Introduction
Volcanic eruptions are important for climate and climate change. They
perturb atmospheric chemistry and radiative transfer. Their signal in
climatic records must be accurately quantified before any attribution of
climate change to anthropogenic sources. Furthermore, by studying the
response of the atmosphere to volcanic eruptions in terms of climate
sensitivity, one can test ideas relating to climate prediction.
Instruments (many of which were flown aboard several different
platforms which are not listed) that have been used to measure volcanic
SO2 in the atmosphere.
Instrument name
Viewing geometry,
Period of
Relevant reference
spectral region
operation
TOMS, TOMS-like instruments (e.g. SBUV/2)
Nadir, UV
1979+
Krueger (1983), Kerr et al. (1980); Krueger et al. (1995, 2008); Guo et al. (2004)
HIRS/2
Nadir, IR
1979+
Prata et al. (2003), this work.
MLS
Limb, IR
1991+
Read et al. (1993, 2009)
GOME, GOME-2
Nadir, UV–vis
1995+
Eisinger and Burrows (1998); Khokhar et al. (2005); Nowlan et al. (2011); Rix et al. (2011)
ASTER
Nadir, IR imager
1999+
Pieri and Abrams (2004); Campion et al. (2010)
MODIS
Nadir, IR imager
1999+
Watson et al. (2004)
SCIAMACHY
Nadir/limb, UV–vis
2002–2012
Bovensmann et al. (1999); Gottwald et al. (2006); Lee et al. (2008)
MIPAS
Limb, IR FTS
2002–2012
Höpfner et al. (2015)
AIRS
Nadir, IR spectrometer
2002+
Carn et al. (2005); Chahine et al. (2006); Prata and Bernado (2007); Prata et al. (2010)
TES
Nadir, IR FTS
2004+
Coheur et al. (2005); Clerbaux et al. (2005, 2008)
SEVIRI
GEO, vis–NIR–IR imager
2005+
Prata and Kerkmann (2007); Thomas and Prata (2011)
IASI
Nadir, IR FTS
2006+
Karagulian et al. (2010)
OMI
Nadir, UV
2006+
Krotkov et al. (2010); Yang et al. (2007)
Suomi NPP OMPS
Nadir/limb, UV
2011+
Yang et al. (2013)
TROPOMI
Nadir spectrometer, UV–vis
2017+
Theys et al. (2017)
The monitoring of volcanic SO2 emissions, the main precursor to
sulfate aerosols, is crucial not only for accurately characterising total emission
estimates but also for understanding plume evolution. Until the mid-1990s,
only one principal instrument (the Total Ozone Mapping Spectrometer, TOMS)
has been able to observe eruptions for an adequate period to generate
something approaching a climate relevant record. The sensitivity of TOMS
limits it to detecting only the larger, explosive eruptions rather than
effusive ones where material remains predominantly in the troposphere.
Satellite instruments that have been used to measure volcanic SO2 are
given in Table 1. From 1996, with the advent of the Global Ozone Monitoring
Experiment (GOME) class instruments (UV–vis spectrometers), sufficient
spectral resolution (and spatial resolution) has enabled the detection of
lower amounts of SO2 with higher accuracy from increasingly smaller
eruptions. This has improved further still with instruments such as the
Infrared Atmospheric Sounding Interferometer (IASI), from which SO2,
sulfate aerosol and ash may be derived simultaneously due to its high
spectral resolution and broad spectral coverage (Karagulian et al., 2010).
Total erupted mass estimates for volcanic eruptions can often differ by
greater than 100 % between instruments, as a result of sampling;
geometry; differences in sensitivity; and assumptions that contribute to algorithms,
such as plume height. For example, Thomas et al. (2009) present a
multi-sensor comparison of the 2005 eruption of Sierra Negra (Galapagos
Islands), using concomitant observations by TOMS, OMI and MODIS. They found
a wide estimate of total erupted SO2 calculated from the three
instruments, ranging from 60 to 1800 kT.
It is still the case that the operational period of these more sensitive,
recent instruments is not yet long enough to constitute a climate-relevant
record. Here we present the methodology for a relatively fast and accurate
volcanic SO2 detection and quantification method for an instrument
originally designed to operationally measure water vapour and temperature
profiles.
The High-Resolution Infrared Radiation Sounder 2 (HIRS/2) has the potential to have captured stratospheric emissions from
explosive eruptions continuously since 1979, and with significantly higher
temporal sampling and greater sensitivity than TOMS. This enables the
35-year volcanic SO2 emission record from satellites to be significantly
enhanced, with potential uses for constraining models and examining in
detail individual eruptions and plume evolution.
HIRS/2 instrument
HIRS/2 is one of three instruments that originally constituted the
Television Infrared Observation Satellite (TIrOS) Operational Vertical
Sounder (TOVS), designed to provide atmospheric profile measurements of
temperature and water vapour structure (Smith et al., 1979). The other TOVS
instruments were the Stratospheric Sounding Unit (a radiometer) and the
Microwave Sounding Unit (a scanning microwave spectrometer). The TOVS suite
of instruments was first launched in 1979 aboard the new NOAA satellites
based on the TIrOS-N (first of its class) design and evolved into the Advanced TOVS (ATOVS)
system. Subsequent replacements have been deployed for the last 30 years
aboard NOAA satellites (NOAA 6–17) (JPL, 2003) and more recently European
platforms including most recently MetOp-A and MetOp-B as HIRS/4. Throughout its
deployment there have been at least two instruments (and occasionally three)
orbiting simultaneously. HIRS/2 has 19 detector channels in the infrared and
one in the visible part of the spectrum for cloud detection during the day.
These channels are relatively broad, spanning between 0.1 and 0.5 µm
depending upon wavelength. The key instrument parameters are given in Table 2.
Two HIRS/2 channels coincide with SO2 spectral absorption features,
these being 7.3 µm (a strong asymmetric stretch vibration band) and 8.6 µm.
The precise central wave number is dependent upon instrument
version, and only HIRS aboard NOAAs 10 and 12 featured an 8.6 µm
channel. These channels were originally chosen to be sensitive to water
vapour for use in sounding and applying corrections for the CO2 and
window channels. The 8.6 µm channel is also reported to be sensitive to
volcanic ash and other aerosols (Kearney and Watson, 2009).
Channel 11 from HIRS/2 aboard NOAA 11, centred on 7.2 µm, is shown in
Fig. 1. Also shown are simulated transmission spectra for water vapour
(which this channel was designed to detect) and SO2, for two column
amounts (1 and 300 DU). It demonstrates both that the channel and spectral
feature coincide well and that for large column amounts of SO2 the channel
would be strongly affected.
Transmission spectra of H2O and SO2 simulated from
Southern Hemisphere mid-latitude water ECMWF ERA-Interim background vapour
profile using the RFM (see text). The SO2 spectra were simulated using
triangular profiles to represent column amounts of 1 and 300 DU, as used in
the forward model.
Previous efforts to retrieve of SO2 with the HIRS
instrument
Prata et al. (2003) demonstrated a method to detect volcanic SO2 from
HIRS, providing the SO2 perturbation is strong enough and located
above any significant sources of water vapour. It is based on a synthesis of
the expected clean atmosphere brightness temperature (BT) for the channel and
the observed deviation from it when contaminated by SO2. This method,
hereafter referred to as either the Prata fit method or after Prata et al. (2003),
uses a linear interpolation between the brightness temperatures of
adjacent channels. It also assumes a fixed height of erupted volcanic
SO2, since theoretically only one piece of information can be obtained
from one channel, and column amount is not insensitive to the height of the
plume. The technique requires the SO2 to be located in the upper
troposphere–stratosphere above most of the atmospheric water vapour, and
there is no information about the height of the plume from the instrument
itself. This information may be gleaned from other types of observations,
but the fit is reliant upon the accuracy of this independent information.
HIRS/2 instrument parameters.
Instrument parameter
Cross-track scan
±49.5∘ (±1125 km) nadir
Number of steps
56
Optical field of view
1.25∘
Step angle
1.8∘
Ground resolution IFOV (nadir)
17.4 km diameter
Ground resolution IFOV (end of scan)
58.5 km by 29.9 km
Distance between IFOV
42 km along track and nadir
A description of how the Prata method operates is detailed in
Prata et al. (2003). Whilst useful in itself, its most significant shortcoming is that, due
to its simplicity, the model is unable to capture atmospheric variability
(other than potentially that of SO2). This particularly alludes to the
variability of cloud, temperature and water vapour. Without independent
height information of the SO2 the radiance relationships are subject to
potentially significant error. Indeed, it is not possible to formally
quantify error of mass estimates from this method as it currently stands.
Its strengths are that the operations required are computationally
inexpensive and straightforward, as it is based on the principles of a band
model. It has also performed well against other observational data sets,
although the previously mentioned uncertainties that contribute to error
make quantifying overall uncertainty difficult. It uses a minimum offset
threshold in brightness temperature for the channel affected by SO2 in
order to predict the presence of SO2 and yet excludes the effects of
atmospheric water vapour variability. As such, its sensitivity to low
amounts of SO2 is limited.
Guo et al. (2004) presented a re-evaluation of the 1991 Pinatubo eruption
using SO2 derived from HIRS/2 using the Prata fit method and compared
it to SO2 derived from TOMS measurements. They were found to be broadly
consistent. The Prata fit method works sufficiently well to suggest that the
7.3 µm SO2 feature it uses is robust enough to make further
exploitation more refined. Use of information arising from other HIRS
channels would constitute an improvement to the Prata fit method, as
multiple-wavelength information can be used to diagnose attributes of the
atmospheric profile such as temperature and the presence of cloud. This
problem is well suited to an optimal-estimation (OE) retrieval, which would
incorporate a forward model (FM) of sufficient complexity to represent these
atmospheric attributes. As with the Prata fit, unavoidably it will require
some estimate of the altitude of an SO2 plume.
Outline of paper
In Sect. 2, an OE retrieval algorithm methodology to
extend the Prata fit method is presented. Section 3 comprises an error study
and presents results of retrievals from simulated measurements in order to
elucidate the sensitivity of the algorithm and potential sources of error.
Section 4 presents a case study of the 1991 Cerro Hudson eruption, where the
algorithm is applied to real data and new eruption mass estimates are
evaluated and compared to existing mass estimates from other
instruments/methods. In Sect. 5 the results are discussed and further work
is suggested.
Methodology
Retrieval algorithm and forward model
The HIRS/2 measurements used here are all-sky brightness temperatures from
the instrument aboard NOAA 11. This was selected to demonstrate the
capability of this version of the instrument with only one channel that is
sensitive to SO2 and two window channels that have some potential to be
used to flag cloud and under some circumstances ash if required (although
only one is used here directly). The brightness temperatures are a product
derived from the raw voltage measurements via a radiance and brightness
temperature conversion and have been subject to calibration factors and some
basic quality control. Further information about the instrument is available
from NOAA (1981) and elsewhere. The data format contains the time in seconds
from midnight of the measurement, the solar zenith angle, 19 IR channel
brightness temperatures, one visible channel albedo, latitude, longitude,
satellite altitude, line number for each orbit and the scan position (see
Table 2).
Retrievals are obtained using the Levenburg–Marquardt minimisation method
after Rodgers (2000), and the full optimal-estimation scheme used here is
described in detail in Miles et al. (2015). The retrieval uses three HIRS/2
channels to derive three products: the SO2 column, a scaling factor for
a water vapour profile and effective cloud top pressure. The 7.3 µm
channel is sensitive to both water vapour and SO2. This channel may be
said to saturate for SO2 columns above 600 DU, where significant
increases in SO2 result in small changes in channel BT below the
envelope of the channel noise and other error terms. The weighting function
for water vapour of the 6.8 µm channel peaks at around 500 hPa (around
5 km) and as such would have some sensitivity to the region where the vast
majority of the water vapour in the column resides. To represent both
channels accurately, some knowledge of cloud is required, which may be
gleaned from the 11.1 µm channel window channel. This channel is highly
sensitive to the emitting temperature of the lowest surface it observes (be
it cloud or the surface); thus with some knowledge of the surface and
atmospheric temperature profile it is possible to obtain an estimate of
cloud top height (CTH). Other atmospheric gases not retrieved but that contribute
appreciably to channel brightness temperature are represented in the forward
model by a climatological value. The potential error that this can introduce
is incorporated into the estimate of forward-model error.
Radiative Transfer for TOVS (RTTOV) is a radiative transfer model (developed
by the UK Met Office; Saunders et al., 1999; ECMWF, 2001) designed to
simulate the instruments of TOVS including HIRS/2, and it is used extensively
(particularly for assimilation) because of its speed. It calculates layer
transmittances for a variety of trace gas species using look-up tables of
parameterised regression coefficients for a range of temperatures and
pressures. It has been further developed since the TOVS system was first
deployed, and version 10 is used here. RTTOV also has the functionality to
compute partial derivatives.
RTTOV estimates channel brightness temperature based on pre-calculated
coefficients for layer transmittances that are generated for a range of
atmospheric profiles. As such, it is extremely fast, but as it stands it
does not incorporate any representation of SO2 other than at a very low
climatological value. To alter the transmittance model to include SO2
would require substantial re-working of program code. It is possible to
calculate a set of predictor coefficients for SO2 and incorporate them
within RTTOV by replacing the properties of another gaseous species that has
negligible impact on the total column transmittance within the selected
HIRS/2 channels (in this case, carbon monoxide). The coefficients were
generated by a “training” methodology using an extensive range of specimen
atmospheric profiles, where the SO2 was represented from very
low/background levels to very large perturbations, after Matricardi (2008,
2010) and Siddans (2011). This approach retains the speed and accuracy
offered by RTTOV and enables the model to be used to represent atmospheric
gases for future instruments not already catered for (ECMWF, 2001).
For this work, the predictors were trained using profiles with up to 300 DU.
Some care is required in the generation of these coefficients for SO2.
They are required to be limited to those that represent a first-order
relationship with SO2 since the more complicated (higher-order)
predictors caused erroneous results. This is thought to be a result of both
the dynamic range that SO2 can exhibit in a volcanically perturbed
atmosphere and the fact that RTTOV was not explicitly designed to model
SO2 for this instrument. The cost in terms of accuracy over this range
of SO2 is shown to be small, as demonstrated in Fig. 2 and to be discussed
in detail later.
Retrievals based on simulations by a line-by-line model (RFM), with
synthetic measurement noise. The error bars for the column retrieval are the
retrieved errors. These simulations use temperature and water vapour from a
cloud-free ECMWF ERA-Interim atmosphere on 15 August 1991, for a grid box
centred at 0∘ N and -60∘ N latitude and
0∘ E longitude. The vertical bars show the retrieved error for the column
retrieval. No error estimates are possible for the Prata fit method.
The column retrieval developed here uses atmospheric profiles from the European Centre for Medium-Range Weather Forecasts
(ECMWF) ERA-Interim product (Dee et al., 2011) to represent atmospheric properties
other than SO2, or as a first guess in terms of the water vapour
profile. These contain profiles on a pressure grid of 37 levels from 1000 to
1 hPa. RTTOV is capable of generating weighting functions, but they
refer to the sensitivity of the simulated measurements to perturbations in
the atmospheric profile, rather than directly to changes in state vector. As
a result, these are evaluated numerically in the forward model by successive
FM calls where each element of the state vector is fractionally perturbed in
turn. RTTOV has certain physical limits for its input values, and when
occasionally the predicted updated state lies outside these they are
constrained in the FM by the physical limits that RTTOV will accept, or that
are appropriate for the forward model. These are 0.01 to 800 DU for
SO2, 1 × 10-6 to 16 times the column water amount predicted by
ECMWF, and a maximum cloud top height of 16 km (a conservative upper limit for
tropopause height). The weighting functions are allowed to make linear
extrapolations beyond these limits, allowing the retrieval more freedom, but
unphysical profiles are suppressed with quality control of the derived
products (discussed later).
Profile definition in forward model
In the absence of any further information, an effective SO2 profile
must be represented in the forward model. The three-element state vector
comprises a scaling factor for the SO2 profile, a scaling factor for a
water vapour profile and a cloud top pressure. A volcanic SO2
perturbation is represented by a vertically localised triangular profile.
This triangular profile is normalised to have an integrated mass of 1 DU.
This was partly done to ease interpretation, since the retrieved scaling
factor would be approximately equal to the total amount of SO2 in the
column. The rest of the profile is prescribed by a background SO2
volume mixing ratio climatology, the total column mass of which is less than
1 DU. In the forward model, a scaling factor applies to a specified height
region of the SO2 profile, scaling all elements within and none outside
this. The expected region of the volcanic plume is estimated using ancillary
information, such as lidar or results from modelling of the eruption
available in the literature. The retrieval sensitivity to how well thickness and altitude of the plume are
modelled as compared to the true state is evaluated using retrievals from
simulated measurements. These are detailed in Sect. 3.
In an analogous way to SO2, H2O is represented in the state vector
by a profile scaling factor, but it applies to the entire profile rather
than a localised height region. The profiles used for retrieval are those
collocated from the ECMWF ERA-Interim product for a given HIRS/2 pixel
(which represents the best guess for the state), but in principle any
climatological profile can be used. In the case where a scaling factor is
close to 1, it would indicate that the H2O profile is similar to that
which produced the measurement.
The third element of the state vector is CTH, or
specifically the geopotential height at an equivalent pressure level. It was
found that the speed of convergence was significantly reduced if the initial
guess of cloud top pressure was reasonably accurate. As such, this is
derived before the retrieval using interpolation between calls to a
radiative transfer model that simulates the 11.1 µm channel BT
for 0–10 km (using associated ECMWF ERA-Interim temperature
profile), and it includes a test for temperature inversions.
Error
An estimate of forward-model error was calculated using the Reference
Forward Model (RFM) – a line-by-line radiative transfer model (Dudhia,
2002), discussed further in Sect. 3. The estimate accounts for
inaccuracies that arise due to modelling the atmosphere at reduced spectral
resolution, limited vertical resolution (100 m versus 1 km as used in the
forward model outside the region of the SO2 perturbation), inclusion of
non-retrieved trace gases at a climatological level or their preclusion
entirely, relative to a reference case. This yields a channel quantity (in
brightness temperature) that is combined in quadrature with the
noise-equivalent differential radiance for each channel and is thus incorporated
into measurement noise for the purposes of the retrieval. The a priori error
associated with cloud height is 10 km. The a priori error for water vapour
is based on the variance of water vapour in the ECMWF atmospheric training
profiles discussed above relative to the mean.
Estimation of SO2 and H2O covariance for HIRS/2
Establishing an appropriate SO2 a priori error is potentially a
non-trivial issue with regard to a retrieval problem where the measurements
have relatively little sensitivity. A volcanically perturbed SO2
profile can contain 2 or 3 orders in magnitude more than a background
profile, and at the centre of a large plume this can be even more. A good a
priori error gives the retrieval the freedom to find a correct minimum in
cost space and can restrict it from converging on a solution that is
unphysical. The variance for a background profile would be very small, as
opposed to a profile where SO2 is expected, which would be very large.
If there is sufficient information contained within the measurements, one
would conventionally use a variance that spans both scenarios. This results
in a poor constraint for an ill-posed problem but is necessarily used here,
where a first guess/a priori error of 100 DU is used and a prior variance is
the first guess squared. A column amount of 100 DU may represent
that from a large, explosive volcanic eruption. Pinatubo, for example, yielded column amounts
of 350–500 DU (depending upon instrument) after 24 h, which reduced to
100 DU after 7 days (Carn et al., 2005). The OMI instrument (see Table 1)
captured column amounts of around 200 DU after the 2008 eruption of
Kasatochi (Prata et al., 2010).
Early results of the retrieval scheme run with real measurements revealed
that there were many “false positives” of SO2 retrieved. Their
structure indicated that they were related to the presence of water vapour,
or errors in the fit for water vapour. This indicated the degree of
covariance between SO2 and water vapour which had to be incorporated
into the retrieval since the 7.3 µm channel is sensitive to both water
vapour and SO2.
The retrieval was applied to one day of “clean” measurements in the Southern
Hemisphere, where no volcanically perturbed profiles were expected. The
retrieval was forced not to retrieve SO2 by artificially constraining
the a priori variance, but nonetheless small amounts of SO2 are
retrieved from that channel because of inadequacies in characterising the
water vapour. The brightness temperature fit residuals in the SO2
channel were very small, but it is expected that nearly all of the SO2
being retrieved on this day is being falsely attributed. The standard
deviation of the 7.3 µm channel brightness temperatures fit residual in
the retrieval of 0.92 K constitutes an estimate of the “real-world” error
covariance of water vapour with SO2 for this instrument. This is
incorporated by adding it in quadrature to the forward-model error for this
channel and resulted in a significant reduction in the occurrence of false
positives.
Error study: retrievals from simulated measurements
There are some sources of error that can be incorporated into and dealt with by
the retrieval. These include measurement noise, the presence of cloud or
ash, SO2 / H2O covariance and an estimate of forward-model error
discussed above. The main sources of error that cannot be adequately
represented in the forward model are errors that impact ill-posed nadir
SO2 column retrievals in general. These are incorrect height assignment
of the SO2 plume; incorrect thickness in the plume represented in the
forward model; and, particularly in the case of infrared measurements,
sensitivity to the presence of cloud and/or water vapour. Their relative
impacts vary, and the sensitivity of the solution to them can be quantified
using simulations. It should be noted that some of these errors (plume
height and profile shape) cannot often be known at the time of retrieval,
and as such the actual impact on the retrieval result also cannot be known.
They are investigated here in order to give a general indication as to the
potential error that can be associated with the results, to give a window of
confidence. Others, such as the impact of cloud or ash on the retrieved
SO2 error, can be investigated for use in quality control.
Spectral precision of forward model
In order to assess the accuracy of the RTTOV-based fast column retrieval
forward model, it is compared to simulations from a model with a higher
accuracy. The RFM is a line-by-line radiative transfer model (Dudhia, 2002)
capable of modelling the atmosphere at a spectral resolution of up to
0.0001 cm-1. The RFM is not suitable for the forward model because it is
computationally expensive and does not inherently represent any effects
of cloud or ash. Figure 2 shows the results of column retrievals from HIRS/2
channel BTs simulated by the RFM, using a sample ERA-Interim cloud-free
meteorology (temperature and water vapour profiles) at 0 and 60∘ S
latitude and 0∘ W longitude, where only the column amount of
SO2 is changed in the simulation. It also shows the SO2 fit by the
Prata fit method. The Prata fit method does not fit SO2 below 5 DU, which
depending upon the atmospheric state can be equivalent to an observed
brightness temperature difference of up to 4 K. The bias of the Prata fit
has a dependence upon latitude, primarily because of the different amount of
water vapour in the profile at the two latitudes shown here. The column
retrieval has a very small bias that only becomes perceptible at SO2
loadings approaching 200 DU, at which point it is of the order of
< 5 DU.
Sensitivity to forward-model representation of SO2 plume
Both the altitude and amount of SO2 affect the 7.3 µm channel
brightness temperature, but as there is only one channel sensitive to
SO2 on NOAA 11 considered here, there is at most one piece of
information that can be retrieved for SO2. Therefore, for an accurate
retrieval of SO2 column, it is important to have some knowledge of the
plume altitude or its vertical profile. The column retrieval developed here
requires some information of the height of the SO2, but this can be
subject to uncertainty and may change with time. As such, the sensitivity of
the retrieval to errors associated with plume height and specification must
be examined.
Altitude
Measurements were simulated for a plume at a range of altitudes from 8 to 18 km.
Figure 3 shows the impact on the retrieved SO2 column at a
specified, fixed altitude of 12 km as a fraction of the true column at these
altitudes. Errors range from typically ±0 to 30 % for most column
amounts up to 100 DU and increase for larger amounts and for particular
altitudes. Whilst the specific error may be state-dependent (upon
meteorological conditions, specifically the water vapour profile), these
simulations do give a general indication as to the magnitude of error that
can result from incorrect height assignment of the volcanic plume in the
forward model. This is the largest source of error in the OE column
retrieval (and the Prata fit method) and is made more challenging because
there is a dependency of the error on column amount. Since height assignment
errors cannot be known, such simulations can at least give a general
indication of potential uncertainty of retrieved amounts, depending on the
quality of information available regarding altitude of volcanic SO2. It
is clear therefore that good prior knowledge of the SO2 plume altitude
is necessary for accurate retrieval or fit of SO2 column amounts from
HIRS/2.
A measurement was simulated for a volcanic plume of triangular
profile centred at a range of altitudes, for a range of total column amounts.
A retrieval is then performed where the plume is assumed to be at 12 km. The
fractional difference, or error, is plotted.
The performance of the column fit was also directly assessed against a
line-by-line model (RFM) for plume altitudes from 8 to 18 km (where the
plume height assignment used in the retrieval was the same as that used in
the measurement simulated by the RFM), and it was found that for altitudes of
over 17 km the column fit was unable to retrieve SO2 columns less than
30 DU, but in all other cases true clear-sky column amounts were retrieved
accurately from simulated measurements.
Profile shape and plume thickness
Figure 4 shows the consequences that can result from retrieving the volcanic
plume with a fixed profile shape that represents the thickness of the plume
incorrectly. Measurements were simulated using a triangular profile centred
at 12 km but with baselines of 1 and 4 km. They were then used in the
retrieval with a fixed profile shape with a triangular perturbation also
centred at 12 km but with a baseline of 2 km (thought to be the best
representation of the plume used in the case study in Sect. 4). The
retrieval simulations suggest that errors are larger when the plume
thickness is overestimated (typically 13 %), with only small inaccuracies
introduced when the plume thickness is underestimated (less than 2 %).
The modelled cloud top height was 3 km in all cases. It is therefore
possible that an underestimate of plume thickness would result in smaller
errors.
The black line indicates how columns from 0.1 to 200 DU are retrieved
on a fixed grid with a scalable triangular profile with base, mid-point and
top at 11, 12 and 13 km respectively, when the true profile shape is given by a
triangular profile at 11.5, 12 and 12.5 km, effectively overestimating the
thickness of the plume. The red line shows the equivalent result for an
underestimate of the plume thickness, the real profile given by 10, 12 and 14
km. The dotted lines show the bounds of retrieved error in each case. The
dashed line is x=y, shown for clarity.
Sensitivity of retrieval scheme to cloud and ash
Some understanding must be obtained of how the column retrieval forward
model behaves in the presence of ash and cloud of different type. The
forward model fits a cloud top pressure using the 11.1 µm channel,
which is expected to work well for most scenes with cloud in the
troposphere. The effect of cloud on the other channels is examined here
using a cloud model, the Oxford-RAL Retrieval of Aerosol and Cloud (ORAC)
model. The model is described in detail by Poulsen et al. (2012), where it
was used as part of an optimal-estimation retrieval of cloud properties for
the Along-Track Scanning Radiometer (ATSR) by simulating radiances in a
combination of visible, near infrared (NIR) and IR channels. The model
parameterises a cloudy scene by ascribing cloud phase, effective radius of a
size distribution, the 0.55 µm optical depth and a cloud top pressure.
It uses the plane-parallel approximation and models cloud as a single layer.
The model represents trace gases at a background climatological level. The
system can also be used to retrieve ash plume properties: plume height,
optical thickness and ash particle effective radius (McGarragh et al.,
2017).
HIRS/2 measurements were simulated for a range of liquid and ice cloud and
ash optical depths, for a range of effective radii and at a range of altitudes when no
volcanic SO2 was present. These channel brightness temperatures were
then used to retrieve SO2 to identify where this resulted in an
erroneous fit.
An example is shown in Fig. 5, which shows that for liquid water clouds
above 5 km the column retrieval erroneously retrieves some SO2 when
there is none, the water vapour and cloud top height become inaccurate and
the fit cost begins to increase. The results indicated that low optical
depth or effective radii for cloud or aerosol can result in poor fitting of
the measurements, resulting in both an underestimate of cloud top pressure
with false positives of SO2 and an overestimation of water vapour.
This yields a crucial quality control threshold where retrieved cloud top
altitudes of greater than 5–6 km should not be trusted, as they are likely
to result in spurious detection of SO2 and a high retrieval cost. This
may imply that very thin cloud beneath 5 km (or incorrectly retrieved to be)
could still contribute to poor fitting of the measurements.
The top left plot shows retrieved cloud top height as a function of
“true” cloud top height as simulated by the cloud model. Black symbols
indicate that the retrieval converged, and purple indicates that it did not.
The top right plot is of the fit residual (measurement minus fit) in the
11.1 µm channel. The bottom left plot shows the retrieved SO2
as a function of the cloud top height in the cloud model, and the bottom
right the equivalent for the water vapour scaling factor.
Quality control
The results of the column retrieval must be subject to some quality control.
In addition to the disregard of non-converged and converged pixels with
cloud retrieved at an altitude greater than 5 km, a retrieved column is only
considered useful if the error is less than the retrieved amount. Quality
control becomes very important when erupted plumes are used to calculate
total erupted mass, where even a small amount of noise can yield a biased
mass total. For the purposes of gridding or summing pixels for deriving a
global/plume mass estimate, a minimum retrieved SO2 threshold may be
applied in deference to the lower detection limit of the retrieval, in order
to avoid spurious low values that the retrieval should not be sensitive to,
such as those relating to water vapour or cloud that are not accounted for
in either the error covariance or the forward model. An effective way of
obtaining this quantitatively is to apply a 2 or 3σ test, where sigma
is the standard deviation of the retrieved SO2 on a day when no
volcanic SO2 is expected to be present. This threshold gives
statistical confidence that a value above it is significantly distinct from
the noise above the 95th or 97th percentile. The sigma threshold for 6 August 1991
(a day when there was no SO2 present in the region relating to the
case study in Sect. 4) was 2.7 DU and is probably a lower estimate of the
detection limit of the HIRS/2 SO2 column retrieval at the
mid-latitudes. Multiples of this value indicate confidence that a retrieval
result is dominated by signal rather than noise.
Case study: Cerro Hudson eruption in 1991
Cerro Hudson (45.54∘ S, 72.58∘ W; elevation: 1905 m) is a
stratovolcano in the south Chilean Andes that erupted explosively in August
1991, 2 months after the Pinatubo eruption. The eruption was estimated to
be 10–20 times smaller than Pinatubo in terms of SO2 that was expected
to be emitted. In this sense, as well as being a non-equatorial eruption, it
has similarities to the 2008 Kasatochi eruption in the Northern Hemisphere.
It is selected here as a case study because it was a relatively large
eruption that has not been studied exhaustively, and it is a very good example of
an eruption in recent satellite history which only TOMS observed with any
significance that can benefit from application of this technique.
Retrieved SO2 columns for 15 August 1991, and retrieved error
for orbits that day. Erupted SO2 from the start of the eruptive phase
(from 8 August 1991) is evident ahead of the larger plume emitted on
15 August. Data are screened at the 2σ level (5.4 DU).
At the time of the 1991 eruption, the only satellite available that could
detect SO2 with any demonstrated accuracy was TOMS. The Microwave Limb
Sounder, a contemporaneous instrument that observed SO2 from Pinatubo
at a higher altitude, produced noisy results in the lower stratosphere at
this latitude (Read et al., 1993). In addition, contemporary lidar
measurements of the Hudson plume were made at the CSIRO (Commonwealth
Scientific and Industrial Research Organisation) Division of Atmospheric
Research, at Melbourne, Australia (38∘ S, 145∘ E) (Young et al., 1992; Barton
et al., 1992). These measurements are sensitive to ash, sulfate aerosol and
meteorological (water) cloud. The backscatter profiles tend to indicate
peaks at around and above 20 km, and frequently at 10–13 km. The higher peak
is attributed to aerosol from the Pinatubo eruption. Young et al. (1992)
interpret the majority of observations that are thought to include Hudson
material as the feature at 12 km in October, with variable cirrus at 10 km.
It is reported by the authors that the plume was observed consistently from
28 August until December 1991 between 10 and 13 km, with a decreasing
scattering ratio. The relative proportions that contribute to the
backscatter measured are expected to be dominated by ash in the first few
weeks after the eruption. Little ash is expected to be present after a month
beyond the eruption, but by this time the vast majority of the SO2 will
have oxidised into aerosol. Whilst lidar is not sensitive to the presence of
gaseous SO2, inferences can be drawn from the height of the aerosol it
eventually becomes. In this case the lidar information is considered to be a
valuable starting point as a guide for estimating the cloud height of the
SO2, in the context of other information. As well as some ground
observations, the Hudson eruption was sensed remotely by AVHRR (ash), lidar
(sulfate aerosol) and incidentally by an aircraft (Barton et al., 1992).
Hofmann et al. (1992) reported possible exacerbation of Antarctic ozone
depletion of 10–20 % of total column due to the presence of Hudson aerosol
in the lower stratosphere for September 1991. The anomalous depletion
occurred within the polar vortex predominantly at 11–13 and 25–30 km, the
respective altitudes of the Hudson and Pinatubo aerosols.
The transport of the Hudson volcanic plume was first numerically modelled by
Barton et al. (1992), to reasonably good agreement with satellite and lidar
observations. The plume was also modelled using an isentropic trajectory
model, initiated by TOMS observations of SO2 (Schoeberl et al., 1993).
These models showed good spatial agreement with observations for the first
8 days after the eruption, which is an indication that the height
assignment of the erupted plume was accurate within the models. The most
explosive eruption began and ended on 15 August. It was at this stage of
its eruptive phase that the majority of the material was injected into the
stratosphere (Constantine et al., 2000).
The top left and top right show the retrieved water vapour scaling
factor and its error from the column retrieval. The bottom left and right show the
equivalent for the retrieved cloud top height.
Results
Using all of this information, the Hudson plume is modelled as a triangular
peaked profile with a baseline of 2 km between 11 and 13 km, peaking at 12 km.
Figure 6 shows an example of the SO2 retrieval applied to a day of
data on 15 August 1991 and its associated retrieval error.
Figure 7 shows results for the same day as Fig. 6, but for the other elements of
the state vector: the retrieved water vapour scaling factor and cloud top
height (with their associated retrieved errors). Only high-cost and
convergence criteria have been applied. In general, the retrieved values of
cloud top height have very small errors. For the water vapour scaling
factor, the largest errors occur in the presence of high or thick cloud,
which is expected. As shown in Sect. 3, the cloud model simulations
suggested that the retrieval struggles in the presence of high cloud and can
on occasion fit spuriously enhanced SO2, potentially because it results
in a poor estimate of water vapour in the correspondingly colder scene.
Regions of very high water vapour scaling factor result in very high errors
in retrieved SO2, and data with cloud top height greater than 5 km are
not considered reliable for SO2.
Progression of main erupted plume from 15 August 1991, using all
orbits (day and night) from HIRS/2 NOAA 11. The eruption began with smaller
amounts emitted from 8 August, which are apparent on the 15th and disassociated
from the main plume. The plume's transport between observations is evident,
particularly from 21 August, where it is captured multiple times by multiple
swaths. Data have been screened at the 3σ level (8.1 DU) for clarity
of the main plume.
Total erupted SO2 rounded estimates for Cerro Hudson.
Eruptive phase
TOMS SO21
TOMS SO22
HIRS/2 Prata fit3
HIRS/2 OE4
8–9 August
700 kT
–
300 kT
500 ± 150 kT
12 August
600 kT
–
400 kT
300 ± 90 kT
15 August
2700 kT
2000 kT
1200 kT
1500 ± 400 kT
1 Constantine et al. (2000), with errors estimated to be circa 30 %.
2 This work, based on updated TOMS algorithm, for total mass as observed
on 16 August (as region was poorly observed on the 15th) with
consideration of pixel overlap within orbit.
3 After Prata et al. (2003), but data reproduced and sampled as OE HIRS/2
product is herein.
4 This work, with retrieved error.
Figure 8 shows 9 days of retrieved SO2 from the 1991 Cerro Hudson
eruption following the largest eruption phase on 15 August. The
eruption began on 8 August, emitting smaller amounts of SO2 into
the upper troposphere–lower stratosphere, which can be seen as already
present in the path of the main plume on subsequent days. The multiple
sampling of the plume by successive orbits (day and night) is quite
apparent, particularly as the plume becomes more distorted after 20 August.
Plume mass estimate
The simplest method to estimate the total erupted mass or mass present in a
volcanic plume is to take the sum of the representative footprint areas of
the satellite that measured SO2. This method presents several problems
relating to sampling of a volcanic plume; particularly with an infrared
instrument that measures both night and day and that could sample the plume more
than once, orbits may partially sample the plume in any one swath, and the
plume will move constantly between sampling. Alternatively, gridding
averages the data into grid boxes on a latitude–longitude grid. Some
care must be taken to account for whether or not the gridded data are
representative of the data resolution, and keeping track of bins with no
data can be a way to estimate under-sampling. Guo et al. (2004) used two
methods of gridding data, that of kriging for TOMS data and nearest-neighbour
interpolation for HIRS/2 (Prata fit method) to account for larger
spatial gaps between points. These methods either impose statistical methods
or manually introduce information based on assumptions. Whilst both can be
utilised in such a way as to indicate an estimate of the error or
uncertainty that this introduces, mass estimates presented here are only
based on the sum of equivalent contiguous footprints represented by each
HIRS ellipse.
Furthermore, if gridding is used, in order to ensure that the data are
sampled fairly, the orbits should first be split into ascending and
descending nodes, with care taken regarding where a plume is in relation to
the date line. This is in an effort to minimise recording the same data
point twice when the plume has moved by the time the region is sampled
again. Other methods are available but often require a model or further
ancillary information.
Comparative measurements of SO2
The plume mass estimate for the HIRS/2 SO2 retrievals for the Cerro
Hudson eruption may be qualitatively compared to the figures for TOMS within
Constantine et al. (2000). Total erupted mass estimates given can be
directly compared, as shown in Table 3, although the methodology by which
the estimates were derived differs. Spatially, HIRS/2 has the advantage of
a smaller footprint than that of TOMS (instrument field of view (IFOV):
1.25∘ × 1.25∘ / 17.4 km × 17.4 km versus
3∘ × 3∘ / 50 km × 50 km),
but the TOMS swath is 50 % wider (3000 km). For a case such as the Hudson plume,
TOMS is more likely to capture the entire plume in one orbit swath and
sample it only once, which on the one hand greatly reduces ambiguity in
deriving total plume mass, but on the other hand the frequency of observation
is reduced, and sometimes only part of the plume is captured. As reported by
Constantine et al. (2000), this was sometimes the case, and a “best”
estimate of the TOMS data was used to contribute to the values in Table 3.
The erupted mass estimates given in Table 3 that relate to HIRS/2 are the
sum of equivalent footprint areas, from nodes that capture the most of the
SO2 plume present each day. Figures are rounded to reflect probable
accuracy. For the total eruptive period, this method has yielded a total
erupted SO2 mass estimate of 2300 kT with an averaged retrieved error
of 27 %. This error does not incorporate error that arises from
uncertainty in the height of the SO2 in the forward-modelled plume (as
demonstrated in Sect. 3), or error that might arise from discounting
pixels where SO2 was retrieved below the 3σ threshold. It does not
account for absent scan lines due to instrument calibration, so it should be
considered a lower limit. As previously discussed, a good estimate of plume
height is an unavoidable requirement in SO2 detection with an
instrument with only one channel sensitive to atmospheric SO2. In the
case of this work, height assignment error of ±1 km introduces a
mass-dependent bias of between 5 and 20 % for a given pixel depending upon
where in the atmosphere the plume is located. For TOMS, the approximate
error suggested for the total erupted mass estimate is 30 % (Krueger et
al., 1995; Constantine et al., 2000).
The TOMS algorithms used in Constantine et al. (2000) have been recently
updated, and a brief comparison is presented here to some initial data from
an updated TOMS algorithm. This algorithm exploits the way ozone and sulfur
dioxide both strongly absorb UV radiation. The new TOMS algorithm builds on
the early heritage of BUV algorithms (Krueger et al., 1995). These
algorithms retrieve both O3 and SO2 by taking advantage of the
large SO2 / O3 cross section ratio (CRS) differences in the
gas-absorbing bands. This approach constructs radiance tables using a forward
model that accounts for both the O3 and SO2 cross sections. The
new algorithm uses the 317 nm channel to retrieve SO2
(CRS ∼ 2.5); the 331 nm channel to retrieve O3 (CRS ∼ 0.15); and the channel at 340 nm to retrieve the spectral dependence,
dR / dλ. This methodology further applies a small second-order
correction that accounts for non-orthogonality between the SO2 and
O3 channels.
A 1-week composite of retrieved SO2 for both instruments is shown in
Fig. 9, where SO2 from the main eruptive phase can be seen
circumnavigating the hemisphere. There is clear complementarity between the
instruments in terms of absolute amount retrieved and characterisation of
the plume. The smaller pixel size of HIRS and more frequent sampling enable
the plume to be observed in finer detail; however the wider swath of TOMS
frequently captures more of the plume in one swath.
Seven-day composite of retrieved SO2 from 15 to 21 August 1991.
For clarity in comparison, TOMS data are screened to have a minimum value of
15 DU, and HIRS/2 data use 3σ (7.1 DU).
For a more detailed comparison, two orbits during the 1991 Hudson eruption
are considered where the plume is almost fully sampled by both instruments,
as shown in Fig. 10. The pixels in the region of the plume were also
relatively cloud-free or had low cloud during the observation.
The main Hudson plume on 17 August 1991 as observed in orbits 5 and
6 by HIRS/2 and 64695 and 64696 by TOMS, 2 days after the main paroxysmal
eruption that occurred on 15 August. Four scan lines in the HIRS/2 panels are
missing due to a routine calibration phase in which no data are provided.
HIRS and TOMS data are both screened at the quality level of 2σ level
(5.4. and 15 DU respectively).
The geographical bounds considered for the mass estimate are between
-53 and -45∘ in latitude and 10 to
60∘ in longitude. Using the method of summing over mass and area
discussed previously, the mass of the plume represented here by HIRS/2 and
TOMS is calculated to be 1398 and 1540 kT respectively, after quality
control has been applied. The missing four scan lines due to a HIRS
calibration phase that coincide with the plume in the region of high
concentration suggest the HIRS estimate is an underestimate. It is apparent
that HIRS/2 is potentially more sensitive to lower amounts of SO2. It
is challenging to directly compare the SO2 retrieved by two instruments
with differing footprint sizes. Gridding might offer an alternative method
of plume mass estimate, but selection of the most appropriate grid box size
relative to the pixels of each instrument coupled with the small size of the
plume with a strong SO2 concentration gradient make it a challenge for
such a comparison to be equitable and account for instrument attributes. A
comparison involving gridding for a larger eruption (c.f. Pinatubo) would be
less problematic.
E-folding time
The e-folding time for erupted SO2 is a measure of the residency of the
material in the atmosphere and is affected by the height the material
reaches and, in the case of very large eruptions, the amount itself. It is
also affected by wind shear (horizontal and vertical) and humidity, which
affects the rate at which the SO2 is oxidised and sulfate aerosols
grow. The measure is more suited to large eruptions (e.g. El Chichn in
1982 or Pinatubo in 1991), in terms of inferring effects upon radiative
forcing, about which Miles et al. (2004) and other works are concerned. This
is because the amount and height that such eruptions reach in the
stratosphere give the SO2 sufficient time to become globally mixed
and as such affect the radiative forcing globally. Equation (1) describes the
process of exponential decay, where N(t) is a quantity at time t, N0 is the
initial quantity at time t=0 and λ is the decay constant.
Nt=N0e-λt
The e-folding time, the time in which the initial quantity is reduced to
1/e of its initial value, is given by the reciprocal of the decay constant.
Using approximate values from the mass estimates derived from Fig. 9 where
the total SO2 can be said to drop from around 1500 kT (the total mass
present on 17 August 1991 associated with main plume) to 500 kT 18 days later,
this yields an e-folding time of around 16 days. Two days after
the largest plume was erupted is used here to minimise potential obscuration
of the plume by the coincident presence of thick ash. In reality the total
mass observed does not decay smoothly but has noise due to the fact that
the plume is not always perfectly sampled, and the number of retrieved
pixels is excluded due to the presence of high or thick cloud or ash varies.
The variability of the mass estimates and the associated retrieval error
make only an estimate appropriate for this approach, but it is not
considered to be an unreasonable one. If the e-folding time is calculated
for the extremes of the retrieved error bounds of the mass estimates, the
e-folding time is 10 days at a minimum and 35 days at its shallowest
descent, but these are considered to be overly generous bounds by this
method. This case is complicated by the fact that about 30 % of the
SO2 released by Hudson was erupted over the 7 days before the main
eruption on 15 August, making the calculation of the decay subject to
further uncertainty. The e-folding time for this SO2 plume as estimated
by Constantine et al. (2000) is around 15 days, but they state that this is
algorithm-dependent. These estimates are somewhat smaller than the e-folding
times for the larger eruptions (e.g. Pinatubo), which is to be expected due
to the considerably lower altitude of the Hudson plume. More recently, Carn
et al. (2016) estimated the e-folding time of Cerro Hudson to be
∼ 7 days, based on mass estimates from TOMS (Constantine et
al., 2000). They attribute this anomalously short e-folding time to the late
Southern Hemisphere winter timing of the eruption. However, since
Constantine et al. (2000) estimate nearly twice the initial total mass
(4000 kT) than that observed by HIRS/2 in this work (and the subsequent TOMS
algorithm discussed here), it is possible that the inconsistency in e-folding
times could be due to an overestimate of initial erupted mass from the
original TOMS algorithms. Total mass estimates (and therefore e-folding time
estimate) would be improved greatly in accuracy if the HIRS/2 instruments
aboard NOAA 10 and NOAA 12 that were also present were used to result in very
comprehensive sampling of this eruption.
Discussion
This OE column retrieval finds a new total erupted mass estimate for the
1991 eruption of Cerro Hudson of 2300 ± 600 kT from the HIRS/2
instrument aboard NOAA 11, where the error is the retrieval noise. This does
not incorporate any error from plume altitude estimation, but the potential
impact has been quantified by forward-model simulations. This total mass
estimate is lower than that of TOMS (Constantine et al., 2000) and that of
Carn et al. (2016) but higher than that derived in a similar way using the
methodology of Prata et al. (2003) for HIRS/2. Reasons for this include (but
are not limited to) differences in sampling, height sensitivity, instrument
differences and attributes or accuracies of the forward model or fit
employed in SO2 detection. From the comparison with the new TOMS
algorithm, the HIRS/2 results presented here are highly consistent, and
further quantitative comparison, for this eruption in particular, is
desirable.
The retrieval precision demonstrated in this case study is slightly smaller
(∼ 3 DU) than that proposed for the TOMS instrument (6–7 DU).
As such, with the increased sampling of the IR instrument it is apparent
that HIRS/2 can offer a positive contribution to the atmospheric SO2
emission record from explosive volcanic eruptions up to and beyond the
launch of GOME and other satellites that followed. Moreover, benefits of the
optimal-estimation approach over and above the more rapid but limited
brightness temperature difference method are significant. They include a
quantified error on individual pixel retrieved values, latitudinal variation
in accuracy, diagnostic indicators of the retrieval performance and
goodness of fit and treatment of cloud and water vapour consistent to the
retrieval of SO2. When summing mass over a large number of pixels, the
precision that these afford becomes increasingly important. Issues that
remain are those endemic to ill-posed problems where there is only one piece
of information on SO2 available and only limited information about the
height or shape of the profile of a volcanic plume. It is conceivable that
further progress might be made by using HIRS/2 aboard NOAA 10 and 12 with the
addition of the 8.6 µm channel in ash-free pixels.
There are clear opportunities for extending this work. In particular, as the
HIRS/2 instrument was present aboard a number of the NOAA platform series
and often simultaneously flown (NOAA 10, 11 and 12 were all in orbit at the
time of the Cerro Hudson eruption), there is the possibility to fully
characterise eruptions with very high temporal sampling. More rigorous
methods for interpolation, sampling and gridding the data can also be used
to reduce errors in the total mass estimates. The application of further
tools such as chemistry transport or trajectory models for understanding
plume evolution would be better constrained by the availability of more
measurements.
The first HIRS instrument was flown aboard TIrOS-N in 1978, and there are
almost continual data available to the present, and for the foreseeable
future of the Met-Op series of satellites, enabling a potential data set
spanning 40+ years. Generating an SO2 data set for the duration would
be an opportunity to maximise the value and legacy of the satellite data.
Such a data set, with an accompanying error covariance estimate, could be
used as input to a climate model to better assess the effects of large
volcanic eruptions on the radiative balance of the atmosphere. For much of
the latter half of that period, there are (and will be) other satellite
instruments capable of measuring SO2 in the limb and the nadir, in
particular high-resolution spectrometers with very much enhanced accuracy
and precision that will provide correlative information about the quality
of the HIRS/2 SO2 column retrievals that may be considered in
retrospective terms. There is also a break in the TOMS record during
1995–1996 that can be filled by HIRS/2 estimates.
It would be highly desirable to extend comparisons from this eruption with
TOMS SO2 in general, comparing a longer record by both instruments
for other eruptions, since both provide a unique record of SO2
potentially spanning many decades. Satellite records of this length for
climatologically important trace gases are rare and would also provide
further constraint to volcanic SO2 emissions in coupled chemistry–climate models.