Introduction
The sounding of planetary atmospheres by observation of astronomical objects
(Sun, Moon, planets, stars) in occultation is a well-established technique.
Spaceborne Earth observation instruments such as SAGE II , SAGE III , ORA , POAM III ,
ACE–Maestro and GOMOS have
clearly demonstrated the possibility to obtain altitude-resolved profiles for
a number of atmospheric gaseous species and particles (aerosols, clouds),
through the combination of occultation transmittance measurements with a
dedicated data inversion algorithm. For obvious reasons, most instruments use
the Sun as light source, although the geographical coverage and temporal
sampling (at most twice per orbit) is limited. Stellar occultation largely
resolves these problems (due to the abundance of stars), however at the cost
of a reduced measurement S/N ratio.
The GOMOS instrument and its 10-year quasi-continuous operation can be
considered a success. An extensive body of papers have been published in the
scientific literature that describe the instrument, data processing, and the
obtained scientific results for the different atmospheric species; a good
overview article has been published by . Notwithstanding
this success, several problems regarding the instrument and the data
processing posed difficulties. Most noteworthy, the imperfect correction of
stellar scintillation due to isotropic turbulence remains
a problem, though the associated residual scintillations have been adequately
characterized in a statistical analysis . The random nature
of these perturbations causes them to disappear after averaging of binned
constituent profiles. More important within the context of this paper,
aerosol–cloud extinction profile retrievals are of good quality at 500 nm
but suffer from unphysical
perturbations at other wavelengths within the GOMOS spectral range. This
problem was already identified earlier but has
been left unexamined until now.
From a retrieval point of view, the importance of good aerosol–cloud
extinction retrievals lies in the fact that they are intrinsically linked
with the retrieval quality of the other species; specifically, upper
troposphere–lower stratosphere (UTLS) ozone values are significantly biased
due to erroneous aerosol retrievals . Scientifically, good
aerosol–cloud extinction observations in the UTLS and stratosphere are of
main importance for atmospheric research, in two ways: (1) the Earth
radiative budget depends on the optical properties of high-altitude clouds
and volcanic sulfate aerosols, and (2) heterogeneous polar ozone chemistry
is driven by the presence of polar stratospheric clouds (PSCs), stratospheric
aerosols and high-altitude cirrus clouds. A good overview of the scientific
significance of aerosols–clouds can be found in the SPARC report
.
Improvement of a long-term aerosol–cloud data record such as the one provided
by GOMOS is therefore important. The European Space Agency (ESA) has
acknowledged this by funding the AerGOM project (Aerosol profile retrieval
prototype for GOMOS). Within this project framework, data inversion problems
have been studied, solutions have been found, and a new Level 2 algorithm has
been developed.
In this article, we summarize the essentials of the GOMOS instrument and its
operational data processing algorithm (currently IPF v6.01). Subsequently, we
present and justify the specific features that have been changed in the
AerGOM code. Finally, the AerGOM aerosol–cloud extinction results are
discussed in a qualitative way; a detailed data validation is presented in a
companion paper .
GOMOS and its operational data processor
Instrument and measurement principle
The GOMOS instrument and measurement principles are described elsewhere (see
e.g. ). GOMOS (Global Ozone
Monitoring by Occultation of Stars), a UV–Vis–NIR grating spectrometer on
board ESA's Envisat satellite, was launched into a sun-synchronous orbit on
1 March 2002. Routine operations started in August 2002, and continued
almost uninterruptedly until the end of the mission on 8 April 2012, when
contact with the satellite was lost. Using the method of stellar occultation,
GOMOS was able to monitor ozone (its main target gas), a number of other
trace gases and aerosols, at altitudes that fall within the range from the
upper troposphere to the top of the atmosphere. In total, almost a million
occultations have been registered by GOMOS during its 10-year mission,
roughly half of them in dark limb conditions (local nighttime).
Spectrally, GOMOS is a medium-resolution instrument, designed with ozone
monitoring in mind. To obtain ozone profiles from the UTLS (using the
Chappuis band) to the upper mesosphere (using the Hartley band), two
spectrometers SPA1 and SPA2 were included, covering the UV–visible wavelength
range (248–690 nm); apart from ozone, this spectral range also allows for the
measurement of optical absorption by NO2, NO3, and the extinction
(scattering) by aerosols and air. Other trace gases such as OClO and Na are
also detectable with specific statistical methods. Furthermore, a
spectrometer B1 (SPB1) was added (spectral range 755–774 nm), with the
purpose of measuring absorption in the O2 A band. Finally, a spectrometer
B2 (SPB2) in the near-IR wavelength range (926–954 nm) allows the measurement
of water vapour. The GOMOS spectrometer characteristics are summarized in
Table .
It was realized in an early stage of the GOMOS development that stellar
scintillation would perturb the measurements considerably. In order to remove
this perturbation, GOMOS was equipped with two fast photometers, sampling the
blue (473–527 nm) and the red (646–698 nm) spectral domain at a frequency of
1 kHz. Apart from the scintillation correction (which was only partially
achieved; see further in the text), the time delay between the two photometer
signals due to chromatic refraction has been used to obtain altitude profiles
of refractive index and temperature.
GOMOS spectral bands. The number of pixels for each band and the optically active species are also indicated.
Spectral band
Wavelength range
No. pixels
Resolution
Major absorbing–scattering species
SPA1 & SPA2
248–690 nm
1416
0.8 nm
neutral density, O3, NO2, NO3, aerosols–clouds
SPB1
775–774 nm
420
0.13 nm
neutral density, O2, aerosols–clouds
SPB2
926–954 nm
500
0.13 nm
neutral density, H2O, aerosols–clouds
The basic principle of a stellar occultation experiment is simple: due to
orbital motion of the satellite, one observes a star setting behind the Earth
horizon; subsequent measurements at different satellite positions therefore
sample different atmospheric layers. The altitudinal distribution of
atmospheric species can in principle be obtained from this sequence of
measurements. The discrimination between different species is of course
achieved by measuring in different spectral regions. The duration of a star
occultation is determined by its obliquity: an occultation within the orbital
plane is vertical and therefore short (about 40 s), while observations
at an angle with the orbital plane are slant, with a long duration (up to
several minutes). It is clear that, for a fixed acquisition time per
spectrum, better altitudinal sampling is obtained for long occultation
durations.
Finally, it should be mentioned that the measurement S/N ratio is largely
determined by the apparent brightness and the temperature of the star; the
catalogue used by GOMOS contains objects with visual magnitudes smaller than
4 and temperatures ranging from 3000–30 000 K (i.e. most stellar
spectral types). The combined effects of varying obliquities and star
characteristics lead to a GOMOS data set that has in a sense an inhomogeneous
nature; during data analysis, the variation in altitudinal sampling and S/N
ratio has to be taken into account.
IPFv6.01 operational data processing
Assumptions and initial processing
It is not the purpose of this paper to describe in detail the GOMOS
operational data processing chain. It is nevertheless necessary to give a
general overview, in order to highlight the differences with the AerGOM
processor further in the text. Detailed descriptions can be found in
. Before the actual data inversion from
measurements to geophysical products is performed, downlinked data are
formatted, ancillary data are added, the necessary calibration steps are
taken and erroneous measurements (e.g. resulting from cosmic ray impacts) are
flagged. The contribution of star scintillation to transmittance is estimated
from the data of the two photometers and is removed from the spectrometer
data. As was mentioned in the introduction, this correction is incomplete
since residual scintillation due to isotropic turbulence is not accounted
for.
The subsequent Level 2 processing steps are based on a number of assumptions
and corrections. (1) The Earth is globally described by a WGS84 reference
ellipsoid . Locally, the Earth is approximated by a tangent
sphere with a radius equal to the one given by the WGS84 model. (2) Chromatic
refraction leads to different tangent points for different wavelengths. A
data reinterpolation is performed such that one entire transmittance spectrum
is associated with the same tangent point. (3) A correction for refractive
dilution is applied. The phenomenon is caused by the altitude gradient of the
air refractive index and consists of the spreading of light rays (divergence)
and an associated decrease in light flux. (4) The finite spectral response of
the instrument is taken into account by applying a convolution of theoretical
or lab-measured cross sections with the instrument response function. (5) Slant
path aerosol optical depth (SAOD) is modelled as a quadratic polynomial
of wavelength:
τaer(λ)=τaer(λref)1+c1(λ-λref)+c2(λ-λref)2,
with λref a reference wavelength of 500 nm, and
τaer(λref), c1 and c2 parameters to be
fitted. A quadratic polynomial can fit a wide range of spectral shapes,
representing small particles (τ∼λ-4), submicron-sized
particles (spectra peaking in the visible wavelength range) to large
particles (τ= constant). (6) The variance of the residual scintillation
component in the signals due to isotropic turbulence is taken into account by
adding an extra term to the measurement covariance matrix. This so-called
full covariance matrix (FCM) method has been described by .
The Level 2 inversion is of course based on the Beer–Lambert law for optical
extinction. Furthermore, the entire inversion is divided in two separate
subproblems: (1) a spectral inversion from individual transmittance spectra
to slant path integrated gas column densities (SGDs; unit: cm-2) and
aerosol optical depths (SAODs; unitless), and (2) a spatial inversion from
these slant path integrated quantities to local gas density and aerosol
extinction altitude profiles. The main advantage of this processing chain
lies in its numerical efficiency: a large number of measurements
(transmittance spectra) are reduced to a small number of slant path
integrated quantities in an early stage of the processing.
Spectral inversion
The SPB1 and SPB2 spectrometers were primarily meant for oxygen and water
vapour measurements. To separate the processing of these two species, it was
decided to obtain all other species exclusively from SPA1 and SPA2 data. As
an initial step, to avoid correlations between the spectrally similar aerosol
and air scattering contributions, the latter is evaluated from ECMWF
(European Centre for Medium-Range Weather Forecasts) temperature and pressure
forecasts and is removed. The other contributions (O3, NO2 and NO3
SGDs; aerosol SAODs) are obtained by fitting the remaining transmittance
Trem with the Beer–Lambert law (using a Levenberg–Marquardt
nonlinear least-squares code). In an early stage of the mission, it was found
that the NO2 and NO3 SGD retrievals suffered badly from the residual
scintillation in the measurements; it was decided to fit both species by
making use of their differential spectral features, in a DOAS-like manner
(differential optical absorption spectroscopy).
At the final iteration of each individual spectral fit, the obtained
covariance matrix is evaluated from the forward model Jacobian. It should be
emphasized that the fit is performed for every tangent altitude separately;
the retrieval covariances between species at different altitudes are
therefore equal to zero.
Spatial inversion
The obtained SGDs and SAODs are equal
to the integral of the local gas densities and aerosol extinction
coefficients along the optical path. An appropriate discretization of this
integral leads to a linear forward model. For example, the model equations
for the column vectors representing altitude profiles for the ozone SGD
NO3 and the 500 nm aerosol SAOD
τaer, 500 equal
NO3=GnO3τaer, 500=Gβaer, 500,
with the nO3 and βaer, 500
vectors representing altitude profiles for the ozone density (molecules cm-3) and 500 nm aerosol extinction (cm-1). The square triangular
matrix G contains optical path length contributions: the matrix
element Gij equals the path length for a ray with tangent point radius
rit through the atmospheric layer centred at rjt.
The spatial inversion then consists of finding a solution for the unknown
local altitude profiles (nO3,
βaer, 500 etc.), using a linear least-squares
method, subject to a Tikhonov smoothing constraint. The associated merit
function to be minimized reads (for ozone, as an example)
M=[NO3-GnO3]TSN,O3-1[NO3-GnO3]+nO3TLTLnO3,
where NO3 now represents actual GOMOS-derived SGDs. The
diagonal of the slant path covariance matrix SN,O3 contains
all variances obtained from the spectral inversion; off-diagonal elements are
zero since the spectral inversion occurs separately for each tangent
altitude. In the second term, the matrix L represents a
first-difference operator, scaled with altitude- and species-dependent weight
factors that tune the profile altitude resolution according to predefined
values. This Tikhonov regularization term was introduced to decrease the
amplitude of the spurious profile perturbations caused by residual
scintillation.
It should be noticed that every individual constituent profile is retrieved
independently from the others. This means that spectral inversion covariances
between different species are discarded, meaning the algorithm assumes
(wrongly) that the obtained SGDs and SAODs after spectral inversion are
uncorrelated.
IPFv6.01 Level 2 data products
The entire data processing chain finally results in dedicated Level 2 data
product files that contain gas SGDs, aerosol SAODs, local gas density and
aerosol extinction profiles, together with respective retrieval error
estimates. Of specific importance to the subsequent AerGOM discussion in this
paper are the so-called residual extinction product files: apart from fit
chi-squared statistics and the transmittance fit, they contain the actual
transmittance measurements, corrected for refractive dilution and
scintillation, and are used as the transmittance data source for the AerGOM
inversions.
Data quality
With respect to the gaseous Level 2 products, several validation studies have
been performed, an overview of which can be found in .
Initial IPFv6.01 aerosol extinction validation results are presented by
. At wavelengths around 500 nm, good agreement was
found within 20 % with SAGE II and SAGE III data (for altitudes from 10 to
25 km) and within 10 % with POAM III (from 11 to 22 km). At other
wavelengths no validation results were published due to the fact that
IPFv6.01 GOMOS aerosol extinction profiles are of very poor quality. More
specifically, strong oscillations are found in the extinction profiles, and
extinction spectra often are very unrealistic. Examples can be found further
in Figs. , and
(discussed below).
The AerGOM algorithm improvements
General approach
AerGOM shares with the GOMOS processor the same basic separation of the data
processing in two distinct steps: a nonlinear spectral inversion, followed by
a linear, regularized spatial inversion. There are however several
significant differences. (1) To improve accuracy, better equations for the
air refractive index and Rayleigh cross section have been used. (2) During
spectral inversion, no differential (DOAS) method is applied to obtain NO2
and NO3 SGDs; all gases–aerosols are retrieved together, using their full
absorption cross-section–spectral model. This is conceptually simpler;
furthermore it ensures that all covariances are retained by the solution. (3) The spectral
behaviour of aerosol SAOD is modelled in a better way. (4) The
algorithm allows the use of SPB1 and SPB2 pixels, hereby increasing the
spectral range and the information content of the solution. (5) The spatial
inversion is applied to all species together, hereby making full use of the
SGD and SAOD variances and covariances. No information is discarded. And (6) for the
spatial inversion, an altitude regularization with a specific scaling
is implemented.
Rayleigh scattering by the neutral density (air)
Equations for the air scattering cross section, approximated for small
refractivities (refractive index m≈1), are still commonly found in
the literature. For optimal accuracy, we use the exact theoretical result
(see e.g. ):
Cair=24π3λ4nstp2mstp(λ)2-1mstp(λ)2+226+3ρ6-7ρ,
with ρ the depolarization ratio that takes into account molecular
anisotropy, and nstp the air number density at standard
temperature and pressure (Pstp=1013.25 mb,
Tstp=288.15 K). The air refractive index mstp is
evaluated using the equation of , which is slightly more
accurate than the still widely used Edlén law (also used
in the GOMOS IPF processor). The factor Fair=(6+3ρ)/(6-7ρ) is known as the King factor. For air, it is commonly
assumed to have a value of 1.06 . The GOMOS IPFv6.01
processor also assumes this value, together with a slightly
modified form of Eq. (). However, Fair
depends on wavelength and the actual composition of air, and this should be
taken into account. A good overview of this subject was given by
. First, we need the partial depolarization of nitrogen and
oxygen as given by :
FN2(λ)=1.034+3.17×10-4λ-2FO2(λ)=1.096+1.385×10-3λ-2+1.448×10-4λ-4.
Furthermore, suggested to take FAr=1,
FCO2=1.15 and to ignore other air constituents. Finally, the
King factor for air can be calculated as a function of wavelength as
Fair(λ)=∑iCiFi(λ)∑iCi,
where the summation runs over the four most abundant gases, and with
concentrations expressed in parts per volume by percent (e.g. use 0.036 for
360 ppm of CO2). The concentration values are CN2=78.084,
CO2=20.946, CAr=0.934 and CCO2=0.036.
Figure shows calculated King factors in the UV–Vis–NIR.
For illustration, Fair equals 1.063 at λ=250 nm and
1.047 at λ=1 µm. The constant value of 1.06 leads to an error
in the Rayleigh cross section of respectively 0.3 and 1.2 %; the impact
on the retrieval of relatively low aerosol extinction coefficients is
significant.
The AerGOM algorithm offers the choice to retrieve the neutral air density
or to remove the contribution from the measured transmittance
Tmeas by making use of ECMWF air density profiles, as provided in
the GOMOS residual extinction files. The resulting transmission T to be
used for the data inversion of all other species is given by
T(λ,rt)=Tmeas(λ,rt)Tair(λ,rt),
with Tair the transmittance by neutral air having SGD
Nair:
Tair(λ,rt)=exp-Cair(λ)Nair(rt).
The wavelength-dependent King factor Fair , together with the commonly used value of 1.06.
Aerosol extinction modelization
Frequently used models
Prior to the actual inversion of occultation measurements, little is known
about the composition, size distribution and morphology of atmospheric
particles. The use of Mie theory to model extinction spectra for data
inversion purposes is therefore limited. In practice, it is usually preferred
to represent aerosol extinction or optical thickness spectra by a smooth
analytical function with a small number of parameters (which are to be
fitted). The well-known Ångström empirical power law (β=Aλ-α) is a prime example. It is however not versatile enough;
researchers are often forced to make the coefficients A and α
wavelength dependent, an approach that seems rather arbitrary. In the current
operational GOMOS Level 2 algorithm (IPFv6.01), a quadratic polynomial of
wavelength (Eq. ) is assumed for the aerosol
SAOD. In the past, retrieval algorithms for other occultation instruments
such as SAGE III and POAM III were
equipped with similar spectral laws for aerosol extinction
βaer; however they are often expressed as a function of the natural
logarithm of wavelength:
βaer(λ)=c0+c1logλ)+c2(log(λ)2.
The formalism can of course be extended to general polynomials of functions
of wavelength. As an example, quadratic polynomials of inverse wavelength
(λ-1) have been found to model realistic extinction spectra quite
well .
AerGOM aerosol spectral law implementation
Inspecting Eq. (), we see that, among the three fit
parameters, only τaer(λref) represents a
physical quantity. There are two reasons for why this formalism is not
optimal: (1) the three coefficients τaer, c1 and c2 have
a different unit and magnitude, giving rise to scaling problems during
numerical inversion, and (2) during the spatial inversion from SAOD to local
extinction values, it is not clear whether or not altitude regularization
constraints on the coefficients c1 and c2 are meaningful. The GOMOS
IPFv6.01 algorithm, making use of this implementation, avoids the second
point by inverting only τaer(λref) with
altitude regularization. It is the main reason why GOMOS aerosol extinction
profiles exhibit strong oscillations for other wavelengths than
λref=500 nm.
The AerGOM solution consists of a fairly simple mathematical reformulation.
The SAOD, modelled as an mth degree polynomial of a function of wavelength
f(λ), can be expressed as a Lagrangian interpolation formula between
a number of discrete SAOD values τ(λi) at different wavelengths:
τaer(λ)=∑i=1m+1qi(λ)τaer(λi),
with spectral base functions
qi(λ)=∏j≠im+1f(λ)-f(λj)f(λi)-f(λj).
For example, a quadratic polynomial of inverse wavelength is specified
by the choice m=2 and three spectral base functions:
qi(λ)=(λ-1-λj-1)(λ-1-λk-1)(λi-1-λj-1)(λi-1-λk-1),
with λi, λj and λk three different wavelengths
that have to be specified in advance. Examples of base functions are given in
Fig. . The spectral behaviour of aerosols is
now parametrized by three SAOD values, having the same order of magnitude and
a direct physical meaning.
Aerosol spectral model: choice based on data
The actual choice of aerosol spectral law should be based on its ability to
model realistic spectra for particle populations that are found in the
atmosphere. By fitting measured or measurement-derived aerosol extinction
spectra with a number of candidate analytical extinction models, it is
possible to single out one of these models that can be used in the AerGOM
retrieval algorithm. We therefore consulted particle size data derived from
measurements that were performed by satellite instruments (SAGE II, CLAES and
POAM), field campaign results (APE-THESEO; Airborne Platform for Earth
observation – contribution to the Third European Stratospheric Experiment on
Ozone; ) and many lidar and in situ instruments
. Measurements of different particle types were considered:
(1) stratospheric sulfuric acid droplets, (2) polar stratospheric clouds
(NAT: nitric acid trihydrate; STS: supercooled ternary solution; water ice)
and (3) cirrus and subvisual cirrus clouds.
Aerosol spectral functions q1(λ) (solid), q2(λ) (dashed) and q3(λ) (dash-dot) for a
quadratic polynomial of inverse wavelength. The three predefined wavelengths are λ1=350 nm, λ2=550 nm, and λ3=756 nm (vertical lines).
Starting from published values of microphysical parameters (typically
lognormal parameters for total number density, mode radius and distribution
width), we simulated extinction spectra with a Mie code (assuming spherical
particles). This of course requires the wavelength-dependent refractive index
of the particles under consideration. For pure-water ice these can be
directly interpolated from tabulated data that were published by
. The other particle types that are to be expected consist of
binary and ternary solutions of sulfuric or nitric acid, of which the weight
percentages (mainly driven by temperature) were obtained from theory: polar
winter temperatures as well as common stratospheric
temperatures were considered. From these weight
percentages, the refractive index was calculated with a code, published by
, which is based on a generalized Lorentz–Lorenz equation for
the refractive index. The various ways we calculated the
refractive index for commonly encountered particle types in GOMOS data are
summarized in Table .
The types of particles that are to be expected in the GOMOS data, with characteristics. The methods used to estimate composition (from temperature) and refractive index are also indicated.
Type
State/morphology/composition
Weight percentage
Refractive index
Background
Liquid/spherical, H2O/H2SO4
Volcanic
Liquid/spherical, H2O/H2SO4
Cirrus
Solid/crystalline, H2O
–
NAT PSC
Solid/amorphous, HNO3/H2O
STS PSC
Liquid/spherical, H2O/H2SO4/HNO3
Ice PSC
Solid/crystalline, H2O
–
Stratospheric aerosols: lognormal particle size distribution parameters rm (mode radius)
and σ (mode width), and aerosol extinction βaer at 525 nm, representative of the
period just before and after the Pinatubo eruption, at two different altitudes, in the 30–50∘ N
latitude band. The data were derived from Figs. 4, 8 and 11 of . A few calculated refractive
indices are also given.
Number
rm
σ
βaer (525 nm)
in Fig.
(µm)
(10-3 km-1)
Altitude = 18.5 km, T= 217 K, H2SO4 weight perc. = 78 %
Refractive index = 1.47 (400 nm), 1.46 (600 nm)
1
0.075
1.4
1
2
0.084
1.8
1
3
0.063
2.2
2
4
0.169
1.8
4
5
0.288
1.6
5
6
0.181
2.0
5
Altitude = 26.5 km, T= 223 K, H2SO4 weight perc. = 82 %
Refractive index = 1.48 (400 nm), 1.47 (600 nm)
7
0.092
1.2
0.05
8
0.151
1.4
0.4
9
0.127
1.8
2
10
0.230
1.6
4
11
0.288
1.6
8
12
0.346
1.6
12
Finally, the obtained spectra were fitted with a range of candidate spectral
laws. Extinction and the logarithm of extinction were fitted with
second- and third-degree polynomials of λ, 1/λ and
log(λ). After comparison of the fit quality, the second-degree
polynomial of inverse wavelength was singled out as a good versatile model
for particle extinction spectra for the bulk of GOMOS measurements.
Stratospheric aerosols: bimodal lognormal particle size distribution parameters
N0 and N1 (aerosol total number density), rm0 and rm1 (mode radius),
and σ0 and σ1 (mode width), representative of the period just before and after the
Pinatubo eruption. The data were obtained from impactor samples on an ER-2 aircraft and were published
by (Table 1a). For optical calculations, we used a H2SO4 weight percentage of
78 %, corresponding to a temperature of 217 K. Examples of refractive indices: 1.47 (400 nm), 1.46 (600 nm).
Number
Date
Latitude
Longitude
Altitude
N0
rm0
σ0
N1
rm1
σ1
in Fig.
(km)
(cm-3)
(µm)
(cm-3)
(µm)
13
28 Feb 1991
40∘ N
123∘ W
18.3
1.0
0.1
1.8
0
0
0
14
14 Oct 1991
39∘ N
123∘ W
20.7
2.8
0.11
1.4
1.9
0.30
1.5
15
14 Oct 1991
66∘ N
123∘ W
18.5
2.8
0.13
1.6
0.6
0.55
1.2
16
2 Nov 1991
41∘ N
107∘ W
20.2
2.1
0.09
1.2
1.2
0.35
1.6
17
20 Mar 1992
48∘ N
71∘ W
20.0
0.4
0.09
1.5
1.8
0.46
1.7
As an example, we used the SAGE II–CLAES stratospheric aerosol climatology of
and converted a few of their values for effective radius
Reff, mode width σ and 525 nm aerosol extinction
βaero (respectively Figs. 4, 8 and 11 in the paper) to the
values in Table . Furthermore, stratospheric in situ
data derived from impactor samples collected onboard an ER-2 aircraft
were used (see Table ). In both
cases, we assumed US76 temperatures at the considered altitudes and derived
corresponding H2SO4 weight percentages with the method of
. Refractive indices were obtained with the method of
. Finally, we calculated the extinction spectra in Fig.
with a Mie code. Also shown are the fits with the
quadratic polynomial of inverse wavelength; the correspondence is quite
good.
Transmittance data
As mentioned before, the GOMOS IPFv6.01 processor uses exclusively SPA1 and
SPA2 data for the retrieval of O3, NO2, NO3 and aerosol extinction
data products, while the SPB1 and SPB2 data are reserved for the retrieval of
O2 and H2O. With respect to aerosol retrievals, this is regrettable; at
longer wavelengths, the relative contribution of aerosol extinction is
stronger (in the lower atmosphere) due to weaker air scattering. Furthermore,
anticipating future research, particle size distribution retrievals improve
if the spectral range is larger .
Measured and fitted stratospheric sulfate aerosol extinction spectra for different aerosol size distributions.
The three panels each cover a different extinction magnitude range. Crosses with dashed lines represent values derived from a
SAGE II–CLAES climatology (red) and in situ impactor measurements (green). Also shown is the fit with the second-order polynomial
of inverse wavelength (black solid lines). The numbers on the plots correspond to the data in Tables and .
Examples of spectra (27 September 2004, 21.17∘ S, 48.62∘ E) for SPB1 (left) and SPB2
(middle) at tangent altitudes of (roughly) 15, 20, 25, 30, 35, 40 and 45 km (from bottom to top). Right panel:
tangent altitude profiles of GOMOS transmittance for spectrometer A: 300 (magenta), 400 (green), 500 (blue), 600 nm (cyan);
spectrometer B1 (black); B2 (red); the B1 and B2 profiles are very rough estimates of what can be expected; they are median
values of the wings left and right of the B1 oxygen band, and the entire B2 spectrum respectively.
We therefore studied the possibility of exploiting SPB1 and SPB2 data in the
AerGOM processor. Of course, care needs to be taken to avoid the use of
wavelengths at which O2 and H2O absorb. Figure shows
one way of doing this. It is intuitively clear that the spectral ranges to
the left and the right of the O2 absorption band in the SPB1 data are
useful to extract aerosol extinction. On the other hand, it is far less
obvious to define SPB2 spectral pixels that are free of H2O absorption
lines. The importance of these spectral regions is nevertheless clear when we
observe the transmittance altitude profiles in the right panel of Fig. ; in the lower stratosphere and upper troposphere (our
main region of interest) a very useful range of transmittance is present in
the SPB1 and SPB2 spectral bands while the SPA transmittance values have
almost dropped to zero. For flexibility, the AerGOM processor offers the
possibility to select SPA/SPB1/SPB2 spectral pixels at will. Due to the
difficulty of finding SPB2 spectral pixels without H2O absorption, and the
fact that AerGOM is at present not able to perform H2O retrievals, SPB2
data are currently not selected for the retrievals. This situation will
likely change for future AerGOM data versions.
AerGOM spectral inversion
In comparison with the GOMOS processor, the AerGOM spectral inversion is
conceptually much simpler. No separate differential method is used to derive
NO2 and NO3 SGDs. Instead, contributions from all molecular/particulate
species to the optical extinction are included in the Beer–Lambert forward
model, which now reads
T(rt,λ)=exp-∑iCi(λ)Ni(rt)-∑jqj(λ)τaer(rt,λj)).
The first term in the exponent indicates a summation over all gaseous species
(O3, NO2 and NO3, if Rayleigh scattering is removed before
inversion), while the second term expresses our new aerosol SAOD formalism
(Eq. ). Once again, a nonlinear Levenberg–Marquardt
inversion is performed at every tangent point individually, and a complete
covariance matrix S is obtained that contains the retrieval dependencies
between all SGDs and SAODs.
AerGOM spatial inversion
AerGOM performs a spatial inversion on all species simultaneously. This
allows the full use of all spectral inversion covariances between different
species, which are discarded by the GOMOS IPFv6.01 processor. The importance
of these covariances is crucial: using them in the spatial inversion
significantly reduces the volume of the state space of possible solutions.
Spatial inversion of all species simultaneously is achieved by expressing the
forward model as
Ntot=Gtotntot,
with Ntot a column vector containing all gas SGDs and aerosol
SAODs obtained from the spectral inversion, ntot a column
vector containing all local gas densities and aerosol extinction
coefficients, and Gtot a matrix containing optical path
lengths, similar to the ones that were discussed in Sect. .
Also here, to control the smoothness of the altitude profiles, the linear
inversion is performed with a Tikhonov regularization constraint. The merit
function M to be minimized reads
M=[Ntot-Gtotntot]TSN,tot-1[Ntot-Gtotntot]+ntotTHtotntot,
with Ntot here representing actual GOMOS-derived SGDs
and SAODs, SN,tot the associated total covariance matrix that
is formed by stacking together all covariance matrices (including
off-diagonal elements) obtained from the spectral inversion, and
Htot the Tikhonov smoothing operator. The solution is
given by
ntot=Sn,totGtotTSN,tot-1Ntot,
with solution covariance matrix
Sn,tot=GtotTSN,tot-1Gtot+Htot-1.
Summary of the main configuration settings for the AerGOM v1.0 processing.
Implementation
Setting
Retrieved species
O3, NO2, NO3, aerosols–clouds
Full covariance matrix (FCM)
no
Top of atmosphere
120 km
Rayleigh scattering
From ECMWF (P> 1 hPa)
and MSIS90 (P< 1 hPa)
τaer(λ)
Quadratic polynomial of 1/λ
τaer parametrized at
350, 550, and 756 nm
Spectral windows selected
248.1–685 nm (SPA)
755–759.3 nm (SPB1)
770–775 nm (SPB1)
Tikhonov parameters μi
Gases: 0.1
Aerosol extinction: 3
Care should be taken to properly scale Htot, since
atmospheric species profiles span several orders of magnitude. A natural
scaling is provided by the unconstrained least-squares covariance matrix of
the solution (obtained by putting the Tikhonov term in Eq. to zero):
Sn,tot, LS=GtotTSN,tot-1Gtot-1=DRD,
where we have also expressed the covariance matrix in terms of the diagonal
standard deviation matrix D and the correlation matrix
R. We then choose the regularization operator as follows:
Htot=LtotD-1TLtotD-1,
where it is understood that Ltot is a composite
operator, consisting of several first-difference operators Li
(one for each gas density and aerosol extinction profile), each one of them
multiplied with its own regularization parameter μi. The functionality
of the applied scaling becomes clear when we rewrite the covariance matrix of
the regularized solution (Eq. ):
Sn,tot=DR-1+LtotTLtot-1D.
We then compare it with the least-squares covariance matrix (Eq. ):
the altitude smoothing operates directly on the correlation matrix
R, which is properly scaled by definition.
A set of 115 randomly chosen GOMOS aerosol extinction profiles, evaluated at three wavelengths,
for the two algorithms. Left column: IPFv6.01; middle column: AerGOM v1.0. Right column: AerGOM v1.0, base 10 logarithm of aerosol extinction.
Aerosol extinction spectra at altitudes 20, 25 and 30 km. The same data set as in
Fig. was used. Left column: IPFv6.01; right column: AerGOM v1.0.
A chronological series of aerosol extinction values at 386 nm, for 1152 GOMOS (blue) and SAGE II (red) collocations.
From top to bottom: altitude = 24, 29 and 34 km. Left column: IPFv6.01; right column: AerGOM v1.0. Correlation coefficients ρ are also indicated in the subplot titles.
Results
AerGOM processing
The entire 10-year GOMOS data set has been processed with the AerGOM
algorithm. The specific configuration that was chosen, taking into account
the required data quality and processing speed, is presented in Table . Notice specifically that for this first tentative
processing the FCM method was not used because it is computationally
expensive. Furthermore, the Rayleigh contribution was not retrieved but
computed and removed, using meteorological data together with the Rayleigh
cross section (Eq. ). Finally, SPB2 data were not used
(since all wavelengths are affected by water vapour, a species that is
currently not retrieved by AerGOM), while only the SPB1 spectral pixels
outside the O2 absorption band were exploited.
By launching several batch processes in parallel, we were able to process the
entire dark limb GOMOS data set in two days. The resulting AerGOM v1.0 data
set (profiles for gas SGD and local densities, aerosol SAOD and extinction
coefficients, retrieval errors, ancillary data and inversion statistics)
occupies about 74 GB of disk space.
A first look at the AerGOM results
A detailed validation will be presented in a companion paper
. Here, we will present a qualitative evaluation of the
obtained AerGOM data by comparison with the IPFv6.01 products; visual
inspection is sufficient to demonstrate the improvement.
Figure shows an ensemble of 115 randomly chosen aerosol
extinction profiles (in a window from April 2002 to April 2005, between
60∘ S and 60∘ N), evaluated at three wavelengths (386, 452 and
525 nm) using the assumed quadratic law. Clearly visible are the IPFv6.01
spurious oscillations, which increase in amplitude for wavelengths farther
away from the reference wavelength of 500 nm. As was anticipated, the
situation improves dramatically for the AerGOM data.
We also observe a larger spread of the aerosol extinction profiles at lower
altitudes (below about 20 km) for both retrieval algorithms. The most
important reason for this increased variability is not related to retrieval
methodology but to the limited signal-to-noise (S/N) ratio of a stellar
occultation experiment. Indeed, at lower altitudes, stronger optical
extinction occurs due to longer optical paths and denser atmospheric layers;
measured signals become comparable to the instrument noise levels. The
altitude region where this happens depends of course on the stellar
properties (mainly magnitude). Furthermore, the presence of clouds in the
troposphere contributes to the increased variability that is observed.
The same set of 115 profiles was used for the plots in Fig. , showing aerosol extinction spectra in the wavelength
range from 300 to 750 nm at three different altitudes. Also here, much more
consistent behaviour with fewer oscillations is exhibited by the AerGOM v1.0
data set. Notice the increased variability of extinction values at short
wavelengths (below 400 nm), reflecting the larger retrieval errors due to the
small aerosol–molecular extinction ratio at these wavelengths. In particular,
the spectral maxima between 300 and 400 nm should not be considered as
physical features but result from the lack of instrument sensitivity to
aerosols.
Ångström exponents (AEs) derived from GOMOS–AerGOM and SAGE II data.
The same data as for Fig. were used. First two columns: 100 examples of AE for
AerGOM and SAGE II at three different altitudes, with error bars. Third and fourth column: AE histograms
for the full set of 1152 GOMOS–SAGE II collocations at three different altitudes. Vertical lines represent
the error-weighted mean of the distribution (central line), and the median experimental error bars
of the AE. The AE weighted mean is also indicated in the subplot titles.
The correspondence between the IPFv6.01 and AerGOM data sets with SAGE II
results is illustrated in Fig. . Shown are
chronologically ordered aerosol extinction values at 386 nm for collocated
GOMOS–SAGE II occultation events (within a window of 500 km and 12 h), at
three different altitudes spanning the middle stratosphere. On average, the
IPFv6.01 data follow the SAGE II values closely but are very noisy. The
amplitude of this noise decreases strongly in the AerGOM v1.0 series, and the
overall agreement between AerGOM and SAGE II values seems to be very good.
This is confirmed when we inspect the correlation coefficients (also given in
Fig. ), which are significantly larger for the SAGE II–AERGOM case, even up to 1 order of magnitude at 29 km. It should be
mentioned that aerosol extinction retrievals at the small wavelength of 386
nm are of limited quality due to the much larger contribution of neutral
density Rayleigh scattering to the total extinction. For example, typical
SAGE II aerosol extinction retrieval errors are 22 % (24 km), 32 % (29 km)
and 45 % (34 km), with similar or larger numbers for GOMOS–AerGOM
retrievals, depending on the magnitude and temperature of the used star. This
limited aerosol information content manifests itself in correlation
coefficients that are still very modest. Nevertheless, the much higher SAGE II–AerGOM coefficients demonstrate the improvement with respect to IPFv6.01.
Coming back to the aerosol extinction spectra in Fig.
we observe that, while the AerGOM results look more consistent than the IPF
ones, quite a large spectral variability (roughly speaking, the slope of the
spectra with respect to wavelength) is still present. At first sight, this
seems to suggest a strong variability of particle size distributions. This
contradicts the fact that the considered period (2002–2005) was remarkably
stable and free from major volcanic eruptions (only background aerosols).
However, the observed spectral variation is just caused by instrument noise,
and the associated extinction error bars are quite large. To demonstrate
this, we have fitted an Ångström power law to the 386, 425 and 525 nm
AerGOM extinction values (evaluated at these wavelengths using the assumed
quadratic polynomial of inverse wavelength), as well as the SAGE II values
for comparison:
log(βaer(λ))=logA-αlog(λ),
with A a constant and α the Ångström exponent (AE) that
describes the spectral shape.
The extinction retrieval errors were taken into account. Results are shown in Fig.
at three different altitudes. We immediately see that the variability of the
AE is for the most part buried in the experimental error and is therefore statistically not
significant. The histograms in the figure for the full GOMOS–SAGE II collocation data set
confirm this finding: the statistical spread of the AE distributions falls largely within
the limits of the experimental error. The findings are valid for AerGOM as well as SAGE II.
Conclusions
The GOMOS aerosol extinction profiles produced by the official
IPFv6.01 algorithm are of good quality around the 500 nm reference
wavelength, but they show pathological behaviour in other spectral regions. This
finding hinted at a conceptual error in the algorithm, instead of a lack of
information in the GOMOS data. Within the framework of the AerGOM project, a
new algorithm was developed that has some similarities with the IPF code but
is equipped with two fundamentally different concepts: an improved aerosol
spectral law and a full spatial inversion that does not discard retrieval
covariances between species. Additionally, a more accurate Rayleigh
scattering cross section and air refractive index has been implemented. The
spectral range has been increased by the possibility to use SPB1 and SPB2
spectral measurements (although only SPB1 data have been selected for the
first data processing presented in this paper).
The entire GOMOS 10-year mission data set has been processed, and the
resulting Level 2 product files (containing altitude profiles for aerosol
extinction and gas densities, with error estimates) have been stored as the
AerGOM v1.0 data set. An initial inspection of the obtained results shows
that the pathological behaviour of the aerosol profiles at wavelengths far
from the 500 nm reference is severely reduced. Furthermore, a coarse
comparison of GOMOS–SAGE II co-locations shows much better agreement for
AerGOMv1.0 than for IPFv6.01 at these wavelengths. Since algorithm
development forms the subject of this paper, a detailed validation study of
the aerosol extinction product has been presented in a separate companion paper . Validation of the other products (O3, NO2,
NO3) will be carried out in the future. Finally, it should be mentioned
that a new algorithm has been developed for the inversion of aerosol–cloud
extinction spectra to particle size distributions. We will also discuss this
algorithm in a separate publication.