Introduction
Methane is the third largest contributing greenhouse gas in the Earth
atmosphere, after water vapour and carbon dioxide
. A quantitative understanding of the
methane cycle is needed to model present and future climate.
Accurate measurements are needed to constrain long-term sources and
sinks .
Methane has both natural and anthropogenic sources, and has an
atmospheric lifetime of approximately 9 years
. Anthropogenic sources, such as
livestock, landfills, and fossil fuels, account for approximately
352±45 Tgyr-1, whereas natural sources total 202±35 Tgyr-1 . Total methane
concentrations are estimated to have risen from 700±25 ppbv in pre-industrial times to 1795±18 ppbv in 2010 . The
largest natural source of methane is from wetlands, which are
concentrated at high northern latitudes
(50–75∘ N) . Models
disagree about the trend and feedbacks for wetland methane
emissions
e.g.. The
northern latitudes where wetlands dominate are poorly sampled by
ground-based measurement networks (either in situ or remote
sensing). Therefore, only spaceborne remote sensing can deliver
the spatial and temporal coverage needed to constrain models. Due
to the difficult nature of satellite remote sensing in an area
where solar elevation angles are low and surfaces are cold and
snow-covered, targeted validation of spaceborne methane
measurements in the Arctic is needed.
Satellite validation is the process of verifying that remotely sensed
geophysical products (such as methane concentrations) are
consistent with a reference “ground” truth while taking into
account accuracy, known biases, and precision
. Validation is carried out
by performing a comparison against a reference that can be
considered as a truth, or that is itself validated. Often, when
such a truth is not available, an alternative is cross-validation.
A cross-validation seeks to verify that measurements reported by
a set of products are mutually consistent within reported error
ranges .
Previous studies have validated spaceborne methane measurements
in different contexts.
A brief overview of the history of spaceborne methane measurements is
included in the broad review by ,
with considerably more detail in the slightly older review by
.
Spaceborne methane measurements use different techniques.
Down-looking (nadir or slant) shortwave measurements (i.e. from reflected solar
radiation), such as from the SCanning Imaging Absorption SpectroMeter for Atmospheric CHartographY (SCIAMACHY) ,
or the Greenhouse Gases Observing Satellite (GOSAT) Thermal And Near infrared
Sensor for carbon Observation (TANSO)-Fourier transform spectrometer (FTS) shortwave
,
are limited to total columns in daytime clear-sky conditions.
Thermal infrared measurements, such as from the Tropospheric Emission Spectrometer (TES)
,
the Atmospheric InfraRed Sounder (AIRS)
,
the Infrared Atmospheric Sounding Interferometer (IASI)
,
or the GOSAT TANSO-FTS Thermal Infra-Red (TIR) band do not depend on the Sun
and have the potential to measure the vertical distribution, although the
latter depends on the spectral ranges used and on sufficient
degrees of freedom for signal (DOFS)
being available in the measurement (at least 2 DOFS are needed
to resolve vertical information).
Even where the measurement contains insufficient information for resolving
features vertically,
thermal infrared can still complement shortwave observations
whose sensitivity generally maximizes lower in the troposphere, and
thus (in the case of methane) closer to the sources.
Measurements in a limb geometry, such as from the Michelson Interferometer for Passive Atmospheric Sounding (MIPAS)
, have a higher vertical resolution
but a less precise horizontal geolocation due to the long path through the
atmosphere, and cannot measure close to the
surface.
One type of limb measurements are solar occultation measurements,
such as those carried out by the Atmospheric Chemistry Experiment (ACE)-FTS .
Looking at a solar source, those measurements have a very high
signal to noise
ratio, at the price of a low number of measurements (two
profiles measured per orbit).
The aim of this study is to cross-validate methane profile products
near Eureka, Nunavut, Canada (80∘ N,
86∘ W). We consider one spaceborne occultation
instrument (ACE-FTS), one spaceborne nadir/off-nadir instrument
(TANSO-FTS, the TIR band), and one ground-based solar absorption
instrument, all described in Sect. . We compare
each pair of products in a round-robin sense (each instrument is
compared against all others), to verify that the differences are
consistent with expected bias, accuracy, and precision.
The paper is set up as follows. Section describes in
detail the instruments involved and the cross-validation methodology
implemented. Section presents results on the vertical
resolution of the different instruments involved, as well as comparisons
of profiles and partial columns. In
Sect. , those results are interpreted and put in a
wider context.
Finally, Sect. contains conclusions
and recommendations for future work.
Methods
Instruments and products
PEARL-FTS
Since 2006, a Bruker IFS 125HR has operated at the Polar
Environment Atmospheric Research Laboratory (PEARL) Ridge
Laboratory at 80.05 ∘N,
86.42 ∘W, at an elevation of 610 ma.s.l. .
As part of the Network for the Detection of Atmospheric
Composition Change (NDACC) (http://www.ndsc.ncep.noaa.gov/)
the Fourier transform infrared (FTIR) makes measurements using
seven narrow-band filters covering the range between
670 and 4300 cm-1 (14.9 and 2.33 µm) with
a spectral resolution of 0.004 cm-1. Methane
retrievals are based on an optimal estimation method in the
framework of , carried out with the
new SFIT4 retrieval code
(https://wiki.ucar.edu/display/sfit4/Infrared+Working+Group+Retrieval+Code,+SFIT).
The retrieval iteratively improves the a priori Volume Mixing
Ratio (VMR) profiles which are based on the mean of
a 40 year run (1980–2020) from the Whole Atmosphere
Chemistry Climate Model (WACCM)
, version 6, for
Eureka. The retrieval strategy is based on the approach presented in
. The retrieval process outputs
methane profiles, averaging kernels, Jacobians for both the
retrieval and forward model parameters, profiles of interfering
species, spectral fits, root-mean-square error of fit, and
retrieval error estimates. Retrievals are performed on a fixed
altitude grid with 47 levels covering 91 kPa–8 mPa.
Pressure and temperature at altitudes below
10 Pa are obtained from daily National Centers for
Environmental Prediction (NCEP) profiles (covering
105–10 Pa), which are calculated for each NDACC
site and available at
ftp://ftp.cpc.ncep.noaa.gov/ndacc/ncep/. At altitudes above
10 Pa, NCEP profiles are not available, and we use the
mean temperature and pressure profiles of the aforementioned WACCM
model run.
Spectroscopic data are obtained from the HITRAN 2008 edition
.
Estimates of the measurement uncertainties are based on the
formulation presented in
.
Uncertainties due to measurement noise and forward model
parameters are calculated for each measurement. Interference
errors account for wavelength shift,
background slope, simple retrieved phase correction and the
profiles of CO2, HDO, NO2, and H2O.
The forward model parameter errors considered are solar zenith
angle uncertainties, temperature uncertainties and spectroscopic
parameter uncertainties. Smoothing error is not included
.
ACE-FTS
ACE (on-board the SCISAT satellite) includes an FTS (henceforth
ACE-FTS) operating at 750–4400 cm-1
(13.3–2.27 µm) with a spectral resolution of
0.02 cm-1 . It was launched
on 12 August 2003, into a circular orbit with an altitude of
650 km and an inclination of 74∘.
ACE-FTS is a Michelson interferometer of custom design built by ABB
Inc. . From two solar occultation
measurements per orbit, profiles of trace gases are retrieved. The
instrument has a vertical resolution of around 4 km,
measuring from the cloud tops up to 150 km. As the
current study focuses on methane, we are primarily interested in
the troposphere and lower stratosphere because this is where the
bulk of the methane is located and these atmospheric regions are
the primary contributors to the greenhouse effect. Retrievals are
performed on either a variable or a fixed altitude grid. Here, we
use the retrievals on the fixed 1 km altitude grid
(oversampled relative to the vertical resolution).
Pressure and temperature are available as retrieved parameters.
Spectroscopic line lists for methane are from HITRAN 2004
.
We use methane profile retrievals from release V3.5.
describe the overall retrieval
strategy for ACE-FTS retrievals. Since then, the algorithm has
been updated several times, with V3.0 described by
. The latest version at the time
of writing is V3.5, which corrects erroneous reanalysis data used
in the processing for V3.0 after September 2010.
As part of a larger validation exercise,
describe validations for
ACE-FTS methane profiles from V2.2, which is the version
immediately preceding V3.0. Differences between V2.2 and V3.0 are
described by .
compare retrieved profiles to
various other sources: 11 ground-based FTIR sites covering
a range of climate zones from Arctic to Antarctic (but not Eureka),
balloon-borne measurements from Spectroscopie Infra-Rouge
d'Absorption par Lasers Embarqués (SPIRALE), and spaceborne
measurements from MIPAS and the Halogen Occultation Experiment
(HALOE). In the high-latitude Upper Troposphere–Lower Stratosphere
(UTLS) region, they find ACE-FTS to be biased low to MIPAS (by
around 0.1 ppmv), but high to SPIRALE (less than
10 %; HALOE has no coverage north of
57∘).
Recently, have empirically
processed ACE-FTS measurements to detect unphysical retrieved
values. They divide values in bins depending on latitude, local
time, season, and altitude level. Within each bin, they fit
a superposition of three Gaussian distributions, assuming the
distribution is at most trimodal. Using these distributions, they
then flag any retrievals determined to be an outlier with
a confidence of 97.5 % or larger. In our study, we have
used version 1.1 of these flags to reject unphysical retrievals
from further processing.
GOSAT TANSO-FTS TIR
GOSAT carries the TANSO-FTS . It was
launched in January 2009 in a near-circular, sun-synchronous orbit
with an inclination of 98∘, a nominal altitude of
666 km, and a local time ascending node of 13:00.
TANSO-FTS scans ±35∘ from nadir, with a footprint
at nadir of 10.5 km. The instrument measures radiation
in four spectral bands. Bands 1–3 measure reflected solar
radiation, and band 4 measures infrared radiation emitted by the
Earth and its atmosphere.
Total column methane is retrieved from shortwave radiances
and validated by
, who find it has a 1.2±1.1 % low bias compared to the Total Carbon Column
Observing Network (TCCON). In this study, we focus on the methane
profiles retrieved from the thermal infrared (band 4,
5.5–14.3 µm or 700–1818 cm-1)
, V1.0x. In
the remainder of this article, TANSO-FTS refers to the TIR band
only, unless otherwise stated.
Processing of level-1 data is described by
. TIR-retrieved temperature and water
vapour validation is described by
. This is the first study to
validate V1.0x-retrieved methane profiles and partial columns
focusing on the northern high latitudes.
V1.0x methane profiles are retrieved on fixed vertical grid levels,
converted to variable pressure levels depending on the ambient
temperature profile, with pressure levels ranging from 94 kPa to
56 Pa. Temperature and water vapour a priori profiles
are obtained from Japanese Meteorological Agency Grid Point Value
data , and methane a priori profiles
are obtained from a National Institute for Environmental Studies
(NIES) transport model
.
Spectroscopic data are obtained from the HITRAN 2004 edition
.
According to thermal vacuum tests of TANSO-FTS before launch, the
signal-to-noise ratio (SNR) was as low as approximately 70 at
around the 7.8 µm CH4 absorption band,
resulting in low information content.
Derived meteorological products
In processing collocations between PEARL-FTS and ACE-FTS, we obtain
scaled potential vorticity (sPV) estimates from Derived
Meteorological Products (DMPs) .
calculate sPV based on Potential
Vorticity (PV) fields from the Goddard Earth Observing System
(GEOS)-5.0 reanalysis , by applying
a height-dependent scaling vector so that profiles have a similar
range of values throughout the stratosphere. Then, they
interpolate sPV values in space and time, to get an estimate at the
location and time corresponding to an instrument measurement. For
details, see .
sPV profiles are reported along a slant path. For ACE-FTS, sPV
values for each altitude correspond to the location of each tangent
point for the occultation measurement. For PEARL-FTS, sPV values
are calculated for altitudes along the line of sight. Details on
why and how we use sPV values are described in
Sect. .
Collocations
Collocations are occasions where different pairs of instruments
observe approximately the same air mass at approximately the same
time e.g.. We calculate
collocations between each pair of instruments; i.e. three sets in
total: PEARL-FTS–ACE-FTS, PEARL-FTS–TANSO-FTS, and
ACE-FTS–TANSO-FTS. A suitable collocation time and distance (for
a level 2 product) depends on the quantity of interest. As methane
is relatively well-mixed and has a lifetime on the order of 9 years , a maximum distance of
500 km and a maximum time interval of 24 h was
selected. This is similar to what previous studies have used. For
example, use 500 km
and 12 h for their polar comparisons, and
use 750 km and
24 h.
In the collocation determination, we consider each profile as
a point measurement, even if the profile is not vertical. For
TANSO-FTS, this is the location where the line of sight intersects
with the surface of the Earth. For ACE-FTS, we use the location of
the 30 km tangent point. For PEARL-FTS, this is the
location of the Ridge Laboratory. In the latter two cases, measurements
are not actually occurring at those locations, but rather along
a slant path with a large horizontal extent. For example, a limb
sounding with a tangent altitude of 10 km has a
715 km path at altitudes between 10 and 50 km
(as a simplified geometrical calculation shows), with a similar
order of magnitude for high PEARL-FTS solar zenith angles. In
Sect. we will discuss what this implies for the
present study.
Collocations between ACE-FTS and TANSO-FTS are limited to the
quadrangle 60–90∘ N,
120–40∘ W, as to remain in roughly the same
geographical area as the collocations with PEARL-FTS.
The larger area compared to the area immediately around PEARL allows
for more collocations and therefore more complete statistics.
A single retrieval from one instrument may collocate with more than
one retrieval from the other. In Sect. , we
describe how this is taken into consideration.
Vertical regridding
Different measurements are reported on different vertical grids, as
described above in Sect. . Therefore, we need to calculate interpolated
profiles before we can perform subsequent processing steps.
To calculate altitude from pressure for TANSO-FTS, temperature and
water vapour fields are regridded onto the retrieval pressure grid
using a b-spline method . This may
introduce some error above 1 kPa. However, as this is at
altitudes above the sensitivity range of the retrieval, this does
not affect subsequent processing. Pressure is converted to
altitude based on the assumption of hydrostatic equilibrium.
For each collocation pair, we choose a shared altitude grid to
which we interpolate profiles of retrieved methane, a priori
methane, averaging kernels, temperature, and water vapour. For the
new altitude grid zn, we (arbitrarily) choose the
arithmetic mean altitude per level for the lower-resolution data set
(i.e. we take all altitude profiles, then calculate the average
hi for i=1…N if each profile has N levels). That
means we have one altitude grid for each of our three comparison
pairs. In regridding, we are careful not to extrapolate any
profiles; any levels outside of the range of the chosen grid are
flagged and not considered in subsequent processing. For the
lower-resolution instrument, averaging kernels are regridded
following ,
Azn≈WAzoW∗,
where A is the averaging kernel matrix,
zn is the new altitude grid,
zo is the old altitude grid, W
is the interpolation matrix between the two grids, and ∗
indicates the Moore–Penrose pseudo-inverse
. Regridding is performed by
linear interpolation, and W is calculated by obtaining
the standard matrix of the linear transformation p. 83,
W=(T(e1)…T(en)),
where T can be any linear vector-valued function (in this case:
linear interpolation), and ek (k=1…n) is
column k of the identity matrix I.
Vertical smoothing
We investigate the information content for each of our data sets by
calculating a histogram of the DOFS for the retrievals, defined as
the trace of the averaging kernel matrix A (we
calculate this before the regridding described above). For each
pair of collocations, one measurement has a higher vertical
resolution than the other. Henceforth, we will refer to the
“higher-resolution” and “lower-resolution” measurements, by
which we mean vertical resolution. The higher-resolution
measurement is smoothed using the averaging kernel and a priori
from the lower-resolution measurement, following
,
x^s=xa+A(x^h-xa),
where x^h is the original
higher-resolution profile, A and
xa are the averaging kernel matrix and the
a priori profile for the lower-resolution profile, respectively,
and x^s is the smoothed
higher-resolution profile, to be compared against the
lower-resolution profile. In cases where
x^h does not cover the full range of
xa, x^h is
extended using xa on both sides, prior to the
application of Eq. () because it follows from
Eq. () that x^s=xa, where rows of A are
0.
Natural variability and coincidence error
Depending on the geophysical quantity of interest, it may or may
not be necessary to consider natural variability. For example,
considers that one needs to
evaluate the coincidence error. He proposes to estimate this by
calculating the expected natural variability based on collocation
distance and time interval, using an independent source, such as
from reanalysis model output. Instead, we choose to investigate
whether this is needed for our methane intercomparison, by
considering the effect of our collocation criteria (time and
distance) on the comparison results. If reducing the collocation
time and distance has no large effect on the difference, an
explicit consideration of natural variability is not necessary.
None of the measurements are point measurements, but all measure
along a path through the atmosphere, as described above. Due to
these considerations, the parts of the atmosphere sampled by
TANSO-FTS, PEARL-FTS, and ACE-FTS are different, even when the
nominal location is the same. This contributes to the coincidence
error described above, but the same reasoning applies.
A coincidence error should be expected to increase when the distance or
time
increases, and decrease when those decrease, ultimately
disappearing in the theoretical case where two instruments sample
exactly the same atmosphere at the same time.
Therefore, where
reducing the collocation distance criterion only has a small impact
on estimated differences between instruments, the coincidence
error is not of major importance, and there is no need to
explicitly take the path through the atmosphere into account.
The presence of the Arctic polar vortex means that even proximate
stratospheric air parcels may sample considerably different
conditions . Therefore, for the
comparison between ACE-FTS and PEARL-FTS, we investigate the effect
of further constraining the collocations by an sPV criterion. This
is not needed for comparisons involving TANSO-FTS because it is
sensitive only to the troposphere. As we choose a single level for
investigating the sPV criterion (potential temperature of 700 K), we do not perform any
interpolation, except when comparing sPV values between two
instruments. The source of our sPV values is described in
Sect. .
Averaging measurements
As mentioned in Sect. , usually the same profile
from one instrument collocates with more than one profile from
another. For example, we have a subset of n collocated pairs
PEARL-FTS vs. TANSO-FTS that all correspond to one unique PEARL-FTS
profile with n different TANSO-FTS profiles. Similar to
, we calculate the arithmetic
mean methane profile of all TANSO-FTS profiles corresponding to the
same PEARL-FTS profile. Note that since we have already performed
smoothing on each PEARL-FTS profile individually, by applying
Eq. () using different TANSO-FTS averaging kernels,
the set of smoothed PEARL-FTS profiles corresponding to a single
original PEARL-FTS profiles now varies. Therefore, we calculate
the arithmetic mean profile for both sets of profiles corresponding
to a unique original PEARL-FTS profile. Note that the same
TANSO-FTS profile can also collocate to more than one PEARL-FTS
profile; i.e. the set of TANSO-FTS profiles collocating with
PEARL-FTS profile k has some overlap with the set of TANSO-FTS
profiles collocating with PEARL-FTS profile k+1. We do no
further processing to account for this.
We perform a similar operation where multiple TANSO-FTS profiles
correspond to the same ACE-FTS profile, or where multiple PEARL-FTS
profiles correspond to the same ACE-FTS profile.
Partial columns
Considering the limited vertical information content for PEARL-FTS
and TANSO-FTS, we compare partial column values. Each of the
retrievals reports VMR. As a first step in calculating partial
columns, we convert volume mixing ratio, x, to number density,
N, according to the ideal gas law
,
Nx=pkT,
where x is the VMR, p atmospheric pressure, T temperature, and
k=1.380653×10-23 JK-1 is Boltzmann's
constant . To convert x to N for both
instruments, there are three reasonable alternatives for temperature
and pressure: one can choose one instrument and use its pressure and
temperature for both, one can convert x to N for each instrument
using its own pressure and temperature, or one can calculate N
using the mean temperature and pressure between the two instruments
(arithmetic mean temperature and geometric mean pressure), resulting
in Nmean. None of those alternatives is perfect and each
has some advantages or disadvantages. We choose to use
Nmean for use in further processing, so that temperature
and pressure are consistent within the comparison ensemble. The
uncertainty due to the differences in pressure and temperature is
then given by
σpT=Nsec-Nprim2,
where Nprim and Nsec are the primary and
secondary number densities corresponding to the primary and
secondary instrument within each collocation pair. For the
temperature, we calculate the arithmetic mean. For the pressure,
we calculate the geometric mean because pressure is very far from
normally distributed and closer to a log-normal distribution.
To calculate partial columns from number density profiles, we need
to determine an appropriate altitude range for the partial columns.
ACE-FTS measurements have a high sensitivity throughout the
vertical range, but PEARL-FTS and TANSO-FTS sensitivities vary as
a function of altitude. For each profile, we calculate as
a function of altitude the sensitivity of the retrieval to the
measurement, by summing the rows of the averaging kernel
. This value, normally between
0 and 1, indicates what fraction of the retrieved value is due
to the measurement (as opposed to the a priori). From this, we
calculate the altitude range (hl,hu) where at least a fraction
f of the profiles have a measurement sensitivity larger than c.
The choice of f and c is an optimization problem. If they are
too large, the altitude range becomes very small and the result is
closer to a single layer retrieval than to a partial column; but if
they are too small, then a large part of the partial columns is due
to the a priori and we are not really comparing measurements.
There is no single obvious solution to this optimization.
Specific criteria for choosing f and c will be presented in
Sect. .
Typically, it is desirable to have c=1 and f=0.5, such that half
the profiles have full sensitivity at a particular altitude.
Once the altitude range is chosen, we define an operator
g such that levels within the range have value 1, and
levels outside it have value 0, and calculate the partial columns
by
npc=gNxx^,
where npc is the partial column estimate, g
is the partial column operator (i.e. a vector consisting of ones at
levels within the partial column range, and 0 elsewhere), and
x^ is the (smoothed) methane profile. We
calculate the difference in partial columns by
δpc=npc,2-npc,1,
where npc,2 and npc,1 are the partial
column values for TANSO-FTS, ACE-FTS, and PEARL-FTS, depending on
the specific comparison set.
Next, we investigate whether the partial column difference is
itself a function of partial column, by fitting a first order
polynomial (y=ax+b) to δpc(xpc,1),
using ordinary least squares, and we calculate the 95 %
confidence band around the predicted regression line. Finally, we
calculate the DOFS of the newly calculated partial columns, by
taking the trace of the sub-matrix of the averaging kernel,
corresponding to the levels used for partial column calculations.
Error analysis
In order to address the core question of a cross-validation study
– are the retrievals consistent? – it is critically important
to address error estimates. If we assume that the
higher-resolution measurement has a much higher resolution than
the lower-resolution measurement, a simplification of
Eq. 22 gives
Sδ12=S1+A1W12S2W12TA1T,
which is identical to the result found by
. Here, S is the
random error covariance matrix, A is the averaging
kernel matrix, the subscript 1 relates to the lower-resolution
retrieval, and the subscript 2 relates to the higher-resolution
retrieval. W12 is the grid transformation matrix
calculated by
W12=W1∗W2
, and ∗ indicates again the
Moore–Penrose pseudo-inverse (see also
Eq. ).
To calculate the variance in the partial column, we use
σPC=gSδ12gT,
where the calculation of g is described in
Sect. .
PEARL-FTS provides the random error covariance matrix directly for
all retrievals, but ACE-FTS and TANSO-FTS do not. As ACE-FTS is
a limb observing instrument, the information content can be
approximated by one degree of freedom per retrieval level.
Consequently, the error covariance between different retrieval
levels for ACE-FTS is far lower than for the other retrievals
considered in this study. Therefore, we neglect those covariances
and approximate SACE-FTS as a diagonal matrix,
with SACE-FTS,i,i=σi2 and
SACE-FTS,i,j=0 where i≠j.
For TANSO-FTS retrievals, error covariances were calculated only
for a limited number of TANSO-FTS retrievals for computational
reasons. For each of the TANSO-FTS profiles where we have not
calculated the covariance matrix, we need to choose a representative
covariance matrix corresponding to a
profile for which one is available. To calculate which
profile to choose, we divide the TANSO-FTS profiles into bins according to
their latitude, longitude, DOFS, retrieved partial column methane
(see Sect. ), time of year, and local time.
Specifically, we used 12 bins for day of year, 5 bins for mean
local solar time, 5 for latitude, 5 for longitude, 10 for
partial column methane, and 10 for DOFS, where the bins are
spanned linearly between the extreme values in the collocation
database. Although this gives a theoretical number of 12×5×5×5×10×10=150 000 bins, only n≪150 000 of those contain a non-zero number of profiles.
For each of those n bins, we select one profile at random,
according to a uniform distribution. For the selected profile, we
calculate the error covariance matrix, which we then use for all
profiles within the same bin.
Secondly, as TANSO-FTS retrievals are performed in logarithmic
space, TANSO-FTS error covariance matrices are in units of
logppmv2 and cannot be directly considered in
Eq. (). To estimate
Cov(x^,x^) from
Cov(log(x^),log(x^)), we
use the approximation
Slin=Cov(x^,x^)≈E(x^)2eCov(log(x^),log(x^))-1,
where Cov(x^,x^) is the
covariance in linear terms, E(x^) is the
expectation value of x^, and
Cov(log(x^),log(x^)) is
the covariance in logarithmic terms. For E(x^),
we use the retrieved state vector x^. See
Appendix A for a derivation of Eq. ().
As described earlier in Sect. , not every
collocation pair is unique. For example, for a single PEARL-FTS
measurement, there may be several matching TANSO-FTS measurements.
Taking the arithmetic mean of a set of TANSO-FTS profiles affects
the effective errors. If we assume the random errors between N
different TANSO-FTS measurements to be uncorrelated, then the
effective Seff=SN. However, we cannot say
the same for the combined error Sδ12,
because for those N pairs, each PEARL-FTS measurement is the
same, so its errors are certainly not independent (their
correlation is equal to 1).
Geographic map showing northeastern Nunavut
(Canada), northwestern Greenland, and surrounding islands, in a Lambert
azimuthal equal-area projection . The
background shows bathymetry in blue tones, elevation in green and brown
tones, and land ice with areas larger than 100 km2 in white, as
calculated by NOAA ETOPO1 . The white circle
with a red edge in the centre of the map shows the location of the PEARL
Ridge Lab near Eureka, Nunavut. The red and blue dots with black edges show
the locations of TANSO-FTS and ACE-FTS profiles within 500 km and
24 h of PEARL, in the time period indicated in
Table .
Results and discussion
In the following sections, we describe the results of the
processing steps described above. This section is structured
similarly to the previous one. First, we describe the results of
collocations, vertical regridding, smoothing, and the investigation
of the coincidence error. Then, we present results for the profile
and partial column comparisons.
Collocation statistics for the different collocation pairs.
Collocations between ACE-FTS and TANSO-FTS are limited to
the quadrangle 60–90∘ N, 120–40∘ W.
The total number of collocations considers all pairs before averaging.
After averaging, the number of collocations is equal to the number
indicated in the row “No. primary”.
“Med. dist” is the median distance for all pairs.
“Dist. mean” is the distance between the arithmetic mean
positions (as calculated using the World Geodetic System (WGS)-84 ellipsoid)
of each instrument in the pair.
Primary
PEARL-FTS
PEARL-FTS
ACE-FTS
Secondary
TANSO-FTS
ACE-FTS
TANSO-FTS
First collocation
24 February 2010
27 September 2006
2 February 2010
Last collocation
19 September 2011
15 March 2013
19 September 2011
No. collocations
20 741
1342
4685
No. primary
939
522
370
No. secondary
2804
149
2916
Med. dist [km]
376.39
313.28
355.09
Dist. mean [km]
33.86
163.11
38.61
Collocations
Figure shows a map of the collocations for the
PEARL-FTS–TANSO-FTS and PEARL-FTS–ACE-FTS pairs.
Table shows the number of collocations between
the three data sets and the period throughout which collocations are
found. The table shows both the total number of collocations, as
well as the number of unique measurements for each data set. From
the methodology of calculating the arithmetic mean where many
profiles from one data set collocate with a single profile from the
other, it follows that after this processing has been performed,
the number of pairs corresponds to the table row “primary”. The
median distance is between 300 and 400 km for each
pair. The distance between the arithmetic geographic mean ranges
from 33.8 km for PEARL-FTS–TANSO-FTS to
163.1 km for PEARL-FTS–ACE-FTS.
Vertical resolution and information content
Figure shows the mean of the averaging kernel
matrices for the entire period of collocations between PEARL-FTS
and TANSO-FTS. As discussed before, the vertical resolution for
ACE-FTS is much higher than for PEARL-FTS or TANSO-FTS, and we
approximate ACE-FTS averaging kernels by the identity matrix.
Note that regridding and smoothing as described in
Sect. is only applied where we are comparing
products directly against each other (profiles or partial columns) and
has not been done for results presented in this section.
Arithmetic mean of all averaging kernels for the set
of collocations between PEARL-FTS and TANSO-FTS. The left panel shows
averaging kernels for PEARL-FTS and the right panel shows averaging kernels
for TANSO-FTS. The white circles with a black edge indicate the nominal
altitude for each retrieval level.
Figure shows a histogram of DOFS for PEARL-FTS and
TANSO-FTS measurements, for all pairs where the two are collocated.
The figure illustrates that whereas PEARL-FTS measurements contain
mostly between 1.5 and 3 DOFS and therefore have some profile
content, the same is not true for TANSO-FTS, where most profiles
have less than 0.5 DOFS, with some below 0.3. Clearly, there
is no profile information here. However, as the DOFS are larger
than 0, there is still some information in the measurement.
Histogram of the total DOFS per retrieved profile
for the set of collocations between PEARL-FTS and TANSO-FTS. The histograms
are normalized such that the total area for each histogram equals 1.
Considering the variable information content for PEARL-FTS and the
very low information content for TANSO-FTS, we investigate how
information content varies as a function of latitude, longitude,
time of year, time of day, and methane partial column. It was
found that for both PEARL-FTS and TANSO-FTS, the most dominant
factor controlling the DOFS is the time of year, followed by the
methane partial column.
Figure shows the information content of the
TANSO-FTS profiles as a function of time of year and methane
partial column. Note that although the figure shows information
content in the entire profile, the vertical axis shows partial
columns. TANSO-FTS retrievals have very low DOFS between September
and May. This period corresponds to a cold and snow-covered
surface in Eureka, and the very low thermal contrast complicates
a retrieval from nadir/off-nadir observations in the thermal
infrared at this time. In July, when the surface is warmer, the
retrievals have a higher number of DOFS; in a few cases up to 0.7
or above.
A different pattern is visible for PEARL-FTS information content as
shown in Fig. . The largest DOFS, with values
up to 3, are found in late February, just after the end of the
polar night, and in late September/early October, just before the
beginning of the polar night. The ground-based PEARL-FTS is not
negatively affected by a cold surface or snow-cover, but rather
benefits from the longer optical path through the atmosphere early
and late in the observing season, when the Sun is closer to the
horizon. Around midsummer, the optical path is shorter, and the
information content in the measurement is smaller. However, even
when PEARL-FTS is at its worst and TANSO-FTS is at its best, the
PEARL-FTS measurement still has more than twice the information
content of the TANSO-FTS one.
Figure shows the fraction of PEARL-FTS
profiles at a particular altitude level that has sensitivity
(defined in Sect. ) larger than c, where c
varies between 0 and 1. We can see that (almost) all profiles
have sensitivity close to 1 below an altitude of approximately
25 km, whereas a much smaller fraction of profiles has
such a high sensitivity at higher altitudes. From the data used to
produce Fig. , we select an altitude range to
use for partial columns. Specifically, for a threshold where
50 % of profiles have at least 50 %
sensitivity, we find a range of 0.9–29.9 km for
partial columns. Note that this relates only to the profiles
collocated to TANSO-FTS.
TANSO-FTS DOFS per profile as a function of season and methane
partial column. The calculation of partial columns is described in
Sect. , and the range of altitudes considered is described in
Table . The vertical axis shows TANSO-FTS partial columns
for 5.3–9.7 km, but DOFS relate to the entire profile. The
figure includes all 2804 TANSO-FTS profiles collocated with PEARL-FTS.
As in Fig. , but for PEARL-FTS. The vertical axis
shows PEARL-FTS partial columns for 5.3–9.7 km, but DOFS relate
to the entire profile. The figure includes all 939 PEARL-FTS profiles
collocated with TANSO-FTS. Note that the range of DOFS here is much larger
than for Fig. .
Sensitivity density (see Sect. ) for PEARL-FTS
retrievals collocated with TANSO-FTS.
Figure shows the same for TANSO-FTS profiles
collocated to PEARL-FTS. In the case of TANSO-FTS, we do not have
any profiles that have a sensitivity close to 1 at any altitude,
and even a sensitivity of 0.5 is rarely reached. TANSO-FTS
sensitivity peaks in the range 7–9 km, and in this
range, at most 16 % of profiles have a sensitivity of at
least 0.5. Therefore, for partial columns including TANSO-FTS,
we cannot use the same criterion as for PEARL-FTS. Rather, we
select the range where at least 20 % of the profiles
have at least 30 % sensitivity, and arrive at a range of
5.2–9.5 km (in comparisons with PEARL-FTS, the lower limit
is 5.3 km, due to regridding and rounding).
Sensitivity density (see Sect. ) for TANSO-FTS
retrievals collocated with PEARL-FTS.
Polar vortex and coincidence error
Figure shows profiles of sPV (see
Sect. ) for the collocations between PEARL-FTS and
ACE-FTS, before selecting pairs based on sPV values. The
PEARL-FTS–ACE-FTS comparison is the only pair that has sensitivity
at stratospheric altitudes, so it is the only pair for which sPV
values are relevant. The figure shows sPV profiles for all
measurements in the comparison ensemble. Broadly speaking, the
range of sPV values increases with increasing elevation, with
values up to 2×10-4 s-1 near the surface and
up to 5×10-4 s-1 at 50 km. At most
elevations, sPV profiles exist at any value between the extrema.
However, between 17 and 32 km, PEARL-FTS clearly shows
a bimodal distribution of sPV values, which are mostly either
smaller than 2×10-4 s-1 or larger than
3×10-4 s-1. For ACE-FTS, the sPV profiles
are more noisy, and the distinction is not as clear; probably due to
the fact that ACE-FTS measurements are spread over a large area,
whereas PEARL-FTS measurements are all from the same location.
Consequently, we do not see the same bimodal distribution in the
difference panel either.
Profiles of sPV as a function of geometric height, for PEARL-FTS
(left panel) and ACE-FTS (centre panel). The right panel shows difference
profiles, i.e. sPVACE-FTS-sPVPEARL-FTS. For
the difference figure, ACE-FTS sPV profiles were interpolated onto the
vertical grid of PEARL-FTS profiles. Only collocated pairs are considered.
Profile comparisons
Figure shows the distribution of methane
profiles for the comparison between PEARL-FTS and ACE-FTS, where
the latter is either smoothed or unsmoothed (in this and subsequent
figures, the unsmoothed profiles and differences are referred to as
“raw”). The figure illustrates the known pattern that methane is
approximately constant as a function of altitude in the
troposphere, but decreases approximately linearly with altitude in
the stratosphere. The raw ACE-FTS profiles show a “wiggle” at an
altitude of around 20–25 km, but this disappears in
the smoothed version and is not visible in the PEARL-FTS profiles
(which, as shown before, have only around 2 DOFS). The figure
also illustrates that the distribution of methane in the
stratosphere is clearly non-Gaussian, as both PEARL-FTS and ACE-FTS
agree that the 1st quartile is considerably further from the median
than the 3rd. This justifies our choice of median and quartiles,
and implies that showing methane distributions using the mean and
standard deviation may be inappropriate.
Figure shows the distribution of
differences between PEARL-FTS and ACE-FTS. In this comparison, we
show an “unfiltered” version and a “filtered” version. The
“unfiltered” version contains all collocated profiles, whereas
the “filtered” version shows only profiles where the sPV values
at the potential temperature level 700 K differ at most
by 0.2×10-4 s-1. The figures show that at
all altitudes, smoothed ACE-FTS measurements are, on average, smaller
than PEARL-FTS measurements, with the median difference
ACE-FTS–PEARL-FTS between -10 and -70 ppbv. The 1st
and 3rd quartile illustrate that the differences are not normally
distributed, something already apparent from
Fig. . For example, between 10 and
20 km, the 1st quartile of the smoothed difference
clearly diverges from the median, whereas the 3rd quartile
approximately follows the pattern of the median. Apart from the
very lowest altitudes, near the lower boundary of the ACE-FTS
measurements, the 3rd quartile of ACE-FTS–PEARL-FTS is positive
with values between 10 and 50 ppbv, which means that
a significant minority of pairs have the smoothed ACE-FTS
measurement larger than the PEARL-FTS measurement. At altitudes
above 30 km, the absolute differences between smoothed
ACE-FTS and PEARL-FTS gradually decreases, as shown by the median
and the distribution. This is expected because with increasing
altitude, both the methane VMR and the sensitivity of PEARL-FTS
decrease. For the comparison between PEARL-FTS and unsmoothed
(“raw”) ACE-FTS, the median of the difference fluctuates
strongly, exceeding -100 ppbv at an altitude of
50 km. Differences with unsmoothed ACE-FTS that are not
seen in differences with the smoothed ACE-FTS are primarily due to
the PEARL-FTS a priori and due to vertical features that PEARL-FTS
cannot resolve.
Distribution of retrieved methane profiles for all collocations
between PEARL-FTS and ACE-FTS. In this and following figures, the solid line
indicates the median value for the set of all collocated profiles as
a function of altitude. The dashed line indicates the 1st and 3rd quartile
(25th and 75th percentile), and the dotted line indicates the 1st and 99th
percentile. The set of thin lines shows the distribution of the unsmoothed
profiles, labelled “raw” and interpolated on a shared altitude grid,
whereas the thick lines show the smoothed profiles. The calculation method is
described in the text.
Distribution of the difference between profiles for
ACE-FTS–PEARL-FTS. Solid, dashed, and dotted lines show the distribution of
the difference as a function of altitude, similar to how they show the
distribution of methane in Fig. . The blue lines show the
differences for all profiles (labelled “unfiltered”), whereas the orange
lines show the differences only for those profiles where ΔsPVθ=700K≤0.2×10-4 s-1,
where sPVθ=700K is the scaled potential vorticity
at a height corresponding to a potential temperature θ of
700 K along the line of sight, labelled “filtered”. See text for
details.
Figure also shows that applying the sPV
criterion has little effect below 25 km, and actually
makes the difference slightly larger above 25 km.
Similarly (but not shown), we find that limiting collocations to
half the distance and half the time interval (i.e.
250 km, 12 h) results in median differences
decreasing by up to 50 % at an altitude of
10 km, but increasing differences by
25–50 % at 20–25 km. This can be
explained by the relatively homogenous distribution of methane in
space and time.
Figure shows the distribution of methane
profiles for collocated measurements between PEARL-FTS and
TANSO-FTS, with PEARL-FTS either smoothed or “raw”/unsmoothed.
Like Fig. , it shows the familiar pattern of
methane, roughly constant below the tropopause, and decreasing with
altitude above it. The distribution is not symmetric around the
median, but the 1st quartile is closer to the median than the 3rd,
a pattern opposite to the PEARL-FTS–ACE-FTS profiles shown in
Fig. . The smoothed PEARL-FTS profile is cut
off at 30 km because TANSO-FTS a priori profiles are
available only up to 1 kPa.
Figure shows the distribution of the
difference TANSO-FTS–PEARL-FTS. Due to the low information
content in TANSO-FTS retrievals, the profiles shown in
Fig. do not contain any profile information,
but are rather a scaled version of the a priori (see also
Sect. ). Therefore, the very small differences for the
smoothed version shown in Fig. do not
mean that the two retrievals agree very well, but rather follows
directly from Eq. (): where TANSO-FTS contains
almost no information (see Fig. ), smoothed PEARL-FTS
tends to be very similar to
TANSO-FTS a priori and therefore to TANSO-FTS itself. Only below
15 km, where TANSO-FTS has some sensitivity, we can see
a nonzero spread in the differences between smoothed PEARL-FTS and
TANSO-FTS, although the median of the differences is still less
than 5 ppbv. The 1st quartile of the difference has
values down to -20 ppbv, whereas the 3rd quartile has
values up to approximately 15 ppbv.
Figure also shows there is a large
difference between the unsmoothed version of PEARL-FTS with
TANSO-FTS, but this is primarily due to differences in the a priori
used.
Figure shows the distribution of methane
profiles for collocations between smoothed ACE-FTS and TANSO-FTS,
with ACE-FTS either smoothed to TANSO-FTS, or not. Median methane
as a function of altitude shows a similar pattern as in the
previous comparisons, and again, it is clear that methane is not
symmetrically (and therefore not normally) distributed.
Figure shows the differences between the
two data sets. The caveat described above, when discussing
Figs. and ,
applies equally to the ACE-FTS–TANSO-FTS comparison. Therefore,
the smoothed difference is essentially zero at altitudes above
15 km. Below 15 km, roughly three-quarters of
TANSO-FTS retrievals are larger than ACE-FTS, with a median bias of
around 20 ppbv in the troposphere. Again, unsmoothed
comparisons show a much larger difference because of the choice of
the a priori used for TANSO-FTS (ACE-FTS retrievals are not
sensitive to any a priori).
As in Fig. , but for PEARL-FTS and TANSO-FTS.
As in Fig. , but for PEARL-FTS and
TANSO-FTS.
As in Fig. , but for ACE-FTS and TANSO-FTS. Note
that collocations are limited to the quadrangle 60–90∘ N,
120–40∘ W.
As in Fig. , but for ACE-FTS and TANSO-FTS.
Note that collocations are limited to the quadrangle
60–90∘ N, 120–40∘ W.
Partial column comparisons
Considering the low measurement information content for TANSO-FTS
and to a lesser degree PEARL-FTS, we also calculate and compare
partial columns as outlined in Sect. . From the
analysis in Sect. , we have calculated an optimal
vertical range for each pair of data sets. Table
shows the vertical range for each data set, as well as
characteristics of the partial column differences. Here,
smoothing (Sect. ) and averaging
(Sect. ) have been applied, but polar vortex
filtering has not, as the profile comparison described above
showed no significant effect.
Figure shows the DOFS for PEARL-FTS and
TANSO-FTS partial columns, when they are collocated to ACE-FTS or
to each other. Each pair that involves TANSO-FTS has DOFS in the
partial columns of less than 0.6 because the inclusion of
TANSO-FTS necessitates a relatively small vertical range of
approximately 5–10 km. TANSO-FTS partial columns
have DOFS between 0 and 0.4 in collocations with either
PEARL-FTS or ACE-FTS. PEARL-FTS partial column information
content is less than 0.6 when collocated with TANSO-FTS (partial
column range 5.3–9.7 km), but in the range of
1.1–2.1 when collocated with ACE-FTS (partial column range
5.3–29.9 km), with a mode of 1.7 DOFS.
Summary of partial column differences.
The upper two rows show the range over which partial columns are
calculated, based on an optimization of the information content as
described in Sect. .
The median Δ shows the median of secondary – primary.
MAD is median absolute deviation.
Unless indicated otherwise, all units are in moleculescm-2.
Primary
PEARL-FTS
PEARL-FTS
ACE-FTS
Secondary
ACE-FTS
TANSO-FTS
TANSO-FTS
Lower altitude (km)
5.3
5.3
5.2
Upper altitude (km)
29.9
9.7
9.5
Median par. col., prim.
164×1021
942×1020
945×1020
Median par. col., sec.
161×1021
942×1020
940×1020
Median Δ (sec.–prim.)
-2.6×1021
0.11×1020
7.4×1020
MAD
2.6×1021
9.6×1020
6.0×1020
Median Δ (%)
-1.6
0.012
0.78
MAD (%)
1.6
1.0
0.64
Offset/intercept
72.3±4.1×1021
467±16×1020
217±39×1020
Slope (no unit)
-0.456±0.025
-0.497±0.017
-0.224±0.041
Figure shows partial column differences
between PEARL-FTS and smoothed ACE-FTS for altitudes in a range of
5.3–29.9 km, with the lower limit determined by
ACE-FTS and the upper limit by PEARL-FTS, based on the method
described in Sect. . We choose to show ΔCH4 vs. PEARL-FTS CH4 rather than ACE vs. PEARL,
so that the difference and its dependences are apparent.
Horizontal error bars show uncertainties calculated from random
uncertainty in PEARL-FTS, propagated to partial columns with an
equation similar to Eq. (), but using
SPEARL-FTS. Vertical error bars show
σtot=σPC+σpT, where the
components on the right hand side are described in
Eqs. () and (), respectively.
Systematic errors are not considered in this error calculation.
Note that data shown here are not filtered by sPV values, since we
did not find that this improved the comparison (see above). The
figure shows that for most collocation pairs, there is
a significant difference between the two retrievals. All
differences lie within a range of ±3×1022 moleculescm-2 for a range of PEARL-FTS partial
columns between 1.3×1023 and 1.9×1023 moleculescm-2. The median difference
ACE-FTS–PEARL-FTS is -2.6×1021 moleculescm-2, which corresponds to
1.6 % of the median PEARL-FTS partial column of
1.64×1023 moleculescm-2.
The median absolute deviation (MAD) is 2.6×1021 moleculescm-2.
The linear
regression has a slope of -0.456±0.25 and an intercept of
7.23±0.41×1022 moleculescm-2.
Information content (DOFS) for partial columns. Each histogram shows
DOFS for a data set collocated with another data set; for example, one of the
PEARL-FTS histograms shows DOFS for PEARL-FTS partial columns collocated with
TANSO-FTS, whereas the other PEARL-FTS histogram shows DOFS for PEARL-FTS
partial columns collocated with ACE-FTS. The histograms are normalized such
that the total area for each histogram equals 1.
Figure shows partial column
differences between smoothed PEARL-FTS and TANSO-FTS for altitudes
between 5.3 and 9.7 km, with the range determined from
TANSO-FTS as described in Sect. . Error bars are
calculated analogously to the case of PEARL-FTS and ACE-FTS
described above. In the figure, the bulk of collocated
measurements are clustered around PEARL-FTS partial column values
in the range of 0.89–0.97×1023 moleculescm-2 with a much smaller number of larger values. For
measurements where PEARL-FTS reports a higher methane partial
column, the difference between TANSO-FTS and PEARL-FTS increases;
indeed, the linear regression has a slope of -0.497±0.17 and
an intercept of 4.67±0.16×1022 moleculescm-2. If TANSO-FTS and PEARL-FTS
reported identical partial column retrievals, the slope of this
regression would be 0. However, if TANSO-FTS retrievals had no
dependency on methane at all, the slope would likely be close to
-1. The observation that the regression slope lies between -1
and 0 shows that TANSO-FTS methane retrievals have some
sensitivity to the actual methane column. This is consistent with
the TANSO-FTS DOFS lying between 0 and 1. The median
difference is 1.1×1019 moleculescm-2 with
a MAD of 9.6×1020 moleculescm-2.
A second regression line shows the same regression excluding any data
points deviating from the PEARL-FTS median by more than 5 times
its MAD (there are 27 points deviating more
than 3 times the MAD, 4 points deviating
more than 5 times, and 1 point deviating more than 10 times).
This reduces the slope somewhat, but there is still considerable
overlap between the confidence bands throughout the range of PEARL-FTS
values (including suspected outliers).
Partial column differences ACE-FTS – PEARL-FTS as a function of
PEARL-FTS partial column. Based on a shared sensitivity calculations, partial
columns are estimated in a range of 5.3–29.9 km. The solid blue
line shows the results of a linear model with the parameters for offset and
slope obtained with a weighted least squares fit. The dashed blue lines show
a 95 % confidence interval around this estimate. The equation in
the upper right describes the linear model fit. See Table
for uncertainty estimates on slope and offset.
As in Fig. , but showing
TANSO-FTS – PEARL-FTS in the range of 5.3–9.7 km. The two
regression lines correspond to a regression with either all points (light
blue), or with suspected outliers excluded from the linear regression (dark
blue) as described in the text.
Figure shows partial column differences
between TANSO-FTS and ACE-FTS for altitudes between
5.2 and 9.5 km. The figure shows ACE-FTS measurements
between 0.87×1023 and 0.99×1023 moleculescm-2, with TANSO-FTS differences
similar to the upper left cluster shown in
Fig. . Based on the small range of
values, it is hard to draw firm conclusions about differences
between TANSO-FTS and ACE-FTS. Here, the linear regression has
a slope of -0.224±0.41 and an intercept of 2.17±0.39×1022 moleculescm-2. The slope is
about half as large as the regression slope for the other two
comparisons. The median difference is 7.4×1020 moleculescm-2 with a MAD of 6.0×1020 moleculescm-2.
As in Fig. , but showing
TANSO-FTS – ACE-FTS in a range of 5.2–9.5 km.
Discussion
Above, we have presented a cross-validation between PEARL-FTS,
ACE-FTS, and TANSO-FTS. Information content, bias, and random
errors, have implications for users. PEARL-FTS retrievals tend to
have DOFS between 1.5 and 3 (Fig. ), which means
there is some vertical information in the measurement. PEARL-FTS
retrieves systematically more methane than smoothed ACE-FTS as
shown by Figs. ,
, and Table . For
partial columns in the range of 5.3–29.9 km (with DOFS
still typically in a range of 1.1–2.2 as shown in
Fig. ), the median difference
ACE-FTS–PEARL-FTS is -2.6±2.6×1021 moleculescm-2, or -1.6±1.6 %. Those differences are robust when only
a subset of the data are considered, as the selection based on sPV
values in Fig. shows. For comparison,
find that ACE-FTS V2.2 profiles
have a difference of 0.3±1.5 % compared to Thule
(high Arctic), 3.0±1.6 % compared to Kiruna
(near the Arctic circle), and 9.8±3.5 % compared to Poker Flat
(sub-Arctic). Thus, our ACE-FTS V3.5–PEARL-FTS comparison
is compatible with comparisons at the only other Arctic site,
Thule, but inconsistent compared to earlier comparisons with Kiruna
and Poker Flat, which exist in different climatic zones. However,
as use V2.2 and we use V3.5,
results are not directly comparable.
The very low information content for TANSO-FTS retrievals
(Figs. and ) shows that these do
not contain vertically resolved information. Information content
for partial columns calculated near peak sensitivity is less than
the information content for complete profiles
(Fig. ). However, even when DOFS are between
0.1–0.4, there is at least some information in the retrieval
due to the measurement. This can be independently confirmed by
considering the partial column differences between TANSO-FTS and
PEARL-FTS. The linear regression for TANSO-FTS–PEARL-FTS, shown
in Fig. , has an estimated slope of
-0.497±0.17, i.e. significantly negative. This confirms
that TANSO-FTS and PEARL-FTS retrievals are both sensitive to what
is reported as methane. Due to the low TANSO-FTS information
content, smoothed PEARL-FTS is necessarily very close to TANSO-FTS.
Indeed, as shown by Table , the bias of methane
partial columns from TANSO-FTS compared to PEARL-FTS is essentially
0 (1.10±9.60×1019 moleculescm-2), but
this says more about the smoothing than about the reliability of
TANSO-FTS.
The very low information content we find for TANSO-FTS is
consistent with , who consider
using the different TANSO-FTS bands to retrieve CO2 and
methane from one or more bands simultaneously, over either ocean or
a desert surface. They find that above a desert surface, methane
retrievals using only the TIR band (that we use here) have 0.84 DOFS, with information content over sea water much lower (they
report 0.51 DOFS when combining TIR with shortwave
bands, but do not report results for TIR-only retrievals over sea
water). Considering that in our study we focus on the more
difficult case of mixed surfaces in the high Arctic, it is
consistent that the DOFS for our retrievals are more often than not
below 0.5.
Errors in methane retrievals – whether accounted for or not –
originate from different sources, but are dominated by
spectroscopy. For example, for the PEARL-FTS methane profiles, the
average error due to spectroscopy overall is 7.88 %,
including an error due to line intensities of 7.52 %.
For comparison, the next largest contributing error is due to the
solar zenith angle, and is 0.55 %. Moreover, the Voigt
line shape as used by many retrievals does not take into account
line mixing effects (for methane), even though those are relevant
. More generally,
spectroscopic transitions for the methane molecule are difficult to
accurately measure in a laboratory or calculate from physics-based
models . Therefore, spectroscopic
differences alone may account for a large part of both random and
systematic differences between different retrievals.
Other error sources are likely not significant. Clear sky bias
should not be an issue for methane retrievals, and even if it were,
it affects all three data sets equally, so it cannot have an effect
on a cross-validation. The same applies for the observation that
collocations only occur at particular times and locations.
Different estimates in temperature and pressure do affect the
retrieval, but we have already quantified those, and those are not
enough to explain the difference.
Conclusions
We have presented an analysis of the differences between methane
retrievals obtained from PEARL-FTS, ACE-FTS, and TANSO-FTS. We
have shown that measurement information content varies considerably
between the three data sets, and that care needs to be taken when
interpreting retrievals from PEARL-FTS and TANSO-FTS as profiles.
In particular for retrievals from the TANSO-FTS TIR band, the
measurement information content is too low for a true profile
retrieval because of the low thermal contrast and the low
signal-to-noise ratio of the CH4 retrieval band of
TANSO-FTS.
Although the measurement information content for TANSO-FTS is very
low and information content for partial columns collocated with
PEARL-FTS or ACE-FTS is even lower, this information content is
non-zero, as confirmed by the slope between the partial column
difference TANSO-FTS–PEARL-FTS and PEARL-FTS partial columns.
Therefore, the measurement is not without value. A future study
should more specifically address detectability: for example, if
there is a significant but spatially concentrated methane emission
somewhere in the Arctic or sub-Arctic, will TANSO-FTS TIR be able
to detect this? This question could be addressed using known
emission events or simulated data. Future work is also needed to
extend the comparisons to be global.
Uncertainties in retrievals arise from a variety of sources.
Ideally, full metrological traceability should be applied in any
satellite validation exercise .
This should also include sensitivity of the retrieval to differences in
spectroscopic data, such as differences between HITRAN 2004 (used for
TANSO-FTS and ACE-FTS) or 2008 (used for PEARL-FTS).
Additional work is needed to assess the impact of these differences.
Another important aspect not considered in this study is stability.
Collocations between PEARL-FTS and ACE-FTS cover a period of at
least 8 years and counting, which may be long enough to
investigate if systematic or random errors vary over time.
A more theoretical question to address is what would be needed to
get a better estimate of methane than we have? As shown, TANSO-FTS
TIR retrievals have very low information content in the Arctic.
What would be needed – in terms of measurement or knowledge of
forward model parameters – to improve this?
provide an overview of studies
estimating what CO2 precisions are needed – similar
studies should be done for methane. This is relevant not only for
pure research, but also for policy, as summarized by
. Overall, more work is needed to
address the use of thermal infrared satellite measurements for
Arctic methane retrievals.