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**Research article**
06 Dec 2018

**Research article** | 06 Dec 2018

Improvement of stratospheric aerosol extinction retrieval from OMPS/LP using a new aerosol model

^{1}Science Systems and Applications, Inc., Lanham, Maryland 20706, USA^{2}NASA Goddard Space Flight Center, Greenbelt, Maryland 20771, USA^{3}Department of Atmospheric and Planetary Sciences, Hampton University, Hampton, Virginia 23668, USA

^{1}Science Systems and Applications, Inc., Lanham, Maryland 20706, USA^{2}NASA Goddard Space Flight Center, Greenbelt, Maryland 20771, USA^{3}Department of Atmospheric and Planetary Sciences, Hampton University, Hampton, Virginia 23668, USA

**Correspondence**: Zhong Chen (zhong.chen@ssaihq.com)

**Correspondence**: Zhong Chen (zhong.chen@ssaihq.com)

Abstract

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The Ozone Mapping and Profiler Suite Limb Profiler (OMPS/LP) has been flying on the Suomi National Polar-orbiting Partnership (S-NPP) satellite since October 2011. It is designed to produce ozone and aerosol vertical profiles at ∼2 km vertical resolution over the entire sunlit globe. Aerosol extinction profiles are computed with Mie theory using radiances measured at 675 nm. The operational Version 1.0 (V1.0) aerosol extinction retrieval algorithm assumes a bimodal lognormal aerosol size distribution (ASD) whose parameters were derived by combining an in situ measurement of aerosol microphysics with the Stratospheric Aerosol and Gas Experiment (SAGE II) aerosol extinction climatology. Internal analysis indicates that this bimodal lognormal ASD does not sufficiently explain the spectral dependence of LP-measured radiances. In this paper we describe the derivation of an improved aerosol size distribution, designated Version 1.5 (V1.5), for the LP retrieval algorithm. The new ASD uses a gamma function distribution that is derived from Community Aerosol and Radiation Model for Atmospheres (CARMA)-calculated results. A cumulative distribution fit derived from the gamma function ASD gives better agreement with CARMA results at small particle radii than bimodal or unimodal functions. The new ASD also explains the spectral dependence of LP-measured radiances better than the V1.0 ASD. We find that the impact of our choice of ASD on the retrieved extinctions varies strongly with the underlying reflectivity of the scene. Initial comparisons with collocated extinction profiles retrieved at 676 nm from the SAGE III instrument on the International Space Station (ISS) show a significant improvement in agreement for the LP V1.5 retrievals. Zonal mean extinction profiles agree to within 10 % between 19 and 29 km, and regression fits of collocated samples show improved correlation and reduced scatter compared to the V1.0 product. This improved agreement will motivate development of more sophisticated ASDs from CARMA results that incorporate latitude, altitude and seasonal variations in aerosol properties.

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Chen, Z., Bhartia, P. K., Loughman, R., Colarco, P., and DeLand, M.: Improvement of stratospheric aerosol extinction retrieval from OMPS/LP using a new aerosol model, Atmos. Meas. Tech., 11, 6495–6509, https://doi.org/10.5194/amt-11-6495-2018, 2018.

1 Introduction

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Accurate estimation of stratospheric aerosol is important because aerosols in the stratosphere have an important influence on climate variability through their contribution to direct radiative forcing, although the magnitude of this term is still uncertain (Ridley et al., 2014). Aerosols also play an important role in the chemical and dynamic processes related to ozone destruction in the stratosphere. Therefore, long-term measurement of the distribution of aerosols is necessary for a better understanding of stratospheric processes.

The Ozone Mapping and Profiler Suite Limb Profiler (OMPS/LP) is one of three OMPS instruments on board the Suomi National Polar-orbiting Partnership (S-NPP) satellite (Flynn et al., 2007). S-NPP was launched in October 2011, into a sun-synchronous polar orbit. The local time of the ascending node of the S-NPP orbit is 13:30. The LP instrument collects limb-scattered radiance data and solar irradiance data on a 2-D charge-coupled device (CCD) array over a wide spectral range (290–1000 nm) and a wide vertical range (0–80 km) through three parallel vertical slits. These spectra are primarily used to retrieve vertical profiles of ozone (Rault and Loughman, 2013; Kramarova et al., 2018), aerosol extinction coefficient (Loughman at al., 2018; Chen et al., 2018) and cloud-top height (Chen et al., 2016). More details about the OMPS/LP instrument design and capabilities are provided in Jaross et al. (2014).

Instruments that measure scattered radiation need to assume some form of aerosol size distribution (ASD) to convert their measured information into aerosol extinction. These instruments include limb-scattered instruments such as the Scanning Imaging Absorption Spectrometer for Atmospheric Chartography (SCIAMACHY) (von Savigny et al., 2015; Malinina et al., 2018), Optical Spectrograph and Infrared Imaging System (OSIRIS) (Bourassa et al., 2008, 2012; Rieger et al., 2014, 2018), OMPS/LP (Loughman at al., 2018; Chen et al., 2018), and space- and ground-based lidars such as Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP) (Winker et al., 2009). By contrast, instruments that employ solar, lunar and stellar occultation techniques such as SAGE II (Chu et al., 1989), SAGE III (Thomason et al., 2010) and Global Ozone Monitoring by Occultation of Stars (GOMOS) (Bertaux et al., 2010) can derive extinction directly from their transmission measurements without assuming an ASD.

In this study, we determine a new ASD by calculating a fit to results produced by the Community Aerosol and Radiation Model for Atmospheres (CARMA; Colarco et al., 2003, 2014) in order to improve the accuracy of aerosol extinction profiles retrieved from OMPS/LP measurements. The revised ASD is used in the new V1.5 OMPS/LP aerosol extinction retrieval algorithm, which demonstrates better performance in internal validation tests (e.g., absolute difference and spectral dependence of calculated radiances vs. measurements) compared to the V1.0 OMPS/LP algorithm. We also validate the revised ASD through comparisons to independent satellite retrievals of aerosol extinction from Stratospheric Aerosol and Gas Experiment on the International Space Station (SAGE III/ISS) solar occultation measurements. This work extends the previous results shown in Chen et al. (2018) to provide improved validation of the LP V1.5 aerosol extinction product.

2 LP algorithm description

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The original LP aerosol extinction retrieval algorithm described in Rault and
Loughman (2013) uses radiance data measured at multiple wavelengths in the
visible and near-infrared spectral region. The updated V1.0 algorithm
described in detail by Loughman et al. (2018) is based on Mie theory, using
radiances from one wavelength at 675 nm. We briefly review the design of
this algorithm here. The aerosol extinction profiles are retrieved from
limb-scatter observations using the aerosol scattering index (ASI) as the
measurement vector. The ASI is the fractional difference between a given
radiance and the calculated radiance assuming a pure Rayleigh atmosphere
bounded by a Lambertian surface. This quantity is roughly proportional to
aerosol extinction, as described in Loughman et al. (2018), and is defined at
wavelength *λ* at altitude *z* in Eqs. (1)–(2):

$$\begin{array}{}\text{(1)}& {\displaystyle}& {\displaystyle}{\text{ASI}}_{\mathrm{m}}\left(\mathit{\lambda},z\right)=[{I}_{\mathrm{m}}\left(\mathit{\lambda},z\right)-{I}_{\mathrm{0}}\left(\mathit{\lambda},z\right)]/{I}_{\mathrm{0}}(\mathit{\lambda},z),\text{(2)}& {\displaystyle}& {\displaystyle}{\text{ASI}}_{\mathrm{c}}\left(\mathit{\lambda},z\right)=[{I}_{\mathrm{c}}\left(\mathit{\lambda},z\right)-{I}_{\mathrm{0}}\left(\mathit{\lambda},z\right)]/{I}_{\mathrm{0}}(\mathit{\lambda},z).\end{array}$$

The measured radiance is denoted by *I*_{m}, while *I*_{c} and
*I*_{0} represent radiances calculated under differing conditions: for
*I*_{c}, the model atmosphere includes the most recently updated
aerosol extinction profile, while the model atmosphere is aerosol-free for
the calculation of *I*_{0}. The radiances are normalized (i.e., divided by
their value at the normalization altitude, 40.5 km) in all cases and form
the basis for the measured and calculated ASI (ASI_{m} and
ASI_{c}, respectively). Normalizing the radiances reduces the
effects of surface/cloud reflectance and errors in sensor absolute
calibration. This formulation removes the first-order effects of both
Rayleigh scattering and reflectivity, though there are second-order effects
which will be discussed later. As discussed in Loughman et al. (2018), the
effect of Rayleigh and aerosol scattering on radiances is not strictly
additive when the optical path along the line of sight (LOS) becomes
optically thick. For example, Rayleigh scattering also attenuates aerosol
scattering, reducing the sensitivity of the ASI to aerosol loading at lower
altitudes (i.e., where Rayleigh scattering is high). The observed limb
radiances are strongly affected by diffuse upwelling radiation and Rayleigh
scattering along the LOS. ASI is far less affected by these effects, so
aerosol signals are much easier to see in ASI.

^{*} *f*_{c} is the coarse-mode fraction, which is the
ratio of the number of particles of the coarse mode to the total number of
particles for a bimodal lognormal distribution (Loughman et al., 2018).

Assuming that optically thin conditions prevail, the radiance sensitivity is
approximately proportional to the change in aerosol extinction *k* at the
tangent point for the LOS. The LP aerosol extinction retrieval therefore
employs a nonlinear iterative technique, based on Chahine's nonlinear
relaxation technique (e.g., Chahine, 1970):

$$\begin{array}{}\text{(3)}& {\displaystyle}{\mathit{x}}_{i}^{(n+\mathrm{1})}={\mathit{x}}_{i}^{\left(n\right)}{\displaystyle \frac{{\mathit{y}}_{i}^{\mathrm{m}}}{({\mathit{y}}_{i}^{\mathrm{c}}{)}^{\left(n\right)}}},\end{array}$$

where ${\mathit{x}}_{i}^{\left(n\right)}$ represents the state vector (i.e., extinction) at
altitude *z*_{i} after *n* iterations of the retrieval algorithm. The
measurement vector ${\mathit{y}}_{i}^{\mathrm{m}}$ represents the measured
ASI_{m} at tangent height *h*_{i}=*z*_{i}. The Gauss–Seidel limb
scattering (GSLS) radiative transfer model (Herman et al., 1994, 1995;
Loughman et al., 2004, 2015) calculates the ASI_{c} vector
${\mathit{y}}_{i}^{\mathrm{c}}$ at each iteration, using the extinction profile
given by ${\mathit{x}}_{i}^{\left(n\right)}$. The cross section and aerosol scattering phase
function are calculated from an assumed ASD using Mie theory assuming
spherical droplets of sulfuric acid (H_{2}SO_{4}). An initial guess for
aerosol profile ${\mathit{x}}_{i}^{\left(\mathrm{0}\right)}$ is constructed by using an aerosol
extinction climatology derived from SAGE II data for the period 2000–2004.
The LP algorithm performs four iterations of Eq. (3) to reach the final
extinction profile. The LP aerosol product provides extinction profiles from
cloud-top height to 40 km. We flag the lowest level of the retrieved aerosol
profile at the cloud-top altitude, which is determined using the algorithm
described in Chen et al. (2016). Potential errors due to stray light or
absolute calibration bias are addressed in part through the use of
altitude-normalized radiances in constructing the ASI measurement vector.
Jaross et al. (2014) discuss possible remaining altitude-dependent errors
from these sources.

The primary change introduced for the LP V1.5 aerosol retrieval algorithm is the revised particle size distribution described in Sect. 3. Other changes with less impact on the retrieved extinction values include the use of vector radiative transfer calculations and the implementation of intra-orbit tangent height adjustments as described by Moy et al. (2017). In addition, the V1.0 retrievals only allowed a factor-of-2 change in extinction for each iteration and executed three iterations, rather than the larger values (factor-of-5 change, four iterations) given in Loughman et al. (2018). Based on inspection of test results, we revised those parameters for the V1.5 algorithm to allow a factor-of-3 change in extinction for each iteration and four iterations of the retrieval.

3 Aerosol size distribution

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Retrieval of aerosol extinction profiles from limb scattering measurements requires the specification of an aerosol size distribution (ASD) to represent the microphysical properties of the aerosol particles. Different functional forms can be selected to represent the ASD. The V1.0 LP aerosol algorithm retrieves extinction profiles by assuming a bimodal lognormal size distribution (BD):

$$\begin{array}{}\text{(4)}& {\displaystyle}n\left(r\right)=\sum _{i=\mathrm{1}}^{\mathrm{2}}{\displaystyle \frac{{N}_{i}}{r\sqrt{\mathrm{2}\mathit{\pi}}\mathrm{ln}{\mathit{\sigma}}_{i}}}\mathrm{exp}(-{\displaystyle \frac{\mathrm{1}}{\mathrm{2}}}[{\displaystyle \frac{\mathrm{ln}(r/{r}_{i})}{\mathrm{ln}{\mathit{\sigma}}_{i}}}{]}^{\mathrm{2}}),\end{array}$$

where *n*(*r*) is the size distribution function (${\mathrm{cm}}^{-\mathrm{3}}\phantom{\rule{0.125em}{0ex}}\mathrm{\mu}{\mathrm{m}}^{-\mathrm{1}}$),
*i* represents the *i*th mode of the distribution (*i*=1 and 2 indicate
fine and coarse mode, respectively), *r* is the particle radius
(µm), *r*_{i} is the median radius, *σ*_{i} is the standard
deviation, and *N*_{i} is the number of the particles corresponding to the
mode *i* (cm^{−3}). The fine- and coarse-mode size parameters of this
distribution (see Table 1) are primarily based on ER-2 measurements made in
August 1991, at 36^{∘} N, 121^{∘} W and 16.5 km (Pueschel
et al., 1994). Since the observed coarse-mode fraction *f*_{c} in the
Pueschel et al. (1994) data was very high following the eruption of Mt.
Pinatubo, we adjusted *f*_{c} downward to provide an Ångström exponent
(AE, defined in Eq. 5) of 2.0.

$$\begin{array}{}\text{(5)}& {\displaystyle}\text{AE}=-{\displaystyle \frac{\mathrm{ln}\left[k\left({\mathit{\lambda}}_{\mathrm{1}}\right)\right]-\mathrm{ln}\left[k\left({\mathit{\lambda}}_{\mathrm{2}}\right)\right]}{\mathrm{ln}\left({\mathit{\lambda}}_{\mathrm{1}}\right)-\mathrm{ln}\left({\mathit{\lambda}}_{\mathrm{2}}\right)}},\end{array}$$

where *k* is the aerosol extinction at wavelength *λ*. We chose AE =2.0 as our reference because it represents the mean value of AE at
20 km altitude estimated from SAGE II (Version 7.0) aerosol extinction data (Damadeo
et al., 2013) at 525 and 1020 nm taken during the period 2000–2005, when
the stratosphere was relatively clean and roughly similar to the present-day
stratosphere (Loughman et al., 2018).

The main motivation for using a bimodal size distribution arose from the desire to make comparisons with the existing in situ optical particle counter (OPC) data set, which generally features a bimodal size distribution at the altitudes where the stratospheric aerosol extinction is greatest (Deshler et al., 2003). However, specifying the five independent parameters (two mode radii, two mode widths and the coarse-mode fraction) needed to define this more complex distribution can be challenging. Most OPC measurements have no independent information at radii less than 0.1 µm, so that the aerosol size distribution between 0.01 and 0.1 µm is poorly defined (Kovilakam and Deshler, 2015). The lack of information in the OPC data gap region results in greater uncertainty in fitting data using the bimodal size distribution function (see Appendix A). As pointed out in Appendix A, the OPC does not count particles smaller than 0.1 µm, but the information on the smaller particles comes from super-saturating the cell so that all particles are lit up and one gets a gross count of the total number. Although a seemingly arbitrary collection of bimodal size distributions would fit the resolved OPC data equally well, the residual uncertainty results in large uncertainty in the phase function. Moreover, internal evaluation of V1.0 algorithm performance with no reference to external data sets (described in Sect. 4) and comparison of retrieved extinction profiles with SAGE III/ISS data (described in Sect. 5) also raised questions about the use of the V1.0 bimodal size distribution.

To select an alternate ASD for use in LP retrievals, we have used results from CARMA. CARMA is a sectional aerosol and cloud microphysics model that has been used to study a wide variety of problems in planetary atmospheres (Toon et al., 1979, 1988; Turco et al., 1979; Bardeen et al., 2008; Colarco et al., 2003, 2014; English et al., 2011, 2012; Yu et al., 2015). The CARMA model is coupled here to the NASA Goddard Earth Observing System (GEOS) Earth system model, a three-dimensional atmospheric general circulation model, as described in Colarco et al. (2014), and provides simulated aerosol distributions over a full range of latitude and longitude, altitude, and season. Colarco et al. (2014) describes how CARMA was implemented initially for dust and sea salt. The usage in GEOS for sulfate aerosols is a relatively new capability, with the sulfur chemistry mechanism and aerosol microphysics as in English et al. (2011) and as described and evaluated in Aquila et al. (2018). The particle size distribution is represented by 22 size bins covering a wide range of radii from 0.000267 to 2.79 µm. For this paper, we use output from simulations in which volcanic eruptions have been turned off, so that the background aerosol distribution reflects anthropogenic and nonvolcanic sources.

The aerosol optical properties can be directly calculated based on a radiative transfer model for each bin of the CARMA size distribution. However, the Mie calculation in the current LP aerosol code requires an analytic aerosol mode, rather than bin data. In this study, we use an analytical model of aerosol particle size distribution which deals with the ASD as a mean of size spectrum to accurately fit a cumulative distribution function (CDF) on the binned data using Deshler's method (Deshler et al., 2003). We have chosen the gamma distribution (GD; e.g., Chylek et al., 1992) to describe the size distribution of aerosols for OMPS/LP retrievals (Chen et al., 2018). This function is described in Eq. (6).

$$\begin{array}{}\text{(6)}& {\displaystyle}n\left(r\right)={\displaystyle \frac{\mathrm{d}N\left(r\right)}{\mathrm{d}r}}={\displaystyle \frac{{N}_{\mathrm{0}}{\mathit{\beta}}^{\mathit{\alpha}}{r}^{\mathit{\alpha}-\mathrm{1}}}{\mathrm{\Gamma}\left(\mathit{\alpha}\right)}}\mathrm{exp}(-r\mathit{\beta}),\end{array}$$

where *n*(*r*) is the number of particles *N*(*r*) per unit volume with a size
between radius *r* and *r*+d*r* (${\mathrm{cm}}^{-\mathrm{3}}\phantom{\rule{0.125em}{0ex}}\mathrm{\mu}{\mathrm{m}}^{-\mathrm{1}}$), *N*_{0}
is the total number density of aerosols (cm^{−3}), *α* and *β*
(µm^{−1}) are the fitting parameters, and Γ is Euler's
Gamma function. At small radii this function follows a power law, while at
large radii it follows an exponential function. In contrast to the BD, which
has five adjustable parameters, the gamma function has only two parameters to be
specified, the shape parameter *α* and the scale parameter *β*.
These parameters have a unique relationship to the effective radius:

$$\begin{array}{}\text{(7)}& {\displaystyle}{r}_{\mathrm{eff}}={\displaystyle \frac{{\int}_{\mathrm{0}}^{\mathrm{\infty}}{r}^{\mathrm{3}}n\left(r\right)\mathrm{d}r}{{\int}_{\mathrm{0}}^{\mathrm{\infty}}{r}^{\mathrm{2}}n\left(r\right)\mathrm{d}r}}={\displaystyle \frac{(\mathit{\alpha}+\mathrm{2})}{\mathit{\beta}}}.\end{array}$$

In order to fit the GD to CARMA results, we calculate the cumulative aerosol size distribution,

$$\begin{array}{}\text{(8)}& {\displaystyle}N\left(>r\right)={\int}_{r}^{{r}_{max}}n\left(r\right)\mathrm{d}r,\end{array}$$

where *N*(>*r*) represents the concentration of all particles larger than *r*.
The integral is performed over a range of sizes from ${r}_{min}=\mathrm{0.01}$ µm to ${r}_{max}=\mathrm{3}$ µm. The two parameters of
the GD are determined by fitting the CDF
of Eq. (8) using a Levenberg–Marquardt nonlinear least squares regression
algorithm. The scattering cross sections and phase functions are then
calculated using Mie theory assuming spherical particles of refractive index
of 1.448+0*i* for hydrated sulfuric acid (Palmer and Williams, 1975), which
is the same as that assumed in the LP V1.0 aerosol algorithm.

We created a subset of CARMA results that is approximately consistent with
the Deshler et al. (2003) long-term measurements by averaging
June–July–August model results to create a climatology, then extracting
aerosol size distribution values for the approximate location
(41^{∘} N, 105^{∘} W) and altitude (20 km) of those
measurements. We then calculated CDF fits to the CARMA results using unimodal
normal distribution (UD), BD and GD functions (described in Eqs. 4 and 6) using the same
fitting method. For consistency with the OPC database, CARMA bins between
0.02 and 0.1 µm were excluded from the fit. Figure 1a shows that,
while these CDF fits are relatively similar, the GD function does give the
best agreement with the excluded CARMA values.

Figure 1b compares the derived differential size distributions from the three
fits, which are plotted as d*N*∕dlog*r* vs. *r* in log–log
scale (here log is the logarithm to base 10). The BD function used for LP
V1.0 processing is also shown for comparison. In contrast to the cumulative
distribution functions shown in Fig. 1a, the differential distributions
differ significantly for *r*≤0.1 µm. Note that the V1.0
bimodal ASD has the largest d*N*∕dlog*r* value among these
distributions at *r*≈0.1 µm. As a result, the
corresponding aerosol scattering phase function for the BD fit is closer to a
Rayleigh phase function at large scattering angles (Θ*>*120^{∘}), as shown in Fig. 2. Fractional differences of 40 % in
this region can lead to up to a factor-of-2.5 larger extinction values at
20.5 km and at low effective reflectivities *ρ* (see Sect. 4), where the
derived extinctions are roughly inversely proportional to the *P*(Θ), as
discussed by Loughman et al. (2018). Conflating Figs. 1b, 2, A1b and A2, it
is concluded that the Mie phase function depends strongly on the peak in
d*N*∕dlog*r*. A larger d*N*∕dlog*r* value at
around 0.1 µm (i.e., narrower distribution width) causes larger
*P*(Θ) value at large scattering angles.

Limb scattering measurements from other satellite instruments have also been
used to retrieve stratospheric aerosol extinction profiles, with their own
choices of particle size distribution. Bourassa et al. (2012) used a unimodal
size distribution based on Deshler et al. (2003) OPC data to retrieve aerosol
extinction from OSIRIS radiance data at 750 nm. Rieger et al. (2014) not only used
the same function and initial parameters but also investigated the addition
of 1530 nm radiance data to enable the simultaneous retrieval of extinction
and mode radius. Rieger et al. (2018) evaluated the errors associated with
both unimodal and bimodal size distributions in the OSIRIS and SCIAMACHY
retrieval algorithms. Von Savigny et al. (2015) used a unimodal size
distribution based on different OPC data (Deshler, 2008) to retrieve aerosol
extinction from SCIAMACHY radiance data at 750 nm, although the radiance
data were not normalized with 470 nm radiance data. Malinina et al. (2018)
used an alternate approach with SCIAMACHY data in which radiances at seven
wavelengths between 750 and 1530 nm were included and the number density
profile was held constant. This allowed the simultaneous retrieval of mode
radius and distribution width for cloud-free observations at tropical
latitudes (20^{∘} S to 20^{∘} N). We include the parameters for
the OSIRIS and SCIAMACHY size distributions in Table 1 and show the
corresponding phase functions in Fig. 2. While we did not create test data
sets using those size distributions, we note that their differences from the
V1.0 phase function in Fig. 2 are in the same direction as the gamma
distribution (i.e., lower value at backscattered angles) but smaller in
magnitude. So we would expect that processing LP data with one of these
unimodal size distributions would yield less change relative to our V1.0
product than the gamma distribution adopted for V1.5. The improved agreement
with SAGE III data for V1.5 extinction data shown in Figs. 10–13 suggests
that we would not want to adopt a size distribution that produces less change
in extinction.

We have selected the gamma size distribution derived from CARMA results in
this work to assess the impact of ASD on stratospheric aerosol extinction
profile retrieval from OMPS/LP limb measurements. The two fitted parameters
(*α*=1.8 and *β*=20.5) determined from the GD fit at 20 km
produce an AE of 2.0 and a *r*_{eff} of 0.18 µm. These
values match the average values determined from SAGE II Version 7.0 data
(Thomason et al., 2008; Damadeo et al., 2013) during the 2000–2005 period.
Hereafter, this resultant ASD derived from the CARMA results will be labeled
as V1.5 ASD, while the ASD assumed in LP V1 will be labeled as V1.0 ASD. The
current LP retrieval algorithm assumes that the size distribution is height
independent, so that one function is used to represent the aerosol size
distribution at all heights. We plan to use CARMA model results in a future
version of the algorithm to incorporate variation in ASD and *P*(Θ) with
altitude, latitude, season and after a volcanic eruption. While we find in
this study a general improvement in the quality of the OMPS LP aerosol
retrievals by adopting the physically based and self-consistent
CARMA-produced particle size distribution, we acknowledge here that the use
of this particular model is not intended as a definitive prescription for the
OMPS LP algorithms. The model is of course subject to a variety of
uncertainties in its own right, in terms of formulation and implementation of
its physical algorithms, and generally speaking the modeling of the
stratospheric aerosol particle size distribution and composition is
nontrivial and a subject of ongoing work by a number of researchers. For
example, the version of the model used here does not yet include the possible
impacts of volcanic eruptions on the background particle distribution,
nor does it include the impacts of nonsulfate aerosols that may be
important in the UTLS (e.g., organics). We recognize that to push the
approach taken here further, for example, to use a model-based climatology of
aerosol properties to define altitude- and location-specific properties to be
used in the OMPS LP algorithms, requires at a minimum a more complete
implementation of the relevant physics in the model (i.e., addition of
missing species) and a thorough and independent evaluation of its
capabilities and quality. Determining the particle size distribution based on
model results is a challenging task. The assumptions inherent in any complex
model can sometimes require arbitrary choices that influence the calculated
results. So the size distribution adopted here for LP V1.5 aerosol extinction
retrievals may not yield equally good results in all situations.

Figure 3a shows the impact on the gamma distribution *P*(Θ) of changing
the mode parameters by ±10 % relative to the baseline mode, for the
range of scattering angles viewed during a single OMPS/LP orbit (Chen et
al., 2018). It is apparent that the phase function is quite sensitive to
*β*. A ±10 % change in *β* can produce a ±10 %
change in the calculated aerosol phase function at moderate scattering angles
(Θ= 70–100^{∘}), whereas a ±10 % change in *α*
only yields a ±3 % change in phase function at $\mathrm{\Theta}>\mathrm{70}{}^{\circ}$. Examination of the corresponding differential distribution
curves (not shown) indicates that increasing *α* produces an increase
in the peak d*N*∕dlog*r* value, whereas increasing *β*
shifts this peak to larger values of *r*. The changes in *P*(Θ)
(Fig. 3a) lead to corresponding significant changes in retrieved aerosol
extinctions, as shown in Fig. 3b. The changes in aerosol extinction are
approximately anti-correlated with the phase function variations, although
smaller in magnitude. The small-scale structures of the extinction data are
caused by the variation in scene reflectivity along the orbit, which is
discussed further in Sect. 4.

It is important to point out that OMPS/LP measurements cover a wide range of scattering angles with a well-defined latitude dependence. Figure 4 shows the variation of Θ with latitude for two dates corresponding to solstice conditions. Note that high values of Θ are always observed in the Southern Hemisphere (SH), while low values of Θ are observed in the Northern Hemisphere (NH). The impact of this sampling on measured ASI is discussed in Sect. 4.

4 Results and discussion

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In Sect. 3, we described the creation of the gamma aerosol size distribution
model derived from CARMA results. To understand the quality of the present
aerosol size distribution and to estimate the uncertainty associated with the
retrieved aerosol extinction, we first perform the aerosol retrieval code
runs for conditions without a significant volcanic eruption. This provides a
baseline situation. To evaluate the performance of the presented aerosol size
distribution, aerosol extinction profiles were retrieved from OMPS/LP
measurements before and after the Calbuco volcano eruption to see if the
volcanic eruption can be captured by the new model. This eruption occurred in
Chile (41.3^{∘} S, 72.6^{∘} W) on 22 April 2015 and had a clear
impact on the stratospheric aerosol distribution.

Figure 5 shows scatter diagrams of retrieved aerosol extinctions at 20.5 and
25.5 km as a function of latitude for the V1.5 ASD (blue) and from V1.0 ASD
(green), as well as their ratios (*k*_{V1.5} ∕ *k*_{V1.0},
black) for the entire month of data following the Calbuco eruption (Chen et
al., 2018). Extinction values from the V1.5 retrievals (top row) have a
similar latitude dependence to the V1.0 retrieval values (middle row) for
both 25.5 and 20.5 km. However, the extinction ratio
(*k*_{V1.5} ∕ *k*_{V1.0}) decreases in magnitude from high
Southern Hemisphere latitudes to high Northern Hemisphere latitudes. The
inverse of the phase function ratio, i.e.,
${\left[{P}_{\mathrm{V}\mathrm{1.5}}\left(\mathrm{\Theta}\right)\phantom{\rule{0.125em}{0ex}}/\phantom{\rule{0.125em}{0ex}}{P}_{\mathrm{V}\mathrm{1.0}}\left(\mathrm{\Theta}\right)\right]}^{-\mathrm{1}}$, is
also shown for comparison in the bottom row of Fig. 5. The observed change in
extinction from the V1.0 ASD to the V1.5 ASD is typically smaller than the
corresponding phase function change at all SH latitudes and at NH latitudes
less than ∼40^{∘} N. This difference is caused in part by the
“smearing” effect of multiple scattering, which becomes more pronounced at
lower altitudes (note the larger scatter of extinction ratio values in
Fig. 5f). The change in extinction ratio is greater than 1.0 at most
latitudes due to the change in phase function presented in Fig. 2 and the
mapping between LP scattering angle and measurement latitude illustrated in
Fig. 4.

Figure 5e and f show significantly more variability in extinction ratio of
*k*_{V1.5} ∕ *k*_{V1.0} at SH latitudes, which is correlated
mainly with the variation of effective reflectivity *ρ*. *ρ* is derived
from the LP measurements at 675 nm to represent Earth surface reflectance.
In the LP retrieval algorithm, *ρ* is determined by comparing the measured
data to model radiances at 40 km using a Lambertian surface (Loughman et
al., 2018). This “Lambert-equivalent” reflectivity (LER) value typically
differs from the true surface reflectivity due to diffuse upwelling radiation
(DUR) contributions from clouds, aerosols and other features within the
scene. As discussed in Loughman et al. (2018), the effect of Rayleigh
scattering and aerosol scattering on radiances is not strictly additive. The
relationship between the large variability in extinction ratio shown in
Fig. 5 and variations in LER is further illustrated in Fig. 6. The dependence
of the extinction ratio (*k*_{V1.5} ∕ *k*_{V1.0}) on *ρ* can
become nonlinear at low reflectivity (*ρ*<0.2), and the slope of the
linear portion of this figure (*ρ*>0.2) varies with latitude. The
nonlinear variation in extinction ratio at *ρ*<0.2 clearly increases in
magnitude when moving from 25.5 to 20.5 km, showing the altitude dependence
of the additional contribution from Rayleigh scattering.

While the altitude normalization used to construct the ASI measurement vector
in Eq. (1) reduces the effect of DUR in the LP aerosol extinction profile
retrieval considerably, there are second-order effects present that make ASI
sensitive to *ρ* at altitudes where there are aerosols. This occurs
because DUR is scattered by the aerosols at an average scattering angle close
to 90^{∘}, while the direct solar radiation is scattered at a wider
range of angles shown in Fig. 4. For singly scattered (SS) radiances,
assuming that the attenuation of SS radiance along the LOS is small, ASI is
proportional to the product of *k* and *P*(Θ). So
in this approximation the spectral dependence of ASI should be determined by
the spectral dependence of *k*⋅*P*(Θ), which is determined by ASD.
Hence, if the assumed ASD is correct, the measured and calculated spectral
dependence of ASI should be consistent.

In Fig. 7, ASI residuals (difference between the measured ASI and the calculated ASI) from V1.0 and V1.5 retrievals at 20.5 km are plotted as a function of latitude for wavelengths not used in the LP aerosol retrieval (352, 430, 508, 600, 745, 869 nm) for the V1.5 test processing of the 1-year data set. Residuals at the retrieval wavelength (675 nm) are not shown because they are very close to zero for both cases. The residuals produced by the V1.5 ASD are closer to zero than the V1.0 residuals for all wavelengths, indicating that the gamma function ASD more effectively represents the OMPS/LP measurements.

Figure 8 shows the ratio of ASI(745 nm) ∕ ASI(508 nm) at 20.5 and
25.5 km as a function of latitude, using LP measurements and the calculated
ASI values from the V1.0 and V1.5 ASDs. The agreement between measured and
calculated ASI ratio is significantly better for the V1.5 ASD, demonstrating
the improved representation of spectral dependence with this function.
Similar figures can be constructed for other combinations of LP wavelengths.
The 1-year results shown in Figs. 7 and 8 demonstrate how internal analysis
of LP aerosol retrieval results can help identify the most appropriate ASD to
use for these retrievals. We note that the ability to distinguish between
ASDs is better in the NH, where LP
scattering angles are lower and the relative uncertainty in *P*(Θ) is
reduced. We therefore use comparisons with external measurements to obtain
additional validation of our choice for the V1.5 ASD.

5 Comparison with SAGE III/ISS

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The Stratospheric Aerosol and Gas Experiment on the International Space
Station (SAGE III/ISS) developed by NASA Langley Research Center (LaRC) was
launched to the International Space Station in February 2017. SAGE III/ISS
provides limb occultation measurements of aerosols and gases in the
stratosphere and upper troposphere (Chu and Veiga, 1998). The SAGE series of
occultation measurements have been extensively evaluated and compared with
other space-based instruments and have been found to have relatively high
precision and accuracy (Bourassa et al., 2012). A general description of the
solar occultation measurement technique is provided by McCormick et
al. (1979). The ISS travels in a low Earth orbit at an altitude of
330–435 km at an inclination of 51.6^{∘}. With these orbital
parameters, solar occultation measurement opportunities cover a large range
of latitudes (between 60^{∘} S and 60^{∘} N). The solar
occultation measurement Version 5 Level 2 data were collected during the
period June–December 2017. SAGE III/ISS scientists have released this
initial data set (which includes retrievals of ozone, aerosols and nitrogen
dioxide from solar occultation measurements) in order to solicit feedback
from the international atmospheric science community. Figure 9 shows the
spatiotemporal coverage of the available data sets used for this study.
Profiles of aerosol extinction at nine wavelengths reported by SAGE III/ISS
(384.2, 448.5, 520.5, 601.6, 676.0, 756.0, 869.2, 1021.2, 1544.0 nm) are
provided from the surface or cloud top to an altitude of 45 km, with a
vertical resolution of 0.5 km at the tangent point location. We have
compared OMPS/LP aerosol extinction retrievals at 675 nm and SAGE III/ISS
aerosol extinction retrievals at 676 nm directly, using SAGE III samples
that correspond to the OMPS/LP 1 km altitude grid. For OMPS/LP, only data
from the center slit were taken into consideration, and all data below the
cloud height were rejected.

Figure 10 shows time series of OMPS/LP and SAGE III/ISS extinctions for six
10^{∘} latitude bins at 20.5 km from June to December 2017. Red and
black dots show individual measurements from sunrise (SR) and sunset (SS),
blue and green dots represent LP V1.5 and V1.0, and pink and yellow lines are the
median of the individual LP extinctions, respectively. SAGE III/ISS data are
available for groups of a few days at each latitude, while OMPS/LP
measurements provide daily global coverage. This time series demonstrates
that reasonable agreement is observed between LP V1.5 data (pink line) and
SAGE III/ISS data (red and black clusters), while LP V1.0 retrievals
typically show lower extinction values except in the Northern Hemisphere
during winter. This difference is consistent with the scattering angle
dependence discussed in Sect. 4, since LP measures at small scattering angles
at this time. Pattern differences between LP V1.5 and V1.0 reflect the impact
of aerosol size distribution on aerosol extinction. Large variability
throughout most of the time series can be explained by differences in spatial
or temporal sampling. The enhanced extinctions at 20.5 km observed by both
LP and SAGE III in September–December in the Northern Hemisphere are likely
associated with the enormous pyrocumulus events caused by the British
Columbia wildfires in August 2017.

Further indication of the level of agreement between OMPS/LP and SAGE III/ISS
is provided by comparing the zonal average profiles. For this comparison, a
relatively broad collocation requirement of ±5^{∘} latitude was used,
and longitudinal differences were ignored in order to maintain a minimal
comparison set size. The variation in SAGE III sampling illustrated in Fig. 9
limits each zonal average to 2–3 consecutive days of measurements. The data
have been binned and averaged to the OMPS/LP reporting altitudes for direct
comparison.

Figure 11 shows the zonal mean extinction profiles between 15 and 30 km
altitude in 6±5^{∘} latitude bins. For each latitude bin, the mean
OMPS/LP profile is usually composed of between 180 and 400 measurements,
while the number of SAGE III profiles used in each average is much smaller,
typically between 20 and 40 profiles. For all latitude bins, the general
agreement between LP V1.5 and SAGE III is quite good except at lower
altitudes (<18 km), where larger differences may indicate limitations in
the LP retrieval algorithm. In contrast, LP V1.0 retrievals are
systematically lower than SAGE III over the entire profile. This improvement
in agreement gives us confidence that the revised ASD used in the V1.5
processing is more appropriate for describing OMPS/LP measurements.

Figure 12 shows relative differences between the mean LP and SAGE profiles using the same latitude bins shown in Fig. 11. The absolute value of the relative differences between LP V1.5 and SAGE III is generally <10 % for 19–29 km, demonstrating good agreement. The relative differences are larger below 18 km, likely due to uncertainties in LP aerosol retrievals at these altitudes.

Figure 13 shows a scatterplot of individual zonal mean extinction values
from each data set between 20.5 and 25.5 km, selected for collocation within
10^{∘} latitude between 45^{∘} S and 60^{∘} N for the entire
comparison period. Linear regression fits between OMPS/LP and SAGE III
extinction data show a clear improvement in correlation coefficient from SAGE
III vs. V1.0 to SAGE III vs. V1.5 (*r*=0.83 to *r*=0.97), with a
concurrent reduction in standard deviation of the differences *σ*
(defined as $\sqrt{{\sum}_{i=\mathrm{1}}^{N}{\left({k}_{\mathrm{LP},\phantom{\rule{0.125em}{0ex}}i}-{k}_{\mathrm{SAGE},\phantom{\rule{0.125em}{0ex}}i}\right)}^{\mathrm{2}}/(N-\mathrm{2})}$) for the V1.5 fit by a factor of
2. These results give further quantitative evidence that the gamma function
ASD is appropriate for OMPS/LP aerosol extinction retrievals. Because of the
large variation of phase function with scattering angle (Fig. 2) and the
strong dependence between scattering angle and latitude for OMPS LP (Fig. 4),
the size distribution determined here is not necessarily the optimum choice
for a satellite instrument with a different measurement geometry resulting
from a different orbit.

6 Summary and conclusions

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This paper describes the derivation of a revised aerosol size distribution function to retrieve aerosol extinction profiles from OMPS/LP limb scattering radiance measurements. We use results from the CARMA microphysical model as a basis for the revised ASD to take advantage of CARMA's large range of particle size information. We find that using an ASD based on a gamma function fit (designated V1.5) requires fewer free parameters than our previous choice of a bimodal lognormal ASD (designated V1.0) and is more consistent with the CARMA particle size results. Evaluation of LP observed radiances is complicated by the measurement geometry (typically backward scattering in the SH, forward scattering in the NH) and the corresponding variation in phase function, as well as variations in scene reflectivity. The V1.5 ASD improves the performance of radiance-based retrieval algorithm internal validation tests, including reducing the magnitude of residuals between calculated and measured radiance and spectral dependence.

We also evaluated our revised ASD by comparing V1.5 retrieved extinction
profiles to SAGE III measurements during June–December 2017. Relative
differences between collocated zonal mean profiles are less than 10 %
between 19 and 29 km, with increased differences below 18 km. Regression fits
to all data between 20 and 25 km show a better correlation coefficient between
SAGE III data and LP retrievals with the V1.5 ASD (*r*=0.97) and a
factor-of-2 improvement in standard deviation of the differences compared to
results using the previous V1.0 ASD. We anticipate using the extensive CARMA
model results in the future to determine additional ASDs for LP retrievals
that can better represent natural aerosol variability in latitude, altitude
and season. CARMA results can also be used to develop a more effective ASD
for aerosol retrievals following a volcanic eruption.

Data availability

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Data availability.

The OMPS LP Version 1.5 aerosol data product will be available through the NASA Goddard Earth Sciences Data and Information Services Center (GES DISC) at https://disc.gsfc.nasa.gov. The DOI for this product (Deland, 2016) is https://doi.org/10.5067/2CB3QR9SMA3F. The SAGE III/ISS Version 5 Level 2 data are available at https://doi.org/10.5067/ISS/SAGEIII/SOLAR_BINARY_L2-V5.0 for the binary version and at https://doi.org/10.5067/ISS/SAGEIII/SOLAR_HDF4_L2-V5.0 for the HDF version, NASA ASDC (2018).

Appendix A: Fitting aerosol size distributions to OPC data

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One of the longest and most comprehensive records of local stratospheric
aerosol conditions comes from the University of Wyoming's optical particle
counters (OPCs) carried on weather balloons at Laramie, Wyoming, USA
(41^{∘} N), at altitudes up to 30 km. The instrument measures the
number of aerosol particles in several size bins, ranging from 0.15 to
2 µm radius. In most cases, a bimodal lognormal size distribution
(BD) is used to fit OPC data if there are enough different particle sizes
measured. For background stratospheric conditions, however, OPC data may not
provide sufficient information about smaller particles (*r*<0.15 µm) to determine a robust BD fit.

An example of this situation is illustrated in Fig. A1, which shows four
bimodal lognormal distribution fits to the same OPC data at 20 km altitude,
all having similar Ångström exponents of approximately 2.4, but each
with a different values of coarse-mode fraction *f*_{c}. The fitted
parameters as well as the calculated AE and *r*_{eff} are given in
Table A1. This topic is discussed further by Nyaku et al. (2018).

All four fits to the OPC data are equally good, but they differ from each other
significantly in the radius range between 0.01 and 0.1 µm because
the gap in OPC size bins limits the ability to constrain a fit. As a
consequence, the differences between the ASDs near 0.1 µm lead to
significant changes in *P*(Θ) for backward scattering conditions, as
shown in Fig. A2. It can be seen that *P*(Θ) is quite sensitive to the
value of d*N*∕dlog*r* around *r*=0.1 µm when
$\mathrm{\Theta}>\mathrm{90}{}^{\circ}$. ASD_1 (black) and ASD_2 (red) have larger values
of d*N*∕dlog*r* around *r*=0.1 µm, shown in
Fig. A1. Larger values of *P*(Θ) derived from the two ASDs in this range
are therefore closer to a Rayleigh scattering behavior.

Competing interests

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Competing interests.

The authors declare that they have no conflict of interest.

Acknowledgements

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Acknowledgements.

We thank the OMPS/LP team at NASA Goddard and Science Systems and
Applications, Inc. (SSAI) for help in producing the data used in this study.
We also would like to thank Tong Zhu for her technical support. Zhong Chen
and Matthew DeLand were supported by NASA contract NNG17HP01C.

Edited by: Piet Stammes

Reviewed by: three anonymous referees

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Short summary

We describe the derivation of an improved aerosol size distribution (ASD) for the OMPS/LP retrieval algorithm. The new ASD uses a gamma function distribution that is derived from CARMA-calculated results. The new ASD also explains the spectral dependence of LP-measured radiances well. Initial comparisons with collocated extinction profiles retrieved at 676 nm from the SAGE III/ISS instrument show a significant improvement in agreement for the LP retrievals.

We describe the derivation of an improved aerosol size distribution (ASD) for the OMPS/LP...

Atmospheric Measurement Techniques

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