Information about the height and loading of sulfur dioxide
(SO2) plumes from volcanic eruptions is crucial for aviation safety
and for assessing the effect of sulfate aerosols on climate. While
SO2 layer height has been successfully retrieved from backscattered
Earthshine ultraviolet (UV) radiances measured by the Ozone Monitoring
Instrument (OMI), previously demonstrated techniques are computationally
intensive and not suitable for near-real-time applications. In this study, we
introduce a new OMI algorithm for fast retrievals of effective volcanic
SO2 layer height. We apply the Full-Physics Inverse Learning Machine
(FP_ILM) algorithm to OMI radiances in the spectral range of
310–330 nm. This approach consists of a training phase that utilizes
extensive radiative transfer calculations to generate a large dataset of
synthetic radiance spectra for geophysical parameters representing the OMI
measurement conditions. The principal components of the spectra from this
dataset in addition to a few geophysical parameters are used to train a neural
network to solve the inverse problem and predict the SO2 layer
height. This is followed by applying the trained inverse model to real OMI
measurements to retrieve the effective SO2 plume heights. The
algorithm has been tested on several major eruptions during the OMI data
record. The results for the 2008 Kasatochi, 2014 Kelud, 2015 Calbuco, and 2019
Raikoke eruption cases are presented here and compared with volcanic plume
heights estimated with other satellite sensors. For the most part,
OMI-retrieved effective SO2 heights agree well with the lidar
measurements of aerosol layer height from Cloud–Aerosol Lidar and Infrared
Pathfinder Satellite Observations (CALIPSO) and thermal infrared retrievals of
SO2 heights from the infrared atmospheric sounding interferometer
(IASI). The errors in OMI-retrieved SO2 heights are estimated to be
1–1.5 km for plumes with relatively large SO2 signals (>40DU). The algorithm is very fast and retrieves plume height in less
than 10 min for an entire OMI orbit.
Introduction
The observation and tracking of emissions from volcanic eruptions are crucial
for both air traffic safety and for assessing climate forcing impacts from
volcanic sulfate aerosols. In the last 10 years, volcanoes have emitted
roughly 20–25 million metric tons of sulfur dioxide (SO2) per year
through passive degassing (Carn et al., 2017). Explosive volcanic eruptions,
however, can additionally release large SO2 amounts high into the
atmosphere. SO2 can be converted to sulfate aerosols within
2–3 d in the troposphere (Lee et al., 2011) and within a few weeks in
the lower stratosphere (von Glasow et al., 2009; Krotkov et al.,
2010). Sulfate aerosols are known to have a cooling effect on climate,
especially if an SO2 plume is injected into the lower stratosphere
and remains there for longer periods of time. This is demonstrated by
significant eruptions such as Mt. Pinatubo in 1991 that temporarily reduced
global temperatures by up to 0.5∘ (McCormick et al., 1995). Aside from
releasing SO2, volcanoes also emit large amounts of ash into the
atmosphere, which can have adverse impacts on air travel. Ash from volcanic
plumes can often interfere with flight paths, greatly reduce visibility near
the ground, and cause damage to aircraft including engine failure (Carn
et al., 2009). In addition, SO2 causes sulfidation in aircraft engines,
an effect that can reduce their lifetimes in the long term. From 1953 to 2009,
over 120 aviation incidents involving volcanic activity were reported, with
roughly 80 of them involving serious damage to the airframe or engine
(Guffanti et al., 2010). There is also the possibility of highly concentrated
volcanic SO2 plumes producing acidic aerosols, which can cause
irritation of the eyes, nose, and respiratory airways of occupants inside
airplanes (Schmidt et al., 2014). In many cases SO2 and ash are
often collocated, thus making estimates of SO2 layer height useful
for aviation hazard mitigation and volcanic plume forecasting. Lastly, the
accurate determination of SO2 height can ideally aid in producing
accurate SO2 vertical column depth (VCD) estimates given that those
retrievals typically use a fixed a priori vertical distribution of
SO2 in the absence of additional information on SO2
height.
With remote sensing, these volcanic plumes can be regularly observed from
space. In particular, hyperspectral spectrometers such as the Ozone Monitoring
Instrument (OMI), GOME-2, OMPS, TROPOMI, and others have provided frequent and
increasingly accurate observations of global SO2 amounts through
retrieval algorithms from backscattered radiance measurements. The OMI
instrument, a Dutch–Finish contribution to the NASA Aura satellite, has been
operational since 2004. OMI has 60 cross-track positions (rows) and has a 13×24km2 spatial resolution at the nadir position (Levelt et
al., 2006). The instrument uses two UV channels and one visible channel to
measure backscattered radiances from the Earth's atmosphere. About half of the
OMI rows are affected by the row anomaly, which affects the quality of OMI
Level 1 and Level 2 data. This anomaly affects individual rows and slowly
evolves over time. It is thought to occur due to a physical obstruction caused
by the loosening of material on the interior of sensor (Torres et al.,
2018). In general, SO2 slant column amounts are retrieved from these
measurements through the differential optical absorption spectroscopy (DOAS)
technique and then converted to vertical columns using air mass factors
(AMFs). The 310.5–340 nm range in OMI's UV2 channel is used in
retrieving SO2, with a focus on the 310.8 and 313 nm
wavelengths. The band residual algorithm (Krotkov et al., 2006) and the linear
fit (LF) algorithm (Yang et al., 2007) were first used as the OMI operational
algorithms for retrieving planetary boundary layer (PBL) SO2 and
volcanic SO2 vertical column densities (VCDs), respectively. These
were replaced with an algorithm based on principal component analysis (PCA) (Li
et al., 2013), which retrieves SO2 amounts directly from spectral
radiance measurements. The same technique was also applied to OMI volcanic
SO2 retrievals (Li et al., 2017). This data-driven approach does not
rely on extensive radiative transfer modeling and has led to reduced biases
and significant improvements (Fioletov et al., 2015). For volcanic retrievals,
algorithms still have uncertainties in SO2 mass in volcanic plumes,
especially in the presence of relatively larger errors in the assumed a
priori profiles.
In addition to column amounts, backscattered radiances can provide important
information about the height of an SO2 layer. Conceptually, a change
in altitude of an SO2 plume alters the number of backscattered
photons going through the layer. If a plume is high in the atmosphere, more
photons that are scattered from below the layer pass through the absorbing
SO2 plume. This results in larger SO2 absorption
structures in the measured radiance spectra, especially in the
310–320 nm range in which Rayleigh scattering is dominant. Relative to
the SO2 amount, obtaining a fast retrieval of the height of a
volcanic plume presents a greater challenge. Until recently, retrieval
techniques have involved a direct spectral fitting approach that uses
backscattered ultraviolet (BUV) measurements in conjunction with extensive
forward radiative transfer modeling. For instance, the iterative spectral
fitting (ISF) algorithm (Yang et al., 2009) for OMI was utilized to determine
the altitude of the SO2 layer by adjusting the height while minimizing
the differences between measured radiances and forward RT
calculations. Another study has utilized an optimal estimation algorithm along
with the VLIDORT radiative transfer (RT) model to retrieve SO2
density and plume height from the GOME-2 instrument (Nowlan et al.,
2011). Sulfur dioxide amounts and plume heights have also been estimated with
the infrared atmospheric sounding interferometer (IASI) through brightness
temperature changes and relative intensities of absorption lines (Clarisse
et al., 2008). For these techniques, extensive radiative transfer modeling is
needed, in addition to a variety of assumptions including a reasonable first
guess for the plume altitude. Newer schemes were later developed for GOME-2
using the SOPHRI algorithm (Rix et al., 2012), a DOAS-based technique that
included minimizing differences between plume height from simulated spectra
and the assumed height from measured spectra. This technique allowed for
reasonably fast retrievals that could be used in near-real time thanks to the
use of pre-calculated GOME spectra stored in a lookup table classified
according to SO2 column, SO2 heights, and other physical
parameters. An updated algorithm was also developed for IASI (Clarisse et al.,
2014), this time implementing an optimal estimation fit approach with
pre-calculated Jacobians. Faster and more efficient methods for GOME-2
(Efremenko et al., 2017) and TROPOMI (Hedelt et al., 2019) have made use of
machine-learning algorithms, specifically neural networks (NNs), to develop a
trained, full-physics inverse learning machine (FP_ILM) for retrieving
SO2 plume height. This approach has shown good accuracy and speed
fast enough for near-real-time operations. The FP_ILM has also been used for
retrieving ozone profile shapes (Xu et al., 2017) and geometry-dependent
Lambertian equivalent reflectivity (Loyola et al., 2020). The primary
advantage of this approach is the execution speed. By separating the training
phase, which involves large quantities of time-consuming radiative transfer
computations and machine-learning model training, from the application phase,
the desired parameter can be retrieved within milliseconds for a single
satellite ground pixel using the inverse model. However, similar methods of
retrieving SO2 layer height have not yet been implemented for
OMI. Now in this study, the FP_ILM has been applied to OMI to estimate
SO2 layer height from backscattered Earthshine radiance
measurements. The retrieval was tested on four past volcanic eruption cases,
and performance was assessed through machine-learning metrics and
comparisons to other datasets such as those from TROPOMI, IASI, and CALIOP
lidar instruments.
Methodology
The FP_ILM approach consists of two parts, the training phase and the
application (or operational) phase. The training phase starts with the
generation of a synthetic training dataset of top-of-the-atmosphere (TOA)
reflectance spectra from a radiative transfer model. This spectral dataset is
then used to train a multi-layer perceptron regression (MLPR) NN model to
predict the SO2 layer height as an output. In the application phase,
the trained inverse model is applied to real OMI radiance measurements. This
inverse model is optimized from the training, and the predictions of
SO2 layer height based on the model are very fast compared with
the time-consuming RT calculations during the training phase. The main steps
of the algorithm are shown in a flowchart (Fig. 1) and discussed in detail in
the next sections.
The flowchart of the FP_ILM methodology
for retrieving OMI SO2 effective layer height. The steps above the
dashed line are part of the training phase done prior to incorporation of
OMI measurements. The application phase involves deployment of the trained
model to the OMI radiance measurements to obtain estimates of effective
volcanic SO2 layer heights.
Forward radiative transfer model
The first step in the training phase is to build a large dataset of synthetic
backscattered Earthshine reflectance spectra from forward radiative transfer
(RT) calculations. These calculations are performed using the LInearized
Discrete Ordinate Radiative Transfer (LIDORT) model with rotational Raman
scattering (RRS) capability (Spurr et al., 2008). This version of the model
treats first-order inelastic Raman scattering in addition to all orders of
elastic (Rayleigh) scattering processes. Rotational Raman scattering occurs
when a photon is scattered at lower or higher energy levels than the incident
radiation. RRS cannot be neglected; it is known to be responsible for the Ring
effect (Grainger and Ring, 1962), a spectral interference signature
characterized by the filling-in of Fraunhofer lines and telluric-absorber
features. Allowing for RRS in the RT model leads to differences in calculated
radiances compared to those made with purely elastic scattering, as
characterized by the filling-in factor. This quantity is generally of the
order of a few percent, consistent with estimates that 4 % of the
total scattering in the atmospheric is inelastic (Young, 1981). Fundamentally
the SO2 layer height information can be retrieved by backscattered
radiance spectra because the amount of scattering occurring in the overlying
atmosphere is determined by the height of the volcanic SO2
plume. This is demonstrated by comparing two otherwise identical RT
calculations with different SO2 layer heights (Fig. 2a). At
shorter wavelengths at which Rayleigh scattering is stronger, there is less
backscattered radiance for the case with higher SO2 plume height,
particularly at shorter wavelengths <320nm (Fig. 2b). Likewise,
the filling-in factor (Fig. 2c) shows the importance of including RRS in the
RT calculations as in some cases there can be 2 %–3 %
difference between the Raman and elastic calculations.
(a) Simulated top-of-the-atmosphere (TOA) Earthshine
radiances for two different SO2 layer heights (10 and 20 km) from
the LIDORT-RRS model. Also shown: (b) the SO2 height Jacobian (change in
radiance per kilometer between the two spectra) along with the absorption
cross sections of SO2 for reference; (c) the filling-in factor. The
filling-in factor is defined as the difference between the total and
elastic-only radiance results divided by the total radiance and expressed as a
percentage. An SO2 column amount of 200 DU was used in the two
calculations, and all other parameters were kept constant except for the
SO2 layer height.
All LIDORT-RRS calculations in this study were performed for the
310–330 nm spectral range, which captures strong SO2 and
ozone absorption features. The model is supplied with ozone (Daumont et al.,
1992) and SO2 absorption (Bogumil et al., 2003) cross sections,
an atmospheric profile, an ozone profile, and a high-resolution Fraunhofer solar
irradiance spectrum. The atmospheric profile has 48 layers and contains a
temperature–pressure–height grid from the standard US atmosphere, with an
increased vertical resolution of 0.5 km below 12 km. The ozone
profile is determined by the total column amount, latitude zone, and month as
specified in the TOMS V7 ozone profile climatology (Bhartia, 2002), while the
SO2 profile is assumed to be a Gaussian shape with a full-width half-maximum (FWHM) of 2.5 km. The solar spectrum is a re-gridded version
of the high-resolution synthetic solar reference spectrum (Chance and Kurucz,
2010), originally with a spectral resolution of 0.01 nm. The
re-gridded version has a resolution of 0.05 nm, which is finer than that for
OMI (0.16 nm sampling for a FWHM spectral resolution of ∼0.5nm). The advantage of using this reference spectrum over the
instrument-measured irradiance is that only one set of calculations is needed;
they can be applied to multiple instruments and instrument cross-track
positions without utilizing unique measured solar flux spectra for each
situation. Using instrument-measured solar flux data may carry less potential
error and be able to better handle issues with instrument
degradation. However, the downside is that the inverse model would need to be
re-trained whenever a new measured solar flux spectrum is used. Since we
expect the retrieval to be primarily sensitive to SO2 absorption
signatures, the radiative transfer calculation was performed for a molecular
atmosphere with no aerosol scattering.
In order to obtain a large number of different spectra, eight key physical
parameters were varied for the LRRS calculations. These parameters include
solar zenith angle (SZA), relative azimuth angle (RAA), viewing zenith angle
(VZA), surface albedo, surface pressure, O3 column amount,
SO2 column amount, and SO2 layer height. The ranges of
these parameters are given in Table 1.
Ranges of the eight physical parameters varied in
LIDORT-RRS for the synthetic spectra calculations.
The number of calculations and the parameter sets for each simulation were
determined through a smart sampling technique (Loyola et al., 2016). A
selective parameter grid with sets of parameters for each simulation was
established through the use of Halton sequences (Halton, 1960) in
eight dimensions. The calculations are continued until the moments of the output
data, mean, and median converged across all wavelengths. In total around
200 000 calculations were done to achieve a sufficiently comprehensive sample
size for the variation in the eight parameters across all rows of OMI. This
sampling was done in order to ensure that (1) each set of parameters was
unique and training data are diverse, and (2) the sample size of the
entire dataset is large enough for the machine-learning application.
Data pre-processing
After the RT calculations are completed, the spectra are convolved with the OMI
slit function. Since each cross-track position of OMI contains a
unique slit function, the appropriate function was applied based on the VZA
input for that particular calculation. The VZA ranges from 0–70∘
across all rows in the OMI swath, with the middle (nadir) rows having a VZA of
close to 0. For each row, only spectra within ±3∘ of the actual
VZA were convolved with the appropriate slit functions. In addition, Gaussian
noise with a signal-to-noise ratio (SNR) of 1000 was added to the
spectra. While the SNR of OMI tends to be lower (Schenkeveld et al., 2017),
adding too much noise can greatly decrease the performance of the machine learning
(Table 2). The root mean squared error (RMSE) and mean absolute difference
(MAE) between the SO2 height from the RT calculation parameter sets
and the height predicted by the neural network were used as metrics (see
Sect. 3). At SNRs of less than 500, the performance starts to increasingly
degrade. Between SNRs of 1000 and 500, there is an increase of around
0.1 km in RMSE. However, adding some degree of noise is necessary to
account for errors in satellite instrument measurements.
The RMSE and the mean absolute difference (km) of all data
points in the independent test set after adding noise as indicated by
different SNR values. All other parameters and input data were kept
constant. SZA < 75∘ and SO2 VCD > 40 DU were
excluded from the test set for these comparisons.
No noiseSNR = 1000750500200100Mean absolute difference0.8940.9040.9390.9961.1141.362(y_known-y_pred) (km)RMSE (km)1.4541.4981.5211.6321.8072.143R coefficient0.9880.9850.9830.9800.9720.955
Next, principal component analysis (PCA) was applied to the spectral dataset
for each row in order to extract the most significant features of the
spectra and to reduce dimensionality. Since each convolved sample consists of
142 wavelength points, the dimensionality of this problem becomes very
large. However, PCA transforms each sample to a set of weights based on eight
principal components (PCs). These principal components explain
99.998 % of the variance in the synthetic dataset
(Fig. 3). Including additional PCs does not add any significant value to the
retrieval and may even lead to overfitting. Prior to starting the machine-learning process, the dataset is split into a training subset
(90 %) and a testing subset (10 %). The training subset
is used for the neural network learning, while the testing subset is only
deployed to verify the performance of the network to predict the output.
Explained variance ratio as a function of the number of
principal components of the spectral dataset.
Machine learning using a neural network
The eight PCs and selected parameters including the SZA, RAA, VZA, surface
pressure, and surface albedo were used as input for training an MLPR, which is
sometimes referred to as a deep neural network. The output layer of the NN
contains the effective SO2 layer height. Column amounts of
SO2 and O3 were not included in the training or in the
application stage because of the large dependency of column amounts on
SO2 layer height and due to biases in OMI ozone retrieval in the
presence of the enhanced SO2 plume, respectively. To improve
stability, the inputs (PC weights, SZA, VZA, etc.) and output (effective
SO2 height) are scaled between -0.9 and 0.9 according to the
minimum and maximum of each input variable prior to input into the NN. In an
NN, the input and output layers are connected by hidden layers containing
neurons (also known as nodes). Each neuron is connected to others by a series
of weights, by means of which the input data are passed to the next level as a
weighted sum of all inputs. Inside the neural network, the Adam optimizer
with a stochastic gradient descent algorithm (Kingma and Ba, 2015) is used to
minimize the loss function, in this case the mean squared error (MSE) between
the result of each iteration and the actual SO2 layer height used to
generate the synthetic spectral sample. With each iteration, the partial
derivative of the MSE with respect to each node is calculated; this is used to
update the weights. The training of an NN progresses by cycling through
iterations of the entire training dataset, called epochs, until the training
and validation MSE is minimized and there is no improvement to be obtained
from further training. Throughout the training, the NN uses 10 % of
the training subset for validation to assess the performance with each
iteration. This validation set is different from the independent test data
that were set aside from training. The “tanh” (hyperbolic tangent) activation
function is applied at the hidden layers to further increase stability in the
NN. Other activation functions (e.g., ReLU and PReLU) were tested; however,
tanh was found to produce slightly better NN performance. There is also
considerable flexibility in the structure of the NN, in particular the number
of hidden layers and nodes in each layer. The final configuration of the NN in
this study includes two hidden layers with 20 and 10 nodes in the first and
second layer, respectively. This was determined through testing and analyzing
the errors of the NN with respect to the synthetic test dataset and the
quality of the retrieval results after application to satellite
measurements. More complex configurations of hidden layers and numbers of
neurons were also tested and found to have worse performance when using OMI
data as input. Hence, the relatively simple configuration was chosen as the
final setup for this study.
In neural networks a common problem known as overfitting often occurs when the
machine-learning model is tuned so closely to the training inputs that it does
not perform well on new data. During training this can be diagnosed if the
validation error is much higher than the training error. To reduce
overfitting, L2 regularization was implemented in the training. The
regularization reduces the effect of small and very large weight values by
penalizing the MSE loss function. For this study, the training was done
separately for each OMI row due to the different VZAs and slit functions
between rows; however, the configuration of the NN was kept constant between
rows. The only difference in the training is the number of training epochs
conducted for each row before the solution becomes optimal for that row. The
number of epochs varies slightly but is in the 200–300 range for all rows.
The final trained version of the NN, the inverse operator, contains the
optimal weights needed to predict the SO2 layer height from an input
of separate test data.
An important aspect for neural network performance is the number of training
samples. Aside from smart sampling, the appropriate number of samples for
training can be determined by comparing errors from training runs wherein
different percentages of training samples were removed (e.g., 10 %,
20 %, 50 %) beforehand. The mean absolute error between
height predicted by the NN and the test set height was calculated when using
different numbers of input samples. With a 50 % reduction in
training samples, the absolute error went up by around 0.3 km. In
contrast, reducing the training set by 10 % had little impact on
the error (see Table A1). These results provide confirmation that for this
case the training data are adequate and that there would likely be
diminishing returns in NN performance with a larger training dataset.
SO2 Height Jacobians (dI/dz) for four different assumed
SO2 column amounts. The Jacobians were calculated from the difference
between two radiance spectra with 10 and 20 kmSO2 height. All other
physical parameters were identical in the calculation of the spectra.
Application to satellite measurements
In the application phase of the retrieval, the inverse operator is applied to
OMI radiance spectra, resulting in a predicted SO2 layer height for
each ground pixel in the OMI swath. For this the OMI L1B geolocated Earthshine
radiance dataset is used. Since OMI only provides absolute radiances, these
data were normalized with respect to the same solar flux spectrum as used in
the generation of the synthetic spectra. In other words, the measured input
becomes the fraction of backscattered radiance to the incoming solar
irradiance (i.e., reflectance spectrum). Prior to normalizing, the irradiance
spectrum was convolved with an OMI slit function for the particular OMI row
and orbit. The irradiance spectrum is convolved with the appropriate OMI slit
function in order to have consistency in wavelength points between the
measured radiances, synthetic radiances, and irradiance of each row. To follow
the same procedure as was used in the training step, the PCA operator from the
training phase is applied to the OMI spectra to perform the dimensionality
reduction and obtain a set of PC weights for each sample. The other inputs are
VZA, SZA, RAA, albedo, and surface pressure parameters from the OMI data
files. As in the training phase, all inputs are scaled to the [-0.9, 0.9]
range. After SO2 heights are retrieved separately for each row, one
height value is given for each pixel (and spectral sample). The application
phase of the retrieval takes only 2–3 s for a given row. This short
duration includes the application of the training phase PCA operator to OMI
measurements, the scaling of inputs, and the deployment of the inverse
operator. The whole process is repeated for each row in order to get a
prediction for an entire OMI swath. For some rows the retrieval is unreliable
due to the row anomaly, which negatively affects the quality of the OMI L1B
radiance data at all wavelengths and consequently L2 retrievals.
Impacts of various parameters on the performance of the trained
inverse model
From the training phase, it becomes clear that the performance of the
algorithm will depend on several factors. As demonstrated in Fig. 3, an
important factor is the SO2 column amount. Overall, the NN makes
better predictions for the test data subset for SO2 amounts >40DU. Below 40 DU, information content on the layer height
to be retrieved becomes increasingly small, as evidenced by large differences
between predicted heights and those in the actual test set (Fig. 5a).
Additionally, larger SO2 loadings result in greater sensitivity
between two heights, as seen by comparisons of SO2 height Jacobians
for multiple amounts (Fig. 4). Quantitatively, if samples with SO2
amounts less than 40 DU are excluded, the RMSE decreases from 1.48 to
1.15 km (Table 3). As with other sensitivity analyses, the RMSE and
MAE in Table 3 are calculated between the predicted output from NN and the
height from the independent test dataset. We can therefore expect the
retrieval to produce reasonable results for moderate to large volcanic
eruptions. In widely dispersed plumes wherein the SO2 VCD is low or
for volcanic degassing events, the retrieval would be less accurate. The
second major dependency is on SZA. The problem here stems from the occurrence
of relatively large errors in RT modeling due to shallow light paths and lower
OMI SNR at the higher SZAs. Reasonably accurate results are to be expected
only for SZA < 75∘. Figure 2b shows significant differences in
predicted and actual heights in spectra associated with large SZAs after
removal of low VCD samples. For the final training approach, it was therefore
necessary to exclude spectra with large SZAs. Dependencies on other physical
parameters are small when compared with these two issues discussed here,
although there is some evidence that high surface albedo also increases
error. If we remove spectra with albedo >0.6 there is a minor improvement
in RMSE from 0.93 to ∼0.89km. However, even with strong
volcanic SO2 signals, we can realistically expect
the absolute error to be at least 1 km on average due to inherent
simplifications in the neural network retrieval approach. The errors in actual
retrievals using OMI data are expected to be larger (see Sect. 4.4).
Dependence of retrieval errors on (a)SO2 amount and
(b) SZA for cases with SO2 VCD > 40 DU. The error is defined
as the difference between the SO2 layer height predicted by the neural
network using inputs from the independent test set and the actual height
from the same samples. The test set comprises 10 % of the original
spectral dataset withheld from training the neural network. The plots show
that the retrieval error is mostly within ±2.5km for SZA < 70,
but it increases significantly for large SZAs.
The RMSE and the mean absolute difference of all data
points in the test set under different conditions. For each condition, the
appropriate points were removed and excluded in error calculations. All
cases in this table used synthetic training spectra with added SNR 1000.
For testing the FP_ILM retrieval on OMI data, four volcanic eruption cases
with sufficiently strong SO2 signals were selected (i.e., with peak
SO2 VCDs greater than 40 DU). Each case is described in
detail in the following subsections. For each case, comparisons were made to
other satellite-derived datasets where available, for example the CALIOP lidar
on board CALIPSO, the IASI SO2 layer height retrieval (Clarisse
et al., 2014), and the GOME-2 (Efremenko et al., 2017) and TROPOMI retrievals
(Hedelt et al., 2019). It is important to note that the CALIOP lidar only
indicates the height of the ash plume and not the SO2
height. Although ash and SO2 plumes are often collocated, this is
not always the case, making direct comparisons difficult.
Kasatochi (2008)
Kasatochi is a volcano located on the Aleutian Islands of Alaska
(52.178∘ N, 175.508∘ W). It underwent a series of eruptions
beginning late in the day on 7 August 2008, which injected great amounts of
ash and SO2 into the stratosphere. Overall the explosion released
roughly 2 million tons of SO2, at the time the highest SO2
loading since the Mt. Pinatubo eruption (Yang et al., 2010). SO2
effective layer heights retrieved using the machine-learning model for OMI
(orbit 21650) on 10 August 2008 were around 11–12 km, with some
portions being slightly lower (Fig. 6a). This is in reasonable agreement with
previous SO2 height retrievals of 9–11 km that used the
ISF algorithm for OMI (Yang et al., 2010) considering that the uncertainty of
both retrievals is around 2 km. Likewise, Nowlan et al. (2011) showed
that the majority of the plume was around 10 km and up to
15 km in some parts. There is also agreement with IASI (Fig. 6b) and
CALIOP data (Fig. 6d), which showed plume heights of 10–12 and 12.5 km,
respectively. It is important to note that the IASI overpass occurred later in
the day than those for OMI and CALIPSO. Another verification source we used
was the GOME-2 SO2 layer height retrieval that uses FP_ILM
(Efremenko et al., 2017). The study found a height of around 10 and
up to 14 km in areas of high SO2 loading for 10 August
(Fig. 6c). The GOME-2 overpass occurred 4 h earlier than OMI. The
mean, median, standard deviation, and inner quartile range (IQR) of the
three retrievals (Table 4) also show good agreement for this case. Although
the OMI results agree well in general with the results of these studies and
datasets, the retrieval is less sensitive with respect to detecting
variability in the SO2 layer height within the plume.
Comparison between the volcanic plume heights from (a)
OMI, (b) IASI, (c) GOME-2, and (d) CALIOP lidar 532 nm attenuated
backscatter for the 2008 Kasatochi eruption. The black dotted line in (a)
shows the CALIPSO track. Some rows of OMI in this case were affected by the
row anomaly, as seen by the gaps in the plume. The red dots in (d) show the
OMI retrieval near the CALIPSO path, and the black dashed line denotes the
height of the ash plume observed by CALIPSO.
Statistical comparisons of the SO2 height retrievals
for 2 d of the Raikoke eruption and the Kasatochi eruption cases.
Raikoke (23 June 2019) Raikoke (24 June 2019) Kasatochi Metric (km)OMIIASITROPOMIOMIIASITROPOMIOMIIASIGOME-2Std. deviation1.670.851.962.380.651.041.390.721.29Median10.609.0012.1010.3010.0013.249.7010.0010.21Mean10.209.6312.1510.009.8313.309.8410.4010.02IQR1.791.002.712.681.001.201.361.001.67Kelud (2014)
Kelud, a stratovolcano located in East Java, Indonesia (7.935∘ S,
112.315∘ E), erupted on 13 February 2014 at 15:50 UTC, in the
process depositing ash in a 500 km diameter around the volcano and
leading to mass evacuations from nearby towns. Even though this case has
somewhat lower SO2 VCDs than those from Raikoke and Kasatochi (see Fig. A1), the
peak SO2 VCDs of ∼60–70 DU should still allow for
retrievals with reasonable accuracy (see Sect. 2). The OMI retrieval results
indicate that the maximum height of the main plume was 18–19 km
(Fig. 7a), although other studies suggest that several smaller layers of
SO2 and ash were located as high as 26 km (Vernier et al.,
2016) on the previous day. However, the SO2 loading at that level
was most likely too low for an accurate retrieval using OMI radiances. CALIOP
lidar detected ash plumes at around 19.5 km, and the IASI retrievals
registered the plume at 17.5 km over the same area as that for
OMI. The height of the ash plume from this eruption was also estimated using
Multifunctional Transport Satellite (MTSAT 2) observations and transport
modeling (Kristiansen et al., 2015). That study found an injected height of
around 17 km, which is in agreement with the OMI result, especially
when considering the most probable heights on the probability density function (PDF) (Fig. 8b). We note here
that only a small portion of the plume was retrieved with our algorithm given
the relatively low SO2 VCDs and interference due to the OMI row
anomaly. It is promising to note that the OMI retrieval was able to identify
heights at the upper end of the height range used in the training phase. On
the other hand, while the retrieval can extrapolate to heights above
20 km, the accuracy would likely degrade due to the lack of training
data with heights outside this limit.
Comparisons of plume heights for the 2015 Calbuco
eruption (a, c, e) and the Kelud eruption (b, d, f) for OMI (a, b), IASI (c, d), and
532 nm total attenuated backscatter from the CALIOP lidar (e, f). For OMI,
only pixels with >30DU of SO2 are shown, and retrievals
were unavailable for some parts of the plume due to the row anomaly. The
black dotted line in (a) and (b) marks the CALIPSO track. The white
rectangles in (e) and (f) show the location of the plume in the lidar
profile. Direct comparison with CALIPSO was not possible due to obstruction
by the OMI row anomaly.
Probability histograms of SO2 effective layer height
retrievals for (a) the Calbuco eruption on 24 April 2015 and (b) the Kelud
eruption on 14 February 2014.
Calbuco (2015)
The Calbuco volcano is located in Chile (41.331∘ S,
72.609∘ W). The primary eruption had a volcanic explosivity index
(VEI) of 4 and occurred on 22 April with little warning. The primary plume
ascended higher than 15 km, while plumes from smaller subsequent
eruptions stayed in the troposphere. The volcanic plume spread northeast in
the following days, resulting in flight cancelations at Uruguayan and southern
Brazilian airports. The OMI-retrieved SO2 effective layer heights in
the area of greatest VCD was in the 15–17 km range. In the same
region, IASI results (Fig. 7c) show similar plume heights of approximately
15 km, although as with the previous events, the overpass times
of the two instruments are different. CALIOP lidar shows the ash plume at
roughly 17 km (Fig. 7e). Unfortunately, the overpass of CALIPSO occurs
over an area of OMI's swath that is affected by the row anomaly, and this
makes a direct comparison unfeasible. Nevertheless, the CALIPSO aerosol layer
height is still comparable to OMI-retrieved effective SO2 layer
heights for the portion of the plume further to the west. The retrieval for
OMI is consistent with the other instruments for SO2 plumes, with
the exception of the part of the plume with SO2 below
30–40 DU (see Fig. A1), for which results were not plotted in Fig. 7a
due to lower biases.
Raikoke (2019)
The eruption of the Raikoke stratovolcano (48.2932∘ N,
153.254∘ E), located on the Kuril Islands of Russia, occurred on
21 June 2019 at 18:00 UTC. A series of explosions during the eruption
sent large amounts of ash and SO2 into the lower
stratosphere. Maximal loadings of SO2 measured by OMI and other
sensors exceeded 500 DU. In the following days the plume underwent
dispersion and spread out over the northern Pacific Ocean and later over
eastern Russia. Early estimates of plume injection height for the eruption
were predominantly in the 10–13 km range, with potentially larger
heights in some areas of the plume. In Fig. 9a and b, the SO2
effective layer heights retrieved from OMI data are shown for the Raikoke
plume on 23 and 24 June, respectively. The plume heights for both days are
predominantly in the range 10–12 km, although some areas of the plume
had estimated peak heights of 13–14 km. In comparison, the TROPOMI
results show slightly larger heights (13–14 km) for 24 June and
similar heights as OMI for 23 June (Fig. 9c and d). The IASI SO2
height product also shows fairly good agreement, with heights mainly at the
10–11 km level (Fig. 9e and f). It is also useful to look at a
distribution of heights predicted for the domain (Fig. 10) in order to get a
more quantitative comparison between the datasets. Based on this distribution,
there is clearly at least 2 km of difference between the most probable
heights from OMI and those from TROPOMI for 24 June (Fig. 10b and d) and
slightly lower heights in the distribution for IASI. This is also displayed in
Table 4, which shows a 2–3 km difference in the mean and median of
retrieved heights between OMI and TROPOMI. Additionally, the IQR and standard
deviation provide a quantitative measure of the variation in the distribution
of the retrieved heights, which can change from one orbit to another. Note
that points with values lower than 30 DU are not included in the PDFs for all
sensors. The results are also compared with the CALIOP lidar on board CALIPSO,
which shows ash plume heights of 12–13 km for both days (Fig. 11a and
b). Although there is overestimation for some OMI pixels, especially for
24 June, the section of the plume with the CALIPSO flyover has similar heights
(around 12.5 km) as lidar-determined aerosol layer altitudes. Lastly,
we note that a recent study highlighted probabilistic height retrievals using
the Cross-track Infrared Sounder (CrIS) for Raikoke. This study found a median
height of 10–12 km across a large part of the plume but with
some areas upwards of 15 km. While there are some notable differences
across all of the datasets, the OMI retrieval for this case falls within the
general consensus of plume height estimates for this volcanic event.
The SO2 layer height retrieval for the Raikoke
eruption plume on 23 June 2019 (a, c, e) and 24 June 2019
(b, d, f) for OMI (a, b), TROPOMI (c, d), and IASI (e, f). For
all three sensors, only pixels for which SO2 VCD > 30 DU are shown.
Probability histograms of SO2 layer height
retrievals for (a, b) OMI, (c, d), TROPOMI, and (e, f) IASI on 23 June 2019 (a, c, e)
and 24 June 2019 (b, d, f). Only pixels with an SO2
column amount greater than 30 DU are included. These plots correspond to the
results plotted in Fig. 4a–f.
CALIPSO lidar 532 nm attenuated backscatter for the
Raikoke eruption on (a) 23 June and (b) 24 June 2019. The
black dashed line symbolizes the height of the ash plume seen by CALIPSO, and red
dots show the results from the OMI retrieval along CALIPSO's flight path.
The flyovers occurred shortly after 01:30 and 00:30 UTC on 23 and 24 June,
respectively, around the same time as OMI.
Discussion of errors
It is clear that predicting SO2 layer height with FP_ILM is an
efficient process, but one that is not flawless in terms of accuracy. As
comparisons between instruments and retrievals have shown, on average there were
1–2 km differences in heights, especially for the Raikoke event,
although we consider this to be good agreement given the estimated MAE and
RMSE associated with this retrieval. In this regard, the retrieval is an
approximate estimate of the SO2 plume height rather than a precise
determination. Differences in the retrieved heights between different
studies and algorithms result from differences in instruments, forward model
assumptions, and retrieval techniques as well as uncertainties in each
retrieval. For instance, IASI is a thermal IR instrument and its retrieval
does not use FP_ILM. Therefore, exact agreement with IASI results is difficult
to achieve, especially since the IASI retrieval itself has a stated error
range of ±2km, although its retrievals serve as a good
verification dataset. The stated uncertainty for TROPOMI retrievals (Hedelt
et al., 2019) is ∼2km for SO2 amounts greater than
20 DU, similar to our estimated uncertainties for OMI. While the
general retrieval approach for TROPOMI (Hedelt et al., 2019) is similar to
that for OMI in the present study, there are also important instrument
differences that can lead to differences in the retrieved heights between the
two instruments, such as the pixel size, noise, radiometric accuracy, and
level of degradation. TROPOMI has a much finer spatial resolution compared to
OMI, with footprints typically 5.5×3.5km2 up to a maximum
size of 7×3.5km2; TROPOMI also has larger maximal
SO2 signals. Consequently, TROPOMI is better able to resolve
localized variations in the height throughout the plume and is likely to be
more accurate overall due to better SNR. However, current TROPOMI L1 data are
known to have issues with instrument degradation and radiometric accuracy in
the UV spectral range (Ludewig et al., 2020); this could be a potential
contributing factor to the differences between the two instruments. OMI
retrievals show more or less uniform height levels across the entire plume,
with the peak heights in areas with the best SO2 signal. Note that
CALIOP lidar profiles sometimes show disagreement with OMI-retrieved heights
because CALIOP only identifies the height of the ash or aerosol plume. It also
offers a comparison for only a single cross section of the entire plume per
orbit. Despite the uncertainties, the consensus provided by different
instrumental datasets can provide a reasonable estimate for the SO2
layer height and, if done in near-real time, can aid in decision-making with
regards to aviation safety.
Another source of error is present in the training phase. One difficulty here
is finding the ideal choice of neural network setup. With many parameters to
consider, such as the number of input PCs, number of layers, number of nodes,
learning rate, regularization, and weight initialization, it is very time-consuming to optimize the neural network setup. We have found a relatively
simply configuration that performed reasonably well with both test data and
real OMI measurements for all scenarios and events considered. However, even
after optimization of the parameters, random error inherently exists in the
neural network. A measure of random error can be obtained by altering the
random state of the neural network whilst keeping other parameters
constant. For 10 trial runs with different random seeds, variations of the
MAE error were around 0.15–0.2 km (see Table A2). Although the
differences in the errors calculated with the synthetic test data are
relatively small, larger changes can be expected during the application
phase. Indeed, when applying the inverse models to OMI, there is noticeable variation of
up to 1 km in the retrieved height for the same pixels. It
is thus difficult to improve results further than ∼1km of absolute
error, even in the training phase. In the application phase, some additional
error comes from the differences between synthetic spectra and real satellite
measurements with noise errors. For example, with an SNR of 500 used in
training, which is a typical noise level for OMI, the RMSE of the neural
network prediction is around 1.25 km (Table 3). This can be considered
the lower limit of retrieval error when the inverse operator is used on OMI
measurements. Lastly, some deviations between the measured and synthetic
training spectra originate from the RT modeling. The calculations contain
several assumptions including the SO2 plume shape, atmospheric
profiles, gas profiles, and a molecular scattering atmosphere. Further testing
is required in order to determine if the inclusion of aerosols in RT
calculations would improve the algorithm performance.
Conclusions
In this study we have introduced a new algorithm for OMI retrievals of the
volcanic SO2 effective layer height from UV Earthshine
radiances. This algorithm is based on an existing FP_ILM method that
combines a computationally time-consuming training phase with full radiative
transfer model simulations and a machine-learning approach to develop a fast
inverse model for the extraction of plume height information from radiance
spectra. Fast performance means that the algorithm can be considered for
operational deployment given that the retrieval of an SO2 layer
height prediction from the inverse model takes only a matter of milliseconds
for a single OMI ground pixel. For the training, a synthetic dataset of
Earthshine radiance spectra was created with the LIDORT-RRS RT model for a
variety of conditions based on choices of eight physical parameters determined
with smart sampling techniques. A dimensionality reduction was performed
through PCA in order to reduce the complexity of the problem and to separate
those features that best capture the majority of variance in the
dataset; eight principal components were sufficient for this
purpose. Dimensionally reduced data together with the associated parameters
were used to train a double hidden-layer neural network to predict
SO2 plume height from any given input data. The PCA from the
training phase and the inverse operator resulting from the optimal NN
framework were then applied to real satellite radiance spectra and parameters
to get retrieved values of SO2 plume heights for several volcanic
eruption events.
Through comparisons with CALIPSO lidar overpasses, as well as TROPOMI and IASI
retrievals, it was shown that the retrieval for OMI can estimate reasonable
SO2 layer height for all the events considered, with absolute errors
in the range of 1–2 km. These results can give an indication of plume
heights achieved during medium- to large-scale eruptions and guide important
decisions in aviation hazard mitigation. For all events treated in this study,
there was general agreement with CALIOP lidar, although SO2 could
not be retrieved for the locations of the CALIPSO flight path for the Kelud
and Calbuco cases due to OMI row anomaly issues.
Uncertainties and sources of error in using this approach open up
possibilities for future work in improving the accuracy of the retrieval. We
assumed that ash and sulfur dioxide plumes are mostly collocated when using
CALIPSO as a source to verify the plume height. Although this is often true,
dispersion of the plume in the days following the eruption can separate the
two components. Therefore, tracking these plumes become challenging when
using reflectance spectra alone; further analysis may need to include
trajectories or wind data. The model was trained on synthetic spectra
calculated for molecular atmosphere conditions in the absence of any aerosol
loading. The impact of including aerosols in the simulations is another
subject for a follow-up study. We also intend to generate datasets of
synthetic spectra by using a vector RRS model to account for polarization.
For improving the performance and efficiency of the machine learning, the
use of neural network ensembles and a further optimized setup of NN
structure and parameters will be explored. Other future work will include
extending the application of FP_ILM to the Suomi-NPP OMPS
instrument and exploring the ability to predict multiple outputs
simultaneously from this approach.
Mean absolute difference and RMSE for different
reductions of the original training dataset. The test was performed on
training sets for five different OMI rows, and the errors were averaged.
Percent of samples withheld01020304050Mean abs. difference0.950.981.021.081.121.24RMSE1.461.451.621.691.792.00
Effect of altering random seed number on error obtained
using the test dataset and the SO2 height retrieval result after
application to OMI. For the results, heights for two different pixels within
the orbit from the Raikoke event (24 June 2019) are shown. Heights
were retrieved using separate inverse models trained using 10 random states.
Random seed12345678910numberNN training errorAbs. mean error0.981.141.031.161.081.181.051.011.120.98RMSE1.691.851.711.781.791.921.711.671.731.70Application (Raikoke –Sample pixel 110.5210.6910.499.729.9810.2310.5310.1910.0710.48OMI orbit 79463)Sample pixel 212.4213.1512.0811.7011.8812.0112.3811.2211.9412.16
SO2 VCD for the four volcanic cases: (a)
Kasatochi on 10 August 2008, (b) Kelud on 14 February 2014,
(c) Calbuco on 24 April 2015, and (d) Raikoke on 24 June 2019. In
these maps, only pixels with SO2> 10 DU are shown.
Data availability
OMI SO2 L1 and L2 data can be accessed via the
Goddard Earth Sciences Data and Information Services Center (GES DISC) at
https://earthdata.nasa.gov/eosdis/daacs/gesdisc (NASA, 2020). IASI SO2 LH data are
available via the IASI AERIS portal at https://iasi.aeris-data.fr/SO2/ (Clarisse et al., 2012). NASA
CALIPSO data can be downloaded from https://doi.org/10.5067/CALIOP/CALIPSO/LID_L1-STANDARD-V4-10 (NASA/LARC/SD/ASDC, 2016), and
images can be found at
https://www-calipso.larc.nasa.gov/products/lidar/browse_images/production (NASA, 2011). TROPOMI L2 SO2 data can be obtained at
https://doi.org/10.5270/S5P-74eidii, (European Space Agency, 2020) while the LH is
experimental and not yet publicly available online. The results of OMI
SO2 layer height retrieval presented in this study can be obtained from the
authors by request.
Author contributions
NMF wrote the paper and performed most of the
computational and model work in this study. The project was conceived and
overseen by CL and NAK. DGL and PH provided the TROPOMI SO2 LH retrieval data
and input on the comparisons in the paper. PH also offered support relating
to the machine-learning aspect of the study. RS is the original developer of
the LIDORT-RRS code and provided related support, as well as input to the
relevant sections of the paper. RRD is an advisor of NMF, provided
additional input to the paper, and was involved in project planning.
Competing interests
The authors declare that they have no conflict
of interest.
Acknowledgements
We would like to acknowledge the NASA Earth
Science Division (ESD) Aura Science Team program for funding the OMI
SO2 product development and analysis. OMI is
a Dutch–Finish contribution to the NASA Aura mission. The OMI project is
managed by the Royal Meteorological Institute of the Netherlands (KNMI) and
the Netherlands Space Office (NSO).
Financial support
This research has been supported by the NASA Earth Sciences Division (grant no. 80NSSC17K0240).
Review statement
This paper was edited by Helen Worden and reviewed by two anonymous referees.
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