AMTAtmospheric Measurement TechniquesAMTAtmos. Meas. Tech.1867-8548Copernicus PublicationsGöttingen, Germany10.5194/amt-10-4601-2017Tomographic reconstruction of atmospheric gravity wave parameters from airglow observationsSongRuir.song@fz-juelich.deKaufmannMartinhttps://orcid.org/0000-0002-1761-6325UngermannJörnhttps://orcid.org/0000-0001-9095-8332ErnManfredhttps://orcid.org/0000-0002-8565-2125LiuGuangRieseMartinhttps://orcid.org/0000-0001-6398-6493Institute of Energy and Climate Research, Stratosphere (IEK-7), Research Centre Jülich, 52425 Jülich, GermanyInstitute for Atmospheric and Environmental Research, University of Wuppertal, 42119 Wuppertal, GermanyKey Laboratory of Digital Earth Sciences, Institute of Remote Sensing and Digital Earth, Chinese Academy of Sciences, Beijing, ChinaRui Song (r.song@fz-juelich.de)30November201710124601461218April201721April201727August201721October2017This work is licensed under the Creative Commons Attribution 3.0 Unported License. To view a copy of this licence, visit https://creativecommons.org/licenses/by/3.0/This article is available from https://amt.copernicus.org/articles/10/4601/2017/amt-10-4601-2017.htmlThe full text article is available as a PDF file from https://amt.copernicus.org/articles/10/4601/2017/amt-10-4601-2017.pdf
Gravity waves (GWs) play an important role in the dynamics of
the mesosphere and lower thermosphere (MLT). Therefore, global observations of
GWs in the MLT region are of particular interest. The small scales of GWs,
however, pose a major problem for the observation of GWs from space. We
propose a new observation strategy for GWs in the mesopause region by
combining limb and sub-limb satellite-borne remote sensing measurements for
improving the spatial resolution of temperatures that are retrieved from
atmospheric soundings. In our study, we simulate satellite observations of
the rotational structure of the O2 A-band nightglow. A key element of the
new method is the ability of the instrument or the satellite to operate in so-called “target mode”, i.e. to point at a particular point in the atmosphere
and collect radiances at different viewing angles. These multi-angle
measurements of a selected region allow for tomographic 2-D
reconstruction of the atmospheric state, in particular of GW
structures. The feasibility of this tomographic retrieval approach is
assessed using simulated measurements. It shows that one major advantage of
this observation strategy is that GWs can be observed on a much smaller scale
than conventional observations. We derive a GW sensitivity function, and it
is shown that “target mode” observations are able to capture GWs with
horizontal wavelengths as short as ∼ 50 km for a large range of
vertical wavelengths. This is far better than the horizontal wavelength limit
of 100–200 km obtained from conventional limb sounding.
Introduction
Miniaturization in remote sensing instrumentation as well as
spacecraft technology allows for the implementation of highly focused
satellite missions, for example to observe airglow layers in the mesosphere
and lower thermosphere (MLT) region. The MLT extends between about 50 and
110 km in the Earth's atmosphere, and is highly affected by atmospheric
waves, including planetary waves, tides, and gravity waves (GWs), which are
mainly excited in the lower atmosphere . Atmospheric GWs
are the main driver for the large-scale circulation in the MLT region with
considerable effects on the atmospheric state and temperature structure
.
Temperature is a key quantity to describe the atmospheric state, and it is a
valuable indicator to identify and quantify atmospheric waves, such as GWs
(e.g. , and reference therein). As GWs displace
air parcels adiabatically both in vertical and horizontal directions, this
process affects the temperature of the atmosphere. Assuming linear wave
theory, GW-related fluctuations in different parameters (wind, temperature,
density, etc.) are directly connected via the linear polarization relations
(e.g. ). Therefore, amplitudes, wavelengths, and phases
of a GW can be determined from its temperature structure .
Over the last few decades, data from satellite and aircraft instruments have
been extensively used to characterize vertically resolved GW
parameters. Utilizing limb soundings, these data sets include temperature or
density data acquired by the Limb Infrared Monitor of the Stratosphere (LIMS)
, the Global Positioning System (GPS) radio
occultation (RO) , Cryogenic Infrared Spectrometers and
Telescopes for the Atmosphere (CRISTA) , Sounding of the
Atmosphere using Broadband Emission Radiometry (SABER) , High Resolution Dynamics Limb Sounder (HIRDLS)
, and Gimballed Limb Observer for Radiance Imaging of the
Atmosphere (GLORIA) aircraft . GWs can be also characterized by nadir-viewing instruments,
such as the Atmospheric Infrared Sounder (AIRS) , and the Advanced Microwave
Sounding Unit (AMSU) .
Typical limb sounders provide middle atmosphere temperature data with a
vertical resolution of 1–3 km assuming a horizontally homogeneous
atmosphere. In most cases, vertical structures of small horizontal-scale GWs
are characterized by separating a background temperature profile from the
measured profiles. The average temperature structure of the atmosphere, the tides (e.g. ) and several different modes of planetary waves (e.g. ) contribute to this background temperature. The final results of this procedure are altitude
profiles of temperature perturbations due to GWs. Temperature data obtained
from limb sounding instruments exhibit a very good vertical resolution, but
suffer from a poor horizontal resolution along the instrument's
line of sight, thus limiting the visibility of waves with short horizontal
wavelengths. proposed to combine the phases provided by the
wave analysis of adjacent temperature vertical profiles to estimate the
horizontal wavelength of GWs. This approach has been successfully applied to
retrieve GWs with vertical wavelengths between 6 and 30 km and horizontal
wavelengths larger than 100 km from CRISTA-2 measurements. The method has also
been used for several other data sets .
A general limitation of all methods based on limb sounding is the
poor along-line-of-sight resolution of this kind of measurement, which is
typically a few hundred kilometres. A few existing and upcoming limb sounders
try to mitigate this general limitation by considering the horizontal
variability of the atmosphere in the retrieval . The GLORIA limb sounder utilizes a tomographic
reconstruction technique, which leads to a horizontal resolution of 20 km
. In this work, we present another measurement strategy
to detect atmospheric small structures, whose spatial dimensions are neither
covered by conventional limb sounding nor satellite- or ground-based nadir
sounding. It is applicable to a low-cost nanosatellite utilizing a remote
sensing instrument to measure atmospheric temperature and a high-precision
pointing system. Simply speaking, the satellite is commanded in such a way
that the instrument observes a certain volume in the atmosphere multiple
times while the satellite is flying by. This results in multi-angle
observations of the target volume, such that a tailored retrieval scheme can
be applied. This differs from classical limited-angle tomography, where only
observations within a limited angular range are taken for the reconstruction.
In Sect. , we present the observation strategy
which we call “target mode” observations. Section
describes the forward modelling of such “target mode” measurements, which is
based on a 2-D ray tracing, an oxygen atmospheric band (A-band) airglow
emission model, a GW perturbation, and the corresponding radiative
transfer. The retrieval algorithm is presented in
Sect. . In Sect. , the
performance of the “target mode” tomographic retrieval is tested with
simulated measurements. A sensitivity study is used to analyse its
performance in deriving GW fine structures compared with pure limb
tomographic retrieval. The conclusion is given in Sect. .
Observation strategy
The detection of small-scale structures in Earth's atmosphere in 2-D requires
new instruments or measurement strategies, as stated above. One of those is
to observe atmospheric volumes from different viewing directions – e.g. by
pointing at one particular region while the instrument is flying by. Such
tomographic retrievals have been demonstrated and implemented in a variety of
measurements for different purposes, including by for
Michelson Interferometer for Passive Atmospheric Sounding (MIPAS),
for MLS, for Process Exploration
through Measurements of Infrared and millimetre-wave Emitted Radiation
(PREMIER), and and for the airborne GLORIA
instrument. In this work, we propose to combine satellite-borne limb and
sub-limb measurements of a nightglow layer in such a way that we obtain
multi-angle observations of a particular air volume as well. The sub-limb
sounding has a similar geometry to limb sounding, whereas the tangent
heights are near or below the surface. We name this combined observation
strategy “target mode”, i.e. we adopt the same expression as for similar
measurements in Earth observations. In the following, the capabilities of
“target mode” observations will be discussed for a specific sequence of
satellite pointing manoeuvres.
Figure illustrates the viewing geometry of the
“target mode” observation, which incorporates limb and sub-limb sounding
measurements. When the satellite is operated in “target mode”, the
instrument will start to observe the target atmospheric volume by forward
limb imaging first. The instrument will continue to measure under limb
geometry for a period of time, and multiple consecutive vertical radiance
profiles will be taken during this time. Then, the instrument will switch to
a forward sub-limb view with a 24.5∘ viewing angle below horizon.
This viewing angle is also constant during the sub-limb observations. In this
way, the volume will be scanned twice by the limb and sub-limb observations.
Depending on the flexibility and possible speed of satellite operations, more
viewing angle positions could be used – for example another position with a
viewing angle > 24.5∘ as indicated in
Fig. . After the satellite overpasses the target
volume, the same measurement sequence will be applied by back-looking at the
target volume.
Viewing geometry of “target mode” observations of a region in a
mesospheric emission layer. This observation mode consists of forward limb,
forward sub-limb and backward sub-limb measurements. The sub-limb
measurements are taken with two different viewing angles – 24.5∘ when
the satellite is far from the target region and 33∘ when it is
closer. The viewing angle is the angle relative to the
instantaneous horizon, with horizon defined as Earth surface for a given but
temporally changing satellite position.
Figure shows how the lines of sight (LOSs) of the
measurements overlap with each other in the orbit plane under limb sounding
and “target mode”, respectively. For an assumed orbit altitude of 600 km,
the corresponding measurement time for taking the measurement sequences for
the limb sounding mode shown in Fig. a is 1.6 min. We
further assume a high measurement frequency of 10 s per vertical profile. As
can be seen in Fig. a, for the limb sounding mode the
LOSs of consecutive limb profiles overlap, which means that the same
atmospheric volume is observed from different directions. In the
“target mode” (Fig. b), sub-limb measurements
contribute further information by intersecting the observed volume at
different viewing angles about 3.3 min after the limb observations were
taken.
Central measurement track of an imaging instrument in the pure limb
sounding and “target mode”. The solid lines represent limb measurements and
dashed lines represent sub-limb measurements. The satellite viewing geometry of
(b) is the same as in Fig. .
Forward modelO2 A-band nightglow emission model
Modelled O2 A-band nightglow emission profile at 30∘ N
and 88∘ E for 22:00 local solar time as simulated by the HAMMONIA
model. The solid curve represents an O2 A-band profile for unperturbed
conditions, and the dashed curve represents a profile perturbed by a GW with
15 km vertical wavelength and 5 K amplitude.
The observation strategy presented in the previous section requires that the
observed emission be restricted to a limited altitude range and that any
emissions from lower parts of the atmosphere or Earth's surface cannot reach
the instrument. This requires that the atmosphere below the emission layer
be optically thick for those emissions. This limits the number of
potential airglow emissions significantly, because most of them are hotband
transitions between two excited vibrational states. The number density of the
lower state of a hotband transition is typically too low to absorb background
radiation from the lower atmosphere. Therefore, we have to search for airglow
emissions, whose lower state is a ground state of a frequent atmospheric
species. This is the case for the O2 A-band nightglow emission. The
emitting electronic state is excited in a two-step Barth process
:
O+O+M→O2*+M,
where M is an O2 or N2 molecule, and O2* is an excited O2
molecule. Then, the O2* state is quenched to a lower electronic state
O2(b1Σ), which emits O2 A-band radiation:
O2*+O2→O2(b1Σ)+O2.
Loss mechanisms for both O2(b1Σ) and its undefined precursor
O2* include quenching by O2, O3, N2, or O and spontaneous
emission. The A-band volume emission rate (VER) η, in
photons s-1 cm-3, is thus η=A1k1[O]2[M][O2](A2+k2[O2]+k3[N2]+k4[O])(CO2[O2]+CO[O]),
where [] refers to the number density of the species within the
brackets. A1 is the A-band transition probability, A2 is the total
transition probability of the zeroth vibrational level of the O2(b1Σ) state . k1 is the reaction coefficient rate
for reaction Eq. () . The quenching rates
for O2, N2, and O are denoted by k2, k3, and k4, respectively.
CO2 and CO describe quenching rates of O2* by
O2 and O. All rate constants utilized in this work are taken from
.
A typical vertical profile of a modelled O2 A-band nightglow emission from
80 to 110 km is shown in Fig. . The temperature
T and number densities of O2, N2, and O are taken from the Hamburg
Model of the Neutral and Ionized Atmosphere (HAMMONIA)
model run at 30∘ N and 88∘ E for 22:00 local solar time.
The intensity of the O2 A-band nightglow limb emission peaks at around
93 km; typical peak values are 3×103 photons s-1 cm-3.
Since the lifetime of the O2(b1Σ) state is more than 12 s, it
can be assumed that the molecule is in rotational local-thermodynamic
equilibrium . This allows us to derive the kinetic
temperature of the atmosphere from the rotational band structure of the
emissions. Under thermal equilibrium conditions, the O2 A-band rotational
excitation follows the Boltzmann distribution at a rotational temperature
T, which is assumed to be equal to the background temperature. The number
of photons that appears in an individual rotational line is given by
ηrotηrot=ηg′Q(T)exp-hcE′kTA1,
where h is the Planck constant, c is the light speed, and k is the
Boltzmann constant. E′ and g′ are the upper state energy and upper state
degeneracy, respectively. A1 is the Einstein coefficient of the
transition. Q(T) is the rotational partition function:
Q(T)=∑g′exp-hcE′kT.
A subset of six emission lines has proven to give an optimal setup for a
potential satellite mission aiming to the derivation of kinetic temperature
from the O2 A band. These six lines show both positive and negative
temperature dependence of rotational structures; also strong, medium and weak
dependence are included, as shown in Fig. .
Temperature dependence of six rotational lines of the O2 A band.
The line centre wavenumbers for the lines are given in the figure legend. The
intensity is normalized around the maximum intensity for a temperature of
230 K.
Wave perturbations
Modelled limb spectral photon radiance for different tangent
altitudes. The background atmosphere is taken from the HAMMONIA model, around
30∘ N and 88∘ E for 22:00 local solar time.
O2 A-band emissions are affected by GWs due to the vertical
displacement of constituents and temperature changes associated with the waves.
Following conventional assumption, we consider an adiabatic and windless
atmosphere. A monochromatic wave perturbation added in background temperature
T0 at position (x,z) can be written as
T(x,z,t)=T0(x,z,t)+Acos(2πxλx+2πzλz-ω^t),
with wave amplitude A, vertical wavelength λz, horizontal wavelength λx, and ω^ the intrinsic frequency
of wave perturbation. We used the following expression to
calculate the vertical displacement δz of an air parcel from its
equilibrium height z+δz:
T(x,z,δz)≈T(x,z)+(Γad-Γ)δz,
where Γ and Γad are the local and adiabatic lapse
rates, respectively. Then, the perturbed density (background density plus
perturbation) ρ′ at fixed height z can be calculated as density at
equilibrium height z+δz:
ρ′(x,z)=ρ(x,z,δz)≈ρ(x,z)exp-κδz/H,
with the scale height H. In the quantity κ=(cp/cv-1), the cp
and cv represent heat capacities at constant pressure and volume,
respectively. Given ρ′, the number densities for perturbed major gases
are calculated as [N2]′[N2]=[O2]′[O2]=ρ′ρ.
Because the mixing ratio of atomic oxygen is not constant with altitude, the
perturbed volume mixing ratio v′ is calculated as follows :
vO′(x,z)=vO(x,z,δz)≈vO(x,z+δz).
Figure shows a perturbed O2 A-band volume
emission rate profile perturbed by a 1-D GW with a vertical wavelength
λz of 15 km and an amplitude A of 5 K.
Ray tracing
To model the instrument's LOS in a 3-D atmosphere we utilize a
module of the Atmospheric Radiative Transfer Simulator (ARTS)
. ARTS is a free open-source software program that
simulates atmospheric radiative transfer. It focuses on thermal radiation
from the microwave to the infrared spectral range. The second version of ARTS
allows simulations for 1-D, 2-D or 3-D
atmospheres. In this study, the relative orientation of LOS is selected to
be parallel to the orbit plane. Thus, it is assumed that the LOS is in the
orbit plane, and a 2-D ray tracing can be applied with ARTS-2.
Radiative transfer
The observed spectral irradiance I(v), in photons s-1 cm-2, is
a path integral along the line of sight:
I(v)=∫-∞∞η(s)rotD(v,s)exp[-∫-s∞n(s′)σ(s′)ds′]ds,
where s is the distance along the line-of-sight, n is the O2 number
density, σ is the absorption cross-section, and D(v) is the Doppler
line shape for the spectral line centred at wavenumber v. In the infrared
the lower atmosphere is optically thick, whereas the upper atmosphere can be
considered as optically thin. Since the O2 A band is a transition to the
O2 ground state, the atmosphere becomes optically thick at stratopause
altitudes. Therefore, any emission from the Earth's surface or tropospheric
altitudes cannot reach the upper mesosphere at these wavelengths. At
nightglow layer altitudes (upper mesosphere/lower thermosphere) the
atmosphere is optically thin for the wavelengths considered. In our case, for
altitudes above 85 km, the atmosphere is assumed to be optically thin and
the self-absorption term in Eq. () can be omitted.
Retrieval result using simulated data. The background atmosphere is
taken from the HAMMONIA run between 30∘ and 36∘ N,
90∘ E, around 22:00 local solar time. The a priori atmosphere is
depicted in panel (a). The difference between the perturbed
atmosphere and the a priori is shown in panel (b). The retrieved
wave perturbation, which is obtained by subtracting the a priori from the
retrieval result, is given in panel (c). The two black dots
correspond to the retrieval points selected for Fig. . The
difference between the retrieval result and the true state of atmosphere is
shown in panel (d).
The spectral range considered in this work is 13 082–13 103 cm-1
and contains six emission lines. The central wavenumbers of these lines are
given in Fig. . In
Fig. , limb spectral photon radiance is simulated
at different altitudes (86–115.5 km with 1.5 km interval). To make a
trade-off between bandwidth and instrument size, a spectral resolution of
0.8 cm-1 is chosen. The temperature dependence of the lines in this
spectral interval is illustrated in Fig. .
Retrieval model
The tomographic retrieval presented here is similar to the widely used
optimal estimation approach . The measurement space is
represented by vector y and the unknown atmospheric state is
represented by vector x. The forward model f(x)
provides the simulated spectrum based on a given atmospheric state x:
y=f(x)+ϵ,
where ϵ is the measurement error. The
inversion problem of Eq. () is generally ill-posed, and
the solution is not unique. Following and
, the cost function J is complemented by a
regularization term:
J(x)=(f(x)-y)TSϵ-1(f(x)-y)+(x-xa)TR(x-xa),
where matrix R is the inverse covariance or regularization matrix,
Sϵ is the covariance matrix of the measurement error,
and xa represents the a priori data. The a priori data are usually
taken as the climatological mean of the retrieved quantities. The second term
in the cost function (Eq. ) ensures that a unique and
physically meaningful solution can be obtained. The inversion of the forward
model (Eq. ) can be formulated as a minimization of the
cost function J(x) given in Eq. (). To
solve the non-linear minimization, we adopt a Levenberg–Marquardt iteration
scheme .
2-D regularization matrix
The design of the 2-D regularization matrix R in
Eq. () is of considerable importance to the retrieval
results. Here, we used a combination of zeroth- and first-order Tikhonov
regularization :
R=α0L0TL0+α1xL1xTL1x+α1yL1yTL1y,
where the weighting parameters α0, α1x, and α1y
control the overall strength of the regularization term added in
Eq. (). Large values of weighting parameters will
result in an over-regularized result, while a small value will give an
unstable solution. The parameter α0, α1x and α1y
also balance the contribution of the zeroth- and the two directional first-order regularization terms. L0 is an identity matrix that
constrains the result to the absolute value of xa. Matrix
L1 maps x onto its first-order derivative in the vertical
and horizontal directions:
L1x(i,j)=1 if j=i+1-1 if j=i0 otherwise ,L1y(i,j)=1 if j=i+m-1 if j=i0 otherwise.
As we convert the 2-D atmospheric temperature to a vector x row by
row, L1x is thus a (l-1)×l matrix, with l the
number of elements in x. L1y is a (l-m)×l matrix
with m to be the number of elements contained in each row of the 2-D
atmospheric volume.
Averaging kernel matrix
Following the concept of , the effect of the
regularization onto the retrieval result can be quantified by the averaging
kernel (AVK) matrix:
A=(R+KTSϵ-1K)-1KTSϵ-1K,
where K is the Jacobian of the forward model f at
atmospheric state x. The measurement contribution vector can be
obtained from the AVK by the sum over each row of A. If the
measurement contribution value is close to 1, most information of the
retrieval result is determined by the measurements and not by the absolute
value of the a priori data. The averaging kernel matrix can also be used to
deduce the spatial resolution of retrieval result. For 1-D retrievals, the
vertical resolution is described by calculating the full width at half
maximum (FWHM) of the corresponding row of the AVK matrix. For 2-D
retrievals, the row needs first to be reshaped into two dimensions, and then
the FWHM method is used to calculate the resolution along each axis
.
Numerical experiments
Averaging kernel matrix for two different retrieval points,
allocated at the geographical position of highest values (red colour).
Panel (a) shows a point coinciding with the observational grid,
while
panel (b) shows a point whose vertical position is in
between two tangent altitudes of the limb observations; for details see
text.
Viewing geometry between the satellite line of sight (LOS)
and the horizontal wave vector. The wave fronts are represented
by the grey shading. The observed horizontal wavelength λx
and the real horizontal wavelength λreal are related by
an angle α: λreal=λxcosα.
GW sensitivity function. The ratio of retrieved wave
amplitude to true wave amplitude as function of horizontal and vertical
wavelength is shown. Panel (a) is the sensitivity function for pure
limb measurements, while panel (b) is for “target mode”
measurements as specified in Sect. .
Simulation setup
In this section, we present the experimental results of tomographic
temperature retrievals using simulated “target mode” measurements with
1 % noise added. Synthetic measurements are generated by imprinting a
GW structure onto a smooth model atmosphere, as described in
Sect. . The temperature, atmospheric density, and
concentrations of various constituents are perturbed by this simulated wave.
As the amplitude is the most important feature of a GW with respect to
energy, the assessment in the next step focuses on how well the wave
amplitude can be reproduced from the retrieval results. The wave vector
investigated in this case is assumed along the direction of line of sight,
where the largest amplitude suppression is provided .
Pure limb sounding (a) and “target mode” (b)
retrieval results comparison. The GW has a wavelength of 250 km in the
horizontal and 40 km in the vertical. The climatological background profile was
subtracted from the retrieval result. The black lines indicate the true
modulated wave structure.
In our study, the spacing of the atmospheric grids is very
important for both the forward and the retrieval model. To reduce the impact
of the discretization on the synthetic measurements, the atmospheric grid in
the forward model should be finely sampled. The atmospheric grid used in the
forward model has a vertical spacing of 250 m and horizontal spacing of
5 km. In the inverse procedure, the sampling can be coarser: 500 m vertical
spacing and 12.5 km horizontal spacing in our case.
Example of a GW parameter retrieval
Figure illustrates the performance of the
tomographic retrieval approach for an atmosphere disturbed by a GW
with a horizontal and vertical wavelength of 300 and 15 km, respectively.
The satellite platform is simulated in an approximately 600 km
Sun-synchronous orbit with an inclination angle of 98∘. The
instrument will employ a 2-D detector array consisting of about
40 × 400 super pixels. It measures in the spectral regions from
13 082 to 13 103 cm-1 within the altitude range from ≈ 60 to
120 km in limb imaging measurements. The atmospheric condition as well as
the sampling patterns are the same as in the previous sections. The
integration time is assumed to be 10 s for limb measurements and 15 s for
sub-limb measurements. The a priori data used in this case study are depicted
in Fig. a. The simulated GW has an
amplitude of 5 K (Fig. b). The retrieved
temperature perturbation is shown in Fig. c. We can
clearly see that the wave structure is well reproduced between 87 and 104 km
height. The horizontal coverage of such a group of “target mode”
measurements is around 800 km. Figure d depicts
the difference between simulated wave and retrieved wave, with an average
error of about 0.5 K.
The spatial resolution of the retrieved data is usually described by the rows
of the averaging kernel matrix, A. The deviation of A
from the identity matrix gives insight into the smoothing introduced by the
regularization. For example, if two adjacent grid points share one piece of
information, the corresponding information content would be 0.5. By
reordering a single row of A according to their vertical and
horizontal coordinates, the influence of each point on the retrieval result
can be revealed. Figure shows the 2-D averaging kernel
matrix of two selected data points, which are marked as black dots in
Fig. c.
Figure a shows the averaging kernel matrix for a point
positioned at 2100 km along track and 95 km altitude. It indicates that the
measurement contribution is sharply centred around this point. A minor part
of the information comes from other altitudes on parabola shaped tracks,
which correspond to the LOSs of observations, whose tangent
altitude is below 95 km or which are sub-limb observations. For
Fig. b, the data point is placed at 2100 km along track
and 99 km altitude. In contrast to (a), this data point is not right on the
tangent altitude of an observation, but in between two observations. Because
this point is not placed exactly at one of the tangent altitudes, main
contributions to the retrieved value come from measurements of adjacent grid
points. According to Fig. a, a vertical resolution of
1.3 km and horizontal resolution of 35 km can be achieved.
Sensitivity study
The quality of a GW amplitude-, wavelength- and phase- retrieval
depends on the wavelength of the wave. The long LOS of limb observations is
ideal for the reconstruction of long horizontal wavelengths, whereas GWs with short horizontal wavelengths are likely underestimated or cannot
be measured at all. A measure to assess the sensitivity of an observation
system to retrieve GW parameters is the so-called GW
sensitivity function . It defines how a wave perturbation
of a given horizontal and vertical wavelength is reproduced by a retrieval.
One option to determine this GW sensitivity function is to perform
the retrieval for the wavelength of interest. However, for a tomographic
retrieval this is computationally very expensive. Alternatively, we can
derive the GW sensitivity function more efficiently by using the
averaging kernel matrix method . The basic idea of this
method is to assume that the forward model can be approximated linearly for a
small perturbation as induced by a GW. In this case, the averaging
kernel matrix A would be identical for the unperturbed atmosphere
and the perturbed atmosphere. If the unperturbed atmosphere xb is
assumed to be the same as the a priori data xa, the retrieval
result xf and the a priori vector xa are related as
follows:
xf-xa=(A(xa+xδ)+(I-A)xa)-xa=Axδ,
with I being the identity matrix and xδ
being the modulated wave structure. Following this equation, the averaging
kernel matrix A maps the true wave perturbations xδ
onto the retrieved wave structure xf-xa. The ratio
between xf-xa and xδ quantifies the
sensitivity to reconstruct the GW.
For this “target mode”, the observed horizontal wavelength is the
wavelength projected along the LOS. In general, there is an angle α
between the LOS and the horizontal wave vector. Therefore, the observed
horizontal wavelength λx is a factor of 1/(cosα) larger than
the real horizontal wavelength λreal, as illustrated in
Fig. . In this sensitivity study, the horizontal
wavelength discussed is the observed horizontal wavelength λx.
Figure shows the results of sensitivity study
adopting this approach for horizontal and vertical wavelengths of 0–400 and
0–60 km, respectively. To illustrate the advancement of the combination of
limb and sub-limb observations for the reconstruction of GW
amplitudes, the sensitivity function for a pure limb measurement was also
calculated, as shown in Fig. a. The retrieval
setup is the same for both cases, but the additional sub-limb measurements
were removed from Fig. b to get the pure limb
simulation in Fig. a.
For pure limb sounding, GWs with vertical and horizontal
wavelengths down to 7 and 150 km, respectively, can be observed. The
sensitivity to detect short horizontal wavelengths decreases for larger
vertical wavelengths, e.g. 250 km at 20 km vertical wavelength, or 325 km
at 60 km vertical wavelength, respectively. In
Fig. b, “target mode” tomography has been
performed which considers sub-limb measurements with 15 s integration time
as well. The GW sensitivity function does not change much for short vertical
wavelength compared to pure limb measurements, but GWs with large
vertical wavelength and short horizontal wavelength become much more visible.
For GWs with vertical wavelengths above 15 km, the increase in horizontal
wavelength sensitivity is typically 50–100 km.
Another advancement of the “target mode” is the reduced altitude
dependence of the observational filter, as is illustrated in
Fig. for a GW with 250 km horizontal
wavelength and 40 km vertical wavelength. Comparing the retrieved wave
structure with the true structure (depicted as the black contour plot), we find that the
“target mode” tomography can reconstruct the wave structure more clearly
than the limb mode tomography.
Conclusions
In recent years, tomographic retrieval approaches have been proposed to
reconstruct 2-D GW structures. However, the spatial resolution of
GWs retrieved from this observation mode is limited by the poor
horizontal resolution along the LOS of these instruments.
In this paper, a novel “target mode” observation combining limb and
sub-limb measurements for retrieval of GW parameters in the mesopause region
is presented. A tailored retrieval scheme for this observational mode has
been presented and its performance has been assessed.
We employed this new approach to simulated measurements of an instrument
measuring the O2 A-band nightglow emissions to demonstrate its advantages
in resolving 2-D atmospheric structures. The retrieval results show that a
combination of limb and sub-limb measurements increases the sensitivity to
detect short horizontal wavelengths by 50–100 km compared to pure limb
sounding. GWs with vertical and horizontal wavelength down to 7 and 150 km
can be resolved. It is shown that its capability of detecting short
horizontal wavelength is dependent on the vertical wavelength of GWs, e.g.
200 km at 20 km vertical wavelength and 260 km at 60 km vertical
wavelength.
All data used in this work are available from
the authors upon request (r.song@fz-juelich.de and m.kaufmann@fz-juelich.de)
The authors declare that they have no conflict of
interest.
Acknowledgements
This work was supported in part by the National Natural Science Foundation of China under grant 41590852 and the China Scholarship Council
(201404910513).The article processing charges for this open-access publication were covered by a Research Centre of the Helmholtz Association.
Edited by: Markus Rapp Reviewed
by: two anonymous referees
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