Measurements of limb-scattered sunlight from the Ozone Mapping and Profiler Suite Limb Profiler (OMPS-LP) can be used to
obtain vertical profiles of ozone in the stratosphere. In this paper we describe a two-dimensional, or tomographic,
retrieval algorithm for OMPS-LP where variations are retrieved simultaneously in altitude and the along-orbital-track
dimension. The algorithm has been applied to measurements from the center slit for the full OMPS-LP mission to create the
publicly available University of Saskatchewan (USask) OMPS-LP 2D v1.0.2 dataset. Tropical ozone anomalies are compared with measurements from the
Microwave Limb Sounder (MLS), where differences are less than 5 % of the mean ozone value for the majority of the
stratosphere. Examples of near-coincident measurements with MLS are also shown, and agreement at the 5 % level is
observed for the majority of the stratosphere. Both simulated retrievals and coincident comparisons with MLS are shown at
the edge of the polar vortex, comparing the results to a traditional one-dimensional retrieval. The one-dimensional
retrieval is shown to consistently overestimate the amount of ozone in areas of large horizontal gradients relative to
both MLS and the two-dimensional retrieval.
Introduction
The Ozone Mapping and Profiler Suite Limb Profiler (OMPS-LP) on board the Suomi National Polar-orbiting Partnership (Suomi-NPP) spacecraft began taking routine
measurements of limb-scattered sunlight in early April 2012 . The limb profiler images the
atmospheric limb every 19 s (∼ 125 km along track) from the ground to approximately 100 km
using three vertical slits that are separated horizontally by 4.25∘. A prism disperser is used to obtain
a spectrally resolved signal in the range 290–1000 nm. These spectrally resolved measurements can be
inverted with a forward model accounting for multiple scattering to obtain vertically resolved profiles of ozone
concentration in the atmosphere.
The standard OMPS-LP ozone product is produced by NASA, and version 1.0 of the retrieval is described in detail by
. The NASA retrieval employs the assumption of horizontal homogeneity, treating each vertical image
separately to retrieve a one-dimensional vertical profile. However, it is possible to take advantage of the long limb path
length and fast sampling capabilities of OMPS-LP to combine multiple images together and retrieve in the orbit track and
altitude dimensions simultaneously. These two-dimensional, or tomographic, retrievals have been used successfully in many
retrievals from limb emission instruments
e.g.,. A two-dimensional retrieval of NO2 and
OCLO was done for limb scatter measurements from the SCanning Imaging Absorption SpectroMeter for Atmospheric
CHartographY SCIAMACHY; by Puķı‾te et al. (), and a preliminary
two-dimensional retrieval study for ozone using a single-scatter radiative transfer model was also performed by
using simulated OMPS-LP measurements. Measurements from OMPS-LP are a natural candidate to attempt
a two-dimensional retrieval due to the relatively finely resolved orbital-track sampling (∼ 125 km) compared
to other limb scatter instruments; for example, the Optical Spectrograph and InfraRed Imaging System (OSIRIS)
has ∼ 600 km along-track sampling.
In this paper we describe a retrieval algorithm for the central slit of OMPS-LP which accounts for inhomogeneity in the
along-orbit direction and present preliminary results. To the authors' knowledge this is the first two-dimensional limb
scatter ozone retrieval applied to real measurements. The algorithm is described in detail in Sect. .
We have applied the algorithm to the entire mission of OMPS-LP, creating a dataset of vertical profiles of stratospheric
ozone from early 2012 to present with near-global coverage (University of Saskatchewan (USask) OMPS-LP 2D v1.0.2 dataset). Section
presents some preliminary results and validation efforts with the dataset. The dataset is compared against the
likewise two-dimensional ozone retrievals from the Microwave Limb Sounder MLS;. Tropical ozone
anomalies are compared against those from MLS for the full mission dataset. Lastly, nearly perfectly coincident
measurements with MLS are investigated.
The retrieval algorithmOverview
Here we follow the optimal estimation framework outlined in and use similar notation. The general goal
of the atmospheric inverse problem is to find the optimal set of state parameters, x, given with a set of
measurements, y, and other a priori information or constraints. The vector x of length n is often called
the state vector, while the vector y of length m is called the measurement vector. In our OMPS-LP ozone
retrieval case, x consists of the logarithm of ozone number density on a two-dimensional grid (altitude and along
the orbital track), and y contains the logarithm of the spectrum for multiple OMPS-LP images at selected
ozone-sensitive wavelengths. A common approach to the inverse problem is to minimize the cost function,
χ2=[F(x)-y]TSϵ-1[F(x)-y)]+[xa-x]TRT⋅R[xa-x],
where Sϵ is the covariance of the measurement vector, F is the forward model, R
is a regularization matrix, and xa is the a priori state vector. A priori information is included through the two
quantities R and xa. Applying a standard Guass–Newton minimization approach to the cost function results in the
iterative step
xi+1=xi+KiTSϵ-1Ki+RTR+γiI-1⋅KiTSϵ-1(y-F(xi))-RTR(xi-xa),
where K is the Jacobian matrix of the forward model, i is the iteration number, and γi is
a Levenberg–Marquardt damping parameter. A relatively small Levenberg–Marquardt type term, γi=0.1 multiplied by
the mean value of the diagonal of KiTSϵ-1Ki, is included to move the solution
step closer to that of a gradient descent method, aiding performance when the Gauss–Newton step is outside the linear
regime.
Equation () forms the basis of the retrieval method used in this work. The tomographic, or
two-dimensional, nature of the retrieval is encoded in the details of the definitions of the state vector and the
measurement vector. The state vector contains information about the atmospheric state for an entire orbit of OMPS-LP and
is described in detail in Sect. . A brief description of the forward model, which must account for
atmospheric variations along the line of sight, is given in Sect. and Sect. . The
exact form of the measurement vector for ozone and minor retrieved species (stratospheric aerosol and surface albedo)
is presented in Sects. and , respectively. Lastly, the form of regularization and a priori
used is given in Sect. .
For this work v2.0–2.4 of the OMPS-LP L1G product
(https://ozoneaq.gsfc.nasa.gov/data/omps/, last access: April 2017) is used.
Conceptual image (not to scale) of the OMPS-LP viewing geometry and retrieval grid. The retrieval grid locations
(gray lines) are chosen to match the average tangent point of the OMPS-LP measurements (red lines).
The state vector
The state vector consists of the logarithm of ozone number density on a discrete grid, referred to as the retrieval grid.
The retrieval grid is two-dimensional in altitude and angle along the orbital plane of OMPS-LP, and is shown in
Fig. . The altitude component of the grid is discretized in 1 km steps with lower and upper bounds
at the tropopause altitude and 59 km, respectively.
The horizontal spacing of the retrieval grid are chosen to match the horizontal sampling of OMPS-LP, which is approximately
125 km. A consequence of the OMPS-LP viewing geometry is that measurements with a higher tangent point are closer
to the instrument than measurements with a lower tangent point. For convenience the absolute locations of the horizontal
retrieval grid locations (gray lines in Fig. ) is chosen to match the average tangent point of each
measurement image. As OMPS-LP measures scattered sunlight, each orbit has a natural start and stop point characterized by
high solar zenith angles. In constructing the retrieval grid we use images with solar zenith angles at the tangent point
of less than 88∘.
A consequence of performing a tomographic retrieval is that there is less information at the edges of the retrieval grid,
simply because there are fewer measurements which sample near the edges. As previously mentioned, our retrieval grid has
hard cutoffs at solar zenith angle 88∘. However, when constructing the measurement vector, we use all images with
solar zenith angle less than 90∘. Under this approach for typical conditions we have not noticed unphysical
effects at the edges of the retrieval, but this is still under investigation. However there is still less information
present at the retrieval boundaries, which is reflected in the resolution and precision estimates described in
Sect. . The latitudinal coverage of OMPS-LP, and thus the retrieval grid, varies throughout the
course of the year as the illuminated portion of the Earth changes. The latitude region 60∘ S–60∘ N is
sampled nearly continuously throughout the year, while coverage extends to 82∘ in each hemisphere's summer.
Example of mismatch between the line-of-sight plane and the tangent point ground track. Black dots show the tangent points (at 25 km) for OMPS-LP orbit 14940. The gray line represents the line-of-sight plane for the tangent point intersecting the line.
Due to the Earth's rotation, there is a slight mismatch between the line-of-sight plane and the retrieval grid as is shown
in Fig. . At the Equator the approximate mismatch is 5∘, resulting in a ∼ 10 km
horizontal distance between the next image's average tangent point and the previous image's line-of-sight plane. The
effect is largest at the Equator, with the mismatch almost completely disappearing at the northern- and southernmost parts
of the orbit (82∘ N and 82∘ S). To perform the retrieval, the horizontal component of the line-of-sight
plane for every image is projected onto the horizontal component of the retrieval grid (orbital-track dimension).
The forward model
The forward model used in this study is SASKTRAN-HR
. SASKTRAN-HR solves the radiative
transfer equation in integral form using the method of successive orders initialized with the incoming solar irradiance.
The model is capable of handling inhomogeneities in the atmospheric state in the line-of-sight direction.
Internally the forward model performs bi-linear interpolation between grid points to create a continuous representation of
the atmosphere. In addition to radiance, the model also outputs the Jacobian matrix with respect to the underlying
two-dimensional atmosphere. Jacobians are calculated analytically taking into account all first-order scatter
terms, with approximations made for higher-order terms. The forward model and the Jacobian calculation are described in depth in
and , respectively.
Computational considerations
In a tomographic retrieval, the length of the state vector, n, and the length of the measurement vector, m, are
significantly larger than those of a one-dimensional retrieval. For example, if the retrieval grid was set up to match the
inherent resolution of the OMPS-LP measurements of a single orbit, for each species n would be on the order of 10 000,
and for each wavelength m would also be on the order of 10 000. Storing these vectors does not pose any computational
challenge; however, it quickly becomes necessary to store the m×n Jacobian matrix using sparse storage
techniques. The Jacobian matrix is naturally sparse in the horizontal direction as sensitivity is largest at the tangent
point and decreases away from it. Elements of the Jacobian matrix for the limb
multiple-scattering problem are never truly zero; every point in the atmosphere should in theory contribute to every measurement.
However, owing to the approximations made in the Jacobian calculation outlined in the section prior, contributions are only
calculated along the line-of-sight and solar planes, resulting in a sparsity factor of ∼ 0.05. The sparsity of the
Jacobian matrix can be improved by artificially allowing only profiles less than some specified distance to the tangent
point to contribute, as is done in . For our retrieval we limit each measurement to contribute to
profiles within 10∘ of the tangent point.
While every matrix in Eq. () is sparse, it is often desirable from a computational-speed point of view to
store some combinations of matrices densely. In particular, solving the linear system requires computing the n×n(KiTSϵ-1Ki+RTR+γiI) matrix. While
it is still somewhat sparse, we have observed significant speed increases by solving the linear system densely. For a full
OMPS-LP orbit this matrix would be 10 000 × 10 000, taking less than 1 GB of memory.
Accounting for the time dependence
Due to an inadequate amount of measurements, we do not account for the time variation of the ozone field in the retrieval.
The reported time for each retrieved profile is calculated by interpolating the measurement times on the tangent points to
the retrieval grid. While it is not perfect, we expect this is a good estimate as the majority of information for a single
retrieved profile originates from the images that have tangent points near it. Nevertheless, there are several other
time-dependent effects which play a role in how the retrieval is performed.
The radiative transfer equation is explicitly time dependent owing to the changing solar conditions. For an imaging
instrument such as OMPS-LP, the natural and most accurate solution to this problem is to re-run the forward model for
every image. That being said, there is potential for large computational-speed improvements by combining multiple images
into the same forward-model calculation. Since SASKTRAN-HR solves the source function of the radiative transfer equation
in a region of interest (nominally a 10∘ cone with the vertex at the Earth's center, but this can be configured)
around the tangent point, there is considerable overlap between the field of interest of one image to the next. However,
there are issues in performing this combination:
Each image happens at a different instant in time; thus the solar conditions have changed.
SASKTRAN-HR's internal atmosphere is specified as a plane in the line-of-sight direction. The lines of sight
from one image do not necessarily lie in the same plane as the lines of sight for the next image. Furthermore, the more
images that are combined together, the larger this plane will diverge from the retrieval grid.
The Earth is represented internally as a sphere with curvature matching a reference ellipsoid at the average tangent
point, which changes from image to image.
The first and the third conditions are not unique to tomographic retrievals; limb-scanning instruments face similar
challenges in one-dimensional retrievals. For example, a single OSIRIS limb scan sequence takes approximately
90 s and is modeled with a single forward-model calculation in operational retrieval algorithms
. Internal tests have been performed to quantify the three conditions by comparing results that
modeled every image separately with retrievals that combined five subsequent images together (95 s variation from the
first image to the last image), which resulted in mostly random differences in retrieved ozone on the order of 0.5 %.
Retrieval ordering
The retrieval is performed for three major parameters: ozone number density, stratospheric aerosol number density, and
surface reflectance assuming a Lambertian surface. While considerable effort has been put into both the aerosol and
surface reflectance retrievals, they are performed primarily as a second-order correction for the ozone retrieval. Each
species is retrieved independently, i.e., holding the other parameters fixed, but the overall retrieval operates in
stages, feeding the results of previous parameter retrievals into the current one. The general retrieval order follows
that of and is first surface reflectance, then aerosol number density, and then lastly ozone number
density. Two passes of this overall procedure are performed, allowing results from the ozone retrieval to couple back
into the other retrievals. The first pass of the procedure can be thought of as obtaining a good first guess for state
vectors, while the second pass finalizes the retrieval.
A fixed number of iterations is performed in each of the passes. The first round of the retrieval procedure performs five
iterations for each of the targeted quantities, while the second round performs two iterations. To verify that convergence
has been reached, at every iteration both the current χ2 value and the expected χ2 value at the next
step, assuming the problem is linear, are calculated. The expected χ2 value at the next step, assuming the problem is
linear, is calculated by performing a step with the Levenberg–Marquardt parameter set to 0, which helps to guard against
situations where premature convergence is detected due to a large damping parameter. A similar technique is used in
. At the end of the fixed number of iterations it was found that the final χ2 value almost
always matches the expected χ2 value calculated at the previous iteration to within 1 %, indicating that the
solution has likely converged. Orbits where convergence has not been seen at a 2 % level are flagged as
suspicious. It is planned for a future version of the retrieval software to stop early if convergence is detected; however
this is not expected to improve the solution, only the computational efficiency.
Ozone measurement vector
The ozone retrieval uses a common technique first suggested by where ozone-sensitive wavelengths in
the Hartley–Huggins and Chappuis bands are normalized by both ozone-insensitive wavelengths and high-altitude
measurements. This technique, sometimes referred to as the triplet or doublet method, has been used successfully in
a variety of limb scatter ozone retrievals e.g.,.
The ozone cross section used in the retrieval is compiled from , , and . While the
triplet/doublet method has previously only been implemented for one-dimensional retrievals, many of the ideas are still
applicable to two-dimensional retrievals with some modifications.
Wavelength triplet/doublets used in the ozone retrieval.
Sun-normalized radiances observed by OMPS-LP event number 90 of orbit 19490.
Our ozone measurement vector consist of seven doublets in the Hartley–Huggins absorption bands and one triplet in the
Chappuis absorption band shown in Table . In one-dimensional retrievals the UV doublets are often forced
to only contribute when the atmosphere is optically thin, i.e., when the area of maximal sensitivity is at the tangent
point. This can be done either through analyzing the diagonal elements of the Jacobian matrix directly
or by only using altitudes above the “knee” of the atmosphere as is done in
. The primary reason to do this forcing is so that the retrieval is most sensitive to the tangent
point, to minimize the effect of the implicit horizontal homogeneity assumption. Since the assumption of horizontal
homogeneity is broken for the tomographic retrieval, we allow all UV doublets to contribute down to some minimum altitude,
chosen to be 22 km. This altitude is approximately the knee of the 350 nm radiance profile; as seen in
Fig. , radiances below this altitude are heavily sensitive to upwelling radiation and in particular
absorbing aerosols.
The unnormalized measurement vector, ỹ, is given by
ỹjkl=1nrefl∑λ∈refllog[Ij(hk,λ)]-log[Ij(hk,sensl)],
where j indexes image along an orbit, k indexes tangent altitude, l indexes the triplet, refl is the set
of reference wavelengths for triplet l from Table with corresponding length nrefl, and
sensl is the sensitive wavelength for triplet l from the same table. Each triplet/doublet is normalized by its
value at a high altitude where the effect of ozone absorption on the observed radiance is minimal. The high-altitude
normalization helps to minimize errors in the absolute calibration of the instrument and reduces the sensitivity to
upwelling radiation. The normalization altitude varies for each doublet/triplet (shown in Table ) and is
pushed low to minimize stray-light errors.
Scaling factors as a function of altitude applied to the UV doublet measurement error covariances.
To avoid discontinuities caused by suddenly introducing UV triplets near 22 km, the diagonal of the measurement
error covariance matrix is artificially scaled during the retrieval:
Sϵ,ii=Sϵ,iiw2,
where the weights, w, are only applied to the UV triplets and only depend on altitude. The applied scale factors are
shown in Fig. .
The initial guess for the ozone profile is taken from ; we have observed negligible
dependence on the choice of initial state (typically less than 1 % on the retrieved ozone values).
Retrieved ozone number density for OMPS-LP orbit 27695 (2 March 2017, 10:30 UTC at Equator crossing).
Figure shows the retrieved ozone number density for OMPS-LP orbit 27695 (2 March 2017,
10:30 UTC at Equator crossing). Several low ozone filaments above the ozone layer are visible in both the Southern
Hemisphere and Northern Hemisphere tropics and midlatitudes. In the Northern Hemisphere a low pocket of ozone can be seen
below and intruding into the ozone layer.
Processing of this orbit took approximately 124 min using eight threads on an i7-4770k cpu. There were 159 vertical images
of radiance data input to the retrieval, giving an approximate processing time of 47 s(verticalimage)-1.
Thus performing the 2D retrieval is not onerous from a computational point of view; two machines of similar computational
power are sufficient to keep up to date with routine processing.
Minor retrieved speciesStratospheric aerosol
The stratospheric aerosol measurement vector definition follows closely the one outlined in and
applied to OSIRIS measurements, with a few minor modifications. The unnormalized measurement vector is given by
ỹjk=log[Ij(hk,745.67nm)].
The altitude of normalization is chosen following the technique described by .
The measurement vector described here differs from that of in that there is no normalization relative
to a shorter wavelength (470 nm for the OSIRIS retrieval). The short-wavelength normalization was included to
reduce the dependence of knowledge of the background Rayleigh atmosphere. However issues were encountered in that the
short wavelength would often be measured on a different gain setting than the longer wavelength, introducing artifacts in
the retrieval seefor more information on the gain settings of OMPS-LP. Since there exist many limb
scatter aerosol retrieval algorithms that operate without a short-wavelength normalization (e.g., Rault and Spurr, 2010), for
simplicity we have opted to remove it. Stratospheric aerosols in the retrieval are assumed to consist of liquid
H2SO4 spherical droplets following a lognormal particle size distribution with a median radius of 80 nm
and a mode width of 1.6. The phase function and cross sections are calculated using a standard Mie scattering code
, using the index of refraction from .
Albedo
The forward model assumes a Lambertian reflecting surface parameterized by the albedo, the ratio of outgoing to incoming
radiance. Typically this quantity does not physically represent actual reflectance from the surface of the Earth but is
used as an approximation for all upwelling radiation from the troposphere. It is important to retrieve the albedo as many
wavelengths used in the ozone retrieval are affected by upwelling radiation.
While albedo in the forward model is allowed to vary in the horizontal direction, several assumptions are made which make
the albedo retrieval similar to a set of independent one-dimensional retrievals. Furthermore the albedo retrieval is not
done under the Rodgers approach described earlier but instead follows the approach of . We define
the albedo state vector xalb as the albedo on the surface of the Earth assuming a Lambertian surface at a set of
latitudes and longitudes defined by the 40 km tangent point of each image. Therefore the state vector is the same
length as the number of images used in the retrieval.
The albedo is iteratively updated with the equation
xalb,ji+1=xalb,jiIj,meas(40km,745.67nm)Ij,mod(40km,745.67nm).
The measurement vector uses the same wavelength as the aerosol retrieval since their effects tend to be coupled together.
The retrieval is one-dimensional in the sense that, at least for one specific iteration, each image is allowed to only
affect one element of the albedo state vector. However the forward-modeled radiance is calculated using the
two-dimensional albedo field, which allows images to couple to other elements of the state vector over the course of
multiple iterations.
The spectral dependence of the albedo is neglected in the present retrieval. estimates that
neglecting realistic surface types (such as desert or savannah type surfaces) can cause systematic biases of up to 4 %
at 10 km for typical ozone retrievals. However these results are likely worst-case estimates, as realistic
tropospheric upwelling radiation is expected to be more spectrally diffuse than a clear surface.
Regularization
The retrieval uses an ad hoc Tikhonov style second derivative constraint applied only in the
horizontal direction of the retrieval grid. The regularization matrix takes the form
R=α-140120-1400…0-140120-140…00-140120-14…⋮⋮⋮⋮⋮⋮⋮⋱,
where α is a constant scaling factor used to control the amount of regularization and 0 indicates a number
of zeros equal to the number of altitude grid points minus 1. The value of α is chosen to control the horizontal
resolution of the retrieved species; for example, the value for ozone is 40, resulting in a 300–400 km horizontal
resolution (see Sect. ). The a priori state vector of Eq. () is chosen to be 0. As
the regularization matrix used only applies in the horizontal direction, the horizontally integrated vertical resolution
of the retrieved profiles matches the vertical resolution of the retrieval grid.
It should be noted that, even though we apply no constraints in the vertical direction, the retrieval software is capable
of doing so. While the above discussion treats the horizontal and vertical dimensions of the grid as separate entities,
the retrieval vertical and horizontal resolutions are inherently coupled together. A lower-resolution horizontal grid
allows for a higher-resolution vertical grid, keeping the total information content relatively constant, and vice-versa.
We make no claims on what is the optimal relationship between these two resolutions, and it is something that we are
actively investigating. It is important to mention that a one-dimensional retrieval makes the trade-off decision for you,
allowing control of only the vertical constraint. The effects of a one-dimensional retrieval on horizontal resolution
have been studied for the Michelson Interferometer for Passive Atmospheric Sounding by .
Pointing correction
Accurate and stable pointing knowledge is of particular importance for limb scatter measurements as it is typically not
possible to simultaneously measure pressure. provide a detailed characterization of the OMPS-LP pointing
errors; however many of these corrections have only been applied to the v2.5 L1G product, and not the v2.0–2.4 L1G
product used in this study. Therefore for the current version of the retrieval a separate pointing analysis has been
performed.
We apply the Rayleigh Scattering Attitude Sensor (RSAS) to the OMPS-LP measurements. The ratio of the
measured radiance at 40 and 20 km near 350 nm is compared to the calculated radiance. At 40 km
the radiance is sensitive to tangent altitude changes, while at 20 km the radiance is not very sensitive since the
line-of-sight path has become optically thick. Based on the difference between the measured and modeled ratios, it is
possible to calculate an effective tangent altitude offset. The RSAS technique is sensitive to both upwelling radiation
and stratospheric aerosol loading, which makes it difficult to apply at low solar zenith angles and in forward-scatter
conditions, respectively.
To minimize the effects of both upwelling radiation and stratospheric aerosols, we only use measurements with solar zenith
angle between 70 and 50∘ with solar scattering angles greater than 90∘. Measurements satisfying
similar criteria have recently been successfully used to apply an RSAS pointing correction to OSIRIS retrievals by
. While measurements with a solar zenith angle greater than 70∘ would have even less upwelling
radiation, it is more challenging to accurately model the multiple scatter component of the radiance. Cutoffs greater
than 50∘ were not found to affect the results; 50∘ was chosen to maximize the number of measurements. The
altitude offsets were daily averaged and are shown in Fig. . Offsets range from approximately 400 to
0 m with a clear seasonal cycle; in April 2013 there is noticeable ∼ 100 m drop due to a known star
tracker adjustment. Being able to clearly observe the star tracker adjustment provides confidence that at least on
a relative scale we are able to detect pointing shifts with the RSAS method.
It is currently unknown whether or not the seasonal structure represents a true pointing shift or if it is an artifact of
the RSAS method – perhaps due to the average latitude of the measurements also varying seasonally and changing cloud cover.
We do not detect any significant pointing drift greater than ±100 m; however later years are affected by
stratospheric aerosols from Kelud and Calbuco, which may skew the RSAS technique. Preliminary validation efforts have
revealed that, on average, there is likely an absolute pointing error present in the OMPS-LP measurements. To calculate
the applied pointing correction (solid line in Fig. ), we take an average value both before and after the
star tracker adjustment. All ozone profiles are shifted downwards by this amount after the retrieval has been
performed. It should be noted that this applied pointing correction is by intention simple. A future version of the data
product will examine the pointing in more depth and apply the correction to the instrument lines of sight rather than
post-shifting the retrieved profile.
Daily averaged pointing offsets calculated with the RSAS technique. The orange line shows the applied pointing correction for v1.0.2 of the retrieved data product.
Error analysis and resolution
Both the random and systematic error components of a limb scatter ozone retrieval algorithm for a similar, but
one-dimensional, retrieval have been studied in . Applying the conclusions of to
our retrieval algorithm suggests that the dominant sources of random error are pointing knowledge and the error due to
measurement noise. have also presented similar findings for a one-dimensional retrieval algorithm
applied to OMPS-LP and in particular showed that the error due to measurement noise is representative of the total
random-error budget. We will not repeat these analyses here; rather we will simply present the technique used to calculate the
reported error estimate for each orbit.
Under the Rodgers framework the gain matrix, G^, is given
by
G^=(K^TSϵ-1K^+RTR)-1K^TSϵ-1,
and the averaging kernel by
A=G^K^,
where the hats indicate that the solution has converged. The solution covariance due to measurement noise only can also
be estimated as
S^noise=G^SϵG^T.
In the current version of the retrieval only the solution covariance due to measurement noise is reported. For the
purposes of the precision estimate we assume that the measurement covariance is diagonal, with the radiance measurements
having a signal-to-noise ratio of 100, an upper bound on the error estimate taken from . Only the
diagonal elements of the solution covariance are used for the error estimate. Since the state vector is the logarithm of
number density, the precision estimate in logarithmic space is propagated to linear space for the reported precision
estimate.
Precision estimate for ozone in percent for OMPS-LP orbit 27695 (2 March 2017, 10:30 UTC at Equator crossing).
Contour levels are indicated by dashed lines on the color bar. The corresponding retrieved ozone profiles are shown in Fig. .
Figure shows an example precision estimate for OMPS-LP orbit 27695 (2 March 2017,
10:30 UTC at Equator crossing). Precision estimates are in the range 2–5 % for the majority of the middle and
upper stratosphere. In the lower stratosphere precision is ∼ 10 %, increasing to 30 % near the tropopause.
Various edge effects of the retrieval are also visible, most noticeably the increase in error at the beginning and end of
the orbit and near where the lower bound of the retrieval changes (due to the lowering tropopause) at midlatitudes.
These are expected effects; edges of the retrieval grid inherently have fewer measurements contributing to them, increasing
the expected noise. The estimate precision varies only slightly between orbits, and the values stated above are generally
valid for the entire dataset.
The resolution of the retrieval is found by analyzing the retrieval averaging kernels. As the retrieval is
two-dimensional, each row of the averaging kernel contains both vertical and horizontal components. Since the
regularization term (Eq. ) contains no vertical information, it can be shown that the horizontally
summed averaging kernel (i.e., the vertical averaging kernel) is the identity matrix. This has also been verified by
calculating the vertical averaging kernel for a set of OMPS-LP orbits, which were all found to be identically unity.
While Eq. () is valid for well-posed, converged retrievals, recent work by
has suggested a modification for cases when a Levenberg–Marquardt term is used to damp the
iterative step. Their formulation involves a recursive definition for the gain matrix, taking into account each iterative
step, and converges to Eq. () in cases where the state vector has reached adequate convergence. It is
not straightforward to apply this technique to a full OMPS-LP orbit due to the memory requirements of storing multiple
gain matrices. However, as a sanity check we have applied the technique of to a 60-image
subset of OMPS-LP orbit 20657 (23 October 2015, 08:50 UTC at Equator crossing).
Vertical averaging kernels at 40∘ S for OMPS-LP orbit 20657 (23 October 2015, 08:50 UTC at Equator crossing) calculated
using the methodology of after one, four, and seven iterations of the retrieval procedure. For clarity only every third row of the vertical averaging kernel is shown for each case.
Vertical averaging kernels from this test are shown in Fig. . As expected, due to the inclusion of the
Levenberg–Marquardt damping term, after one iteration rows of the averaging kernel are far from unity, with peak values
on the order of ∼ 0.4. After four iterations the rows are close to unity with peak values of ∼ 0.95. At the
end of the retrieval the averaging kernel rows are nearly identical to unity with peak values of ∼ 0.99 in the worst
case. Therefore, we can say that the retrieval is sufficiently converged for Eq. () to be valid.
Considering the vertical averaging kernel contain little information, we will focus on the vertically integrated, or
horizontal, averaging kernel.
Figure shows the rows of the horizontal averaging kernel for two orbits in different seasons at
0 and 55∘ N. In both cases the horizontal full width at half maximum (FWHM) is smallest near 40 km with values of
∼ 250 km. For the majority of the altitude range the FWHM is less than 400 km, with the exception of
the region near the tropopause where it can increase to 500 km. Only minor differences in the FWHM are seen
between the tropical and midlatitude averaging kernel rows, with the majority of the differences occurring near the lower
bound of the retrieval. Averaging kernels are not stored for every orbit due to size constraints; however it was found
that deviations from orbit to orbit are small enough that the above resolution estimates are representative for the entire
dataset.
Horizontal averaging kernels from OMPS-LP orbit 20657 (23 October 2015, 08:50 UTC at Equator crossing)
and OMPS-LP orbit 11915 (14 February 2014, 04:35 UTC at Equator crossing) for 55∘ N (a, c)
and 0∘ N (b, d). Data are masked below the lowest retrieval altitude. Vertical
black lines show the FWHM boundaries, while the vertical gray line
indicates the location of the retrieval. Distance from the retrieval location is defined as
negative towards the start of the orbit in the Southern Hemisphere and positive towards the
end of the orbit in the Northern Hemisphere.
As previously stated, the vertical averaging kernels are identity, suggesting that the vertical resolution of the
retrieval is 1 km, the same as the retrieval grid. However, the instrumental vertical field of view
∼ 1.5 km; see is neglected in the retrieval process, treating each measurement with
a single line of sight. Therefore we estimate the vertical resolution of the retrieved profiles to be 1–2 km.
Including the vertical field of view in the retrieval process to obtain a better estimate of the vertical resolution is
currently under investigation. It is not currently possible to fully account for the vertical field of view as the
OMPS-LP L1G product is a gridded data product that does not provide an estimate of the vertical field of view.
Preliminary simulation studies including an instrumental vertical field of view of 1.5 km have indicated that
neglecting the vertical field of view leads to biases less than 2 %, with the majority of differences seen in the
20–25 km region.
Preliminary resultsSimulations on the edge of the polar vortex
To test the retrieval method, a one-dimensional retrieval method that assumes horizontal homogeneity has also been
developed to compare against. The one-dimensional retrieval has been designed to be as similar to the two-dimensional
retrieval as possible. The measurement vectors for ozone, albedo, and stratospheric aerosol are the same as those for the
two-dimensional retrieval, with the only difference being that the number of images used is one instead of an entire
orbit. The state vector is modified to be one-dimensional in altitude, representing a horizontal homegenous atmosphere
with 1 km vertical spacing. As the Tikhonov regularization is only applied in the horizontal direction for the
two-dimensional retrieval, no regularization is used in the one-dimensional retrieval. The same iterative procedure is
also used for the one-dimensional retrieval.
To test the ability of the two-dimensional retrieval to resolve horizontal gradients in the ozone field, simulated
retrievals have been performed. For the simulations, measurements from a full OMPS-LP orbit are simulated using
a two-dimensional ozone field. The resulting radiances are then used in both the one- and two-dimensional retrievals. To
isolate the effects of horizonal ozone gradients, the input aerosol and albedo fields are assumed to be known and
horizontally homogenous.
Simulated retrieval results for OMPS-LP orbit 20657 (23 October 2015, 08:50 UTC at Equator crossing). The left column
shows the true ozone field (a), tomographically retrieved ozone (b), and one-dimensionally retrieved
ozone (c). The right column contains a horizontal slice of the retrieved ozone at 15.5 km(d),
the percent difference between the tomographic retrieval and the truth (e), and the percent difference between the
one-dimensionally retrieved ozone and the truth (f). For the percent-difference panels contours are shown every ±5 %.
Figure shows the results of the simulated retrieval for OMPS-LP orbit 20567. Qualitatively there is good
agreement between the one- and two-dimensional retrievals and the true ozone field, providing confidence in both methods.
The two-dimensional retrieval agrees to better than 5 % with the true ozone profile almost everywhere, with a few
exceptions below 20 km. Looking at the 15.5 km slice of the retrieval (top right panel of
Fig. ), it can be seen near 50∘ S that the two-dimensional retrieval smooths out some of the fine
oscillatory structure of the true profile, which is expected from the form of the averaging kernel. That being said, the
two-dimensional retrieval captures the large ozone gradient in the
60∘–75∘ S region very well.
Overestimation by the one-dimensional retrieval can be seen in the
60∘–75∘ S, 10–20 km
region. The 15.5 km slice reveals that the one-dimensional retrieval assigns the horizontal gradient to the wrong
location, leading the true profile by ∼ 2∘. Consistent overestimation by the one-dimensional retrieval is
what would be expected by the measurement geometry and input ozone field. As OMPS-LP looks backward in the orbital plane,
measurements near the edge of the polar vortex consistently look through high ozone values into lower ozone values. For
limb scatter measurements ozone sensitivity is larger on the instrument side of the line of sight for an indepth
discussion of this effect see; the high ozone values near OMPS-LP are incorrectly assigned to tangent
points inside or near the vortex.
Same as Fig. but for OMPS-LP orbit 12300.
To assess the impact of viewing geometry on the retrieval, a second simulation has been performed with a large horizontal
ozone gradient present in the Northern Hemisphere. For this simulation the geometry from OMPS-LP orbit 12300
(14 March 2014) was used. The simulated ozone field was taken from 14 March 2011 to obtain a realistic scenario with
large polar ozone depletion. The results of the simulation are shown in Fig. .
The one-dimensional retrieval consistently underestimates the true ozone profile in the 60–70∘ N region.
In this gradient region the instrument's line of sight is looking through low ozone values into high ozone values, opposite of the prior simulation; thus
underestimation is expected. As before, the one-dimensional retrieval leads the true profile, which can be seen in the
17.5 km slice (top right panel of Fig. ). The magnitude of the underestimation
(10–20 %) is less than the overestimation of the prior simulation (50 %), primarily because the gradient is
weaker and does not extend into the lower altitudes. The two-dimensional retrieval captures the structure of the gradient
quite well; as before, some horizontal smoothing errors on the order of 5–10 % can be seen at altitudes below
20 km.
Monthly zonal mean ozone anomalies in the 5∘ S–5∘ N bin for OMPS-LP (a), MLS v4.2 (b), and their absolute difference (c). Anomalies are calculated relative to the common overlap period, and data are masked outside the common overlap period.
Percent difference comparing monthly zonal mean values from OMPS-LP and MLS v4.2. Dashed black contour lines are the ±5 % levels, while solid black contour lines are the ±10 % levels.
An example of nearly perfectly coincident measurements from OMPS-LP and MLS. The dashed orange line shows the retrieval grid points for OMPS-LP orbit 11915 (14 February 2014, 04:35 UTC at Equator crossing),
while the blue line shows the retrieval locations for the near-coincident MLS measurements. The time difference at the crossing point is ∼ 16 min.
(a) shows the retrieved ozone field for OMPS-LP orbit 11915 (14 February 2014, 04:35 UTC at Equator crossing) from the USask 2D v1.0.2 retrieval;
(b) shows the corresponding coincident MLS v4.2 retrieved values for the coincident measurements shown in Fig. ; and (c) shows the percent difference between
the two, with gray and black contours indicating the ±5 and ±10 % levels, respectively.
Mean differences ((OMPS-LP - MLS) / MLS ⋅ 100 %) in latitude bins for all coincident orbits between 2012 and 2013 (see text for coincidence criteria). The shaded blue region shows the SD of the differences, while the shaded red region is the predicted SD using the precision estimate from both retrievals. Dashed vertical lines indicate the ±5 % levels.
Retrieval results for OMPS-LP orbit 20657 (23 October 2015, 08:50 UTC at Equator crossing) near the polar vortex. The left column shows the coincident MLS v4.2 ozone (a), tomographically retrieved ozone (b),
and one-dimensionally retrieved ozone (c). The right column contains a horizontal slice of the retrieved ozone at 15.5 km(d), the percent difference between the tomographic retrieval and MLS (e),
and the percent difference between the one-dimensionally retrieved ozone and MLS (f). For the percent-difference panels, contours are shown every ±5 %. The dashed black box indicates the area in which the two-dimensional retrieval is expected to show improvement based upon the simulations of Sect. .
Monthly zonal mean anomalies
As a zeroth-order validation effort, monthly zonal mean relative ozone anomalies have been performed against the MLS v4.2
ozone measurements. The MLS retrievals' native product is volume mixing ratio on pressure
surfaces; for these comparisons we have converted MLS v4.2 measurements to number density on altitude levels using ERA-Interim
reanalysis . The MLS data have been screened according to the recommendations of .
Figure shows the result of these comparisons in the tropical 5∘ S–5∘ N latitude
bin. Qualitatively there is excellent agreement; the anomalous change in the Quasi-Biennial Oscillation beginning at the end of 2015 can clearly
be seen in both datasets. Quantitatively, above 25 km observed differences in relative anomaly are less than 0.05
(∼ 5 % change in ozone) for all time periods. Below 25 km differences on the order of 0.1 are seen,
which could be related to larger variability in the tropical upper thermosphere and lower stratosphere. Anomalies from the dataset in other latitude bands
have been studied in detail by .
As a second check, the raw monthly zonal mean values are compared to those from MLS for the same latitude band in
Fig. . In the 25–45 km range, differences are generally less than 5 %. Below
25 km differences on the order of 10 % can be seen in the 2014–2015 and early 2016 time periods. It is
thought that these differences could be retrieval artifacts caused by the large stratospheric aerosol loading following the
Kelud and Calbuco eruptions in 2014 and 2015, respectively. Large high biases can be seen at the lowest altitudes
(16–18 km), which could be explained by the retrieval lower bound being set to the tropopause, causing a sampling
bias. Values used to calculate the monthly zonal mean for MLS could consist of both tropospheric and stratospheric air,
while monthly zonal means from OMPS-LP are purely stratospheric, leading to higher observed values. Above 45 km
OMPS-LP is low relative to MLS; however these results are not representative as both day and nighttime measurements are
used to calculate the MLS monthly zonal means, which causes differences when the diurnal variation of ozone is
significant.
Nearly perfect coincidences with MLS
MLS on board Aura and OMPS-LP on board Suomi-NPP are both in sun-synchronous orbit with similar inclination and local
crossing times; however Suomi-NPP orbits near ∼ 800 km, while Aura is at ∼ 700 km. The slight
difference in orbital periods causes the measurement ground tracks to drift relative to each other, with near-perfect
overlap, in both space and time, every 2–3 days. Figure shows the measurement track of OMPS-LP orbit
11915 (14 February 2014, 04:35 UTC at Equator crossing); also shown are the available measurements from MLS which
are nearly perfectly coincident to the OMPS-LP measurements. At the crossing point there is a time difference of 16 min,
and the differences in longitude are less than 1∘ for the entire orbit track. It should be mentioned that
sampling differences in latitude do not play a large factor as both the MLS and OMPS-LP retrievals are
two-dimensional, with the horizontal along-track resolution being poorer than the sampling frequency. For example, at 20 km, the
OMPS-LP retrieval has a horizontal sampling of ∼ 125 km with an estimated horizontal resolution of
350 km, while MLS v4.2 samples every ∼ 150 km with a horizontal resolution of 300 km.
The MLS retrieval is also two-dimensional and has similar along-track resolution to the two-dimensional OMPS-LP
retrieval; thus we have not applied horizontal averaging kernels for these tests. To account for differences in vertical
resolution, the procedure recommended by has been used. The OMPS-LP data are degraded to the MLS pressure
grid with a least squares fit and then converted back to the altitude grid in a consistent fashion; however internal
tests have shown that this makes negligible differences. A full validation of the dataset is intended for a forthcoming
publication; however an initial validation check has been performed by examining near-coincident orbits between Aura (MLS)
and Suomi-NPP (OMPS-LP).
Figure shows the retrieved ozone for OMPS-LP orbit 11915 (14 February 2014, 04:35 UTC at
Equator crossing) and coincident MLS measurements. Qualitatively there is excellent agreement between the two retrievals.
A triple ozone peak at low altitudes is seen in both retrievals in the Northern Hemisphere, and both retrievals resolve
a break in the ozone peak near 40∘ S. Some slight horizontal oscillations are observed (∼± 5 %) in
the USask OMPS-LP retrieval near the Equator. The exact cause of the oscillations is currently unknown, but initial
investigation suggests that it could be caused by the combination of cloud cover affecting the large amount of upwelling
radiation observed due to low solar zenith angles (∼ 20∘) seen in the tropics.
Quantitatively agreement between the two retrievals (bottom panel of Fig. ) is better than 5 %
for the majority of the stratosphere. Differences greater than 10 % are seen at the lowest altitudes of the retrieval
grid; it is possible that these are caused by the nonlinearity involved in applying the pointing correction to the
retrieved profile rather than the measurement tangent altitudes themselves. At the northern edge of the retrieval grid
there are also differences on the order of 5–10 %, which could be indicative of an edge effect in the two-dimensional
retrieval. Above 45 km there is a large amount of variance observed; however this is reflected in the MLS
precision estimate (∼ 20 % at 0.5 hPa).
Next, 251 coincident orbits were identified that are uniformly distributed from the 2012–2013 time period, where the time
difference at Equator crossing was less than 20 min and the average longitude difference for the full orbit was less than
1∘. Figure shows the results of these comparisons in various latitude bins. Generally
agreement is within 5 %, with the exception of altitudes below 18 km in the tropics, where OMPS-LP is biased
low at the 10–20 % level. Low biases are also observed near 50 km in most latitude bins; however the effect
is most noticeable at 60∘–90∘ S, where differences reach 8 %. Also shown
in Fig. is the observed standard deviation (SD) and the predicted SD using the supplied precision values for both data
products. While the observed SD does also include natural variability since the two measurements are not perfectly
temporally/spatially co-located, we do not expect this to be a noticeable effect due to the tight coincidence criteria.
The generally good agreement seen between the observed and predicted SD provides confidence in the supplied precision
values for the dataset.
Lastly, results are shown for OMPS-LP orbit 20657 (23 October 2015, 08:50 UTC at Equator crossing), which
are also nearly perfectly coincident to measurements from MLS. For this orbit we also apply the one-dimensional retrieval
described in Sect. , and the retrieval results are shown in Fig. . Similar to
the previous orbit, agreement in the middle stratosphere is typically better than 5 % between MLS and the
two-dimensional retrieval. The one-dimensional retrieval also agrees favorably with MLS in the middle stratosphere.
Inside the vortex there is larger disagreement; however this is expected due to the low absolute ozone values and the
inherent variance of the retrievals.
Highlighted in Fig. (dashed lines) is the 60∘–75∘ S, 10–20 km region,
which is the region where the one-dimensional retrieval performed poorly in the simulations of Sect. .
In this region the two-dimensional retrieval agrees better with MLS than the one-dimensional retrieval, with the
one-dimensional retrieval consistently overestimating the ozone values. The 15.5 km slice (top right panel of
Fig. ) shows the one-dimensional retrieval leading both MLS and the two-dimensional retrieval, which
is consistent with the prior simulation results. If we interpret the difference between the profiles at 15.5 km
entirely as a latitudinal offset, then the difference between the two-dimensional retrieval and MLS is
∼ 0.5∘, while the difference between the one-dimensional retrieval and MLS is ∼ 2∘ at 65∘ S.
Conclusions
A two-dimensional retrieval algorithm which directly accounts for atmospheric variations in the along-orbital-track
dimension has been developed for use with limb scatter measurements from OMPS-LP. The retrieval algorithm combines all
measurements from the sunlit portion of the orbit and simultaneously fits the full ozone profile for the portion of the
orbit with solar zenith angle less than 88∘. The vertical resolution of the retrieved profiles is estimated to be
1–2 km, while the along-track resolution is controlled with a Tikhonov type second squared difference constraint
and is typically 300–400 km for retrievals from OMPS-LP. The estimated precision of the retrieved ozone product
is 2–5 % for the middle and upper stratosphere, with values increasing to 30 % just above the tropopause.
Simulated retrievals were shown indicating that the retrieval is working as expected and offers improvement over
traditional one-dimensional retrievals in areas of large horizontal gradients.
The retrieval algorithm has been applied to all measurements from the center slit of OMPS-LP from early 2012 to present to
create a multi-year near-global ozone time series. Tropical ozone anomalies from the dataset agree well with those from
MLS v4.2, with differences greater than 5 % of the ozone mean value only observed below 25 km.
A preliminary validation effort is presented comparing coincident measurements from MLS. These measurements are
nearly perfectly coincident with time differences of less than 20 min and longitude differences of less than 1∘. For
the majority of the stratosphere differences are less than 5 %; larger differences are seen at the edges of the
retrieval grid. Qualitatively the precision estimate matches the observed scatter seen in the differences. Coincident
comparisons during the 2015 ozone hole indicate that the two-dimensional retrieval and MLS agree qualitatively well at
the edge of the polar vortex, whereas a traditional one-dimensional retrieval is shown to systematically overestimate in
this area.
Data availability
The USask OMPS-LP v1.0.2 2D dataset is available in HARMOZ format from the
Odin-OSIRIS FTP server (see http://odin-osiris.usask.ca/?q=node/280).
Competing interests
The authors declare that they have no conflict of interest.
Special issue statement
This article is part of the special issue “Quadrennial Ozone Symposium 2016 – Status and trends of
atmospheric ozone (ACP/AMT inter-journal SI)”. It is a result of the Quadrennial Ozone Symposium 2016, Edinburgh, United
Kingdom, 4–9 September 2016.
Acknowledgements
This work was partially funded by the Canadian Space Agency, the Natural Sciences and Engineering Research Council of
Canada; Science Systems and Applications, Inc.; and the National Aeronautics and Space Administration's Goddard Space
Flight Center. We would also like to thank the OMPS-LP team for assistance and for providing a high-quality L1 data
product. The manuscript was greatly improved through the helpful comments of one anonymous referee and Alexei
Rozanov.
Edited by: Mark Weber
Reviewed by: Alexei Rozanov and one anonymous referee
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