Introduction
Carbon dioxide (CO2) and methane (CH4) are the most
important anthropogenic greenhouse gases. Anthropogenic
CO2 and CH4 are produced in the troposphere and
then, due to their long lifetimes, eventually transported upwards
into the stratosphere.
Tropospheric concentrations and/or total column averages of
CO2 and CH4 are available from both ground-based
networks like the Total Carbon Column Observing Network (TCCON,
) and satellite measurements (from 2002 to
2012 by the SCanning Imaging Absorption spectroMeter for
Atmospheric CHartographY, SCIAMACHY on Envisat,
, and since 2009 by
TANSO
onboard GOSAT, ).
However, especially during the last decade, there has been only
very little information available on the stratospheric distribution
of CO2 and CH4. Since the end of the Envisat
mission in 2012, the Atmospheric Chemistry Experiment Fourier
Transform Spectrometer (ACE-FTS) on SCISAT ,
launched in 2003, is the only instrument providing CH4
profiles in the stratosphere . On Envisat,
the Michelson Interferometer for Passive Atmospheric Sounding
(MIPAS, see e.g. ) also provided
measurements from which stratospheric CH4 profiles can be
inferred see e.g..
CO2 profiling from space is in many cases limited.
In particular, the assumption of a known
CO2 volume mixing ratio (VMR) is quite commonly used to
determine the altitude at which the instrument is pointing. As
a consequence, it is difficult (though not impossible) to determine
CO2 VMRs in these cases. For example, ACE-FTS retrievals use
CO2 to determine pressure and temperature
profiles, and thus the altitude grid of the measurements, but
CO2 data in the altitude range between 5 and 25 km
and in the mesosphere and
lower thermosphere can still be derived.
For this purpose, N2 continuum-induced absorption instead of
CO2 absorption is utilised at lower stratospheric altitudes,
whereas at mesospheric/thermospheric altitudes the geometrical pointing
information is used.
SCIAMACHY pointing information is derived completely independently
from CO2. For the solar occultation data we make use of
the method developed by , which determines
the precise pointing from scans over the solar disk to determine the
position of the solar centre which is then compared to the astronomical
position.
From this we get an individual pointing correction for each solar occultation
measurement which does not depend on the attitude information of the
satellite.
Therefore,
CO2 concentrations and tangent altitudes can be determined
independently from each other.
In this study we present stratospheric profiles of CH4
and CO2 which have been derived from solar occultation
measurements of SCIAMACHY on Envisat. The retrieval is performed
using a method called onion peeling DOAS (ONPD) which is based
on an onion peeling approach (see
e.g. ) in combination with a weighting
function DOAS (differential optical absorption spectroscopy) fit
(see e.g. ).
A first implementation of this method has been used to retrieve
water vapour profiles from SCIAMACHY data . In
a later step, the method had been successfully adapted to
CH4 retrievals . Within this CH4
retrieval, CO2 was also fitted as a secondary absorber.
However, in this previous study, not much attention was paid to the quality
of the derived CO2 profiles. Another shortcoming of the
retrieval described in (and the related
CH4 data set V3.3.6) was its restriction to the altitude
range from 20 to 40 km.
In the context of the ESA Greenhouse Gas Climate Change Initiative
(GHG-CCI), the SCIAMACHY CH4 and CO2 profile retrieval has
been further improved. The data set used in the present manuscript (V4.5.2)
is part of the Climate Research Data Package (CRDP) generated in the
context of this project and available via the GHG-CCI web site
(www.esa-ghg-cci.org).
We describe the data sets used in this study in Sect. , followed
by a description of the improved ONPD retrieval (inversion algorithm in
Sect. and
applied a posteriori corrections in Sect. ). In
Sect. we present the new CH4 and CO2
data sets, compare them with independent data and – as an example
for a possible application – estimate trends from the derived time
series.
Data sets used in this study
SCIAMACHY data
The SCIAMACHY instrument on Envisat measured
backscattered earthshine and solar and lunar spectra in nadir, limb
and occultation geometry between 2002 and 2012.
In this study we use SCIAMACHY radiance spectra measured in solar
occultation mode taken from the current level 1 data set,
i.e. V7.04, consolidation degree W.
SCIAMACHY measures from the UV (about 214 nm) to the SWIR (about
2386 nm).
Here we use the spectral interval between 1559 and 1671 nm in which
mainly CO2 and CH4 absorb light.
The SCIAMACHY solar occultation measurements are performed once per
orbit in the Northern Hemisphere during local sunset. However, due
to the orbital motion of Envisat, SCIAMACHY sees a rising sun.
During a solar occultation measurement, regular scans over the solar
disk are performed (see Fig. ). One upward or
downward scan takes 2 s. Typically 16 readouts are taken
during one scan, looking at different regions of the sun. The
observations start when the sun is still below the horizon
by scanning a fixed tangent altitude of around 17.2 km.
After the centre of the sun is observed at this tangent altitude, the centre
of the scan follows the rising sun until about 100 km.
Illustration of the solar scan strategy modified version of
Fig. 2 in.
The orange/yellow area indicates the size of
the refracted/geometrical sun. The black curve shows the scan as function of
time, relative to the time where the geometrical sun reaches 17.2 km (which
is the sun-fixed event used in mission planning for this measurement).
The white dots indicate (as an example for one upward scan) the position of
individual readouts.
The corresponding reference readout for an upward scan is also shown.
Above 100 km, two different measurement configurations
(so-called “states”) were used: for state 47 (executed for
typically two orbits per day) the measurement ends with pointing to
the solar centre, while for state 49 (executed during the other orbits)
the scan over the sun is continued until almost 300 km.
In contrast to the algorithm of Noël et al. (2011) the analysis described
here uses only data below the 100 km tangent altitude and therefore is
applicable to both measurement states.
During a scan over the sun the measured signal varies strongly,
because only a small horizontal stripe of the sun (with varying
area) is seen during one readout. Furthermore, successive scans
over the sun overlap in altitude.
In order to avoid large fluctuations with altitude caused by too noisy
data, we select a subset of SCIAMACHY occultation data to be used in the
retrieval.
The basic idea for this selection is to preferably use the data with the
highest signal in one scan and to avoid large fluctuations
with altitude.
The following procedure is used to determine the
subset of data to be used in the retrieval.
First, for each readout at a tangent altitude below 60 km
the transmittance is computed. For this, we take the measured
spectrum and divide it by a reference spectrum measured at around
95 km tangent height. To account for possible systematic
differences between upward and downward scans, we use two different
reference spectra.
An upward reference spectrum is obtained by selecting the spectrum, for one upward scan
around this altitude, which has the highest signal outside the
absorption (i.e. at the lower edge of the fit window at about
1560 nm).
The same is done for a corresponding downward scan to determine the downward
reference spectrum.
We then divide the altitude range between 0 and 60 km into
0.5 km bins and select the spectrum with the highest
transmittance within each bin. Furthermore, the following
additional constraints are applied:
In order to exclude too noisy data, the transmittance has to be higher than 0.01.
Without absorption, the transmittance should (at least roughly) increase
with altitude.
Therefore, a valid transmittance has to be higher than the previous valid
transmittance minus 0.02 (when starting from the bottom).
The resulting vertical sampling of data points varies with altitude
between about 0.5 and 3 km, with typical average values
less than 2 km. This is illustrated in
Fig. .
Illustration of selection of data.
The transmission at about 1560 nm, i.e. outside the strong
absorption, is shown as a function of altitude.
Red points show all readouts, connected by lines to illustrate the temporal sequence.
Black points show readouts used in the retrieval.
The basic idea for the selection is to take the measurements with the
highest transmission within one vertical bin of 0.5 km (indicated by horizontal black
lines).
ECMWF data
The ONPD CH4 and CO2 retrieval (see
Sect. ) uses pressure and temperature
profiles taken from the ECMWF ERA-Interim data set
as input. These data are available every 6 h on
a 1.5∘×1.5∘ spatial grid.
For the retrieval, the model data closest in time and space to an actual
measurement are used; no interpolation is performed.
ACE-FTS CH4 data
To assess the quality of the derived SCIAMACHY stratospheric
CH4 profiles they will be compared in Sect.
with data measured by other sensors. One of these sensors is the
Atmospheric Chemistry Experiment Fourier Transform Spectrometer
(ACE-FTS) on SCISAT which has provided
scientific data since February 2004. In this study, we use the
actual ACE-FTS V3.5 CH4 data product seefor
a description of the retrieval method. The ACE-FTS
V3.5 data set is a successor of the V2.2 data, which have been
extensively validated see e.g.for
CH4. state that
the overall accuracy of the ACE-FTS V2.2 stratospheric CH4
product is about 10 % in the upper troposphere and lower
stratosphere and about 25 % in the middle and higher
stratosphere. There are no validation results for ACE-FTS V3.5
CH4 data published yet.
For the comparison with SCIAMACHY, we take about 1300 collocated ACE-FTS
V3.5 data between 2004 and 2012 based on a maximum spatial distance of 500 km.
The maximum temporal distance of these data is usually below 1 h
(maximum distance 1.2 h).
This is because both ACE-FTS and SCIAMACHY measure in solar occultation
geometry and only local sunset data are used, which automatically results in a
similar measurement time for collocated data.
HALOE data
The Halogen Occultation Experiment (HALOE;
) on the Upper Atmospheric Research
Satellite (UARS) provided the longest stratospheric CH4
time series so far (1991–2005). HALOE measured in solar
occultation viewing geometry both during sunset and sunrise. In
this study, we use HALOE
sunset data v19 for the comparison with SCIAMACHY, because SCIAMACHY solar occultation spectra are
also measured during sunset. The precision of HALOE CH4
profiles is in the order of 7 %, while the total uncertainty
including systematic errors is about 15 %
based on v17 HALOE data.
Because the HALOE time series ends in August 2005, the temporal
overlap with SCIAMACHY is only three years.
To achieve a suitable number and temporal
distribution of collocations, we chose a maximum spatial distance of
800 km, which results in about 300 collocations.
We only use HALOE sunset data; therefore the temporal mismatch to
SCIAMACHY is also very low here (<1 h).
MIPAS data
The SCIAMACHY CH4 data have also been compared with
stratospheric CH4 profiles obtained by the Michelson
Interferometer for Passive Atmospheric Sounding (MIPAS;
), which is also part of the Envisat
atmospheric chemistry payload. MIPAS performed measurements in
limb viewing geometry. The MIPAS measurements cover the time
interval between 2002 and 2012. Until 2004 MIPAS was operated in
the so-called high-resolution (HR) mode, but later on in reduced-
resolution (RR) mode, i.e. with lower spectral resolution but
higher spatial resolution.
The MIPAS profiles used in this study were derived with the research
processor developed at the Institute of Meteorology and Climate Research
and at the Instituto de Astrofísica de Andalucía (CSIC)
.
Versions are V5H_CH4_20 for the time interval from 2002 to 2004 in
combination with V5R_CH4_222 (for January 2005–April 2011)
and V5R_CH4_223 (for May 2011–April 2012). Note that the
only difference between V5R_CH4_222 and V5R_CH4_223 is the
source of ECMWF data used as a priori in the temperature
retrieval, which has a negligible impact on the CH4
product. The accuracy of the MIPAS CH4 profiles is
expected to be high in the middle stratosphere as no clear bias to
other sensors is observed; however, below about 25–30 km
MIPAS CH4 seems to have a high bias on the order of
0.2 ppmv .
For the selection of collocated data from MIPAS we used the same maximum spatial
distance of 800 km as for HALOE, but the maximum temporal distance
was chosen to be 9 h, taking into account that MIPAS performed
about 72 limb measurements per orbit in HR and 96 in RR at varying
local times, whereas there was only one SCIAMACHY solar occultation
measurement per orbit at local sunset.
Because of the different viewing geometries, it is not possible to restrict
the maximum temporal offset to about 1 h (as for ACE-FTS and HALOE), as this would
result in no collocations with MIPAS.
With the chosen criteria, we usually obtained several MIPAS measurements which match with
one SCIAMACHY measurement, from which we selected the closest one (spatially).
This results in more than 25 000 collocations between August 2002 and April
2012, which essentially cover all seasons.
ACE-FTS CO2 data
One of the stratospheric CO2 data sets used in this study
is derived from ACE-FTS measurements and based on the algorithm by
.
It is a research data product which covers the years 2009 to 2011.
Profiles are available for altitudes below 25 km.
There are about four data points above 17 km.
The data set used here is a combination of V4.3 and V4.4 data; these versions
only differ in the choice of pressure and temperature profiles below
15 km, which are not relevant for this study.
We use the same collocation criteria as for the ACE-FTS CH4 data, i.e. only
sunset data with a maximum distance of 500 km.
This results in about 100 collocations.
CarbonTracker data
To our knowledge there are no measured stratospheric CO2
profiles covering the full spatial and temporal range of the SCIAMACHY
solar occultation data.
The standard ACE-FTS CO2 product only contains measurement results
at mesospheric altitudes (above about 70 km), whereas the CO2
values below are based on a simple equation see.
The stratospheric CO2 data from ACE-FTS used in this study are
based on a research product and only
cover altitudes below 25 km (see above).
In addition to a comparison with these data, the quality of the ONPD
CO2 profiles is assessed in Sect. by
comparison with data derived from the CarbonTracker model
. Here, we use the latest version
of these model data (CT2013), which cover the time interval until
the end of 2012.
For each SCIAMACHY measurement the spatially and temporally
closest CT2013 profile has been selected, resulting in
a collocation for each of the SCIAMACHY profiles. The
CarbonTracker VMR data, which have a quite coarse sampling of about
5 km in the
stratosphere, have then been interpolated to the 1 km
altitude grid of the SCIAMACHY data.
Inversion algorithm
The ONPD algorithm is essentially based on
a weighting function DOAS fit (see e.g. ) in combination with an onion peeling
approach (see e.g. ).
We divide the atmosphere into N spherical layers. The absorptivity
of the whole atmosphere can then be written as the sum of the
absorptions of these individual altitude layers. Let ci,k be
the atmospheric parameter associated with the absorption features in
atmospheric layer i. This could, for example, be the number
density of an absorber k. It is then the task of the retrieval
to determine the vertical profile of c as a function of height
(index i) for each absorber (index k). As typical for an onion
peeling approach, the retrieval starts at the top layer and
propagates downwards, taking into account the results of the upper
layers.
The basic equation of the ONPD method for a tangent altitude j is then given by the following:
lnIjI0=Pj+lnIj,refI0,ref+∑k=1M∑i=1Nwij,kai,k,
where M is the number of absorbers; Ij is the measured radiance for
tangent altitude j; I0 is the
corresponding radiance obtained at the reference altitude, i.e. at
an altitude which is high enough that atmospheric absorption can be
neglected.
The ratio Ij/I0 is therefore the measured atmospheric
transmittance. Ij,ref and I0,ref are the
corresponding values calculated for a reference scenario (i.e. for
a reference set of parameters cref).
The quantity wij,k describes – similar to a relative
weighting function – the change of the (logarithmic) transmittance
when changing the atmospheric parameter (evaluated at ci,k,ref):
wij,k:=ci,k,ref∂ln(Ij/I0)∂ci,kci,k,ref,
where wij,k is determined using the radiative transfer model
SCIATRAN 3.3 in transmission mode . The solar
irradiance spectrum used in this context has been derived from an
empirical solar line list provided by G. Toon (NASA Jet Propulsion
Laboratory). The SCIATRAN calculations take into account the
effects of refraction and the vertical size of the SCIAMACHY field
of view (0.045∘). A main advantage of the weighting
function DOAS method is that it is possible to handle dependencies
on pressure and temperature in a similar way to absorbers,
i.e. by definition of appropriate weighting functions. The
parameter c can therefore be any parameter on which the measured
transmittance depends. This may be the number density of an
atmospheric constituent as well as pressure or temperature.
The scalar ai,k is defined as the relative change of
ci,k:
ai,k:=Δci,kci,k,ref=ci,k-ci,k,refci,k,ref.
As typical for DOAS-type retrievals, broadband absorption features (e.g. from
aerosols) and uncertainties in the radiometric calibration are handled via a
low-order (in the present case second-order) polynomial Pj.
Furthermore, uncertainties in the spectral calibration are
accounted for by fitting additional spectral shift and squeeze
factors.
The retrieval starts at the top of the atmosphere and then
propagates downwards. A non-linear least squares fit (Levenberg–Marquardt
algorithm) is used to determine from Eq. () for each tangent
altitude the shift and squeeze parameters, the coefficients of Pj and
the corresponding aj,k.
The noise of the measurement data is not considered in the fit.
Note that – in contrast to the previous retrieval version
described by – the summation over altitude
(index i in Eq. ) now also includes altitudes below
the tangent height.
With this we account for effects due to refraction and the vertical
smearing of the signal by the instrument field of view.
Because of refraction, the light path through the atmosphere is no longer a
straight line but bent such that atmospheric layers from below the
tangent altitude also affect the measured signal.
However, because of the onion peeling
approach, there is no information about altitudes below the current
tangent height j. As an approximation, we therefore assume in
the retrieval that ai,k=aj,k for all altitudes i<j.
This means that we assume that all parameters c below the current
altitude j scale the same way as for j. Noting that the
contributions from altitudes below the current tangent height are
typically small and limited to a few kilometres, this is
a reasonable assumption. This means that for each atmospheric
parameter only one aj,k needs to be determined in one
retrieval step.
From the retrieved aj,k the parameter cj,k (e.g. the
number density of the absorber k at altitude j) can then be
determined (see Eq. ):
cj,k=(1+aj,k)cj,k,ref.
This type of retrieval may in principle be applied to all kinds of
species/spectral regions. The selected fit window and the
related absorptions determine the number of absorbers to be
considered. In the present case we choose the fit window to be
1559–1671 nm. We consider CH4 and CO2 as
absorbers, and temperature and pressure as additional parameters.
However, only CH4 and CO2 number densities are
determined in the fit; adequate pressure and temperature profiles
are provided as input to the retrieval and kept unchanged to reduce
the impact of correlations between the weighting functions
(especially regarding pressure and CO2). For the current
product version (V4.5.2), the radiative transfer database has been
calculated assuming the 1976 US Standard Atmosphere with background
stratospheric aerosol and an altitude-independent CO2 VMR
of 380 ppmv. In the retrieval, input temperature and
pressure profiles are taken from collocated ECMWF ERA-Interim data
. Weighting functions are then used to correct
differences to the settings in the radiative transfer
calculations.
The ONPD retrieval has several advantages. First of all, it is
a simple method which may be applied to various spectral regions.
Furthermore, no individual radiative transfer model calculations are
required during the retrieval, because a pre-calculated database can be
used for the weighting functions and the reference transmittances. This
database has been calculated on a high spectral sampling grid, which is
then interpolated in the retrieval to the wavelength grid of the measured
spectra.
This makes the method numerically very fast.
In the present case, the retrieval uses an altitude grid which
reaches from 0 to 50 km in 1 km steps. The
retrieval is then performed for all altitudes above 10 km
(starting at 50 km), but due to tropospheric effects,
e.g. strong refraction at lower altitudes and low
signal-to-noise at higher stratospheric altitudes, useful results for
CH4 and CO2 are only achieved between 17 and
45 km.
Because the onion peeling method uses a pre-calculated radiative
transfer database, it is necessary to interpolate the logarithms
of the SCIAMACHY measured transmission spectra to the 1 km
retrieval grid. To increase the stability of the interpolation
towards e.g. noise effects, we normalised each spectrum before the
interpolation to its average value. This is possible, because the
ONPD retrieval is not sensitive to absolute radiometric calibration
(which is handled via the polynomial). The vertical interpolation
is then done using Akima splines.
An example for a fit at 25 km and the corresponding
residual is shown in Fig. . The two absorption
features between 1560 and 1620 nm are attributed to
CO2. The absorption above 1620 nm is mainly due to
CH4, with some underlying contributions from CO2.
As can be seen from this plot, the amplitude and variability of the
residuals are higher above about 1590 nm and largest around
1645 nm. This is due to a change in the SCIAMACHY detector
material, which results in higher measurement noise at the longer
wavelengths. This already implies that the precision of the
derived CO2 is higher than for CH4.
Example of a spectral fit. Top: normalised measured spectrum (red) and fitted spectrum (green) at 25 km tangent altitude.
Bottom: resulting residual, i.e. relative difference between measurement and
fit.
After the retrieval, we apply some additional corrections. These
are described in Sect. . Finally, we derive VMRs
from the retrieved number densities using the same pressure and
temperature profiles which we assumed in the retrieval, i.e. the
corresponding ECMWF data for this measurement.
Corrections
Error correction
In the onion peeling approach only the density scaling factors for
the actual tangent height j are fitted, i.e. the aj,k for
each absorber k (see Eq. () and the description
given in the previous section). For a fit at tangent height j it
is assumed that all ai,k from below (i<j) are identical to
aj,k and all ai,k from altitudes higher than j are
known from previous fits.
The error for aj,k is the fit error, which is derived from the
covariance matrix of the fit parameters obtained in the fit and scaled with
the root mean square of the fit residual.
This accounts for the unweighted fit.
Calculating the error in this way implies that all ai,k for
i>j are assumed to have no error (although the error is in fact
determined in previous fits). The error for aj,k derived from
the fit is therefore overestimated because it also includes the errors
from the upper altitudes.
To account for this effect, the retrieved errors have been
multiplied by a factor of 0.66.
This value has been derived by application of standard error propagation to
about 10 000 retrievals on measurement data.
In this context, the error obtained from the retrieval at one altitude has
been propagated downwards in an onion peeling way.
From this it turns out that the required error
correction factor is quite independent from the observed scene and
almost constant over altitude. The factor is also the same for
CH4 and CO2, thus indicating that the correlation
of the fit parameters is about constant with altitude and thus
essentially determined by geometry.
Note that, although the average error correction factor is
constant, the exact determination of the individual errors
introduces, especially at higher altitudes (where measurement noise
is larger), additional oscillations in the retrieved errors, which
is a typical problem of onion peeling methods (see also the following
section). This is why we prefer to use an average error correction
here.
Vertical smoothing
Although the retrieval is performed on a 1 km altitude
grid, the vertical resolution of a single SCIAMACHY measurement is
limited by the vertical size of the field of view (0.045∘),
which corresponds to about 2.6 km at the tangent point.
The size of the field of view has been considered in the radiative
transfer calculations, which effectively results in a vertical
smoothing of the reference spectra profiles and the weighting functions profiles.
In contrast to many optimal estimation type retrievals, the
ONPD method does not include a regularisation. This especially
means that the smoothness of the resulting profiles is not
constrained in the retrieval, such that artificial oscillations
over altitude are not suppressed. This is a general problem of the
onion peeling approach: if, for example, a too high value is
retrieved at one altitude, this is compensated by a too low value
at the next altitude. In the present case we account for this lack
of regularisation by vertically smoothing the retrieved profiles
(scaling factors) using a boxcar of width 4.3 km. This
width has been chosen because it corresponds to the approximate
vertical range covered by the scan over the sun during one
integration time. However, this is in fact an arbitrary choice
resulting from a trade-off between vertical resolution and
amplitudes of oscillations in the profiles.
Since boxcar smoothing is similar to averaging, the error of the retrieved
scaling factors is reduced after smoothing.
Assuming that the error is random and the underlying data are
uncorrelated, this would result in a factor of 4.3.
This is in fact a conservative estimate since – as explained above –
adjacent altitudes are typically anti-correlated.
On the other hand, smoothing does not affect systematic errors contained in
the spectra, but since the systematic errors are unknown, there is no way to
quantify this effect.
On a best effort basis, the error of the final data product is therefore
estimated to be reduced by 4.3 due to smoothing.
This error reduction factor is considered to be of similar quality as the
broadband error correction described in the previous section, which assumes a
constant scaling factor for all altitudes.
As can be seen from Fig. , the smoothing is quite
efficient although the smoothing procedure cannot fully remove
oscillations of the correction factor (and therefore derived
densities) with altitude. This issue will be addressed further
below.
Example for derived profile scaling factors a from SCIAMACHY solar
occultation for CH4 (left) and CO2 (right). Red shows the original fit
result,
green shows vertically smoothed data.
Saturation correction
Atmospheric absorbers like CH4, CO2, O2 or water vapour
have strongly varying absorption lines which are not resolved by
the SCIAMACHY instrument because of its too low spectral
resolution. The signal measured by SCIAMACHY is therefore
comprised of a convolution of saturated and non-saturated lines.
As a consequence, the relationship between absorber amount and
absorption depth becomes non-linear, which is usually referred to
as saturation effect. Thus, the weighting function depends on the
chosen linearisation point, i.e. the reference concentration
assumed in the radiative transfer calculations.
We account for this effect by application of a saturation
correction function. This function is determined from retrievals
on a set of simulated spectra, which are based on scaled profiles
of the absorber to be corrected. The ratio of the true to the
retrieved number density then gives the saturation correction. We
store the (simulated) true and retrieved densities in a look-up
table and then derived the actual density at a certain altitude by
interpolation to the retrieved number density.
The determined correction functions are shown in
Fig. a for CH4 and Fig. d
for CO2.
(a) Saturation correction factors for CH4.
(b) Pressure correction factors for CH4.
(c) Temperature correction factors for CH4.
(d) Saturation correction factors for CO2.
(e) Pressure correction factors for CO2.
(f) Temperature correction factors for CO2.
The weighting functions – and through this, the retrieved CH4
and CO2 density – also depend slightly on the actual
pressure and temperature, which might differ from the assumptions
in the radiative transfer calculations. Note that although the
CO2 VMRs are rather constant, the CO2 number
densities vary with temperature and pressure. We therefore
determine additional corrections for CH4 and CO2
depending on the actual pressure and temperature. These
corrections are multiplicative factors (shown in
Fig. b, c, e and f). They are determined in
a similar way as the saturation correction (i.e. we apply the
retrieval to a set of simulated data, but now we keep CH4
and CO2 fixed and vary (scale) pressure or temperature
profiles).
These correction factors are also stored in a look-up table from
which actual factors are obtained by interpolation to the retrieved
quantity for each altitude. Since pressure and temperature are not
retrieved in the fit but taken from ECMWF data, the applied
pressure and temperature corrections account for the difference
between the ECMWF pressure/temperature used as input profiles in
the retrieval and the pressure/temperature assumed in the radiative
transfer calculations (i.e. 1976 US Standard Atmosphere).
As can be seen from Fig. , saturation and
temperature corrections have the largest effect. We also checked
the dependence of the retrieved CO2 amount on the retrieved
CH4 (and vice versa). These dependences are small (even
lower than the pressure dependence) and are therefore neglected.
Please note that at a fixed altitude seasonal variations of
stratospheric temperature and pressure (and by this CO2
number density) are typically less than about ±20 %.
The effective corrections to be applied are therefore usually quite
small,
typically not larger than a few percent.
The correction factors are derived from radiative transfer calculations and
are therefore in principle as accurate as these calculations.
The main uncertainties arise from (1) their calculation via scaled profiles
and (2) the later interpolation of the database.
Using scaled profiles is a valid approximation, considering that the vertical
resolution is about 4.3 km, which is essentially determined by the
vertical smoothing, and that most information is derived from altitudes
close the tangent height.
The interpolation error is quite small (typically below 0.1 %) and could be
further reduced by extension of the database.
Overall, the contribution of the uncertainties of the correction factors to
the error of the derived profiles is considered to be in the sub-percent range.
Results
Example profiles
The effect of the algorithm improvements can be seen in
Fig. , which shows the resulting
CH4 on the left (both for version 3.3.6 and 4.5.2) and the
CO2 VMRs for an example measurement on the right (same orbit as in
previous figures). For comparison, collocated data from ACE-FTS
CH4 and CarbonTracker CO2 profiles are also shown.
The ACE-FTS error bars represent the retrieval statistical fitting error.
Example for resulting VMR profiles for CH4 (left) and
CO2 (right).
Red shows the results for the current product version (V4.5.2).
For comparison, the CH4 profile from the previous product version (V3.3.6) is
also shown in the left plot in blue.
Green (left) indicates collocated CH4 profiles from ACE-FTS V3.5.
Black (right) indicates the CO2 profile from CarbonTracker (CT2013).
Error bars denote the errors given in the products. No error is given for
the CarbonTracker model data.
The ONPD CH4 profiles are
in good agreement with the ACE-FTS data above about 20 km.
Below this altitude, the previous product version 3.3.6 CH4
drops off significantly, whereas the new version 4.5.2 product is
still very close to the ACE-FTS results. The error of the
SCIAMACHY V4.5.2 data is significantly lower than for V3.3.6. This
is mainly due to the correction factors applied to the errors as
explained above.
For CO2, there is no V3.3.6 product. The comparison of the
new SCIAMACHY V4.5.2 CO2 product with CarbonTracker model
data shows a systematic positive offset of the
SCIAMACHY data of about 10 ppmv above 25 km for this orbit; below
this altitude the agreement is better. Especially at these lower
altitudes, the SCIAMACHY data show a pronounced oscillation which
is not expected from CarbonTracker data and larger than the
estimated error of the SCIAMACHY product. This oscillation could
already be observed in the derived correction factors
(Fig. ). It is probably a retrieval artefact and
does not represent true CO2 variations in the stratosphere.
However, CarbonTracker is mainly designed to model tropospheric
CO2 and has only very few data points in the stratosphere
(as can be seen from Fig. ). Therefore no clear
conclusion can be drawn at the moment; further investigations are
needed.
Comparison with independent data sets
The complete SCIAMACHY occultation data set reaching from August
2002 until the end of the Envisat mission in April 2012 has been
processed with the updated ONPD algorithm. From these, about 2000
orbits of reduced instrument performance (mainly related to
instrument switch-offs or decontamination periods) have been
excluded, resulting in more than 43 000 CH4 and
CO2 profiles. In order to assess the quality of the
derived SCIAMACHY ONPD CH4 and CO2 profiles, it is
necessary to compare them with independent data.
The SCIAMACHY methane data have been compared with results from ACE-FTS, HALOE
and MIPAS.
The vertical resolution of these data products is quite similar (ACE-FTS about
4 km, MIPAS about 2.5–7 km, HALOE about 2.5 km).
This is why we did not consider differences in vertical resolution explicitly
in the comparisons (e.g. by application of averaging kernels).
This approach is consistent with the one used in , who
state that the inclusion of averaging kernels in similar comparisons has an
effect of only about 2 %.
SCIAMACHY CO2 profiles have been compared with data from ACE-FTS
for altitudes below 25 km and with data from the CarbonTracker model
(CT2013).
The top plot of Fig. shows, as an example,
a time series of the SCIAMACHY CH4 data at 30 km
altitude. In the middle figure, the corresponding collocated
ACE-FTS, HALOE and MIPAS data are displayed. The bottom figure
shows the SCIAMACHY and CarbonTracker CO2 data sets.
ACE-FTS CO2 data are not included in this plot, because they are
not available at this altitude.
Top:
time series of SCIAMACHY CH4 VMRs at 30 km.
Middle:
time series of collocated MIPAS (blue), HALOE (grey) and ACE-FTS (green) CH4 VMRs.
Bottom:
time series of CO2 VMRs at 30 km.
Red: SCIAMACHY data.
Black: collocated CarbonTracker data.
Comparison of retrieved SCIAMACHY CH4 profiles (ONPD V4.5.2) with
ACE-FTS data (V3.5).
(a) Mean absolute difference (green) plus/minus one standard deviation (shaded
area) and mean absolute error of SCIAMACHY data (dotted red line).
(b) Mean relative difference (green) plus/minus one standard deviation (shaded
area) and mean relative error of SCIAMACHY data (dotted red line).
(c) Mean profiles and standard deviations (red: SCIAMACHY, green: ACE-FTS).
(d) Correlation between SCIAMACHY and ACE-FTS data.
The overall temporal behaviour of the different time series is
quite similar. All CH4 data sets show a large seasonal
variation and a significant scatter, except for HALOE, where the seasonal
coverage of the collocations is not sufficient to draw this conclusion.
The variability is largest
in winter/spring, due to the influence of the polar
vortex (as already discussed in ). Both the
SCIAMACHY and CT2013 CO2 time series show a continuous
increase with time (as expected from rising tropospheric
CO2), but the scatter in the SCIAMACHY data is much larger
than in the model data. One possible explanation for this scatter
is of course the error of the SCIAMACHY CO2 data (which is
about 10 ppmv at this altitude, see
e.g. Fig. ). On the other hand, CarbonTracker is
a model which uses fully consistent information about the
atmosphere, whereas e.g. pressure and temperature profiles used in
the calculation of the SCIAMACHY VMRs are derived from the closest
ECMWF data and thus never fully match the actual conditions.
Results from a more quantitative comparison between the different
data sets is given in the following subsections.
Same as Fig. , but for comparison of retrieved
SCIAMACHY
CH4 profiles (ONPD V4.5.2, red) with HALOE v19 sunset data (grey).
Comparison with ACE-FTS CH4
The results of the intercomparison between SCIAMACHY and ACE-FTS
CH4 are shown in Fig. . Overall, the
two data sets agree within about 5–10 %. Between 25 and
40 km the SCIAMACHY data are typically higher than ACE-FTS
data; the mean offset over all altitudes between 17 and
45 km is about 3 %. This is within the expected
accuracy of the products and better than the mean difference
between the previous product version and ACE-FTS V2.2 data which
was about 10 % . The differences show
a small oscillation with altitude (especially below about
25 km), which might be related to the onion peeling
approach as discussed above. The mean profiles (shown in
Fig. c) indicate that this oscillation of the
differences is caused by the SCIAMACHY data. The estimated mean
error of the SCIAMACHY CH4 product (single profile at
1 km vertical sampling) is about 0.05 ppmv between
17 and 35 km (which is about two times smaller than the
standard deviation of the difference between the two data sets)
and increasing to about 0.1 ppmv for higher altitudes.
Especially below 40 km the correlation between SCIAMACHY
and ACE-FTS CH4 (Fig. d) is high,
reaching about 0.95 between 30 and 35 km. This indicates
that both instruments see a similar temporal variability in
CH4, which is also in line with the similar standard
deviations shown in Fig. c.
Comparison with HALOE
The results of the comparison between SCIAMACHY and HALOE
CH4 profiles are shown in Fig. .
Above 20 km, the relative and absolute differences are very
similar to those from the comparison with ACE-FTS
(Fig. ). Between about 25 and 40 km
and at the lowest altitudes, SCIAMACHY VMRs are up to about
10 % higher than those from HALOE; the overall agreement
is quite good above 40 km. Some oscillation is visible in
the differences and the mean SCIAMACHY profile. The correlation
between SCIAMACHY and HALOE CH4 is somewhat smaller than
between SCIAMACHY and ACE-FTS, which is probably related to the
specific temporal sampling
(see top plot of Fig. ), resulting in less
variability. This is in line with the smaller standard deviations
of the mean profiles.
Comparison with MIPAS
Figure shows the results of the
intercomparison between SCIAMACHY and MIPAS CH4 profiles
in a similar way to the comparisons with ACE-FTS and HALOE. As
can be seen from this plot, the systematic differences between SCIAMACHY
and MIPAS are near zero above 25 km. Below this
altitude, the deviation between SCIAMACHY and MIPAS data increases
with decreasing altitude, reaching about -0.2 ppmv
(10–15 %) at 17 km. This negative bias of
SCIAMACHY towards MIPAS is in line with the about 0.2 ppmv
positive bias of MIPAS in this altitude range .
Especially at these lower altitudes the correlation between MIPAS
and SCIAMACHY is somewhat smaller than between ACE-FTS and
SCIAMACHY. The maximum correlation occurs at around 30 km,
reaching almost 0.9.
Same as Fig. , but for comparison of retrieved
SCIAMACHY
CH4 profiles (ONPD V4.5.2, red) with MIPAS data (blue).
Comparison with ACE-FTS CO2 data
The results of the comparison between the ONPD CO2 data and the
ACE-FTS CO2 data, derived using the algorithm by
,
are shown in Fig. .
The agreement between SCIAMACHY and ACE-FTS data is within about 2%.
The small increase in the ACE-FTS CO2 above about 22 km is related to
a high bias in the ACE-FTS data, due to a HDO interference which is not
properly taken into account in this product version.
The correlation is quite low, but this can be expected, because the
expected natural variability in CO2 is typically of the same
magnitude as the errors of the individual profiles.
The vertical range where the data sets overlap (17–24 km) is about the
typical wavelength of the vertical oscillations seen in the SCIAMACHY profiles
(or even smaller),
such that the differences are dominated by the oscillations in the SCIAMACHY
data.
The fact that such oscillations are not seen in the ACE-FTS data is a further
indication that these are a SCIAMACHY retrieval artefact.
Same as Fig. , but for comparison of retrieved
SCIAMACHY CO2 profiles (ONPD V4.5.2, red) with ACE-FTS CO2
after (violet).
Same as Fig. , but for comparison of retrieved
SCIAMACHY
CO2 profiles (ONPD V4.5.2, red) with CarbonTracker CT2013 data (black).
Comparison with CarbonTracker
The ONPD CO2 profiles have been compared with the CT2013
data derived from the CarbonTracker model .
The results of the CO2 comparison are shown in
Fig. . As for CH4, a variation of the
differences with altitude can be clearly seen, similar to the
example shown in Fig. . Except for these
oscillations with altitude, there is no apparent
altitude-independent systematic bias between SCIAMACHY ONPD
CO2 and CarbonTracker, meaning that such a bias would be
significantly lower than the amplitude of the oscillations of about
10 ppmv (3 %). The mean error of the SCIAMACHY
CO2 product is about 4 ppmv (1 %) at
17 km, increasing to about 16 ppmv (4 %)
at 45 km. At higher altitudes the error is even slightly
larger than the standard deviation of the difference between both
data sets, which is over the whole altitude range about
10–15 ppmv, i.e. less than about 4 %. This
indicates that above about 32 km the estimated error of the
CO2 profiles might – despite the additional corrections
performed after the retrieval as described above – still be
overestimated.
Probably because of the generally low variability of
stratospheric CO2 VMRs and the larger variability of the
SCIAMACHY data (see standard deviations in Fig. c),
the maximum correlation with CarbonTracker CO2 is only
about 0.45.
Time series of SCIAMACHY CH4 and CO2 data
To reduce the impact of the scatter between the individual
measurement results, daily averages of the SCIAMACHY VMR data have
been computed. These are based on up to 15 individual profiles at
different geographical longitudes but – because of the sun-fixed
Envisat orbit – at almost the same geographical latitude, so these
are essentially zonal means.
Time series of daily averaged CH4 (a) and CO2
(b)
profiles August 2002–April 2012.
Areas with reduced instrument performance (decontaminations,
switch-off, etc.) are masked out by grey bars.
The lower, black curve shows average tropopause height derived from
ECMWF data.
Top graph of each sub-figure shows the tangent latitude
of observation.
The resulting time series for daily averaged CH4 and
CO2 are shown in Fig. . For each gas,
a contour plot shows the change of the VMRs with time and altitude,
together with the average tropopause height derived from ECMWF
data. Above the contour plots the variation of the geographical
latitudes of the SCIAMACHY measurements with time is displayed.
The time series for CH4 (Fig. a) shows
a clear variation with latitude and/or tropopause height. This
variation is very similar to that observed for the previous product
version and is attributed to the direct
and non-separable relation between time and latitude of the solar
occultation measurements imposed by the sun-fixed Envisat orbit.
In Fig. b the complete SCIAMACHY time series of
daily averaged CO2 profiles is given. This figure shows
a similar variation of the CO2 VMRs with latitude and/or
tropopause height as observed for CH4. In addition, there
is a pronounced variation of the CO2 VMRs with altitude.
Highest CO2 VMRs occur between about 25 and 30 km.
As mentioned before, this variation, which was also visible in the
comparison with CarbonTracker (Fig. ), is assumed
to be related to the ONPD retrieval, but this issue is still under
investigation. Furthermore, a general increase of stratospheric
CO2 over time is observed, which is expected as tropospheric
CO2 also increases with time.
Preliminary trend analysis
The ONPD method uses the solar transmittance as input, which is
computed from the ratio of two radiance measurements at different
altitudes. Furthermore, a polynomial is fitted to the data.
Therefore, the ONPD retrieval is very insensitive to systematic
instrumental errors (like degradation) or uncertainties in the
radiometric calibration. This makes the SCIAMACHY ONPD data
especially suited for trend analyses.
However, as shown in the previous sections, the temporal variability is
large
and the data seem to be affected by a currently unexplained
systematic effect resulting in an unexpected vertical oscillation
in the derived profiles. For the estimation of trends from the
SCIAMACHY data set, we therefore first determine monthly anomaly
profiles by the following procedure:
Monthly average VMR profiles are computed from the daily average data shown
in Fig. .
For each month, an average profile is computed resulting in a mean
profile (e.g. all January profiles are averaged to get a mean
January profile for the time series).
The mean profile for one month is then subtracted from all corresponding
profiles (e.g. the mean January profile is subtracted from all individual
January profiles).
All these operations are performed independently for each altitude
for all data from January 2003 to December 2011. Retrieved
profiles from August to December 2002 and January to April 2012
have been excluded to avoid different weighting of different
seasons.
The resulting VMR anomalies are less affected by noise and
short-term variability. Furthermore, regular seasonal/latitudinal
effects have been removed from the data by this procedure. Since
the observed vertical oscillations are very stable with time, they
are also essentially eliminated. This can be seen from
Fig. , which shows time series of the
resulting VMR anomalies for both CH4 and CO2.
Time series of CH4 (a) and CO2 (b)
monthly VMR anomaly
profiles January 2003–December 2011.
Time series of SCIAMACHY CH4 (a) and CO2
(b) VMR
anomalies at 30 km.
Red lines show the daily averaged data.
Green lines show the linear trend.
The CO2 anomaly plot
(Fig. b) is especially much smoother than the
corresponding daily data (Fig. b). Except for
some small regions, e.g. around 20 km at the end of 2003
and 2011, a continuous increase with time is observed
at all altitudes. There are also indications for some remaining
instrumental influences, e.g. due to thermal instabilities after
a decontamination like in January 2009. The lower CO2
values at the lowest altitudes in the second half of 2009 are most
likely due to a remnant sensitivity of the retrieval to increased
aerosol, related to the eruption of the Sarychev volcano on 12 June
2009 see e.g..
Furthermore, the variability in the derived CO2 anomalies
is somewhat higher in 2003 (before the update of the Envisat
on-board orbit model) and after the Envisat orbit change end of
2010. This is because during these times the vertical sampling
pattern of the SCIAMACHY solar occultations measurements was
slightly different such that (systematically) spectra at other
altitudes were selected as input for the retrieval. The additional
spatial and temporal variations in the anomalies at the beginning and
the end of the mission are therefore an estimate of the sensitivity
of the ONPD retrieval to the vertical sampling. The fact that the
vertical distribution can be influenced by the sampling of the
measurement data is also an indication that the observed unexpected
vertical oscillations in the CO2 data may be a retrieval
artefact.
In contrast, the CH4 anomalies
(Fig. a) show no clear trend, but
some distinct features. For example, the year-to-year variability
of the polar vortex can be seen from the higher variability in the
CH4 anomalies during winter/spring time. Due to the
downward transport of upper stratospheric/mesospheric air
CH4 VMRs inside the vortex are usually lower than outside
the vortex. The average monthly CH4 profile depends
therefore on the number of contributing profiles from
inside/outside the vortex. For example in February 2009, there are
(based on potential vorticity derived from ECMWF data) only very few profiles located inside the vortex in contrast
to other years,
which results in a positive anomaly for this month.
In addition, there is a pattern of alternating positive and
negative anomalies occurring around 30 km before 2009 and
somewhat above and below after that time. This pattern has an
approximate frequency of two years, therefore we assume that it is
caused by transport effects related to the
quasi-biennial oscillation (QBO), see e.g. .
It is probably worthwhile to look deeper into these effects during
further studies. However, in the present work we only want to show
that such information is contained in the ONPD data, which
makes them useful for stratospheric studies.
From the monthly anomalies we obtain a linear trend by simply
fitting a straight line to the data for each altitude. As an
example, Fig. shows time series of
CH4 and CO2 monthly anomalies at 30 km
altitude and the corresponding fit results. For CO2
a significant positive trend of 1.5 ppmvyear-1 is
obtained at this altitude. No clear CH4 trend is visible
by eye; the fit results in a small but insignificant positive trend
which is much smaller than the variability in the data.
Figure shows the derived 2003–2011 linear
trends as a function of altitude on an 1 km grid. The left
panel of this figure shows the calculated altitude-dependent trends of
CH4, the right panel those of CO2.
As can be seen from the
2σ ranges, all of the CO2 trends are significantly
different from zero, whereas for CH4 only trends below about
20 km are usually larger than two times their error. The
CH4 trends show an oscillation with altitude which seems
non-erratic but is within the estimated error of the trends.
Calculated trends of CH4 (left, red curve) and CO2
(right, red
curve) VMRs 2003 to 2011 as function of altitude.
Shaded areas denote the 2σ error range of the derived trends.
For comparison, the corresponding trend derived from CarbonTracker CT2013
data is also shown in black. Note that the 2σ range for
CarbonTracker is smaller than the thickness of the trend line and therefore
not visible in the plot.
Especially because of the very specific temporal and spatial
sampling of the SCIAMACHY solar occultation measurements,
a quantitative comparison of the derived ONPD trends with other
data sets is in general not easy.
However, the ONPD CH4 trends below 20 km of about
3 ppbvyear-1 are roughly in line with total column
trends derived from nadir measurements. For example,
determined from SCIAMACHY data a total
dry-air column-average CH4 linear change in the Northern Hemisphere of about 8 ppbvyear-1 between 2007 and 2009
and an almost zero trend before. report
– also based on SCIAMACHY data – an increase of about
20–25 ppbv total dry-air column-average CH4
between 2003 and 2009 at northern latitudes.
The ONPD CO2 trends depicted in the right plot of
Fig. vary between about 1.3 and
1.9 ppmvyear-1. For comparison, CT2013 trends are also
shown. The CarbonTracker trends have been calculated in the same
way as the SCIAMACHY CO2 trends, i.e. based on monthly
anomalies derived from the collocated profiles. The SCIAMACHY
CO2 trends are somewhat lower than the corresponding
CarbonTracker changes of about 1.9 ppmvyear-1 and show
a slight decrease with altitude which is less pronounced in the
CT2013 trends. Some oscillations with altitude are also visible in
the SCIAMACHY CO2 trends, but these are much smaller than
the trends. For the CO2 total dry-air
column-average determined a northern
hemispheric trend of about 1.8 ppmvyear-1 between 2003
and 2009, which is – considering different temporal and spatial
sampling, different altitudinal ranges and different ways of
calculating the trend – consistent with the lower stratospheric
values resulting from the ONPD data.
Conclusions
The SCIAMACHY ONPD retrieval has been further developed in the
context of the ESA GHG-CCI project, resulting in improved
CH4 stratospheric profiles now covering the altitude range
between 17 and 45 km. Furthermore, the first
SCIAMACHY CO2 stratospheric profiles have been obtained.
The complete SCIAMACHY time series has been processed, resulting in
a stratospheric CH4 and CO2 data set (V4.5.2)
covering the time interval from August 2002 to April 2012. Because
of the sun-fixed orbit of Envisat, the SCIAMACHY solar occultation
measurements are restricted to latitudes between about
50 and 70∘ N. However, measurements
of the stratospheric distribution of greenhouse gases are generally
sparse. Therefore the new SCIAMACHY data sets, which cover almost
ten years, can provide valuable information about stratospheric
changes.
Intercomparisons with correlative data (ACE-FTS, HALOE and MIPAS
CH4; ACE-FTS and CT2013 CO2) indicate an accuracy of the
new products of about 5–10 % for CH4 and
2–3 % for CO2. At most altitudes, this is in fact
similar to or even better than the estimated mean (statistical)
error of the single profile products. However, at least for
CO2 there are indications that the error at
altitudes above about 30 km is still overestimated.
First estimates of CH4 and CO2 trends have been
derived from the SCIAMACHY ONPD time series (2003–2011). Above
20 km no significant CH4 trends are observed. At
the lowest altitude (17 km) a small CH4 trend of
about 3 ppbvyear-1 has been determined.
The derived CO2 trends are significant at all altitudes and on the
order of about 1.7 ppmvyear-1, slightly varying with
altitudes between 1.3 ppmvyear-1 (at 39 km) and
1.9 ppmvyear-1 (at 21 km).
Considering the specific spatial and temporal sampling of the
SCIAMACHY occultation data, these trends are in reasonable
agreement with total dry-air column-average trends of CH4
and CO2 obtained from SCIAMACHY.
The main issue to be resolved in the future is an unexpected
vertical oscillation in the resulting CH4 and CO2
profiles. These oscillations are currently considered to be the
most limiting factor for the accuracy of the ONPD products and need
further investigation.
A possible way forward in this context is to use the ONPD method to
derive pressure and temperature data from SCIAMACHY solar
occultation measurements in the atmospheric O2(A) band around
760 nm. These data could then be used in the CH4
and CO2 retrievals instead of the ECMWF data. This way,
potential systematic errors might be cancelled and the ONPD data products
would be less dependent on ECMWF data. However, this would
require high-quality ONPD pressure and temperature products, which
are not yet available. This will be subject to future studies.
Especially for CO2, another option to be followed in the
future is the application of alternative retrieval algorithms.
Possible candidates for this would be a two-step approach used e.g. in GOMOS
stellar occultation retrievals or the use of
a full optimal estimation-based retrieval, including online radiative transfer
calculations to the SCIAMACHY solar occultation data see
e.g..
The latter kind of retrieval is in particular computationally much more expensive,
but vertical oscillations can be better handled via appropriate regularisation
and the retrieval is less sensitive to non-linear effects arising from
e.g. saturation or varying temperature and pressure.