The global variability of clouds and their interactions
with aerosol and radiation make them one of our largest sources of
uncertainty related to global radiative forcing. The droplet size
distribution (DSD) of clouds is an excellent proxy that connects cloud
microphysical properties with radiative impacts on our climate. However,
traditional radiometric instruments are information-limited in their DSD
retrievals. Radiometric sensors can infer droplet effective radius directly
but not the distribution width, which is an important parameter tied to the
growth of a cloud field and to the onset of precipitation. DSD heterogeneity
hidden inside large pixels, a lack of angular information, and the absence of
polarization limit the amount of information these retrievals can provide.
Next-generation instruments that can measure at narrow resolutions with multiple
view angles on the same pixel, a broad swath, and sensitivity to
the intensity and polarization of light are best situated to retrieve DSDs at
the pixel level and over a wide spatial field. The Airborne Hyper-Angular
Rainbow Polarimeter (HARP) is a wide-field-of-view imaging polarimeter
instrument designed by the University of Maryland, Baltimore County (UMBC),
for retrievals of cloud droplet size distribution properties over a wide
swath, at narrow resolution, and at up to 60 unique, co-located view zenith
angles in the 670 nm channel. The cloud droplet effective radius (CDR) and
variance (CDV) of a unimodal gamma size distribution are inferred
simultaneously by matching measurement to Mie polarized phase functions. For
all targets with appropriate geometry, a retrieval is possible, and
unprecedented spatial maps of CDR and CDV are made for cloud fields that
stretch both across the swath and along the entirety of a flight
observation. During the NASA Lake Michigan Ozone Study (LMOS) aircraft
campaign in May–June 2017, the Airborne HARP (AirHARP) instrument observed
a heterogeneous stratocumulus cloud field along the solar principal plane.
Our retrievals from this dataset show that cloud DSD heterogeneity can occur
at the 200 m scale, much smaller than the 1–2 km resolution of most spaceborne
sensors. This heterogeneity at the sub-pixel level can create artificial
broadening of the DSD in retrievals made at resolutions on the order of 0.5
to 1 km. This study, which uses the AirHARP instrument and its data as a
proxy for upcoming HARP CubeSat and HARP2 spaceborne instruments,
demonstrates the viability of the HARP concept to make cloud measurements at
scales of individual clouds, with global coverage, and in a low-cost,
compact CubeSat-sized payload.
Introduction
Clouds are one of the most uncertain aspects of our climate system. Clouds
are highly variable, yet well-dispersed across the globe and play a dual
role in distributing energy: they trap infrared radiation in our atmosphere
and reflect shortwave radiation back to space (Rossow and Zhang, 1995). This
energy distribution is the key unknown in predicting climate change, as the
interplay between longwave trapping and shortwave reflection of radiation by
clouds may change significantly as the planet warms. The relative strength
of these impacts depends strongly on cloud macrophysical and microphysical
properties, such as cloud optical thickness, thermodynamic phase, cloud-top
temperature, height, and pressure, liquid and ice water path and content, and
droplet size distributions. Measuring these elements in a global context and
over long temporal scales is crucial to improving our understanding of how
cloud properties translate to a radiative impact on climate.
Clouds also share a delicate relationship with aerosols. Aerosols drop the
energy barrier required for condensation, serving as condensation nuclei
(Petters and Kreidenweis, 2007) for liquid water and ice clouds in our
atmosphere. When aerosols are entrained into a cloud, they can set off a
condensation feedback loop, but in some cases, the opposite occurs: they dry
out the local atmosphere and evaporate smaller droplets (Hill et al., 2009; Small et al., 2009). Aerosols can invigorate convective clouds
(Altaratz et al., 2014) and suppress the development of other clouds (Koren
et al., 2004), depending on the aerosol and meteorological properties of the
local atmosphere. This complexity is a major source of uncertainty related
to understanding global radiative forcing and predicting climate change
(Boucher et al., 2013; Rosenfeld et al., 2014; Penner et al., 2004; Coddington
et al., 2010).
A major link between the radiative and microphysical climate impacts of liquid
water clouds is the droplet size distribution (DSD). A common mathematical
representation of the liquid water cloud DSD is a gamma distribution
(Tampieri and Tomasi, 1976; Hansen, 1971; Alexandrov et al., 2015). This DSD is
formed by two parameters, cloud droplet effective radius (CDR or reff) and effective variance (CDV or
veff; Hansen and Travis, 1974), which represent the mean droplet size and
dispersion relative to the scattering cross section. Aerosol effects on cloud
microphysics are strongly tied to the CDR (Twomey, 1977; Albrecht, 1989). In a
general example, aerosol loading generates competition for condensation
sites and leads to smaller droplets. This process can delay rainout but
increase the overall liquid water content, extending the lifetime of the
cloud. An abundance of smaller droplets scatters shortwave radiation
efficiently, creating a brighter cloud, and finally the excess of radiation
to space results in a net cooling of the planet (Haywood and Boucher, 2000;
Lohmann et al., 2000, and references therein). Typically, studies that connect
the microphysical and radiative properties of clouds do so by tracking changes
in CDR only, with no direct sensitivity to CDV (Feingold et al., 2001;
Platnick and Oreopoulos, 2008). Because CDV is a measurement of the breadth
of the DSD, it may encode information on cloud growth processes:
collision–coalescence, aerosol or dry air entrainment, evaporation, and the
initiation of precipitation on cloud cores or peripheries. Not all clouds
share the same relationship between microphysics and radiation, but the key
to understanding the connection lies in the microphysics described by these
two DSD parameters. Only satellite instruments allow us to make these
long-term connections between radiation and the evolution of cloud DSDs for
different cloud types and over large spatial and temporal periods. Also,
satellite studies best improve global models that examine both future
climate scenarios and cloud feedbacks (Stubenrauch et al., 2013).
There are currently two methods used to retrieve CDR from spaceborne
instruments. The first is the widely used radiometric bi-spectral retrieval,
first proposed by Nakajima and King (1990) and employed operationally to the
MODerate resolution Imaging Spectroradiometer (MODIS) and other multi-band
radiometer data (Platnick et al., 2003, 2017; Walther and Heidinger, 2012).
The bi-spectral retrieval uses the difference in cloud information content
observed by shortwave infrared (i.e., 1.6, 2.1, or 3.7 µm) and visible
(i.e., 0.67 or 0.87 µm) channels to retrieve CDR and cloud optical
thickness (COT) simultaneously for a cloud target. The second method is the
multi-angle polarimetric retrieval, which is relatively new. The
polarimetric retrieval corresponds to a parametric fit to a multi-angle
polarized cloudbow (or rainbow by cloud droplets) structure that is
sensitive to both CDR and CDV simultaneously (Breon and Goloub, 1998;
Alexandrov et al., 2015; Di Noia et al., 2019). COT can also be retrieved with
assistance from an external radiative transfer simulation (Alexandrov et al.,
2012a). The 3D multiple scattering effects of shadowing and illumination
(Marshak et al., 2006; Varnai and Marshak, 2002) bias the radiometric method,
whereas the polarimetric retrieval is sensitive to scattered photons from a
COT up to ∼3, lessening the impact of this effect (Miller et
al., 2018). Sub-pixel clouds and spatial heterogeneities can affect both
methods, as discussed in later sections (Zhang and Platnick, 2011; Breon and
Doutriaux-Boucher, 2005; Shang et al., 2015). Furthermore, the bi-spectral
technique is not sensitive to CDV and uses a preestablished value (0.1,
Platnick et al., 2017) that may not be valid for all liquid water cloud
targets and all regions of the world.
Multi-angle polarimetric measurements have other advantages for cloud
characterization beyond the retrieval of the two DSD parameters. We find that
retrievals of cloud thermodynamic phase (Riedi et al., 2010; Goloub et al.,
2000), ice crystal asymmetry (van Diedenhoven et al., 2013), aerosol above
cloud (Waquet et al., 2013), and COT (Xu et al., 2018; Cornet et al., 2018) are
considerably improved with the addition of polarized observations. At the
time of this writing, only the Polarization and Directionality of the
Earth's Reflectances (POLDER; Deschamps et al., 1994) instruments have
demonstrated the polarized retrieval of cloud DSD properties from space, though
several aircraft instruments, including the Airborne Multi-angle
SpectroPolarimetric Imager (AirMSPI; Diner et al., 2013), the Research
Scanning Polarimeter (RSP; Cairns et al., 1999), and the subject of this
paper, the Airborne Hyper-Angular Rainbow Polarimeter (AirHARP; Martins et
al., 2018), have demonstrated improved sampling schemes, resolution, and
accuracy (Knobelspiesse et al., 2019; van Harten et al., 2018).
Mie scattering simulations for liquid water cloud droplets, with solar light incident, for the four HARP wavelengths at 10 µm CDR and 0.02 CDV (a), the 0.67 µm channel for variable CDR and constant CDV (b), and constant CDR with variable CDV (c).
Not all polarimetric measurements will achieve a high-quality retrieval of
cloud DSDs. Multi-angle sampling at high angular density and moderate pixel
resolution is an essential element of an accurate single-wavelength
retrieval. Figure 1 shows theoretical Mie simulations that mimic the
polarized cloudbow for particular values of CDR, CDV, and wavelength. To
resolve the cloudbow patterns from space and retrieve the CDR and CDV of the
cloud, the multi-angle polarimetric instruments must satisfy a minimum
viewing angle density (Miller et al., 2018), which is directly related to
scattering angle coverage. The location of the supernumerary peaks in scattering
angle encode CDR in the 0.67 µm example shown in Fig. 1. To resolve the CDV,
the amplitude of the supernumerary peaks must be detected. Polarimeters with coarser
viewing angle separation for a single wavelength (i.e., >3∘ at 0.67 µm for typical droplets <15µm; Miller et al., 2018) may not distinguish these cloudbow
oscillations. Instruments like POLDER, which samples at 14 unique viewing
angles separated by 10∘, do not provide enough native angular
resolution (Shang et al., 2015) and, as a consequence, may not be able to
identify wide versus narrow DSD clouds at specific geometries (Miller et al.,
2018). Only when sampling all native 6×7km POLDER pixels inside a 150 km
superpixel can they access the full scattering angle coverage in Fig. 1 and
perform an accurate retrieval (Breon and Goloub, 1998). However, this limits
their retrievals to large-scale, homogenous marine stratocumulus clouds with
narrow DSDs. In a study by Breon and Doutriaux-Boucher (2005), a comparison
between POLDER polarized and MODIS radiometric retrievals showed a CDR bias
of 2 µm that could not be fully decoupled from the large POLDER
superpixel. Later evaluation by Alexandrov et al. (2015), with the RSP and
the Autonomous Modular Sensor spectrometer, found that the CDR values
retrieved by the two methods agree at narrower resolution. Shang et al. (2015) improved the POLDER retrieval by reducing the superpixel to 42 km.
Even though sampling at higher resolution produced gaps in cloudbow
coverage, they still found heterogeneity inside the original 150 km
superpixel using this improved method. In a follow-up paper, Shang et al. (2019) showed that the POLDER retrieval is sensitive to a wider CDR and CDV
range and can be done at a lower 40–60 km resolution when considering all
three polarized wavelengths (490, 670, and 865 nm) in the retrieval. Even so,
no instrument thus far has performed a polarimetric cloud retrieval from
space with both co-located pixel resolution less than 40 km and high native
angular density (<10∘). These goals are essential to
studying the spatial distribution of DSDs for heterogeneous, broken, and
popcorn cumulus cloud scenes other than the conventional retrievals from
marine stratocumulus cases.
The benefit of aircraft instruments like RSP, AirMSPI, and AirHARP is to
demonstrate new technologies that improve upon the POLDER retrieval
heritage. RSP, in particular, samples at 150+ viewing angles, separated on
average by ∼0.8∘, and does so for a co-located
250 m along-track pixel (Alexandrov et al., 2012b, 2015, 2016b). This
advancement removes any large-scale homogeneity assumptions and allows for a
rainbow Fourier transform on the data, one that retrieves the DSD itself, including multiple modes,
without any assumptions on the distribution shape (Alexandrov et al., 2012b).
RSP can sample other kinds of clouds, including broken and popcorn cumulus
clouds, with high angular and spatial resolution and does so with high
polarimetric accuracy (Cairns et al., 1999). The single-pixel cross-track
swath of RSP, however, restricts its spatial coverage: RSP cannot form an
intuitive image of the scene, requires specific solar angles for cloudbow
coverage (Alexandrov et al., 2012b), and requires input from other
coincident instruments for off-nadir context (Alexandrov et al., 2016a).
Conversely, the AirMSPI instrument is a highly accurate push-broom imager
capable of discrete, programmable viewing angles on the same target, but it has
the same angular limitations as POLDER in this step-and-stare mode. AirMSPI also samples in
a continuous sweep mode that trades co-located information for scattering angle coverage
(Diner et al., 2013). This mode gives full visual coverage on the cloudbow
but limits the retrieval to a line cut of binned pixels along the solar
principal plane. A study by Xu et al. (2018) extended the AirMSPI line-cut
retrieval to the entire continuous sweep image of the cloudbow with assistance from
image-specific empirical correlations between COT, CDR, and CDV. This
line-cut polarimetric technique requires a droplet size homogeneity
assumption over the full line cut of the cloudbow, which may blur
heterogeneity that exists at the pixel level and steer the retrieval towards
wider DSDs.
There is a strong interest in the Earth science community in a multi-angle
polarimeter concept for aerosol and cloud retrievals with a wide swath for
spatial context, high accuracy in polarization, high angular density for
cloudbow retrieval, and narrow ground resolution (Remer et al., 2019; Dubovik
et al., 2019). The Earth and Space Institute (ESI) at the University of
Maryland, Baltimore County (UMBC), designed, developed, and deployed the
Airborne Hyper-Angular Rainbow Polarimeter (AirHARP), a next-generation
wide-field-of-view (FOV) imaging polarimeter specifically for this purpose.
AirHARP is the aircraft demonstration of spaceborne technology that will fly
on a stand-alone CubeSat platform in 2019 in the orbit of the International
Space Station and an enhanced HARP sensor for the NASA
Plankton–Aerosol–Cloud–ocean Ecosystem (PACE) mission, called HARP2, in the
early 2020s.
In this paper, we will first describe the HARP concept and frame the
AirHARP instrument and its data as a proxy for upcoming HARP CubeSat and
HARP2 space instruments throughout the rest of the work. We then explain the
cloud droplet retrieval framework in Sect. 3, followed by applications of
the retrieval on a stratocumulus cloud deck observed by AirHARP during the
NASA Lake Michigan Ozone Study field campaign in 2017 in Sect. 4. In
Sect. 5, we make use of the fine spatial resolution of the retrieved DSD
parameters to explore the information content of the retrieval itself and
relate the spatial variability of the results to cloud processes. Section 6
discusses the uncertainties and current limitations of the procedure, and we
conclude the paper in Sect. 7, looking ahead to HARP CubeSat and HARP2
deployment and data content.
Panels (a), (b), and (c) illustrate the current HARP VNIR polarimeter family consisting of the AirHARP airborne system (a), HARP CubeSat (b), and HARP2 for the NASA PACE mission (c). The HARP concept comprises a wide-field-of-view imaging polarimeter that images the same ground target from up to 60 distinct viewing angles at 0.67 µm(d) and up to 20 viewing angles at 440, 550, and 870 nm. The wide cross-track swath (94∘) of HARP2 allows for global coverage from space within 2 d.
Airborne Hyper-Angular Rainbow Polarimeter
The AirHARP concept, and the HARP family of polarimeters in general, was
developed with a wide swath, fine angular resolution, and high polarization
accuracy to address some of the limitations of modern polarimeters. The
three HARP instruments, shown in Fig. 2, are amplitude-splitting, wide-FOV
polarimetric cameras. Incident light enters through the wide-FOV front lens,
passes through telecentric optics, and is split by a Phillips prism toward
three detectors. Before reaching each detector, this light passes through a
polarizer oriented at 0, 45, or 90∘. The polarizers are
oriented at 45∘ separations such that the I, Q, and U Stokes
parameters of the scene can be retrieved in a single co-aligned pixel from
an orthogonal basis set of polarization states (Fernandez-Borda et al., 2009). AirHARP
images a ground scene with a ±57∘ (±47∘)
along-track (cross-track) FOV, and a custom stripe filter over the detector
assigns 120 along-track portions, or view sectors, of the FOV to four visible channels
(bandwidths): 440 (14), 550 (12), 670 (18), and 870 (37) nm. A view sector
specifically defines a segment of the detector that corresponds to a unique
average viewing angle at the front lens. The hyper-angular 670 nm band
samples at 60 view sectors at an average 2∘ separation, and the
other three channels sample at 20 each at an average 6∘
separation. In this way, the 60 670 nm view sectors can sample the cloudbow
oscillations at high angular density without large-scale homogeneity
assumptions or degrading the measurement for scattering angle coverage. The
wide FOV also allows for broad scattering angle coverage from space during
the daylit portion of an orbit. The 20 view sectors in the other three
channels ensure multi-angle coverage on aerosols; several studies show that
fewer than seven unique views in a single channel are appropriate for high-accuracy retrieval of aerosol optical properties (Hasekamp and Landgraf,
2007; Hasekamp et al., 2019), though the details are beyond the scope of this paper.
AirHARP is a push-broom imager, meaning that consecutive measurements from a
single view sector can be stitched together to form an image of a ground
scene as observed only from that angle. These push brooms can have any
along-track length but a cross-track swath proportional to the flight
altitude multiplied by a factor of 2.14. This factor accounts for the
maximum AirHARP cross-track view angle, ±47∘. A
unique push broom is made for each of the 120 view sectors, and
post-processing registers all of them to a common grid.
A target, either on the ground or in the atmosphere, will be viewed from a
subset of the 120 view sectors with its reflected apparent I, Q, and U
measured in each view sector and wavelength. From these measurements, the
polarized reflectance as a function of scattering angle can be compared with
theoretical Mie calculations, as in Fig. 1. The hyper-angular capability of
the 670 nm channel with its 2∘ viewing angle resolution can best
measure the supernumerary location and amplitude of the cloudbow structure
and is therefore best for retrieving the CDR and CDV of the target cloud. Note
that because AirHARP is an imager, each pixel in the image is a potential
target viewed by multiple angles. Therefore, each pixel in the image can
produce its own polarized reflectance and can be used to retrieve CDR and
CDV, granted that the range of view angles spans a sufficient range of
scattering angles. Note that the scattering angle range is dependent on both
the view angle range (fixed by the instrument) and solar geometry (not fixed).
If a large number of pixels in the image are viewed at the correct geometry
then a spatial map can be made of the DSD parameters across and along the
swath, wherever a cloud pixel is found. Depending on the observation
altitude and binning scheme, ∼0.2 to 6 km native retrieval
resolutions are possible. Therefore, the microphysics of individual fair-weather cumulus clouds can be retrieved across a cloud field stretching tens
to hundreds of kilometers. This capability is unprecedented for any existing
multi-angle polarimeter instrument.
In HARP's current configuration, all of this retrieval potential fits
entirely inside a 10×10×15cm enclosure. The flagship version of HARP is a
spaceborne CubeSat, a stand-alone payload funded by NASA's Earth Science
Technology Office (ESTO) In-space Validation of Earth Science Technologies
(InVEST) and in collaboration with the Space Dynamics Laboratory (SDL) in
Logan, Utah, USA. The HARP CubeSat satellite was launched on 2 November 2019 to the International Space Station (ISS) (400 km, 51.6∘ inclined
orbit) and then dispatched from the station for an autonomous year-long
mission in February 2020. Cloud retrievals on HARP CubeSat data will be
possible at a minimum 4 km superpixel, a capability demonstrated in this
paper using AirHARP, a near-identical copy of the CubeSat instrument for
aircraft. A third HARP concept, HARP2, is currently under development for
the PACE mission to launch in the early 2020s. The HARP CubeSat will be the
first satellite to perform wide-swath polarized cloud retrievals at sub-5 km
co-located resolution from space, and HARP2 will continue this capability
forward and expand it to provide global coverage in 2 d.
The remainder of this paper will discuss the information content retrieved
from complex cloud scenes observed by AirHARP. The study below refers
specifically to AirHARP datasets, but the HARP term may be used when
discussing general performance expected from any of the HARP instruments.
Retrieval framework
A simple treatment of the parametric retrieval is described below, with main
components derived from Breon and Goloub (1998), Alexandrov et al. (2015),
and Diner et al. (2013). The interaction between incident light and
a liquid water cloud droplet is described by a scattering matrix:
IQUsca=σsca4πR2P11P120P12P22000P33IQUinc,
where a Stokes column vector describes the incident beam (subscript “inc”), in
total radiance (I) and polarized radiance (Q, U), and the scattered beam by a
similar vector with subscript “sca”. In general, 16 elements describe the
scattering matrix, but since circular polarization in the atmosphere is
negligible (Cronin and Marshall, 2011) and not measured by AirHARP, the
fourth column and row are neglected. Cloud-top liquid water droplets are
spherical, randomly oriented, and mirror symmetric: any matrix elements in
Eq. (1) that describe asymmetry are neglected and the others mirror across
the main diagonal (Hansen and Travis, 1974). The unitless Pmn matrix
elements scale by the droplet scattering cross section (σsca)
weighted by the inverse of droplet surface area.
Sunlight incident on the atmosphere is unpolarized (Qinc,Uinc=0).
For single-scattered photons, the scattered intensity (Isca) is
proportional to the first matrix element, P11 and its polarization
(Qsca) to the second, P12, called the polarized phase function. Usca does not
contain any structural information in the scattering plane, though it may
show a weak linear slope in the presence of non-cloud scatterers (Alexandrov
et al., 2012a). For this reason, Qsca in the scattering plane represents
the entire polarized signal.
At the top of the atmosphere (TOA), remote sensors do not observe the
scattering from individual droplets but the bulk behavior of the droplet
distributions due to measurement resolution and scale limitations. The bulk
Mie polarized phase function, 〈P12〉, is a weighed sum of optical
properties:
〈P12(λ,θ,CDR,CDV)〉=∑iP12,iλ,θ,CDR,CDVωiλCext,iλ∑iωiλCext,iλ,
where ω is the single-scattering albedo (SSA, 1 for water droplets),
and Cext is the scattering cross section, which itself is composed of the
scattering efficiency and a size distribution weighted by droplet
cross section. This study uses the same unimodal gamma size distribution
function as Breon and Goloub (1998). Polarized reflectance observed at TOA
from liquid water cloud droplets is proportional to P12, after a
correction for viewing geometry:
Robs=4πμ0+μ-πQscaμ0F0,
where the cosines of the view zenith angle (μ0) and solar zenith
angle (μ) and the band-weighted extraterrestrial solar irradiance
(F0) rescale the polarized radiance (Qsca). The bracketed term is
the polarized reflectance (ρP), and a similar expression gives the total reflectance
(ρ) using the Stokes parameter Isca in place of -Qsca.
Subsequent figures use L670nm for Isca and LP,670nm for
Qsca radiances, where applicable, and anytime the term intensity is used, it
corresponds to a radiance measurement, not reflectance, unless explicitly
noted. Because we are only using a single wavelength in our retrieval,
radiance and reflectance are interchangeable in terms of the information content
shown in the figures. Corrections to Eq. (3) for Rayleigh scattering at
observation height are performed in prior studies (Breon and Goloub, 1998;
Diner et al., 2013), but the necessity is disputed (Alexandrov et al., 2015):
this study accounts for Rayleigh effects in a weak cosine term described
below.
The retrieval compares Eq. (3) to a parametric model and infers the CDR
and CDV from the best-fitting P12 simulations:
Rfitλ,ϑscat=αP12λ,ϑscat,CDR,CDV+βcos2ϑscat+γ.
The parametric fit scales the theory, Eq. (4), to observations, Eq. (3),
inside the polarized cloudbow scattering angle range (135∘<ϑscat>165∘; Di Noia et al.,
2019; Shang et al., 2015) with three free parameters (α, β, γ). Corrective factors for aerosol above cloud, cirrus, sun glint, molecular
scattering, and surface reflectance signals comprise weak functions of
scattering angle (Diner et al., 2013; Alexandrov et al., 2015). The parameter
α is related to cloud fraction (Breon and Goloub, 1998) and is
therefore accounted for by Eq. (4).
A prescribed lookup table (LUT) in CDR and CDV drives the parametric fit,
ranging between 5 and 20 µm in CDR (Δ=0.5µm), and CDV
values of 0.004 to 0.3 at variable intervals, similar to Alexandrov et al. (2015), with Δ values indicating the step size. The LUT is dense for
CDV<0.1: the majority of supernumerary bow sensitivity exists
below this level and is considerably reduced for CDV>0.1, as shown
in Fig. 1. Polarized reflectance measurements are corrected via Eq. (3) and
fit in a nonlinear least-squares process to Eq. (4), checking all possible
combinations of CDR and CDV in the LUT. The root mean square error (RMSE)
and reduced chi-square statistic χred2 of the least-squares process verify all LUT
comparisons:
RMSE=1n∑inRfit,i-Robs,i2,
and
χred2=1n-5∑in(Rfit,i-Robs,i)2σobs,i2.
The χred2 verifies that the data are
best described by the fit in Eq. (4) with n-5 degrees of freedom (for three fit
parameters, CDR, and CDV), where n is the number of measurements in the
cloudbow scattering angle range for that pixel. Like Alexandrov et al. (2015), a fine-scale interpolation is performed on the LUT at 10 times the
original resolution in CDR and CDV. Retrievals are accepted immediately for
χred2 values 0.5 to 1.5. In this
range, our error estimate is consistent with the minimized fit. If the
χred2is outside this range, our error
may lead to an overfit (χred2<0.5) or underfit (χred2>1.5). However, large χred2 does not always mean the fit is poor in our
case: the physics of the cloud field may justify solutions with
χred2 beyond 1.5. Therefore, we also
check to see if the fit satisfies an RMSE threshold of 0.03. If not, the fit
is rejected and the pixel is flagged. These diagnostics were found by a
sensitivity study on synthetic AirHARP cloudbow retrievals and an estimation
of the error in the actual data.
There are several reasons for this two-factor authentication. First, we
recognize that the signal-to-noise ratio of the superpixel is not the only error
that contributes to the measurement. Optical etaloning (andor.oxorinst.com, 2020) that remains in this
AirHARP dataset will also add uncertainty. This effect is weak compared to
the signal and nearly random angle to angle, so we estimate an extra 1σ
contribution in each superpixel to account for it. Therefore, the superpixel
uncertainty, σobs, used in Eq. (6) represents 2 times the
standard deviation of the superpixel bin. Because the χred2 value depends heavily on a correct error
estimation, it is important that all artifacts in the data are
well accounted for. Second, there is evidence in the literature that when
multiple DSDs exist inside the same superpixel, the polarized signal will
not agree completely with a signal that represents a single DSD (Shang et
al., 2015). This retrieval will still attempt to find a representative DSD in
the measurement, however. Here, the χred2 may be higher than 1.5, but the RMSE
threshold can still find a solution if the measurement residuals are not too
far from the best-fit curve. This may also occur for observations of
multi-layer cloud fields. Because the χred2 depends strongly on the uncertainty of the
individual measurements, there is also a possibility that pixels that
represent narrow size distributions may give a valid retrieval, while
producing χred2 values beyond 1.5.
Figure 6a is one such example. The cloudbow oscillations are well-defined
and AirHARP data clearly capture the pattern, though the χred2 is 2.52. While the error bar on several
AirHARP data points does not touch the best-fit polarized reflectance, the
overall curve fit does represent the information content in the measurement.
It is therefore important to include the RMSE as a two-factor
authentication. Third, Breon and Goloub (1998) noted that secondary and
tertiary scattering events in the primary bow region (137–145∘ in
scattering angle) can widen the polarized signal here relative to Mie
simulations. Here, the RMSE may preserve a strong fit in the supernumerary
region, where the majority of the DSD information content lies, even if the
χred2 is beyond our threshold. These
diagnostics also account for any artifacts that arise from rotating our
reference frame of polarization into the scattering plane and retrievals
that converge artificially to the edges of the LUT. When the uncertainty is
high relative to the measurement, both χred2 and RMSE will also be high and the retrieval will be
rejected if both values exceed their expected ranges. More details on some
of these effects are discussed in Sect. 6.
The focus of this paper is on the application of AirHARP cloud datasets and
not the retrieval algorithm itself; therefore, we use a simple treatment of
the classic parametric model. This retrieval will be extended to multi-modal
DSDs and take into account both multi-angle and multi-spectral sampling in
future studies.
The scattering angle coverage typical of an instantaneous AirHARP wide-FOV observation, projected to simulate a scene over Lake Michigan on 19 June 2017 at 15:22 Z (a). The cloudbow in this simulation represents a simulated cloudbow at 670 nm, with CDR 10um and CDV 0.01, with scattering angle isolines from 90 to 165∘ shown (solid lines). Note that the cloudbow pattern occurs within 135–165∘ in scattering angle, and the location of the cloudbow in the FOV depends on time of day, flight orientation, and solar geometry. Note that the only portion of the image that is eligible for retrieval lies inside the region defined by along-track lines tangent to the 165∘ scattering angle isoline (yellow dotted lines).
Hyper-angular polarized cloud retrievals from AirHARP
Before we discuss how the retrieval is applied to the AirHARP data, we will
first walk through an AirHARP measurement. As the AirHARP instrument images
a scene for a particular solar geometry, each view sector captures a range
of scattering angles unique to each of the 120 view sectors and
wavelengths. Figure 3 shows an example of the AirHARP instantaneous
scattering angle coverage for a simulated observation at 15:22 UTC over Lake
Michigan on 19 June 2017 during the NASA Lake Michigan Ozone Study (LMOS)
field campaign. This target was chosen because of the cloud conditions
present during the observation, and the solar geometry allows for retrievals
across the swath and along the entire length of the observation. Figure 3
shows a simulated cloudbow as it would appear in a single AirHARP snapshot
if the entire detector was capable of sampling at 670 nm. This cloud field
was simulated using a CDR of 10 µm and CDV of 0.01, with the same solar and
viewing geometry of the LMOS observation. Note that this is the scattering
angle coverage for a single snapshot, and when AirHARP flies over a cloud
deck, it is taking two snapshots a second. This means a different portion of
the detector is imaging the same cloud target from image to image, which
also suggests that the scattering angle observed at the target changes image to
image as well. From the perspective of the detector, the target travels from
the front of the detector to the back during a full angle observation,
reflecting solar light at different scattering angles as the instrument
flies over it. Therefore, only along-track pixel columns inside the
yellow dotted lines in Fig. 3 contain pixels that are eligible for a
polarimetric DSD retrieval. This work does not perform a retrieval on any
targets observed outside these lines. Outside these lines, the reduced
scattering angle coverage at the upper end of the cloudbow range begins to
truncate the signal from the supernumerary bows. Because the majority of the
size distribution information is encoded in the supernumerary bows (145–165∘), it is important that the full scattering angle range is preserved.
The same simulation as Fig. 3, now with along-track view sector (zenith angle) isolines (a). A push broom is made when a view sector images consecutive information along-track, shown for seven view sectors, separated by 7.5∘ each (b). Because cross-track pixels represent a cross section of the cloudbow, they are also proxies for scattering angle. Note that the cloudbow distribution is different for each view sector push broom. Since each push broom is projected on a common grid, any pixel or superpixel in common to all of the views can generate a discrete polarized structure. This measurement can be compared to Mie simulations to retrieve CDR and CDV at the target resolution.
Figure 4 shows the view sector isolines of AirHARP over the same snapshot
from Fig. 3. The AirHARP wide FOV covers view sectors from ±57∘, but note that the cloudbow only covers a subset of these.
Push brooms are made from individual view sectors as the instrument flies
over the cloud field. Figure 4b shows examples of push brooms built from
cloudbow content in Fig. 4a isolines. If AirHARP was to fly over this
simulated field, the cloudbow would transition from a concentric space in
the raw image to a linear one in the push brooms. This occurs because each
view sector only observes a specific cross section of the cloudbow at any
one time, and the structure of the cross section is maintained due to the
geometry of a single view sector. Figure 5 shows the actual AirHARP
observation during LMOS, in total (top) and polarized reflectance (bottom),
at view sectors near +38∘ during the time and day used to simulate
Figs. 3 and 4. The red–green–blue (RGB) composite image of the polarized reflectance
displays the cross-track cloudbow structure of the segment near +38∘
in the Fig. 4b simulation. The polarized reflectance image shows the
wavelength dependence in the polarized cloudbow structure, which is absent
from the total reflectance image. Also, the appearance of the cloudbow in
this push broom is highly variable compared to the simulation in Figs. 3
and 4, which reflects the heterogeneity in the cloud field seen in total
reflectance.
AirHARP data taken at the same time, location, and geometry as Figs. 3 and 4 reveal a heterogenous cloud field in total reflectance (a) and a cloudbow in polarized reflectance (b). The linear distribution of cloudbow oscillations is heterogenous compared to the Fig. 4b simulation and reflects the variability in the cloud field. Both images are RGB composites of push brooms from 440, 550, and 670 nm view sectors near +38∘, presented without axes for visual purposes only. A single gridded pixel in this image represents 50 m, and the scene stretches approximately 37 km along-track by 5 km cross-track.
Since a single target moves across the detector in consecutive snapshots,
there will always be a location in each of the 120 push brooms that
represents that target on the ground, and any cloudbow target appearing in
multiple sector views having sufficient scattering angle range can be used
in a polarimetric cloud DSD retrieval. Figure 6 shows several examples of an
AirHARP 200 m superpixel retrieval of different regions of the LMOS cloud
field shown in Fig. 5 using hyper-angular, co-located information. Error
bars represent 2 times the standard deviation of the polarized reflectance
measured by the pixels inside the superpixel bin. Superpixels are
constructed from finer-resolution native pixels to increase SNR and mitigate
other potential artifacts in the data. These artifacts will be discussed in
Sect. 6. Note that Fig. 6a and b both represent narrow DSDs with low
CDV values, though the difference in CDR causes a shift in the location of
the observed supernumerary bows. Figure 6c and d are wider DSDs with
higher CDV values, with eroded supernumeraries. As the DSDs become wider and
wider, this retrieval method becomes less and less accurate at inferring
CDV, as the supernumerary region becomes monotonic and linear. The CDR
values retrieved in Fig. 6 are typical of non-precipitating stratocumulus
cloud fields (Pawlowska et al., 2006), and CDV values are similar to those
found by Alexandrov et al. (2015) using RSP measurements over marine
stratocumulus.
Several examples of the traditional parametric fit retrieval applied to AirHARP hyper-angular polarized reflectance measurements for 200 m superpixels. Panels (a) and (b) signify narrow DSDs with small CDV values. In panels (c) and (d), the eroded supernumerary bows suggest wider DSDs. Error bars represent the 2σ standard deviation of the measurements inside the superpixel. Note that while the χred2 in (a) is larger than our 1.5 threshold, the overall fit to measurement generates a valid RMSE.
The hyper-angular retrieval requires data that are captured over a short time
window as AirHARP flies over a cloud: it takes time for the AirHARP backward
angles to image the same location on the ground as the forward angles. The
differences in time depend on the instrument-level flight speed and
the difference in altitude between the instrument and target. For the LMOS
campaign, the difference between ±57∘ observations was 112 s (∼2min) for a nominal UC-12 flight speed of 133 ms-1 at 4.85 km of altitude above the cloud deck. Note that the actual aboveground
altitude was 8 km, but the cloud deck was geolocated to be 3150 m on
average. Therefore, the hyper-angular retrieval requires cloud constancy
over this time interval. If we only include the angles used in the cloudbow
retrieval, the time interval between the views with the largest angular
separation is reduced to a minute. A study with the HARP CubeSat at an estimated
400 km orbital altitude and 7.66 kms-1 ISS speed requires ∼160s (∼2.5min) for the same full-angular coverage
over the same cloud target. In this way, the HARP hyper-angular retrieval
still requires an assumption of homogeneity in a short time window over a
narrow pixel.
Nadir push-broom images for 670 nm of total intensity (a) and polarized intensity (b), as well as for the retrieved CDR (c) and CDV (d) for 200 m (4×4) gridded superpixels with access to 135–165∘ in scattering angle using hyper-angular co-located data. Quality-flagged retrievals are screened out (white). Note that the polarized reflectance is smoother compared with the reflectance image, and both represent nadir (-0.003∘) view sector push brooms. The general locations of each retrieval from Fig. 6 are identified in red. The scene stretches 3 km cross-track and 34 km along-track.
With this in mind, any liquid water cloud pixel in the AirHARP wide FOV that
samples scattering angles between 135 and 165∘ can be used to retrieve
CDR and CDV. This constraint is used in several other polarimetric studies,
though with a slight discrepancy on the start of the lower bound (Di Noia et
al., 2019; Alexandrov et al., 2015). Shang et al. (2015) found that using
a 137–165∘ scattering angle range as opposed to the operational
POLDER 145–165∘ improved many of the CDR and CDV retrievals,
specifically for CDR>15µm (Shang et al., 2019). The upper
bound of 165∘ is consistent between studies dating back to Breon
and Goloub (1998): the bulk of the microphysical information lies in the
supernumerary bows, and the assumption of a structureless Usca breaks
down after this point (Alexandrov et al., 2012a). Figure 7 shows an example
of how individual pixel retrievals generate a spatial distribution of CDR
and CDV for those that access this cloudbow scattering angle range. Each
pixel is first conservatively masked for non-clouds using the nadir 670 nm
intensity push broom (-0.003∘ VZA) using a conservative threshold
of 0.06 Wm-2sr-1nm-1 to avoid cloud holes and views of
Lake Michigan below. All pixels are aggregated to 4×4 resolution (200 m), and
the polarized radiances (LP,670nm) are converted into polarized
reflectances via Eq. (3) before entering the retrieval process. The portion
of the image capable of retrieval stretches 34 km along-track and 3 km
cross-track.
A zoom of two sectors of the AirHARP polarized cloud retrieval for the LMOS cloud field. The intensity image (top) shows both a heterogeneous (a) and a homogenous region (b), defined by the distribution of CDR and CDV, as well as visual cues from the total reflectance. Large-eddy simulations of clean clouds (c), performed by Miller et al. (2018), show that high CDV (veff) and low CDR (reff) typify cloud periphery regions, and low CDV and higher CDR occur in the core of the clouds. Similar CDV–CDR relationships are seen in the AirHARP retrievals (a) at 200 m resolution.
The distribution of CDR and CDV in AirHARP data is consistent with prior
studies and physical phenomena. Because the cloud case observed during LMOS
was heterogenous, there are several examples of how cloud substructure can
give different retrievals. Figure 8 takes a few areas from Fig. 7 and
zooms in on their retrieval results. Figure 8b shows a uniform sector of the
cloud field, described this way because of its visual homogeneity in both
intensity and CDR as well as the narrow and consistent CDV retrievals over many
pixels. The results here suggest that the supernumerary bows are well-defined and
the cloud pixels have narrow size distributions. Figure 8a shows a region of
the same leg that is heterogeneous in CDV, and the intensity and CDR
distribution suggest that this area is a region of convection: larger CDR in
the cloud core, or central area of the cloud, and smaller CDR retrieved on
the periphery, where the intensity is lower. We will look at this phenomenon
in more detail in the AirHARP data in the sections below. Here we point out
that large-eddy simulations (LESs) of similar heterogenous clouds show
similar spatial distributions of intensity, CDR, and CDV (Miller et al.,
2018), with one representative case shown in Fig. 8c. Miller et al. (2018)
simulate LES clouds using vertical weighting functions that take into
account the distribution of reflectance at the edges of the cloud, echoing
theoretical recommendations made by Platnick (2000).
While these simulations can assume any resolution, the AirHARP retrievals
are performed at 200 m in this study and even coarser resolutions from space.
The small-scale variability in the cloud field can also be missed by MODIS
radiometric analyses, for example, which assumes constant CDV in their
droplet size retrieval. This is one of the strongest benefits of polarized
cloud retrievals: a quantitative measurement of heterogeneity through CDV
information, which is not possible with traditional radiometric methods.
This has serious implications for climate in terms of quantifying cloud
development, brightness, and lifetime, aerosol–cloud interaction, and
reducing the uncertainty in global radiative forcing due to clouds and
aerosols. In the following section, we explore how we can extend the AirHARP
spatial retrievals of CDR and CDV to study changes in size properties along
the cloud field and the impact of resolution on the retrieval itself.
Analysis of intensity (blue), CDR (red), and log (CDV) (green) anomalies from the mean following the black transect along the nadir intensity push broom for a segment of the cloud field measured by AirHARP (bottom). Using the spatial distribution of intensity as a proxy for cloud optical thickness (COT), we can visually identify what appear to be cloud cores (blue blocks) and cloud periphery (orange blocks) regions. CDV trends are opposite to intensity and CDR in both regions, but wider DSDs with smaller CDR appear at cloud peripheries, while larger CDRs with narrow DSDs appear in cloud cores. The label X to the left of the intensity image is an abbreviation for cross-track distance from the image center line.
Spatial scale analysis
Because the AirHARP retrievals of CDR and CDV are images, any sector of the
cloud field can be analyzed by taking a transect of pixels along- or
cross-track. In Fig. 9, we take a 34 km pixel transect of the cloud field
(shown in the inset intensity image with a black line) and compare the
anomaly from the mean along the track for intensity, CDR, and CDV. The CDV
is log-scaled to linearize its several orders of magnitude range. Positive
CDR anomalies describe larger droplet sizes, and positive CDV anomalies
correspond to wider distributions. Any position along the transect of the
cloud field lines up exactly with three unique points in the plot, and the
correlation between the three curves suggests information about the nature
of the cloud field. It is important to note that we are using the cloud
intensity as a proxy for COT, which is orthogonal to CDR (Nakajima and King,
1990). In some locations in the plot, intensity (COT) and CDR are correlated
with each other and anticorrelated with CDV. Blue blocks define
unambiguous locations in the cloud field where intensity and CDR have
positive anomalies while the CDV anomaly is negative, whereas orange blocks
give the opposite: intensity and CDR are negative and CDV is positive. If we
define cloud cores as the pixels brightest in intensity (blue) and cloud
peripheries as darkest in intensity (orange) then cloud cell sizes appear
to be of the order 1–4 km, both comparable to and slightly larger than
traditional MODIS cloud droplet size retrieval products (1 km). Comparison
to the traditional cloud product resolution is notable because, in some
regards, the 1 km resolution is adequate to resolve cloud microphysics of
the cloud cores. However, when cores and peripheries are found in the same 1 km pixel, issues in separating DSDs will arise. Since AirHARP is an aircraft
instrument and flies beneath 20 km, its resolution will be better than an
equivalent AirHARP instrument in space, so this fine-scale
variability will likely not be captured by HARP CubeSat or HARP2. Regardless, this
result emphasizes the importance of small-scale sub-kilometer sampling of
cloud fields because cloud heterogeneity and microphysical processes may be
lost in the large spatial resolutions of spaceborne instruments.
There are physical explanations for the relationships we see between
intensity, CDR, and CDV on the spatial scales of Fig. 9. Liquid water
droplets that form at the base of adiabatic clouds, such as cumulus and
stratocumulus, see their largest sizes at cloud top (Platnick, 2000)
and further grow by longwave radiative cooling, small-scale turbulence, and
collisional processes (de Lozar and Muessle, 2016). On the periphery,
evaporation removes smaller droplets, and at the same time, the entrainment of
warm air and/or aerosol here may enhance droplet growth. There are many
competing theories as to the net effect of aerosol entrainment on droplet
growth (Small et al., 2009, and references therein), but these two opposing
effects may create a larger DSD variance on the periphery. Alexandrov et al. (2015) and Platnick (2000) suggest that CDR changes occur vertically
in the cloud periphery. Therefore, multi-angle polarimeters that can sample
deeper into the periphery could retrieve a larger CDV in these areas. The
above LES study of broken marine stratocumulus by Miller et al. (2018) also
shows higher CDV (lower CDR) in the cloud periphery and lower CDV (higher CDR) in
cloud cores, as shown in Fig. 8c. In the present study, all of these
processes cannot be decoupled, but these promising results show that AirHARP
retrievals are consistent with current research and theories of cloud
microphysics.
Scale analysis for the scene in Fig. 5 with 200 m(b) and 600 m(c) resolutions. The Mie P12 curves retrieved from the AirHARP data are shown with gray lines in panels (d), (e), and (f), and the direct 600 m superpixel P12 retrieval is shown in red for three difference cases: narrow (d), two-regime (e), and mixed (f) DSDs. The boxes to the right-hand side show CDR and CDV results for each of the nine 200 m pixel retrievals within the outlined 600 m superpixel. Results of the direct retrieval at 600 m resolution are shown on the top of the boxes. The location of each retrieval site is given as corresponding colored blocks in the retrieval image for narrow (red), two-regime (peach), and mixed (yellow). Note that the 600 m retrievals shown in (e) and (f) give wider CDV results than (d), mainly due to competing size properties at the 200 m level.
Furthermore, the AirHARP pixel resolution can be degraded and used to
understand the effect of sub-pixel variability on the DSD retrieval itself,
as shown in Fig. 10. Figure 10a and b are repeated from Fig. 7a and
b, and both represent the 200 m CDR retrieval, while Fig. 10c shows the
CDR product at 600 m resolution. To calculate the 600 m product, the gridded
polarized reflectance data at the original 50 m resolution are aggregated
into 600 m superpixels. Next, the superpixels pass through a screening
process: this eliminates low-intensity superpixels that represent cloud
holes and marginal situations. Third, the superpixels enter the retrieval
process. Thus, Fig. 10c is not a resampling of Fig. 10b but a new
retrieval using a different resolution as input. This study does not examine
the effect of cloud screening at the different resolutions, only the effect
of the degraded resolution using pixels that have been properly identified
as clouds at the finer resolution.
The plots on the left-hand side of Fig. 10d–f are the retrieved
P12 curves, which emphasize how the nine 200 m retrievals, shown as gray
lines, compare to the single 600 m retrieval, which is shown as a red line.
The two boxes to the right of each of the retrieved P12 curve plots in
Fig. 10d–f represent the retrieved CDR (middle column) and CDV (right
column) for the colored superpixel boxes located in Fig. 10a–c. The 600 m
CDR or CDV result is given in the title above each box and represents the
retrieval for the entire nine-box square underneath, whereas the 200 m CDR or
CDV results are shown inside each colored sub-box.
Figure 10d shows that the narrow DSD retrievals are robust against
resolution degradation; if we take the 200 m retrievals as truth, the 600 m
result agrees within community standards (10 % σCDR and
50 % σCDV; Mishchenko et al., 2004). The 600 mP12
resembles the 200 mP12 curves, both in the location of supernumerary peaks
and overall structure. Figure 10e shows a retrieval that appears to
represent the cloud periphery, as the intensity image shows the appearance
of a cloud cell near the superpixel. Here, the CDR retrieval gives higher
values in the center of the structure and smaller values on the sides,
consistent with prior studies. Figure 10e shows two conflicting P12 regimes. Here, 200 m DSDs with CDR between 6.6 and 7.5 µm separate into two
modes: CDV>0.08 and CDV between 0.048 and 0.028. While the
primary bow around 143∘ is preserved between retrieval scales, the
600 m retrieval gives a CDV of 0.047, a value that appears to represent the
mean of the nine pixels but satisfies neither regime. Shang et al. (2015)
and Miller et al. (2018) show similar results in theoretical and
observational mixed DSDs. Note that the combination of gamma distributions inside
a superpixel is not itself a gamma distribution, though retrievals that
contain sub-pixel heterogeneity in the DSD still attempt to infer gamma
distribution properties from a signal that may not represent one (Shang et
al., 2015). The rainbow Fourier transform method (Alexandrov et al., 2012b) may distinguish these two
modes at the 600 m scale, but the result could not be independently
validated if it was performed with RSP single-pixel sampling, as it is here
with AirHARP data. Figure 10f shows another retrieval done close to the
cloud periphery, but this time, the retrieved 200 mP12 curves show a wider
spread of CDV values compared to the results shown in Fig. 10d–e.The
retrieved 600 m fit generates a curve that does not represent any of the
sub-pixel results. The consequence is a broad 600 m CDV that reflects the 200 m variability but not the mean magnitude of the nine sub-pixels, as the 600 m
retrieved value for CDV is 0.284, while the nine individual pixels return
values 0.086 to 0.186. Here, the sub-pixel variability smears out the
supernumerary bows. This result is a well-known consequence of mixed DSDs in
a large superpixel, but it does not provide any information as to which parts
of the cloud inside the superpixel contain narrow vs. wider DSDs. The
interpretation of CDR and CDV at large pixel sizes is still widely debated,
but fine-resolution spatial data provided by AirHARP and its retrievals can
provide a meaningful advancement in this direction.
Discussion of limitations and uncertainty
The first limitation of this method concerns the parametric retrieval, which
assumes a single-mode DSD that can be described by CDR and CDV alone.
Situations that do not fit this assumption may not be retrievable, as
mentioned above. We note that other retrieval methods will overcome this
limitation. However, for the purposes of this initial demonstration, the
assumptions of the parametric retrieval seem to be met by our example.
This being said, we cannot ignore the possibility of optically thin upper-level clouds (τcld<1) moving over the geolocated cloud
deck. If these clouds exist, they will appear to “move” from angle to
angle, as our current geolocation algorithm, discussed later on, focuses on
the layer of clouds that is producing the dominant signal. This also means
their impact on the cloud retrieval will change from angle to angle but
will likely affect only two or three view sectors at most, with a weak
contribution to the measurement. Therefore, this is not expected to
significantly contribute to the overall cloudbow fit. All fits shown in this
paper lie beneath our successful RMSE threshold, supporting this claim,
though other retrieval methods could tease out the signals from both cloud
layers when properly geolocated (Alexandrov et al., 2012b, 2016b).
This limitation, the need to map the different angular measurements to a
target elevation, is a significant challenge with AirHARP data. If the
target were Earth's surface, then a digital elevation map could be used, but
clouds appear at a range of altitudes and are not always easily predictable
in height, distribution, time, or space. Therefore, an iterative method
determines, within a gridded pixel, the altitude that provides zero parallax
displacement in the cloud field. We use the location of several
distinguished cloud features, as observed from at least two view sectors, to
determine the average cloud height of the dataset. Currently, this single
cloud height estimate is applied to the entire dataset during the Level 1
geolocation process. Because there is no such thing as a plane-parallel
cloud, both the parallax method and the assumption of constant cloud-top height
introduces uncertainty in the retrieval. Where possible, the altitude of the
scene is verified with heights retrieved from data from other coincident
instruments. Conservative cloud identification and binning pixels to 200 m
(4×4) resolution further mitigates the error introduced by using this mean
height. In the case shown in Fig. 5, the derived height is (3150±50) m, for which the uncertainty is the resolution that guarantees no
movement from view sector to view sector. A self-check on the validity of
these assumptions is the goodness of fit of each retrieval. In our example,
while the RMSE of the cloud field varies, all retrievals shown successfully
fit the RMSE threshold defined above. Therefore, we believe errors in our
geolocation do not contribute significantly to the results of our study
shown at 200 or 600 m resolutions. However, when studying broken or popcorn
cumulus clouds, a proper 3D geolocation of the cloud will be required. The
HARP science team is currently developing an optimized pixel-level
topographic algorithm to mitigate any multi-layer or cloud projection biases
in future retrieval studies, as well as other quality assurance corrections
beyond the scope of this work.
During an aircraft campaign, it is also important to maintain calibration
accuracy in flight as many factors such as temperature, pressure, vibration,
and humidification can alter the quality of the measurements. AirHARP did
not have an in-flight calibration mechanism during LMOS, so it is
challenging to verify the accuracy of the in-flight data. We also realized
in lab studies that AirHARP generates internal optical etaloning. The
etaloning produces concentric fringes on the raw image, which transform
into linear bands at the push-broom level. Typically, a lab flat field
corrects for this effect, but our flights show that the etaloning occurs in new
locations at the detector during flights. The fringes are variable in
strength and size across each view sector but are easily removed over
homogenous targets with our current correction scheme. Because the cloudbow
also transforms from a concentric to linear space at the push-broom level,
cloudbow cases are especially tricky to correct. Luckily, the effect of the
fringes on the hyper-angular retrieval is nearly random: the retrieval is a
structural fit from angular data that covers many unique positions in the
detector. Therefore, the etaloning can be treated as a decrease in SNR in
the measurement, which we estimate as an extra 1σ error contribution.
Due to the well-resolved retrievals in Figs. 6–10, it is clear that the
etaloning does not contribute significantly to the CDR and CDV products,
though the fringe contribution would make it more difficult to retrieve
above-cloud aerosol signals hidden inside the cloudbow measurement, if
applicable. For this reason, we are currently developing a new correction
algorithm to remove the fringing from heterogenous datasets and an internal
calibrator for HARP2 on the PACE mission. With frequent flat-field
calibrations, the etaloning can be immediately corrected in a variety of
environments. Also, there is evidence that the cloudbow retrieval itself
could be used to remove the fringe signal from AirHARP data. While the cloud
signal changes across multiple full-size images, the fringe structure is
stable for the same view sector. This allows for the characterization and
removal of the fringes uniquely from cloudbow datasets. This is a promising
correction technique that will be explored in future work.
Finally, the results of the retrieval presented in this paper are
challenging to validate and even difficult to compare with other
retrievals. The MODIS Terra and Suomi-NPP VIIRS radiometers passed over the
same location on the ground as our example over an hour after the AirHARP
observation, and while the GOES-R Advanced Baseline Imager (ABI) radiometer
is coincident, its 1–2 km CDR retrieval resolution is difficult to reconcile
with the variability observed in the cloud field at finer AirHARP
resolution, as suggested by our study presented in Fig. 10. Intercomparing
GOES-R and AirHARP retrievals will be performed in a future study; the
constant coincidence of GOES-R makes it very attractive for field campaigns
that once relied on the sparse coincidence of polar-orbiting or
ISS-based sensors. AirHARP was also the only Earth-observing polarimeter
present on aircraft or in space during LMOS with these capabilities for cloud
retrieval. None of the field experiments in which AirHARP has flown (LMOS or
ACEPOL in 2017) focused on clouds, allowing for only a few cloud targets of
opportunity during both campaigns. For example, the observation presented in
this paper was the only one in which AirHARP achieved full angular coverage
over a continuous cloud field and one that could be geolocated to a
constant height over the full push broom with little impact to the retrieval
itself. A dedicated future aircraft campaign for clouds, specifically one
that allows coincident AirHARP observations with other compatible
cloud-measuring or -retrieving sensors at similar spatial resolution, would
be beneficial for validation. Optimally, coincident HARP space and AirHARP
aircraft observations would greatly improve our ability to validate the
differences in retrieval resolution for cloud cores and peripheries, across a
wide swath, and for unique global locations and aerosol source regions.
Conclusion
We used the AirHARP hyper-angular measurements at a single wavelength
(670 nm) in a traditional parameterization scheme to demonstrate the ability
of the HARP concept to characterize cloud microphysical parameters across a
cloud field at sub-kilometer spatial resolution. HARP measurements can also
be applied to the four polarized wavelengths, akin to Breon and Goloub
(1998) and Shang et al. (2019), but this type of retrieval is more sensitive
to resolution and calibration than the hyper-angular technique presented
here and most importantly requires homogeneity at cross-track scales (3 km). In the hyper-angular method, we can achieve the same results at the
pixel scale (0.2 km) and resolve the spatial inhomogeneity across the track.
Variability within a 3 km scale retrieval can easily steer the parametric
retrieval towards larger CDV (Fig. 10e; Shang et al., 2015; Miller et al.,
2018), and calibration biases that affect an individual view sector (i.e.,
etaloning) will be much more prominent and systematic in this approach than
in the hyper-angle retrieval. Using data from multiple channels (Shang et
al., 2019) serves as an excellent cross-calibration and intercomparison with
other instruments over narrow DSD marine stratocumulus (Alexandrov et al.,
2015; Knobelspiesse et al., 2019), all of which will be explored in future
work.
The HARP concept enables highly resolved, hyper-angular polarimetric
retrievals of liquid water cloud microphysical properties. Using a
heterogenous cloud field from the NASA LMOS campaign as an example, AirHARP
datasets allow for sub-kilometer spatial retrievals of CDR and CDV across the
full swath and along the entire flight track. These analyses reveal cloud
substructure and the spatial distribution of DSDs for cloud cores and
periphery regions, which can be easily extended to marine stratocumulus,
trade-wind, and popcorn cumulus clouds. Because of the wide HARP FOV, these
retrievals are possible off the instrument nadir scan line and during nearly
all daytime hours if geometry allows. Combined, these capabilities position
HARP as an instrument capable of cloud DSD retrieval at scales relevant to
climate study and with global coverage from space.
Because of relatively fine-spatial-resolution retrievals across a broad
swath, we were able to perform scale analysis on retrieved DSD parameters by
degrading the resolution and subsampling the hyper-angular polarimetric
retrieval. At the pixel level, we note that large pixel sizes blur DSD
variability, resulting in a retrieval that tries to account for all sub-pixel
regimes but ends in producing an entirely different DSD altogether. The
sub-kilometer retrievals were able to identify small-scale DSD variability
in our heterogenous cloud field. Specifically, we found that there is a
correlation between intensity (a proxy for COT) and CDR and an
anticorrelation with CDV. For places where intensity is high (high COT),
assumed to be cloud cores, droplets were large and size distributions
narrow. The opposite is found along the cloud periphery. These findings may
be related to entrainment and droplet evaporation on cloud edges and
collision–coalescence processes in cloud cores, but further theoretical
study and targeted campaigns are needed. Some of these results are not
limited to the HARP design: producing spatial images of both DSD parameters
can be achieved by other imaging multi-angle polarimeters. Producing these
images with a spatial resolution sufficiently fine to illuminate cloud
processes along with the spatial coverage to encompass an entire
two-dimensional cloud field is unique to the HARP concept.
Future work anticipates extending these concepts to multi-modal size
distributions and combining multi-spectral and multi-angle sampling to
retrieve cloud size properties and other information: aerosol-above-cloud
microphysics, cloud height, and thermodynamic phase, as well as a stronger
definition of CDR and CDV for large superpixels that contain internal DSD
variability. With the upcoming launch of HARP CubeSat in 2019 and HARP2 in
the early 2020s, the same retrieval concepts applied here on AirHARP data
can be used to connect cloud properties to global radiative forcing, improve
radiometric retrievals, and provide strong science rationale for including
high-resolution, hyper-angle imaging polarimetry on future Earth science
space missions.
Data availability
Quality-assured AirHARP data from the NASA LMOS campaign to Version 000 can
be found at https://www-air.larc.nasa.gov/cgi-bin/ArcView/lmos (last access: 4 April 2020).
Future version updates are planned, as is the delivery of more LMOS datasets
to the archive in 2020. Data used in this paper and L2 products can be
found at
https://www.dropbox.com/sh/imd9quoloeqhsum/AADeyvMchZSrabM8nJ7VEgi-a?dl=0 (last access: 4 April 2020, McBride, 2020).
Author contributions
BAM actively participated in the NASA LMOS field campaign by operating AirHARP
in the aircraft, performing ground calibrations, and L1 processing the
datasets used in this paper. BAM wrote the retrieval code, conducted error
analysis, and contributed to the interpretation of the results in this paper. LAR, JVM, and
HMJB provided substantial editing support, and the latter developed the
general algorithm used for AirHARP L1 processing of LMOS datasets. WB was
the first to use the algorithm developed by BAM to generate the first spatial
CDR and CDV products from this cloud field, which were quality-assured and
optimized in this paper.
Competing interests
The authors declare that they have no conflict of interest.
Disclaimer
The statements contained
within the research article are not the opinions of the funding agency or the U.S. government, but
reflect the author's opinions.
Acknowledgements
The authors would like to thank Dominik Cieslak, Roberto Fernandez-Borda, Kevin Tonwsend, and Paul Pongsuphat for their contributions to supporting AirHARP in the lab and the field, as well as
Jassim Al-Saadi, Charles Stanier, and R. Bradley Pierce for hosting the participation of the AirHARP
instrument during LMOS. The authors also thank Graham Feingold, Michael Garay, and Daniel Miller for
insight and fruitful discussions.
Financial support
This study is supported and monitored by the National Oceanic and Atmospheric
Administration – Cooperative Science Center for Earth System Sciences and Remote Sensing Technologies
(NOAA-CESSRST) (grant no. NA16SEC4810008). Brent A. McBride has been supported by the City College of New York, the NOAA-CESSRST program, and NOAA Office of Education
(Educational Partnership Program). Brent A. McBride has received funding from the NASA Earth and Space
Science Fellowship (grant no. 18-EARTH18R-40) under the NASA Science Mission Directorate. Henrique M. J. Barbosa has received funding from FAPESP (grant no. 50 2016/18866-2) and from CNPq (grant no. 308682/2017-3).
Review statement
This paper was edited by Alexander Kokhanovsky and reviewed by Gerard van Harten and two anonymous referees.
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