AMTAtmospheric Measurement TechniquesAMTAtmos. Meas. Tech.1867-8548Copernicus PublicationsGöttingen, Germany10.5194/amt-10-1511-2017Merged ozone profiles from four MIPAS processorsLaengAlexandraalexandra.laeng@kit.eduvon ClarmannThomasStillerGabrielehttps://orcid.org/0000-0003-2883-6873DinelliBianca Mariahttps://orcid.org/0000-0002-1218-0008DudhiaAnuhttps://orcid.org/0000-0003-4619-8545RaspolliniPierahttps://orcid.org/0000-0002-5408-1809GlatthorNorbertGrabowskiUdoSofievaViktoriahttps://orcid.org/0000-0002-9192-2208FroidevauxLucienWalkerKaley A.https://orcid.org/0000-0003-3420-9454ZehnerClausInstitut für Meteorologie und Klimaforschung, Karlsruhe Institute of Technology, Karlsruhe, GermanyISAC-CNR, Bologna, ItalyEarth Observation Data Group, Oxford University, Oxford, UKIFAC-CNR, Florence, ItalyFinnish Meteorological Institute, Helsinki, FinlandJet Propulsion Laboratory, California Institute of Technology, Pasadena, USAUniversity of Toronto, Toronto, CanadaESA ESRIN, Frascati, ItalyAlexandra Laeng (alexandra.laeng@kit.edu)21April20171041511151816July201617October201614March201731March2017This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://amt.copernicus.org/articles/10/1511/2017/amt-10-1511-2017.htmlThe full text article is available as a PDF file from https://amt.copernicus.org/articles/10/1511/2017/amt-10-1511-2017.pdf
The Michelson Interferometer for Passive Atmospheric Sounding (MIPAS) was an
infrared (IR) limb emission spectrometer on the Envisat platform. Currently,
there are four MIPAS ozone data products, including the operational Level-2
ozone product processed at ESA, with the scientific prototype processor being
operated at IFAC Florence, and three independent research products developed
by the Istituto di Fisica Applicata Nello Carrara (ISAC-CNR)/University of Bologna, Oxford University, and the
Karlsruhe Institute of Technology–Institute of Meteorology and Climate
Research/Instituto de Astrofísica de Andalucía (KIT–IMK/IAA). Here we present a dataset of ozone vertical profiles obtained by
merging ozone retrievals from four independent Level-2 MIPAS processors. We
also discuss the advantages and the shortcomings of this merged product. As
the four processors retrieve ozone in different parts of the spectra
(microwindows), the source measurements can be considered as nearly
independent with respect to measurement noise. Hence, the information content
of the merged product is greater and the precision is better than those of
any parent (source) dataset.
The merging is performed on a profile per profile basis. Parent ozone
profiles are weighted based on the corresponding error covariance matrices;
the error correlations between different profile levels are taken into
account. The intercorrelations between the processors' errors are evaluated
statistically and are used in the merging. The height range of the merged
product is 20–55 km, and error covariance matrices are provided as
diagnostics. Validation of the merged dataset is performed by comparison with
ozone profiles from ACE-FTS (Atmospheric Chemistry Experiment–Fourier
Transform Spectrometer) and MLS (Microwave Limb
Sounder). Even though the merging is not supposed to remove the biases of
the parent datasets, around the ozone volume mixing ratio peak the merged
product is found to have a smaller (up to 0.1 ppmv) bias with respect to
ACE-FTS than any of the parent datasets. The bias with respect to MLS is of
the order of 0.15 ppmv at 20–30 km height and up to 0.45 ppmv at larger
altitudes. The agreement between the merged data MIPAS dataset with ACE-FTS
is better than that with MLS. This is, however, the case for all parent
processors as well.
Introduction
The Michelson Interferometer for Passive Atmospheric Sounding (MIPAS) was an
infrared (IR) limb emission spectrometer onboard the ENVISAT platform. It
measured during day and night at 6 to 70 km (up to 170 km in special modes),
pole-to-pole, producing more than 1000 profiles per day. Around 30 species,
temperature, and cloud composition could be derived from these measurements.
In 2002–2004, the instrument operated in full spectral resolution, with a
vertical resolution of about 3.5–6 km for the retrieved ozone product; this
period of MIPAS operations is referred to as the full resolution (FR) period.
Due to a failure of the instrument's mirror slide in 2004, the operations
were suspended during almost a year and were resumed in 2005 with reduced
spectral, but improved vertical, resolution. The corresponding period, until
the loss of communications with the ENVISAT platform in April 2012, is
referred to as the reduced resolution (RR) period of MIPAS operations.
MIPAS Level-2 data are operationally processed at ESA, with the scientific
prototype processor at IFAC Florence . Beyond this,
there are three independent scientific Level-2 processors: at the Istituto di Fisica Applicata Nello Carrara (ISAC-CNR)/University
of Bologna , at Oxford University
(http://www.atm.ox.ac.uk/MORSE/), and the Institute of Meteorology and
Climate Research/Instituto de Astrofísica de Andalucía (IMK/IAA) processor at KIT, Karlsruhe Institute of
Technology . Henceforth, the
four processors will be referred to as the ESA, Bologna, Oxford, and KIT
processors. The existence of these four products often leads to confusion in
the scientific community about their differences and which one to use. The
unified description of the four processors is given in .
The main similarities and differences between the four processors can be
summarized as follows:
all four processors use the same Level-1b spectra provided by ESA, but the Level-2 retrieval algorithms are different;
all four processors use microwindows instead of the full spectrum, but microwindow selection differs; for the rationale behind this approach see , , and ;
all four processors apply a global fit approach in a sense that the tangent altitudes of a limb scan are processed simultaneously rather than
sequentially ; however, they use different regularization approaches;
the Bologna processor uses a full 2-D-approach, that is, all measurements in a complete orbit are processed simultaneously; the horizontal variation
of the atmospheric state within the orbit plane is considered; the KIT processor accounts for horizontal temperature gradients along the line of sight
direction in the ozone retrieval; the other processors consider atmospheric variation in the altitude domain only.
In the frame of ESA's Ozone Climate Change Initiative project, a round robin
evaluation of ozone products from the four MIPAS processors was performed.
Comparison with ground-based instruments revealed that all four processors
reproduce on average the correct ozone distribution in a similar way, with
small differences in bias appearing most clearly in the troposphere. The KIT
bias was shown to be less than ±25 ppbv, depending on latitude, compared
to a systematic positive bias of roughly +50 ppbv for the other products.
In the stratosphere, all four products are positively biased by 2–5 %
relative to ozonesonde, lidar, Aura–MLS (Aura–Microwave Limb
Sounder), and ACE-FTS (Atmospheric Chemistry Experiment–Fourier Transform
Spectrometer) observations. Comparison with satellite instruments showed that
the KIT product is biased high only above 35 km, while the other products
start to be biased high at somewhat lower altitudes. This was tentatively
attributed to the use of the MIPAS AB band (1020–1170 cm-1) which is
more restrictively used by the KIT processor below 35 km. The MIPAS datasets
are generally in better mutual agreement than each of them with other ozone
records. The good resemblance of the biases, for example, is a strong
indication that the biases are not caused by one particular retrieval
processor but come from the instrument itself, from the Level-1 processing or
from the spectroscopic data used in the Level-2 retrievals. The details of
this analysis are reported in . Given the availability of
four independent MIPAS ozone data products, the question arose of how to
optimize the use of all MIPAS data products. This gave rise to the title
activity of this paper: to demonstrate the feasibility of merging the ozone
data from the four MIPAS datasets. Contrary to the merging of data from
multiple sensors, the following issues do not apply to the merging of
multiple data products of a single sensor: sampling issues in space and time,
and insufficient time overlap. Further, as follows from
, the degradation of the MIPAS instrument in the parts
of the spectra used by different MIPAS processors is similar. Since different
processors analyze different parts of the spectrum (microwindows), the source
(parent) measurements can be considered as nearly independent with respect to
the primary measurement errors. The microwindows used by the four MIPAS
processors are reported in the Table .
The use of different data points by the four processors gives rise to the
expectation for the merged product to have a better precision than the
individual contributing datasets. However, it should be treated with caution:
this expectation relies on the assumption that the dominating source of
uncertainties coming with the data is measurement noise, or any other source
of random error which is uncorrelated between the parent datasets. It is, of
course, not expected that systematic error components will necessarily
average out by the merging operation. The merging was performed on the MIPAS
data provided for the round robin exercise only, namely ozone data for the
years 2007 and 2008.
Spectral analysis windows used by the four MIPAS processors for
ozone retrieval.
The merging is performed on a profile per profile basis. Parent ozone
profiles are weighted based on their corresponding random error covariance
matrices; the correlations between different altitude levels of the profiles
are taken into account. The intercorrelations between the processors' errors
are evaluated statistically and are used in the merging. The small sample
size (four processors only) is an obstacle to the identification of outliers.
It only takes one processor to significantly deviate from the true profile,
and the merged product will be worse than any of the other three. Our choice
is, however, to always use all four processors' values.
The merged profile is constructed as a weighted mean of the four parent
profiles. For each processor, the errors at different height levels are
correlated because of error propagation patterns typical for limb sounding.
Therefore, the value of the merged profile at each level is a linear
combination of all the levels of all four processors, with weights defined by
corresponding error covariance matrices. This means that the weights depend
on the uncertainties' size: the smaller the error of a processor are, the
larger its contribution to the merged profile is. The merging is performed on
a fixed pressure grid which corresponds approximately to the MIPAS RR nominal
tangent altitude grid. At the upper and lower ends of the profiles, it occurs
frequently that not all four processors provide data. The height range was
hence limited to 62–0.8 hPa (∼ 20–55 km). We note n as the number
of vertical levels in the profile. The merged profile is obtained as
xmerged=eeeeC-1eeee-1eeeeC-1x1x2x3x4,
where e is n×n identity matrix, xi,i=1,2,3,4 is a
column vector representing the profile from the processor i, and C is
the processor intercorrelation 4n×4n matrix defined as follows:
C=Sx1S12TS13TS14TS12Sx2S23TS24TS13S23Sx3S34TS14S24S34Sx4,
where Sxi is the random retrieval error
covariance matrix of processor i, Sij (i and j correspond to
processors) are n×n matrices defined by
Sij=rijdiagSxidiagSxj,
with rij being n×n matrices representing the
correlation of errors on different levels of two processors; the calculation
of rij is discussed below in Sect. .
The random error covariance matrix of the merged profile is given by
Sxmerged=eeeeC-1eeee-1.
As the vertical resolutions of the four processors are very close (see
for details), our choice is not to take the averaging
kernels into the merging formalism. See for a merging
formalism involving the averaging kernels but omitting the correlation
between the random errors of the parent datasets.
Correlation coefficients
A retrieved atmospheric profile x^ can be decomposed into
the contribution from the true profile and the contribution from bias and
random error:
x^=x+ϵbias+ϵrandom,
where x^ is the retrieved profile, x is the true
profile, and ϵbias and ϵrandom are respectively the bias
and random components of the error. We pragmatically define “biases” as the
average over time at a given altitude and latitude and “random components”
as all other error components which survive the subtraction of the bias. Partly
correlated errors contribute both to the bias and the random error component.
We expect that the random errors in tendency cancel out by the merging, while
the bias component of the error will survive the merging. Our approach does not
require that the bias components are isolated beforehand, because we
statistically evaluate the inter-processor error correlations using debiased
differences, as outlined below.
We evaluate the intercorrelation of random errors of different processors by
examining the statistics of differences between each pair of processors in
the
following way.
The random errors of processor i at height p and of processor j at
height q, i, j=0, 1, 2, 3, p, q=1, ... , n are deduced from the
Eq. () as
ϵrandom,ip=x^ip-xp-ϵbias,ip, and ϵrandom,jq=x^jq-xq-ϵbias,jq.
By definition, the correlation coefficient xX,Y
between random variables X and Y is
ρX,Y=cov(X,Y)σXσY=EX-μXY-μYσXσY,
where cov stands for covariance, E stands for mathematical
expectation operator, μX stands for the expectation
values of X, μY stands for the expectation values of
Y, σX stands for the standard deviation of X, and
σY stands for the standard deviation of Y. In
our case, the random variables would be the random error of the values of
processor i at height p and the random error of the values of processor
j at height q (i=0, 1, 2, 3). Since the aim of our merging operation is to
improve the precision, the weight of each parent profile shall be associated
with the its precision and not with its accuracy. Thus, we use debiased
differences to infer the inter-profile correlation coefficients. N is the
number of profiles in the whole 2007–2008 sample. On each geolocation k,
k=1, ..., N, we will use the best estimate of the truth x that we
have, namely the mean profile of the four processors on this geolocation; we
note it by x‾k, k=1, ..., N, and its pth level is
noted by x‾kp. The expectation of X (or Y) is
estimated as the mean debiased difference between the retrieved profile and
the truth over all geolocations:
μX=1N∑l=1Nx^i,lp-xlp and μY=1N∑l=1Nx^j,lq-xlq,
where the vector x^i,l is the profile retrieved by processor
i on the lth geolocation and x^i,lp is its pth
level; xl is the true profile on the lth geolocation and xlp is
its pth level. Then the realization of X-μX on the kth geolocation is
X-μXk=x^i,kp-xkp-1N∑l=1Nx^i,lp-xlp=x^i,kp-x‾kp-1N∑l=1Nx^i,lp-x‾lp
(the true profile xk was replaced by its estimate
x‾k), and similarly the realization of Y-μY on the kth geolocation is
Y-μYk=x^j,kq-x‾kq-1N∑l=1Nx^j,lq-x‾lq.
We use hence the following estimator of the correlation between the random
errors ϵrandom,ip and
ϵrandom,jq. The correlation coefficient
rijpq between the random errors of processor i at height p and
the random errors of processor j at height q is
rijpq=∑k=1Nx^i,kp-x‾kp-1N∑l=1Nx^i,lp-x‾lpx^j,kq-x‾kq-1N∑l=1Nx^j,lq-x‾lq∑k=1Nx^i,kp-x‾kp-1N∑l=1Nx^i,lp-x‾lp2x^j,kq-x‾kq-1N∑l=1Nx^j,lq-x‾lq2.
In this formula, the third term in each outer sum is the bias of
corresponding processor, by taking it out of the first term we obtain a
debiased profile, and the second term in the bracket is the mean around which
the variation of debiased profiles is calculated.
Note that the obtained matrices are not symmetric, which is to be expected:
there is no reason why the random errors of Bologna at height 20 km and
random errors of KIT at height 35 km would be correlated exactly as the
random errors of Bologna at height 35 km and random errors of KIT at height
20 km.
Figure shows that the errors are correlated for all six
pairs; this correlation is not negligible: with a minimal value of -0.6 and
maximum of 0.26. This means that the coefficients rijpq can not be
assumed zero and must be taken into the merging formula.
Figure also demonstrates that error correlations between
the retrieved profiles from different processors are not mostly due to error
correlations in the measured spectra: Oxford and ESA use identical
measurements (see Table ), but the highest correlation is
observed in Bologna–Oxford and KIT–Oxford cases. However, the
similarities/differences in the retrieval algorithms seem to also play a
role, and that could explain some high absolute values of the coefficients. A
gain in precision of the merged product can be expected if these correlations
are adequately taken into account.
Statistical covariance matrices
In the previous section we have discussed how the inter-processor
correlations were diagnosed. Now we turn to the inter-level error covariances
of each single processor. These error covariance matrices are needed for each
single processor to construct the processor intercorrelation matrix as given
by Eq. (2). Only two processors, ESA and KIT, provide the covariance matrices
for each profile. For the other two processors, only statistical error
covariance matrices can be evaluated empirically. The error covariance
matrices are taken into the merging for controlling the weight of each
processor in the average. Thus, it is more important to evaluate the
covariance matrices in a consistent way than to have a particularly good
covariance matrix for a subset of profiles. Therefore, we have decided to use
statistical covariance matrices for all four processors. In order to reduce
the correlation due to natural atmospheric variability, we calculate it on
summer profiles in the 20∘ S–20∘ N latitude band. The mean of
all summer tropical stratospheric profiles of a processor i is noted x‾i,mean. The error covariance matrix of a processor
i is evaluated from the sample of debiased summer tropical stratospheric
profiles:
Sxi=1N∑k=1Nxi,kp-x‾i,meanp-1N∑l=1Nxi,lp-x‾i,meanp×xi,kq-x‾i,meanq-1N∑l=1Nxi,lq-x‾i,meanq.
Correlation of errors of four processors calculated by
Eq. (). Obtained matrices are not symmetric, which is to be
expected. The errors are non-negligibly correlated for all six pairs, which
means that the coefficients can not be assumed zero and must be taken into
the merging formula.
Note that this formula can also be obtained from the formula for the
correlation of errors by taking i=j and replacing the mean of four profiles
at each geolocation by the mean of the processor in the summer tropical
stratosphere. The obtained error covariance matrices are shown in
Fig. . The results obtained are consistent with the
error bars validation from .
Merged profiles and their validation
Figure shows an example of the merging of the four
individual parent profiles into one merged profile for the tropical summer
geolocation 33441_20080723T072843Z (0.2∘ S, 40.5∘ E).
Statistical covariance matrices of four parent MIPAS processors. The
white areas in Bologna and Oxford plots are for values bigger than 0.3: up to
0.82 for Bologna and up to 0.44 for Oxford processors.
Parent MIPAS profiles and the resulting merged MIPAS profile on
geolocation 33441_20080723T072843Z (0.2∘ S, 40.5∘ E). The
profile from the Bologna processor is the blue line; from the ESA processor, red; from the KIT processor, green;
and from the Oxford processor, pink. The merged profile is the brown line.
Mean profiles (a), bias (b), and precision
validation (debiased standard deviation of the differences, c) of
the four parent datasets and merged MIPAS dataset with respect to ACE-FTS
ozone profiles in 2007–2008.
Mean profiles (a), bias (b), and precision
validation (debiased standard deviation of the differences, c) of
the four parent datasets and merged MIPAS dataset with respect to MLS ozone
profiles in 2007–2008.
Merging of various data products from the same instrument is not necessarily
supposed to remove the bias of the parent datasets. Instead, it is supposed
to ameliorate the precision of the product since the parent processors rely
on different spectral information (different microwindows). At heights where
the precision of the merged product is better than the precision of any of
the parent datasets, the merging is successful. Figure
shows simultaneous comparison of the four parent MIPAS datasets and the
merged MIPAS dataset with ACE-FTS version 3.5 ozone dataset, for collocation
criteria 5 h and 500 km. In terms of precision, hence, the merging is a
success at 20–28 and 39–43 km. At 28–38 km, KIT's precision in terms of
the standard deviation of the differences is better than the precision of the
merged product. At 44–52 km, ESA's precision is better than the precision
of the merged product. All these conclusions are conditional to the
assumption that ACE represents the truth. Although the merging is not
supposed to remove the bias, it can change the bias through the averaging,
and depending on the signs of biases of parent profiles, this could lead to
the improvement of the bias. This is what is happening in the comparison with
ACE-FTS: at 24–28 and 33–37 km, the merged product agrees with ACE
∼ 1 % better than KIT, while at all other heights, KIT agrees
better. Interestingly, in integrated view over the altitude range around the
ozone VMR (volume mixing ratio) peak, where all four processors
have a known positive bias , the merged product is
performing ∼ 0.8 % better than any of the four processors
(Fig. b).
Figure shows simultaneous comparison of the four parent
MIPAS datasets and the merged MIPAS dataset with MLS version 3.3 dataset,
for collocation criteria 4 h and 250 km. At 20–25 km, the precision of
the merged product is better than the precision of any individual dataset.
When looking at the whole height range, the overall precision of the merged
product is better than the precision of any of the parent datasets. The
overall agreement of the merged product with MLS is not as good as that with
ACE-FTS; this is also the case for all parent datasets. In terms of bias, the
merged product performs ∼ 1.5–2 % better at 24–33 and 41–45 km, while
KIT performs better at the remaining heights. In particular, unlike for the
comparison with ACE, around the ozone VMR peak, the agreement of KIT is ∼ 2.5–2.8 % better than the agreement of the merged dataset.
Conclusions
We created a 2-year dataset of merged ozone profiles from four independent
MIPAS Level-2 processors. The novelty of the product is a mathematically
clean way of performing the merging: the weighting of parent profiles
is realized by corresponding inverse error covariance matrices, the
correlations between different profile levels are considered, and the
intercorrelations between processors' errors are evaluated statistically and
are used in the merging. In comparison to the individual parent datasets, the
merged product has a restricted height range (20–55 km) and only a
statistical covariance matrix can be provided. Validation of the merged
dataset is performed by comparing with ozone profiles from ACE-FTS and MLS.
Comparison with ACE-FTS looks better than with MLS. This is, however, the
case for all parent processors as well. Despite the fact that the merging is
not supposed to remove the bias, the high bias around the ozone VMR peak
known for the parent profiles is reduced in comparison with ACE-FTS (but not
with MLS). The overall precision of the merged product is better than that of
any of the four processors. This product could therefore be of use in
specific studies requiring improved precision of the MIPAS ozone record.
The merged MIPAS data product is available at
http://www.esa-ozone-cci.org (Laeng, 2016).
The authors declare that they have no conflict of
interest.
Acknowledgements
This work was performed in the frame of European Space Agency
(ESA) project Ozone_cci. All four MIPAS teams acknowledge ESA for
providing MIPAS L1b data. The ACE mission is supported primarily by
the Canadian Space Agency. Work at the Jet Propulsion Laboratory
was performed under contract with the National Aeronautics and
Space Administration.
We acknowledge support by Deutsche Forschungsgemeinschaft and
the Open Access Publishing Fund of Karlsruhe Institute of Technology.
The article processing charges for this open-access publication
were covered by a Research Centre of the Helmholtz Association.
Edited by: M. Weber
Reviewed by: two anonymous referees
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