-
Atmos. Meas. Tech., 11, 5471–5488,
2018https://doi.org/10.5194/amt-11-5471-2018© Author(s) 2018. This
work is distributed underthe Creative Commons Attribution 4.0
License.
Retrieval of snowflake microphysical properties
frommultifrequency radar observationsJussi Leinonen1,2, Matthew D.
Lebsock1, Simone Tanelli1, Ousmane O. Sy1, Brenda Dolan3, Randy J.
Chase4,Joseph A. Finlon4, Annakaisa von Lerber5, and Dmitri
Moisseev5,61Jet Propulsion Laboratory, California Institute of
Technology, Pasadena, California, USA2Joint Institute for Earth
System Science and Engineering, University of California, Los
Angeles, California, USA3Department of Atmospheric Science,
Colorado State University, Fort Collins, Colorado, USA4Department
of Atmospheric Sciences, University of Illinois at
Urbana-Champaign, Urbana, Illinois, USA5Radar Science, Finnish
Meteorological Institute, Helsinki, Finland6Institute for
Atmospheric and Earth System Research/Physics, Faculty of Science,
University of Helsinki, Helsinki, Finland
Correspondence: Jussi Leinonen
([email protected])
Received: 14 March 2018 – Discussion started: 27 March
2018Revised: 29 August 2018 – Accepted: 12 September 2018 –
Published: 5 October 2018
Abstract. We have developed an algorithm that retrieves thesize,
number concentration and density of falling snow frommultifrequency
radar observations. This work builds on pre-vious studies that have
indicated that three-frequency radarscan provide information on
snow density, potentially improv-ing the accuracy of snow parameter
estimates. The algorithmis based on a Bayesian framework, using
lookup tables map-ping the measurement space to the state space,
which allowsfast and robust retrieval. In the forward model, we
calculatethe radar reflectivities using recently published snow
scat-tering databases. We demonstrate the algorithm using
multi-frequency airborne radar observations from the OLYMPEX–RADEX
field campaign, comparing the retrieval results tohydrometeor
identification using ground-based polarimetricradar and also to
collocated in situ observations made us-ing another aircraft. Using
these data, we examine how theavailability of multiple frequencies
affects the retrieval ac-curacy, and we test the sensitivity of the
algorithm to theprior assumptions. The results suggest that
multifrequencyradars are substantially better than single-frequency
radars atretrieving snow microphysical properties. Meanwhile,
triple-frequency radars can retrieve wider ranges of snow
densitythan dual-frequency radars and better locate regions of
high-density snow such as graupel, although these benefits are
rel-atively modest compared to the difference in retrieval
perfor-mance between dual- and single-frequency radars. We
alsoexamine the sensitivity of the retrieval results to the fixed
a
priori assumptions in the algorithm, showing that the
multi-frequency method can reliably retrieve snowflake size,
whilethe retrieved number concentration and density are
affectedsignificantly by the assumptions.
1 Introduction
Atmospheric ice formation and growth processes have a ma-jor
impact on the Earth’s radiative balance and on the hy-drological
cycle. Ice clouds and snowfall occur nearly every-where, as ice
processes occur at high altitudes even in ar-eas where freezing
temperatures at the surface are rare (Fieldand Heymsfield, 2015;
Mülmenstädt et al., 2015). Ice cloudshave also long been a
challenge for weather and climatemodels (Waliser et al., 2009).
Improving the microphysicsschemes, which describe nucleation of
small ice crystals andtheir transformation into precipitation-sized
particles, is alsocurrently an active area of model development in
which con-ceptually new schemes have been recently introduced
(Har-rington et al., 2013; Morrison and Milbrandt, 2015).
Observational data are needed to evaluate the represen-tation of
ice and snow in models. While direct measure-ments of ice particle
properties can be made in situ, suchmeasurements only produce
limited samples and are diffi-cult and expensive to make,
especially when surface ob-servations are not possible and
aircraft-based measurements
Published by Copernicus Publications on behalf of the European
Geosciences Union.
-
5472 J. Leinonen et al.: Retrieval of snowflake microphysical
properties
are needed. Remote-sensing instruments are able to samplefar
larger volumes. Radars, in particular, can make range-resolved
measurements and thus map the vertical structureof the ice
cloud–precipitation column. However, the inter-pretation of radar
signatures of ice particles is subject touncertainties because the
microwave scattering properties oficy hydrometeors depend on their
size, shape and structure.These are extremely variable, as
deposition growth alone re-sults in diverse and often complicated
shapes, and furthergrowth through aggregation and riming adds to
the complex-ity (Pruppacher and Klett, 1997; Lamb and Verlinde,
2011).
Multifrequency radars have emerged as a potential tool forice
microphysics investigations. It has been recognized fora while that
snowflake size can be constrained with collo-cated measurements at
two different frequencies (Matrosov,1993, 1998; Hogan et al., 2000;
Liao et al., 2005). More re-cently, several studies have shown,
using detailed numeri-cal scattering simulations and empirical
evidence, that triple-frequency measurements provide information on
both thesize and density of icy hydrometeors (Kneifel et al.,
2011,2015; Leinonen et al., 2012a; Kulie et al., 2014; Stein et
al.,2015; Leinonen and Moisseev, 2015; Leinonen and Szyrmer,2015;
Gergely et al., 2017; Yin et al., 2017). The availabilityof this
information has been expected to enable more accu-rate quantitative
estimation of ice water content (IWC) andsnowfall rate and to
provide a method to remotely distinguishand characterize icy
hydrometeor growth processes.
Studies on the triple-frequency signatures of snow have, sofar,
been mostly limited to numerical and theoretical inves-tigations,
as well as empirical studies that demonstrated theplausibility of
the concept. Only very recently have databasesof snow scattering
properties covering a wide range of snowgrowth processes (e.g.,
Leinonen and Szyrmer, 2015; Kuoet al., 2016; Lu et al., 2016)
become available, enabling thedevelopment of a versatile radar
forward model that can pro-duce the radar signatures of many types
of snowflakes. This,together with the expanded availability of
collocated triple-frequency measurement datasets from field
campaigns, hasprovided the prerequisites for the development of a
practicalsnowfall retrieval algorithm for triple-frequency
radars.
In this paper, we introduce a method for retrieving
certainmicrophysical properties of snow – namely, the number
con-centration, size and density – from multifrequency radar
ob-servations. The algorithm is based on a Bayesian frameworkand
uses radar cross sections from detailed snowflake mod-els that
cover a wide range of sizes and densities. In Sect. 2,we describe
the algorithm formulation. Section 3 describesthe datasets used for
demonstrating and evaluating the algo-rithm, and Sect. 4 describes
how the a priori distributionsused in the retrieval were derived.
In Sect. 5, we investigatecase studies of airborne radar data from
the Olympic Moun-tain Experiment–ACE Radar Definition Experiment
2015(OLYMPEX–RADEX’15) coordinated by NASA and com-pare the
retrieval results to ground-based polarimetric radarobservations.
Section 6 describes comparisons to collocated
in situ measurements. Section 7 presents statistical analysesof
the sensitivity of the algorithm to the number of frequen-cies
available and to the a priori assumptions. Finally, we dis-cuss the
implications of the results and summarize the studyin Sect. 8.
2 Algorithm
2.1 Physical basis
The objective of a radar retrieval algorithm for snowfall is
toprovide the best estimate of the microphysical properties ofthe
snowflakes based on the received radar signals. The unat-tenuated
equivalent radar reflectivity factor Ze for a givenwavelength λ
is
Ze =λ4
π5|Kw|2
∞∫0
σbsc(D)N(D)dD, (1)
where σbsc(D) is the backscattering cross section as a func-tion
of the maximum diameter D, N(D) is the particle sizedistribution
and Kw is the dielectric factor defined as Kw =(n2w−1)/(n
2w+2), where nw is the complex refractive index
of liquid water assumed at a reference temperature and
fre-quency.
The attenuation of the radar signal must be accounted forin
radar-only retrieval algorithms. The attenuated reflectivityat
distance r from the radar is given by
Z′e(r)= Ze(r)exp
−2 r∫0
∞∫0
σext(D,r′)N(D,r ′)dD dr ′
, (2)where σext is the extinction cross section. The resulting
re-flectivity is usually expressed in logarithmic units of
decibelsrelative to Z (dBZ), defined by
Z′dB = 10log10Z′eZ0, (3)
where Z0 = 1mm6 m−3. The attenuated reflectivity can bewritten
as
Z′dB(r)= 10log10Ze(r)
Z0−
r∫0
AdB(r′)dr ′, (4)
where AdB is the two-way specific attenuation, that is,
theattenuation in decibels per unit length.
It was shown as early as Hitschfeld and Bordan (1954)that
weather radar attenuation correction is subject to mathe-matical
instabilities that can lead to small errors multiplyingin a
positive feedback loop. Namely, overestimation of at-tenuation in
one radar range bin leads to overcompensationin all subsequent bins
away from the radar, causing overes-timation of the precipitation
signal, which in turn leads to
Atmos. Meas. Tech., 11, 5471–5488, 2018
www.atmos-meas-tech.net/11/5471/2018/
-
J. Leinonen et al.: Retrieval of snowflake microphysical
properties 5473
further overestimation of the attenuation. In
multifrequencyradars, the lower-frequency signals are generally
attenuatedless. In the case of snowfall, the W-band signal can be
sig-nificantly attenuated, the Ka band much less so, and the Kuband
is practically unattenuated by the snowflakes. Thus, theKu-band
radar reflectivity can be used to correct the Ka- andW-band signals
in a stable manner.
We use a technique similar to Kulie et al. (2014) for
at-tenuation correction: we draw samples from the a priori
dis-tribution (described in Sect. 4), calculate both the
Ku-bandreflectivity and the specific attenuation at the Ka or W
bandfor each sample, and fit a function between the reflectivityand
the attenuation. We found that a linear function betweenZdB and ln
AdB fits the relationship well. We validated thisapproach by
computing attenuation afterwards from the re-trieved microphysical
values; the root-mean-square (RMS)difference in the total
attenuation, calculated over all binsin the case shown in Sect.
5.2, is only 0.27dB, so this ap-proximate approach to attenuation
correction seems to workadequately.
Attenuation also results from atmospheric gases and
fromsupercooled liquid water. The gaseous attenuation was
cal-culated and corrected for with the ITU-R P.676-11 model(ITU,
2016), using radio sounding data for the temperature,pressure and
humidity required by the model. The gaseousattenuation varies
spatially since it is dependent on water va-por, but the error
introduced by this is likely small given thatthe maximum two-way
gaseous attenuation in the cases an-alyzed in this study is only
1.1dB at 94GHz (W band), andmuch less at the lower frequencies.
However, supercooledliquid water found in mixed-phase clouds can
cause signifi-cant radar attenuation. However, the radar echo of
the super-cooled water is very weak because of the small size of
thedrops, making it practically impossible, using radar
signalsalone, to detect supercooled water coexisting with ice.
Thus,we do not correct for attenuation caused by supercooled
wa-ter, while acknowledging its role as a potential error
source.
In order to manage the dimensionality of the problem,
themicrophysical properties of the snowflakes must be
parame-terized. We utilize two common assumptions for this.
First,we assume that the particle size distribution (PSD)
followsthe exponential distribution
N(D)=N0 exp(−3D), (5)
where N0 and 3 are the intercept and slope parameters,
re-spectively. Although gamma distributions, and other formsthat
introduce additional parameters, are sometimes used,the exponential
distribution has been found to describesnowflake size distributions
well (Sekhon and Srivastava,1970; Heymsfield et al., 2008). We also
found it to be a goodmatch to the in situ airborne size
distribution measurementsused in this study (see Sect. 6).
Therefore, we find it prefer-able over more complicated
alternatives. Second, we assumethat the mass of snowflakes is given
as a function of the di-
ameter as
m(D)= αDβ (6)
as has been commonly done in microphysics literature
(e.gPruppacher and Klett, 1997). In the following section,
weexplain how these assumptions are used to compute the
radarreflectivities.
2.2 Forward model
The forward model in an inversion algorithm is responsi-ble for
calculating the measurements that correspond to agiven state vector
– in our case, the radar reflectivity at eachwavelength given the
microphysical parameters. The simu-lation of radar reflectivity
from snowflakes whose diametersare comparable to or larger than the
wavelength is knownto require calculations that account for the
internal struc-ture of the snowflake (Petty and Huang, 2010; Botta
et al.,2011; Tyynelä et al., 2011). Recently, such calculations
havebeen used for a wide variety of model snowflakes in orderto
establish databases of scattering properties. We chose acombination
of two such datasets as the basis of our for-ward model: the rimed
snowflakes of Leinonen and Szyrmer(2015) and the OpenSSP database
of Kuo et al. (2016). Thedataset of Leinonen and Szyrmer (2015)
covers a wide rangeof snowflake densities, but due to the
relatively coarse reso-lution of the volume elements, it mostly
contains moderate-and large-sized snowflakes. The Kuo et al. (2016)
dataset wasused to augment the set of snowflakes used by the
forwardmodel at small sizes, D < 1mm.
While there have been considerable recent advances onthe problem
of modeling snowflakes produced by differentice processes and
calculating their scattering properties, theabundance of available
snowflake models leads to anotherquestion: which set of snowflakes
should be used by the for-ward model in a particular situation? We
use an approachthat does not force us to select any one dataset.
Instead, thescattering properties are given as a function of mass
andsize: σ(D,m), where σ can be one of σbsc, σsca or σabs, thelast
two being the scattering and absorption cross
sections,respectively, with σext = σsca+ σabs. The function
σ(D,m)is constructed by organizing all model snowflakes from
thecombined scattering database into bins by D and m; we use128×
128 logarithmically spaced bins to cover the range ofdiameters and
masses found in the dataset. For each bin, wecompute the average of
σnorm ≡ σ/mγ , where γ = 2 for thebackscattering and scattering
cross sections, and γ = 1 forthe absorption cross section. The
reason for the normaliza-tion by m2 or m is that in the Rayleigh
scattering regime(D� λ) σbsc and σsca are proportional to m2, and
σabs isproportional to m (Bohren and Huffman, 1983). It followsthat
the normalized cross sections are roughly constant atthe
small-particle limit. To smoothen the binned values, thesamples
used in the averaging are weighted using a Gaussianfunction of the
distance from the bin center, with a standard
www.atmos-meas-tech.net/11/5471/2018/ Atmos. Meas. Tech., 11,
5471–5488, 2018
-
5474 J. Leinonen et al.: Retrieval of snowflake microphysical
properties
deviation of 0.15 for both lnD and lnm. A continuous func-tion
of the form
ln σnorm(ln D, ln m) (7)
is then formed by interpolation among the bin centers. Notall
bins have snowflakes in them; for those we are unableto do the
averaging and instead assign the scattering prop-erties to zero.
This means that the limits of the coverage ofthe snowflake database
in the (D,m) space are effectively as-sumed to be the limits of the
natural variability in snowflakes.While this is not exactly true,
the combined database doescover a wide range of microphysical
processes. The assump-tion that the cross section goes to zero (as
opposed to, forinstance, extrapolating it) outside the coverage
area also ef-fectively truncates the integrals in Eqs. (1) and
(2).
With a method to calculate the cross sections as a functionof D
and m, it is relatively straightforward to compute
radarreflectivities from the microphysical inputs. As can be
seenfrom the previous section, the input parameters for the
for-ward model are N0, 3, α and β. We start with a fixed set of1024
logarithmically spaced integration points that span theinterval
[Dmin,Dmax]. The parameters α and β are used tofind the
corresponding masses using Eq. (6). The cross sec-tion for each
integration point is then found from the lookuptable using
interpolation. The cross sections are multipliedwith the size
distribution determined by N0 and3, which al-lows us to compute the
integral in Eq. (1) with fixed-pointnumerical integration.
2.3 Retrieval
A radar retrieval algorithm needs to invert Eqs. (1) and (2)such
that an input ofZ′e at one or more wavelengths yields theproperties
of N(D) and m(D). The inversion is unavoidablyinexact, as the wide
variety of snowflake number concentra-tions, size distributions and
densities leads to a variability toolarge to constrain with a few
radar reflectivities. The retrievalmust be performed in a
probabilistic sense, deriving the mostlikely solution from the
possible alternatives, using the priorinformation about snowflake
properties as a constraint.
The retrieval problem is commonly stated as finding a
statevector x that explains a given measurement vector y. The
for-mulation of the state vector depends on which variables
arechosen for retrieval and which ones are simply assumed. Inour
experimentation with different combinations, we foundthat the most
stable solution was to retrieve N0, 3 and α.The β parameter was
fixed at 2.1. While β varies in na-ture, many experimental and
modeling studies (e.g., Mitchellet al., 1990; Pruppacher and Klett,
1997; Westbrook et al.,2004; Leinonen and Moisseev, 2015; Delanoë
et al., 2014;Erfani and Mitchell, 2017; Moisseev et al., 2017;
Mascioet al., 2017; Mascio and Mace, 2017) have found exponentsnear
this value for various types of snowflakes; we will ex-amine the
sensitivity of the results to this assumption inSect. 7.3. We
retrieve the logarithm of each microphysical
parameter because the dynamic ranges of the retrieved valuesare
large and because using the logarithmic values makes theforward
model more linear; this was examined analyticallyfor the simpler
case of cloud water retrieval by Leinonenet al. (2016). The state
vector then becomes
x = [ln N0 ln 3 ln α]T . (8)
In our multifrequency radar retrieval algorithm, the
moststraightforward way to formulate the measurement vectorwould be
to use each of the three radar reflectivities. How-ever, earlier
studies (e.g., Kneifel et al., 2011; Leinonenand Szyrmer, 2015)
have shown that combinations of dual-wavelength ratios (DWRs), such
as simultaneous measure-ments of Ka–W-band and Ku–Ka-band DWRs,
contain infor-mation about the size and density of the snowflakes.
Follow-ing this concept, we form the measurement vector with
theKu-band reflectivity and the Ka–W-band and Ku–Ka-bandDWRs. The
measurement vector is then
y =[ZdB,Ku DWRKa/W DWRKu/Ka
]T. (9)
The choice of the Ku-band reflectivity is somewhat arbitrary,as
any of the three bands could be used, but the Ku band doesbenefit
from that band being the least attenuated of the three.In studies
in which we omit one of the radar bands, insteadoperating with a
dual-frequency radar, y consists of the re-flectivity from the
lowest-frequency radar and the DWR. Forsingle-frequency retrievals,
y simply contains ZdB at the sin-gle band.
The measurement vector must be accompanied by an er-ror
estimate, which should include not only the radar instru-ment error
but also the error due to the forward model as-sumptions. In our
case, the latter includes the errors due tothe assumptions of an
exponential size distribution, a fixedmass–dimensional exponent β
and the orientation distribu-tions assumed in the scattering
databases. The extent of theseerrors is difficult to quantify, but
their effect should be simi-lar on each collocated radar frequency:
for example, the radarcross section will increase with increasing
particle size for allfrequencies, and thus the errors in radar
reflectivity at differ-ent frequencies will partially cancel out
when computing theDWRs. This suggests that the DWRs can be assumed
to havesmaller errors than the absolute value of the reflectivity.
Ac-cordingly, we assign 3dB of error standard deviation for
theabsolute value of the radar reflectivity and 1dB for each ofthe
DWRs.
In atmospheric remote sensing, the inversion problem isoften
solved using optimal estimation (OE; Rodgers, 2000).This is a
Bayesian method that assumes that x and y arejointly distributed
according to the multivariate normal dis-tribution and which is
solved using optimization methods.We found this technique to be
problematic for our retrieval,partly due to the limited and
discrete nature of the snowflakescattering database used in the
forward model. The optimiza-tion in OE often converged to local
minima, especially near
Atmos. Meas. Tech., 11, 5471–5488, 2018
www.atmos-meas-tech.net/11/5471/2018/
-
J. Leinonen et al.: Retrieval of snowflake microphysical
properties 5475
the extreme values supported by the snowflake database,
in-troducing sudden changes to the retrieved values.
Despite the shortcomings of OE, a Bayesian approach wasstill
desirable in order to constrain the retrieved microphysi-cal
parameters. We found that the retrieval can be performedin a robust
way through a global calculation of the expectedvalue of the state
x given a measurement y. This is given by
E[x|y] =∫
x p(x|y)dx =1
p(y)
∫x p(y|x)p(x)dx, (10)
where p(y) is the marginal probability of y, p(y|x) is
theconditional probability of a measurement y given a state xand
p(x) is the a priori probability of x, described in detail inSect.
4. This approach is slightly different from the commonstrategy of
finding the most likely solution given the priorand the
measurement: That method aims to find the mode ofthe conditional
distribution; ours determines the mean.
Using Eq. (10), we can construct a lookup table that
mapsdiscrete values of y to the corresponding expected
valuesE[x|y]. Multilinear interpolation is used to estimate
E[x|y]for values of y that fall between the discrete values usedin
the table. The errors associated with the discretizationcan be
reduced to be arbitrarily small by making the inter-vals between
the values finer. In the studies presented here,the lookup table
for E[x|y] ranged between 0 and 35dBZfor ZdB,Ku, between −2 and
14dB for DWRKa/W, and be-tween −2 and 9dB for DWRKu/Ka, with 0.25dB
discretiza-tion for each dimension. The integral in Eq. (10) was
com-puted by evaluating the integrand at approximately
10000discrete points, which were distributed uniformly across
afinite search space spanning (xi − 3σi ,xi + 3σi) along
eachvariable, where xi is the prior mean of the ith variable in
x,and σi is its prior standard deviation. Making the
discretiza-tion finer than this did not seem to change the
retrieval resultssignificantly in our case, although we encourage
those usingthis approach for other problems to establish the
appropriatediscretization for their problem.
Error estimates for the retrieved values can be computedusing
the same technique. The error covariance matrix of thestate given
an observation, Sx|y , can be computed as
Sx|y = E[x⊗ x|y] −E[x|y]⊗E[x|y], (11)
where “⊗” is the outer product. E[x⊗x|y] can be evaluatedusing a
lookup table and interpolation in the same manner asexplained for
E[x|y] above.
The method described above allows the state and its co-variance
to be retrieved robustly and very quickly, with onlya table lookup
and an interpolation needed for each measure-ment. This comes at
the cost of a relatively expensive ini-tialization of the tables
before the retrieval is started. How-ever, with our parameters for
the discretization, this only tookabout 1 min on a modern laptop
computer with no paral-lelization, so it does not present a major
computational bur-den.
2.4 Derived variables
The results of the retrieval are the parameters of Eq. (8),
butfor further analysis of the results, it is useful to derive
othervariables that are important for microphysics or more
intu-itively understood by end users. Perhaps most importantly,the
IWC (denoted by Wice), which expresses the ice mass ina unit volume
of air, is given by
Wice =
∞∫0
m(D)N(D)dD. (12)
Consistently with the calculation of the scattering
properties,we set m(D)= 0 in the integral (and other integrals in
thissection) where no snowflake samples are available for the(D,m)
combination. If this truncation is not used, the as-sumptions of
Eqs. (5) and (6) give Wice in the simple form
Wice =N0α3−β−10(β + 1), (13)
where 0 is the gamma function.When discussing the snowflake
size, 3−1 gives the aver-
age diameter for the untruncated exponential size distribu-tion,
but it is often clearer and more convenient to state thediameter
that contributes most to the IWC. This is the mass-weighted mean
diameter
Dm =
∫∞
0 Dm(D)N(D)dD∫∞
0 m(D)N(D)dD. (14)
Similarly, the total number concentration of snowflakes maybe a
more meaningful quantity than N0. This is given simplyby
NT =
∞∫0
N(D)dD. (15)
Also, the density of the snowflakes depends on the diameter,but
a bulk density for the snowflake ensemble can be com-puted by
dividing the IWC by the volume spanned by theenclosing spheres of
the snowflakes in a unit volume:
ρbulk =Wice∫
∞
0π6D
3N(D)dD. (16)
We use this definition for simplicity; a somewhat higher
den-sity would be obtained by using the volume of the
enclosingspheroid or ellipsoid in the integral in the denominator,
butthe shape of this ellipsoid is in general dependent on D andm,
which would complicate the calculation.
The quantities in Eqs. (12)–(16) are nonlinear functionsof the
state x, and consequently estimating their errors isnot completely
straightforward. Since our algorithm returnsa probability
distribution function (PDF) for x, we can obtainstatistically valid
error estimates by computing the standarddeviation of a quantity
over the PDF. This can be estimatedquickly with Gauss–Hermite
quadratures; see Appendix A.
www.atmos-meas-tech.net/11/5471/2018/ Atmos. Meas. Tech., 11,
5471–5488, 2018
-
5476 J. Leinonen et al.: Retrieval of snowflake microphysical
properties
3 Data
The main source of data that we use to demonstrate
thetriple-frequency retrieval is from the Airborne Third
Genera-tion Precipitation Radar (APR-3; Sadowy et al., 2003)
flownonboard the NASA DC-8 aircraft during the OLYMPEX–RADEX
experiment, which took place around the OlympicMountains of
Washington State, USA, in late 2015 (Houzeet al., 2017). The RADEX
involvement in this field cam-paign was intended specifically to
assess the the capabili-ties of multifrequency radar observations
for satellite remotesensing of precipitation processes. APR-3
acquired simul-taneous measurements at three frequencies: 13.4GHz
(Kuband), 35.6GHz (Ka band) and 94.9GHz (W band). APR-3is a
scanning polarimetric cloud-profiling radar with Dopplercapability.
With a vertical resolution of 30m, it provideshigh-resolution 3-D
measurements of clouds and precipita-tion. OLYMPEX was the first
time it was deployed in itstriple-frequency configuration.
We investigated the ability of the triple-frequency algo-rithm
to identify snowfall processes qualitatively by compar-ing the
results to collocated ground-based dual-polarizationradar
observations. These observations were made by theNASA S-Band
Dual-Polarimetric Radar (NPOL), which wasdeployed 2km from the
coast at 47.277◦N, 124.211◦W,157m above mean sea level (m.s.l.).
The NPOL scanningstrategy interleaved planned position indicator
scans (PPIs)with a series of high-resolution range-height indicator
(RHI)sector scans to the west over the ocean and to the east over
theQuinault River valley (Houze et al., 2017). During OLYM-PEX, the
NASA DC-8 aircraft frequently flew directly alongNPOL RHI azimuths,
making it relatively straightforward tocollocate with the
nadir-pointing scans from APR-3. We col-located NPOL data to the
APR-3 radar coordinates using thePython ARM Radar Toolkit (Helmus
and Collis, 2016) byfirst identifying RHI scans whose time and
direction coin-cided with the APR-3 overpass, then copying data
from thenearest NPOL bin to each APR-3 bin. We used two
variablesfrom NPOL: the radar reflectivity and the hydrometeor
iden-tification (HID) product (Dolan and Rutledge, 2009). The
lat-ter uses fuzzy logic to assign the most likely hydrometeorclass
to each radar bin based on temperature and the radarreflectivity
and polarimetric parameters. We use this productto provide
independent estimates of the type of icy hydrom-eteors and compare
them to the microphysical properties re-trieved by our
algorithm.
During the OLYMPEX campaign, the University of NorthDakota
Citation aircraft often flew in the same area as theNASA DC-8.
Typically, the Citation flew at lower altitudesthan the DC-8, and
consequently there are many data pointswhere the Citation
measurements are collocated with theAPR-3. A total of 16 cases from
OLYMPEX were analyzed.The APR-3 gate closest to the Citation is
found using a k-dimensional-tree search algorithm. The Citation
measuredthe PSD using the 2D-S (Stereo) Probe (Lawson et al.,
2006)
in the range of 225µm≤D < 1mm and the High-VolumeParticle
Spectrometer (1mm≤D ≤ 3.25cm). To eliminateshattered artifacts
created from ice crystals colliding withthe probe housing,
anti-shattering tips are used in conjunc-tion with the University
of Illinois Oklahoma Optical ArrayProbe Processing Software
(Jackson et al., 2014). In additionto the optical array probes, the
Citation also carried a Nev-zorov probe (Korolev et al., 1998) to
measure bulk total watercontent.
The ground-based observations of snowfall microphysicsused to
derive the a priori distribution were gathered at theHyytiälä
Forestry Field Station (61.845◦N, 24.287◦E, 150mabove mean sea
level) of the University of Helsinki, Finland,during the Biogenic
Aerosols – Effects on Clouds and Cli-mate (BAECC) campaign (Petäjä
et al., 2016) and the fol-lowing winter of 2014–2015. The weather
conditions dur-ing BAECC and the following winter were mostly mild,
andmost of the snowfall observations were collected at
temper-atures above −4 ◦C. Both aggregation and riming
occurredfrequently during the measurement period (Moisseev et
al.,2017). The PSDs were measured with a video disdrometer,the
Snowflake Video Imager (SVI; Newman et al., 2009), asa function of
the disk-equivalent diameter (the diameter of adisk with the
projected area of the particle image). The meanPSD was calculated
for every 5 min period. The resolutionof the SVI is 0.1mm, although
in practice, the smallest disk-equivalent diameter used in the
computations was approx-imately 0.2mm. The PSD was divided into 120
bins with abin size of 0.2mm; the highest bin is for diameters
larger than26.0mm. A linear scaling factor between the
disk-equivalentdiameter and the maximum diameter was determined by
an-alyzing SVI images of snowflakes from each case and uti-lized to
give the PSD as a function of maximum diameter.The mass retrievals
were obtained by combining SVI obser-vations with a collocated
precipitation gauge. Based on theparticle fall velocity and shape
measurements provided bythe SVI, the masses of individual falling
snow particles wereestimated with hydrodynamic theory (Mitchell and
Heyms-field, 2005; von Lerber et al., 2017). The
mass–dimensionalrelation in the form of Eq. (6) was determined for
every 5minwith mass as a function of maximum diameter and with a
lin-ear regression fit in the log scale.
We also used balloon sounding data to support the anal-ysis of
the case studies. These data were derived from pub-licly available
operational soundings launched daily at 00:00and 12:00 UTC from
Quillayute, Washington, near the areawhere the radar measurements
took place.
4 A priori assumptions
Bayesian retrievals depend on the availability of a priori
data.We based our a priori values on two sources of in situ
data:the Citation dataset from OLYMPEX and the
ground-basedmeasurements from BAECC. Both of these datasets can
be
Atmos. Meas. Tech., 11, 5471–5488, 2018
www.atmos-meas-tech.net/11/5471/2018/
-
J. Leinonen et al.: Retrieval of snowflake microphysical
properties 5477
used to derive theN0,3 and α parameters. For both datasets,N0
and 3 can be derived from the binned PSDs. The α pa-rameter can be
derived by fitting a curve defined by Eq. (6)to the mass as a
function of diameter; this is included inthe BAECC data, in which
the mass was derived from thesnowflake fall velocity (von Lerber et
al., 2017). In calculat-ing α from the BAECC dataset, we fixed β to
2.1, consistentwith the assumptions in the retrieval algorithm. For
the Ci-tation data, mass is not directly available as a function
ofdiameter, but Wice is estimated with the Nevzorov probe andthus α
can be roughly estimated using Eq. (13).
For the purposes of demonstrating the algorithm, we basedthe a
priori distribution used in this study on a combinationof the two
datasets, taking an equal number of samples fromeach for a total N
≈ 6000. We recognize that this is an im-perfect solution, and a
further analysis using these and otherdatasets should be conducted
to establish a priori distribu-tions suitable for remote-sensing
retrievals of snowfall undervarious atmospheric conditions. Doing
this rigorously willlikely require an entire study of its own.
The analysis resulted in means of ln N0 = 15.4, ln 3=7.50, and
ln α =−2.30 and standard deviations ofStd[ln N0] = 1.67, Std[ln 3]
= 0.52 and Std[ln α] = 0.69.Because the two datasets cannot be
expected to cover theentire natural distribution of these
parameters, basing the apriori distribution on them would likely
result in an overlyrestrictive prior. To compensate for this, we
increase the stan-dard deviations given above by a factor of 1.5,
acknowledg-ing that this choice is somewhat arbitrary. The
correlationmatrix of x derived from the datasets is
Ca =
1 0.46 −0.070.46 1 0.54−0.07 0.54 1
, (17)from which the a priori covariance matrix can be
computedas
Sa = DCaD, (18)
where D is a diagonal matrix with the standard deviationsof x on
the diagonal. The resulting distribution, used as theprior in all
retrievals in this study, is then given by the meanxa and
covariance Sa:
xa =[
15.4 7.50 −2.30]T, (19)
Sa =
6.28 0.90 −0.180.90 0.61 0.44−0.18 0.44 1.07
. (20)In Sect. 7.2 we examine the sensitivity of the results to
thechoice of prior.
We assume that the a priori distribution is multivariatenormal.
Given the limited scope of the datasets used to de-rive the prior
distribution in this study, we cannot rigorouslytest this
assumption, but the choice is motivated by proba-bilistic arguments
that the normal distribution is the most
124.5 124.0 123.5 123.0
47.00
47.25
47.50
47.75
48.00
48.25
48.50 (a) 3 Dec 2015
NPOL
16:17:2316:20:24
16:25:49
16:32:17
124.5 124.0 123.5 123.0
(b) 4 Dec 2015
NPOL
14:53:53
14:59:18
15:05:1915:06:28
Figure 1. The paths of the flights used in Sect. 5.1 (a) and 5.2
(b).The darker sections of the paths show the flight data used in
thisstudy (the rest of the measurements were discarded for the lack
ofuseful data). The time stamps (UTC) denote the beginning and
endof each flight and the beginning and end of the data that were
used.The gray background shows the outline of the Olympic
Peninsula,with Vancouver Island to the north.
natural choice for an unknown distribution (Jaynes, 2003).Global
distributions for microphysical quantities have alsooften been
found to be lognormal (e.g., Kedem and Chiu,1987; Leinonen et al.,
2012b), meaning that the distributionsof their logarithms (we use
the logarithmic values in the statevector) are normal. Thus a
multivariate normal distributionis a reasonable assumption for this
study, although largerdatasets should be analyzed in this manner in
order to deriveappropriate global priors.
5 Case studies and comparison to NPOL
5.1 3 December 2015
The first of the two cases that we examined together withNPOL
data took place on 3 December 2015. The APR-3flight leg started at
16:17:23 UTC over the Olympic Moun-tains, from where the DC-8 flew
towards the coast, passingdirectly over the NPOL site. A map of the
flight path is shownin Fig. 1a. The case consisted primarily of
prefrontal strati-form precipitation; see Houze et al. (2015a) for
details. Weonly used data from regions above the melting layer,
whichwe identified just below 3km in altitude based on the theradar
bright band; this also agrees with the 0 ◦C isothermof 2.85km in
the 12:00 UTC balloon sounding from nearbyQuillayute,
Washington.
The retrievals from the case are shown in Fig. 2a–e. Onthe left
side of Fig. 2a–c, an orange box delineates a col-umn in which Dm
increases significantly with decreasing al-titude, accompanied by a
rapid decrease in ρbulk. Together,these changes point to the onset
of aggregation, which re-sults in rapid growth of snowflakes
accompanied by a de-crease in density as single ice crystals stick
together to formaggregates, whose density decreases as a function
of size.The transition can also be seen in Fig. 2e, in which
orangedots denote the data points from the orange box in Fig.
2a–c.
www.atmos-meas-tech.net/11/5471/2018/ Atmos. Meas. Tech., 11,
5471–5488, 2018
-
5478 J. Leinonen et al.: Retrieval of snowflake microphysical
properties
0 20 40 60
8
7
6
5
4
Altit
ude
[km
](a)
0.5
1.0
2.0
5.0
Dm [mm]
0 20 40 60
8
7
6
5
4
(b)
10.020.0
50.0100.0200.0
500.01000.0
bulk [kg m 3]
0 20 40 60Distance [km]
8
7
6
5
4
Altit
ude
[km
]
(c)
0.0050.010.02
0.050.10.2
0.51.0
Wice [g m 3]
0 20 40 60Distance [km]
8
7
6
5
4
Altit
ude
[km
]
(f)
10
20
30
40
50
NPOL dBZ0 20 40 60
8
7
6
5
4
(d)
Wet snow
HD graupel
LD graupel
Aggregates
Ice
Vert. ice
NPOL HID
0.5 1.0 2.0 5.0Dm [mm]
10.020.0
50.0100.0200.0
500.01000.0
bulk
[kgm
3 ]
(e)
RimingAggregationOther data
Figure 2. Data from the 3 December 2015 case described in Sect.
5.1. (a) The mass-weighted mean diameter Dm (Eq. 14). (b) The
bulkdensity ρbulk (Eq. 16). (c) The ice water content (Eq. 12). (d)
The NPOL hydrometeor identification. (e) A scatter plot ofDm and
ρbulk from(a) and (b), with the red and orange points identifying
the data inside the boxes of corresponding colors shown in those
panels. (f) The radarreflectivity observed by NPOL.
The transition from ice crystals to aggregates is also de-tected
at around 5 km in altitude, 20–45km on the distancescale, by both
the triple-frequency retrieval, which shows asudden increase in Dm
(Fig. 2a), and by NPOL, which iden-tifies a change in the
hydrometeor type at roughly the samealtitude. According to NPOL
HID, the hydrometeors abovethis altitude consist mostly of a
mixture of ice crystals andaggregates, while the hydrometeors below
it are identified asaggregates. While the altitude at which
aggregation initiatesappears to be similar between NPOL and our
retrieval, smalldiscrepancies are to be expected because the APR-3
obser-vations are not perfectly simultaneous with the NPOL scan.The
time difference ranges from 4min at the beginning ofthe
observations shown in Fig. 2 to 14min at the end. Fur-ther evidence
for aggregation is provided by sounding data,which indicate a
temperature between−15 and−12 ◦C in thelayer at 5.0–5.5km in
altitude, a common temperature rangefor the onset of aggregation
driven by dendritic growth ofice crystals at these temperatures
(Bailey and Hallett, 2009;Lamb and Verlinde, 2011).
Another interesting feature found in this case is denotedby the
red boxes in Fig. 2a–c. In this region, the retrieved
mi-crophysical variables indicate moderately sized snowflakes
with relatively high ρ, which suggests that rimed
snowflakesoccur in the area. The data points located within this
box areshown in red in the scatter plot of Fig. 2e, which
confirmsthese attributes. It is interesting to note that the red
regionand the bottom of the orange region have similar IWCs, butthe
sizes and densities are very different. NPOL also detectssome
graupel in this region, which suggests that the three-frequency
retrieval detects snowflake riming and graupel for-mation. In the
following case, we further explore this capa-bility.
5.2 4 December 2015
On 4 December 2015, precipitation originated mostly
frompostfrontal convection following the passage of the fronton the
previous day (Houze et al., 2015b). The DC-8 fol-lowed a flight
path similar to in the previous case (Fig. 1b);APR-3 data
collection for the dataset shown here started at14:53:21 UTC. We
collocated two NPOL RHIs to APR-3 co-ordinates, one pointing toward
land and the other toward theocean. For the ocean-pointing scan, we
selected an RHI thatis offset by 4◦ from the optimal collocation
with APR-3 in or-der to better capture a convective plume that was
observed by
Atmos. Meas. Tech., 11, 5471–5488, 2018
www.atmos-meas-tech.net/11/5471/2018/
-
J. Leinonen et al.: Retrieval of snowflake microphysical
properties 5479
APR-3 but had moved before being scanned by NPOL 2 minlater.
This shifted the location of the scan by only 500 m at thedistance
of the plume. The sounding data and the radar brightband both
placed the melting level at around 1.3km, lowerthan on the previous
day. We again only used data points lo-cated above the melting
layer.
The large convective plume found by APR-3 in this case ismarked
with a red box in Fig. 3a–c. As with Fig. 2, the datapoints from
this box are denoted with red dots in Fig. 3e. Inthis case, the
data points from the plume are particularly dis-tinct from the rest
of the joint distribution of Dm and ρbulk,indicating moderately
large particles with high density, char-acteristic of graupel. NPOL
also indicates a similarly sizedplume of graupel in this region.
The time separation of thescans in the region to the right of NPOL
in Fig. 3 is only2min, so it seems likely that the same plume was
capturedby both radars. The spatial shift between the plumes
observedby APR-3 and NPOL appears to be 1–2km; this is
consistentwith the 13ms−1 wind speed measured by the sounding at3km
in altitude, which translates to a 1.5km distance over2min.
On the left side of NPOL, another graupel-containing re-gion is
denoted by an orange box. This region is also ac-companied by an
NPOL detection of graupel in the vicinity.The time separation in
this region was longer, between 4 and8min, so the plume had more
time to move away from thevertical cross section before being
observed by APR-3. Re-gardless, the two radars agree on location of
the plume towithin 2km and on its height to within 0.5km.
Our retrieval and the NPOL HID also seem to be in rea-sonably
good agreement regarding the transition from icecrystals to
aggregates. Both indicate the presence of ice crys-tals (i.e.,
small, relatively dense hydrometeors) at higher alti-tudes and
aggregates at lower altitudes (below approximately4km), with the
transition point varying considerably withinthis case. Both
products also identify the presence of smallerparticles at 2–3km in
altitude in the region, around 20km onthe horizontal scale.
6 Comparison to in situ data
As described in Sect. 3, the UND Citation aircraft
gatheredparticle probe measurements simultaneously with the
NASADC-8 radar observations during OLYMPEX. This resulted ina set
of collocated radar and in situ data. The retrieval algo-rithm was
run using the collocated and attenuation-correctedradar
reflectivity values. The retrieved microphysical quanti-ties were
then compared to those measured in situ. The avail-ability of
variables from the in situ dataset is somewhat lim-ited: while the
number and projected sizes of the ice particlescan be measured
quite accurately using the imaging probes,the two-dimensional
nature of the imager limits the accuracyof the maximum dimension as
this must be estimated from aprojection of the particle. The
snowflake masses are also dif-
ficult to determine. The bulk IWC can be estimated with
theNevzorov probe, but its inlet is only 8mm in diameter,
whichcauses it to underestimate IWC when the maximum particlesize
exceeds approximately 4mm (Korolev et al., 2013). Un-fortunately,
the cases with large snowflakes are where onewould expect the
largest benefits from multifrequency meth-ods because of the
stronger resonance effects involved inscattering. Thus, this
limitation of the Nevzorov probe some-what diminishes its value in
validating the retrievals. Whilethe Citation measurements do not
give the masses of individ-ual particles, α can be estimated from
Eq. (13) if the IWCgiven by the Nevzorov probe is assumed to be
correct.
To filter out outliers and poor collocations, we applied
twofilters. First, to ensure an acceptably accurate collocation
be-tween the two measurements, the time separation betweenthem was
required to be less than 2min. Second, for adequatesampling, the
total number concentrationNT was required tobe more than 103 m−3.
These criteria successfully removedmost outliers that we found in
the unfiltered comparisons.
The comparisons of the retrievals against the in situ valuesare
shown on the top row of Fig. 4 (the same analysis runwith reduced
frequencies, shown on the other rows of Fig. 4,is discussed in
Sect. 7.1). The figures show that retrievalsof the slope parameter
3 compare considerably better to thein situ values than do the
retrievals of the intercept param-eter N0, which in turn are better
than those of the mass–dimensional factor α. The 3 parameters agree
well through-out the range of values (for ln3, root-mean-square
error isRMSE[ln3] = 0.41, bias is bias[ln3] = 0.023 and
correla-tion is Cor[ln3] = 0.70), showing that particle sizing
canbe carried out reliably using the multifrequency retrieval. N0is
also quite well matched (Cor[ln N0] = 0.56), but the rela-tive
errors are much larger than for3 (RMSE[ln N0] = 3.01,bias[ln N0] =
−0.73). The α parameters are poorly matchedbetween the two
datasets, although the retrieval producessome variation in this
parameter. In any case, one should beskeptical of the α comparison
as the in situ values have beenderived from the Nevzorov probe
data, which suffers fromthe abovementioned problems, and using Eq.
(13), which isan approximation. Furthermore, fixing the β parameter
mayfurther exacerbate the problem with estimating α.
The retrieved IWCs Wice correspond quite well to thein situ
values (RMSE[lnWice] = 0.72, bias[lnWice] = 0.30,Cor[lnWice] =
0.67). Interestingly, the IWC, which is afunction of N0 and α,
appears to be better retrieved than ei-ther of those parameters.
Opposite errors in N0 and α, seenin their respective scatter plots,
suggest that their retrieval er-rors compensate for each other in a
way that allows Wice tobe constrained better than either N0 or α
alone. This is alsosupported by the correlation matrix of the
retrieval errors, forwhich the error correlation between ln N0 and
ln α is −0.30on average. The red dots in Fig. 4 correspond to
larger iceparticles, where the Nevzorov probe might be prone to
un-derestimation. However, there does not appear to be a
signifi-cant difference inWice between the small and large
particles.
www.atmos-meas-tech.net/11/5471/2018/ Atmos. Meas. Tech., 11,
5471–5488, 2018
-
5480 J. Leinonen et al.: Retrieval of snowflake microphysical
properties
0 20 40 60
7
6
5
4
3
2
Altit
ude
[km
](a)
0.5
1.0
2.0
5.0
10.0Dm [mm]
0 20 40 60
7
6
5
4
3
2
(b)
10.020.0
50.0100.0200.0
500.01000.0
bulk [kg m 3]
0 20 40 60Distance [km]
7
6
5
4
3
2
Altit
ude
[km
]
(c)
0.002
0.0050.010.02
0.050.10.2
0.51.0
Wice [g m 3]
0 20 40 60Distance [km]
7
6
5
4
3
2
Altit
ude
[km
]
(f)
10
20
30
40
50NPOL dBZ
0 20 40 60
7
6
5
4
3
2
(d)
Wet snow
HD graupel
LD graupel
Aggregates
Ice
Vert. ice
NPOL HID
0.5 1.0 2.0 5.0 10.0Dm [mm]
5.010.020.0
50.0100.0200.0
500.01000.0
bulk
[kgm
3 ]
(e)
Graupel region 1Graupel region 2Other data
Figure 3. As Fig. 2, except for the 4 December 2015 case
described in Sect. 5.2. The location of NPOL on the flight track is
marked by thearrow in panels (a)–(d) and (f).
However, the large particles stand out in the α scatter
plot,where they are clearly the worst match between the in situand
retrieved values.
7 Sensitivity analysis
7.1 Sensitivity to the number of frequencies
In the assessment of a multifrequency algorithm, one
inter-esting question is what are the benefits of introducing
addi-tional frequencies? To evaluate this, we reran the analysis
ofSect. 6 with subsets of the frequencies used in the full
anal-ysis. We examined all the possible combinations of
availablebands, always using the lowest frequency for the absolute
re-flectivity, combined with the DWRs that were available (oneDWR
for dual-frequency retrievals and two DWRs for thetriple-frequency
retrieval).
The scatter plots of the in situ and retrieved
microphysicalparameters are shown in Fig. 4. These plots suggest
that theresults of the triple-frequency retrieval are similar to
those ofthe dual-frequency retrievals. However, the
multifrequencyretrievals clearly outperform single-frequency
retrievals. Thetriple- and dual-frequency scatter plots are
visually similarfor all two- and three-frequency combinations for
3, and
to a lesser extent N0. The dual-frequency retrieval using
theKa–W bands seems to be limited in its ability to determinethe
size of large particles (small 3), presumably because
thedual-frequency ratio saturates at large sizes, while the
Ku–Ka-band retrieval suffers from a similar problem with
smallparticles. The Ku–W-band retrieval and the
triple-frequencyretrieval do not suffer from this problem.
Meanwhile, thesingle-frequency retrievals all have poor sensitivity
to N0.Ku- and Ka-band single-frequency retrievals have some
sen-sitivity to 3 for small particles, while the W-band
retrievalalso cannot discern this parameter particularly well. None
ofthe retrievals perform adequately with α, although the
multi-frequency retrievals, especially the triple-frequency
retrieval,permit considerably more variation in the values of that
pa-rameter: α is almost constant with the single-frequency
re-trievals, while its relative standard deviation is about 60 %
inthe triple-frequency results, indicating that the retrieval
algo-rithm is confident enough in the signal to estimate α as
some-thing other than the a priori mean. The results for α should
beinterpreted skeptically because of the issues with the
deriva-tion of α, as explained in Sect. 6. The single-frequency
re-trievals appear to constrain Wice much better than they
con-strain any of the individual microphysical parameters.
Atmos. Meas. Tech., 11, 5471–5488, 2018
www.atmos-meas-tech.net/11/5471/2018/
-
J. Leinonen et al.: Retrieval of snowflake microphysical
properties 5481
103
104
106
107
108
Retri
eved
Ku+K
a/W
+Ku/
Ka
N0 [m 4]
400
1600
6400
[m 1]
102
101
100
105
104
103
Wice [kg m 3]
103
104
106
107
108
Retri
eved
Ka+K
a/W
400
1600
6400
102
101
100
105
104
103
103
104
106
107
108
Retri
eved
Ku+K
u/Ka
400
1600
6400
102
101
100
105
104
103
103
104
106
107
108
Retri
eved
Ku+K
u/W
400
1600
6400
102
101
100
105
104
103
103
104
106
107
108
Retri
eved
Ku
400
1600
6400
102
101
100
105
104
103
103
104
106
107
108
Retri
eved
Ka
400
1600
6400
102
101
100
105
104
103
103 104 106 107 108In situ
103
104
106
107
108
Retri
eved
W
400 1600 6400In situ
400
1600
6400
10 2 10 1 100In situ
102
101
100
10 5 10 4 10 3In situ 1
05
104
103
Figure 4. Scatter plots of in situ measured (horizontal axis)
and retrieved (vertical axis) microphysical values from the
collocated Citation–APR-3 dataset. The columns correspond to
different microphysical parameters: from left to right, the
intercept parameter N0, the slopeparameter 3, the mass–dimensional
prefactor α and the ice water content Wice. The rows correspond to
different combinations of radarfrequencies and DWRs used to run the
retrieval, as shown to the left of each row. The color denotes the
size of the snowflakes: blue dotscorrespond to small particles
(largest 25% of 3), orange to medium-sized particles and red to
large particles (smallest 25% of 3). In eachplot, the black line is
the 1 : 1 line. Note the logarithmic scales on the axes.
www.atmos-meas-tech.net/11/5471/2018/ Atmos. Meas. Tech., 11,
5471–5488, 2018
-
5482 J. Leinonen et al.: Retrieval of snowflake microphysical
properties
ln N0 ln ln ln Wice ln NT ln Dm ln bulk
Ku+Ka/W+Ku/Ka
Ka+Ka/W
Ku+Ku/Ka
Ku+Ku/W
Ku
Ka
W
1.17 0.28 0.70 0.78 1.11 0.27 0.90
1.24 0.41 0.79 0.80 1.12 0.41 1.10
1.75 0.36 0.76 0.92 1.54 0.35 0.96
1.10 0.31 0.84 0.79 1.11 0.30 1.08
2.43 0.58 0.81 1.05 1.92 0.58 1.17
2.34 0.62 0.81 0.95 1.81 0.61 1.19
2.13 0.67 0.82 0.79 1.55 0.67 1.22
0.0
0.5
1.0
1.5
2.0
Figure 5. The average posterior retrieval errors of the
logarithmsof microphysical variables with different combinations of
radar fre-quencies. The data from the 4 December 2015 case (Sect.
5.2) areused in this figure.
Another way to evaluate the sensitivity to the number
offrequencies is to examine the a posteriori errors reported bythe
algorithm itself. These errors, derived from the 4 Decem-ber 2015
case, are shown in Fig. 5 for the different frequencycombinations.
According to the error estimate from the algo-rithm, the
three-frequency retrieval seems to yield a modestbut fairly
consistent improvement over the dual-frequency re-sults. These,
like with the in situ data comparison, are clearlybetter than the
single-frequency results for all parameters,although the
differences for α, Wice and ρbulk are less pro-nounced.
The errors in the single-frequency retrievals are all sim-ilar;
the W band seems to have somewhat smaller errorsfor Wice and N0
while the Ku band is slightly better withthe particle size.
Notably, the a posteriori errors for thesingle-frequency retrievals
are not much smaller than the apriori errors of Stda[ln N0] = 2.45,
Stda[ln 3] = 0.83 andStda[ln α] = 1.13, which emphasizes the poor
informationcontent in the single-frequency retrievals. Regardless,
withWice the single-frequency retrievals perform nearly as well
asthe multifrequency ones, consistent with what was shown inthe
comparison to in situ values. None of the dual-frequencyoptions are
significantly better than the others, either, al-though the
Ku–Ka-band configuration underperforms theKa–W-band and Ku–W-band
configurations in retrievals ofN0 and NT , and to a lesser extent
Wice. The Ka–W- and Ku–W-band configurations are nearly equally
good.
We have additionally created plots of the
microphysicalparameters shown in Fig. 3 using each of the frequency
com-binations found in Fig. 5. Due to the large number of
plotsresulting from this analysis, these plots are not shown
here,but can be found in Figs. S1–S21 of the Supplement
accom-panying this article. A notable feature of these plots is
thehigher level of detail and wider range of variation found in
ln N0 ln ln ln Wice ln NT ln Dm ln bulk
ln N0, a 2.51
ln N0, a + 2.51
ln a 0.78
ln a + 0.78
ln a 1.04
ln a + 1.04
-0.68 -0.05 +0.10 -0.43 -0.62 +0.05 +0.05
+0.88 +0.08 -0.11 +0.51 +0.78 -0.08 -0.04
-0.03 +0.00 +0.12 +0.09 -0.03 -0.00 +0.12
+0.03 +0.01 -0.10 -0.09 +0.02 -0.01 -0.09
+0.26 -0.12 -0.49 +0.13 +0.39 +0.12 -0.60
+0.05 +0.18 +0.49 +0.00 -0.16 -0.17 +0.65
0.6
0.3
0.0
0.3
0.6
Figure 6. The root-mean-square changes in the microphysical
pa-rameters in response to changes in the prior. The change in the
prioris indicated on the left side of each row. The data are from
the 4 De-cember 2015 case (Sect. 5.2).
the triple-frequency plots of Dm and especially ρbulk com-pared
to the dual-frequency plots. The Ka–W band dual-frequency retrieval
appears to capture the plume found by thetriple-frequency approach,
albeit with a more subdued signal;the other two dual-frequency
configurations miss the plumealtogether. Consistent with the
results of other comparisonsshown in this section, the
dual-frequency plots capture moredetail than the single-frequency
plots. This is especially strik-ing for the plots of ρbulk, in
which the single-frequency re-trievals appear to always give nearly
the same density. Incontrast to Dm and ρbulk, Wice has only small
differences,and similar levels of detail between the
single-frequency andmultifrequency retrievals. This is again
similar to the findingsin Fig. 4.
7.2 Sensitivity to prior assumptions
In order to examine the sensitivity of the results of the
re-trieval algorithm to the prior assumptions, we ran the case of4
December 2015 with shifted prior means. We changed themean of each
variable in the state vector x, one at a time, by±1 standard
deviation of that variable. The results are shownin Fig. 6. The
results are consistent with the retrievals in thesense that a shift
in the prior of a variable causes a smallershift of the same sign
in the a posteriori value of that variable.
The effects on other variables from adjusting the prior ofone
variable are not straightforward to interpret. These areconnected
in a complicated way due to the significant a pri-ori correlations
among the different variables, as well as thenecessity of
explaining the observed reflectivities with otherparameters when
one of them is shifted. The dependenciesare clearly not linear. The
shifts in the prior also interact withthe limits of the scattering
database, which further compli-cates the interpretation. The IWC is
the most sensitive tothe prior of ln N0. The results are the least
sensitive to theprior assumption of ln 3, indicating that ln 3 is
very well
Atmos. Meas. Tech., 11, 5471–5488, 2018
www.atmos-meas-tech.net/11/5471/2018/
-
J. Leinonen et al.: Retrieval of snowflake microphysical
properties 5483
ln N0 ln ln Wice ln NT ln Dm ln bulk
= 1.9
= 2.3
= 2.5
-0.01 +0.18 +0.11 -0.24 -0.25 +0.85
+0.90 -0.09 +0.35 +1.00 +0.15 -0.92
+1.86 -0.14 +0.71 +1.93 +0.26 -1.721.6
0.8
0.0
0.8
1.6
Figure 7. The root-mean-square changes in the microphysical
pa-rameters in response to changes in the mass–dimensional
exponentβ. The standard assumption of this paper, β = 2.1, is used
as thebaseline. The value of β is indicated on the left side of
each row.The analysis is based on the 4 December 2015 case (Sect.
5.2).
constrained by the observations. Changes to the priors of
ei-ther ln N0 or lnα induce considerably larger changes in
theresults. Thus, the triple-frequency algorithm is clearly
stillsomewhat dependent on the a priori assumptions, althoughthe
changes in the posterior values are much smaller than
thecorresponding changes in the prior, showing that the radarsignal
constrains them quite effectively.
In Figs. S22–S28, we repeat this analysis with the re-duced
frequencies. These clearly show the increasing depen-dence on the
prior assumptions with fewer available frequen-cies. Again, the
difference between triple and dual frequencyis fairly modest, while
the single-frequency retrievals shiftmuch more in response to
changes in the prior.
7.3 Sensitivity to mass–dimensional exponent
The most significant fixed parameter in the retrieval is the
ex-ponent β of the mass–dimensional relationship (Eq. 6). Simi-lar
to Sect. 7.2, we carried out an analysis of the sensitivity ofthe
retrieval results to the choice of β. We used the value usu-ally
adopted in this paper, β = 2.1, as the reference and com-pared the
results obtained with β = 1.9, β = 2.3 and β = 2.5to the reference
retrieval. The values were chosen based onexponents found in the
literature for single crystals, aggre-gate snowflakes and rimed
particles (e.g., Mitchell et al.,1990, their Tables 1 and 2);
higher exponents such as thoseclose to 3.0 often found for graupel
(Locatelli and Hobbs,1974; Heymsfield and Kajikawa, 1987) were not
tested be-cause the distribution of particles in the scattering
databasesdoes not support such high exponents well. The results
areshown in Fig. 7. This figure is similar to Fig. 6, but we
haveomitted the changes in the mass–dimensional prefactor α
be-cause this parameter does not have a physical meaning
inde-pendent of β.
The changes in the retrieval results for different values of
βexhibit patterns similar to those resulting from the change
inprior values: The parameters corresponding to number
con-centration (N0 and NT ) and density (ρbulk) are the most
sen-sitive to the assumptions. Meanwhile, parameters related to
particle size (3 and Dm) and, to a lesser extent, the IWCWice
are less affected by changes in β. The changes in re-trieved
parameters with changing β can be substantial, sug-gesting that a
good estimate of β is important for quantita-tively correct
retrievals. However, the changes are predictableand reasonable,
which suggests that the algorithm is robustand can function with
different values of β without majorproblems. A notable exception to
the predictable behavior isthat of Wice, whose retrieved value
increases in response toboth increase and decrease in β from
2.1.
8 Conclusions
In this study, we described and evaluated an algorithm forsnow
microphysical retrievals using multifrequency radarmeasurements.
The probabilistic method is based on directapplication of Bayes’
theorem using lookup tables. We exam-ined the capabilities and
limitations of the retrieval algorithmusing data from the
OLYMPEX–RADEX measurement cam-paign, comparing the results to
ground-based radar measure-ments from the NASA NPOL radar and to in
situ measure-ments from the UND Citation aircraft, both of which
werecollocated with the APR-3 measurements. We also examinedthe
sensitivity of the algorithm to various assumptions usedin its
formulation.
The results indicate that, at least for the retrieval ap-proach
presented here, triple-frequency radar retrievals pro-vide modest
benefits over dual-frequency retrievals of snow-fall properties.
The probabilistic error estimates from thetriple-frequency
retrievals are generally only slightly smallerthan those from
dual-frequency retrievals, but closer exami-nation of the retrieved
values shows that the triple-frequencyapproach produces more
detailed retrievals with higher de-grees of variability than the
dual-frequency retrievals. Thetriple-frequency method can also
determine particle sizethroughout the range of snowflake sizes
studied here, avoid-ing problems with some of the dual-frequency
methods withsizing either small or large particles. Multifrequency
re-trievals significantly outperform those using only one
fre-quency, and none of the three dual-frequency configura-tions
studied (Ka–W-, Ku–Ka- and Ku–W-bands) appearto be decisively
better than the others, although the Ka–Wband combination was found
to have more sensitivity to thesnowflake density than the Ku–Ka- or
Ku–W-band combina-tions. Similarly, we found the relative
performances of Ku-,Ka- and W-band single-frequency retrievals to
be approxi-mately equal. Thus, information content analysis appears
tosuggest that multifrequency radars are preferable to
single-frequency radars in snowfall retrievals, but it does not
pro-vide much insight into the exact choice of frequencies;
thischoice should probably be more dependent on other factorssuch
as achievable sensitivity and resolution, the importanceof
attenuation, and cost.
www.atmos-meas-tech.net/11/5471/2018/ Atmos. Meas. Tech., 11,
5471–5488, 2018
-
5484 J. Leinonen et al.: Retrieval of snowflake microphysical
properties
The triple-frequency technique appears to be useful
atidentifying graupel, that is, ice particles that are heav-ily
rimed and thus considerably denser than most aggre-gate snowflakes,
providing a sufficient signal for the triple-frequency retrieval to
detect. This was confirmed in this studywith the comparison to
polarimetric observations with theNPOL ground-based radar.
Globally, graupel occurs in rela-tively rare events that represent
only a small fraction of snowcases, and consequently graupel events
do not impact thestatistics much. However, graupel (and hail, which
is evendenser) can have a substantial societal impact where it
oc-curs, and thus detecting it can be valuable even though it
onlyoccurs in a small percentage of icy precipitation.
Detectinggraupel plumes, together with accurate snowflake size
deter-mination elsewhere in a precipitating region, can also
shedlight on the processes involved in the formation of
graupel.These plumes are usually small in their horizontal extent,
ofthe order of 1km, requiring a fairly high spatial resolution
inthe radars used to detect them, which can be challenging
toachieve if multifrequency radars are considered for
satelliteapplications.
Despite the improvements in retrieval precision in
mul-tifrequency retrievals, the retrieved results are still
depen-dent on the assumptions regarding the a priori distribution
ofthe retrieved microphysical parameters, as well as the
mass–dimensional exponent β. Different retrieved parameters
havewidely different sensitivities to the assumptions: the
retrievedsnow particle size changes only modestly in response
tochanges to the prior and to β, indicating that the size canbe
retrieved robustly with the multifrequency method. Incontrast, the
retrieved number concentration and density aremuch more sensitive
to the assumptions and therefore po-tentially susceptible to
retrieval errors caused by inaccurateprior data. Therefore, it is
still vital to constrain the algorithmusing in situ measurements
that provide not only the sizeand number concentration of
snowflakes but also their mass–dimensional scaling parameters α and
β. Later versions ofthe algorithm should include β as a retrievable
parameter andincorporate it in the multivariate prior so that the
retrieval er-rors originating from the uncertainty of β can be
properlyquantified.
The findings of this study concern the retrieval accuracyof
multifrequency radars and do not address their other po-tential
benefits. For instance, multifrequency radars can uti-lize
lower-frequency channels (e.g., Ku band) to penetratedeeper into
precipitation, particularly heavy rain that can at-tenuate higher
frequencies (e.g., W band) heavily enoughto block detection
altogether. Conversely, higher-frequencyradars can generally be
made more sensitive, allowing de-tection in regions below the
sensitivity thresholds of low-frequency bands. These benefits
should be considered to-gether with the retrieval performance when
decisions aboutinstrument specifications are made; see, e.g.,
Leinonen et al.(2015) for a quantitative assessment of retrieval
capabilitiesof a potential spaceborne triple-frequency radar.
This work builds on earlier experimental and modeling re-sults
that suggested that triple-frequency radars can be usedto constrain
snowflake habits and examines this capabilityin practice with a
prototype retrieval algorithm. Based onthe experience gained in
this study, we can identify two re-quirements for future research
that need to be fulfilled in or-der to use such an algorithm in an
operational setting. First,the snowflake scattering database, while
more extensive thanthose previously available, is still limited in
its scope, andits coverage of snowflake sizes, densities and habits
shouldbe expanded in order to support the forward model in all
sce-narios. Second, the a priori distributions used in the
retrievalsin this study are based on relatively few data points. An
abun-dance of in situ data from ice clouds and snowfall
currentlyexists as a result of many ground- and aircraft-based
fieldcampaigns; analyses of the data from these are needed
tosupport retrieval algorithm development by providing
rep-resentative a priori distributions of snowfall properties.
Thesubstantial cross correlations found in this study among thesnow
microphysical properties (Eq. 17) emphasize the needfor a
multivariate analysis of these datasets.
Data availability. The APR-3 data files can be down-loaded from
the OLYMPEX data repository
athttps://doi.org/10.5067/GPMGV/OLYMPEX/APR3/DATA201(Durden and
Tanelli, 2018), and the NPOL data
fromhttps://doi.org/10.5067/GPMGV/OLYMPEX/NPOL/DATA301(Wolff et
al., 2017). The Citation data are available
athttps://github.com/dopplerchase/Chase_et_al_2018 (last ac-cess: 1
October 2018), maintained by Randy J. Chase
(email:[email protected]). The BAECC campaign data are
availableat
https://github.com/dmoisseev/Snow-Retrievals-2014-2015(last access:
1 October 2018). The sounding data can beobtained from the
University of Wyoming collection
athttp://weather.uwyo.edu/upperair/sounding.html (last access:1
October 2018). The retrieval results, used to generate the
plots,are available in numerical form from Jussi Leinonen
(email:[email protected]).
Atmos. Meas. Tech., 11, 5471–5488, 2018
www.atmos-meas-tech.net/11/5471/2018/
https://doi.org/10.5067/GPMGV/OLYMPEX/APR3/DATA201https://doi.org/10.5067/GPMGV/OLYMPEX/NPOL/DATA301https://github.com/dopplerchase/Chase_et_al_2018https://github.com/dmoisseev/Snow-Retrievals-2014-2015http://weather.uwyo.edu/upperair/sounding.html
-
J. Leinonen et al.: Retrieval of snowflake microphysical
properties 5485
Appendix A: Fast derivation of error estimates forretrieved
quantities
Consider a scalar Q(x) that is a function (not necessarily
alinear function) of the vector x of normally distributed ran-dom
variables, whose probability distribution p(x) is givenby the mean
〈x〉 and the covariance S. For example, Q canbe ln Wice or the
logarithm of any variable introduced inSect. 2.4. Then, a
probabilistic error estimate is given by thestandard deviation
1Q= Std[Q] =√〈Q2〉− 〈Q〉2, (A1)
where the expectation, denoted by 〈·〉, is taken over the PDFof
x. The expectation can be estimated efficiently using
aGauss–Hermite quadrature. For a three-variable x (general-ization
to other numbers of variables is straightforward), theexpectation
〈Q〉 is obtained as follows:
〈Q〉 =
∫x
Q(x)p(x)dx ≈∑i,j,k
wiwjwkQ(xijk), (A2)
wi =1√πwGH,i, (A3)
xijk = 〈x〉+√
2V31/2[xGH,i xGH,j xGH,k
]T, (A4)
where
– V is a matrix whose columns contain the normalizedeigenvectors
of S,
– 3 is a diagonal matrix containing the correspondingeigenvalues
of S,
– xGH and wGH are the points and weights of a Gauss–Hermite
quadrature that gives the approximation
∞∫−∞
exp(−x2)f (x)dx ≈N∑i=1
wGH,i f (xGH,i), (A5)
where the approximation is exact if f is a polynomialof at most
degree 2N − 1; xGH and wGH can be foundin many tables (e.g., Beyer,
1987) and in scientific soft-ware packages (e.g., SciPy; Oliphant,
2007).
〈Q2〉 can also be estimated using the above method, thus giv-ing
the error estimate when substituted into Eq. (A1). Thisis derived
by computing the Gauss–Hermite quadrature forthe standard
multivariate normal distribution with zero meanand identity
covariance, then mapping the quadrature pointsto the corresponding
points in the distribution of x.
www.atmos-meas-tech.net/11/5471/2018/ Atmos. Meas. Tech., 11,
5471–5488, 2018
-
5486 J. Leinonen et al.: Retrieval of snowflake microphysical
properties
Supplement. The supplement related to this article is
availableonline at:
https://doi.org/10.5194/amt-11-5471-2018-supplement.
Author contributions. JL planned the study, formulated and
imple-mented the retrieval algorithm, and performed the analysis
pre-sented in this paper. He also led the preparation of this
article, withcontributions from all authors. MDL advised on the
algorithm for-mulation and data analysis. ST and OOS calibrated and
quality con-trolled the APR-3 data and provided support for using
them; ST alsoparticipated in the collection of the APR-3 data
during OLYMPEX–RADEX. BD processed the NPOL data, provided advice
on theiruse and participated in the NPOL operations during
OLYMPEX.RJC and JAF analyzed and processed the Citation data,
collocatedthem with APR-3, and advised on the comparisons to the
retrievals.AvL and DM coordinated the collection of the BAECC in
situ dataand processed them for use in this study.
Competing interests. The authors declare that they have no
con-flicts of interest.
Acknowledgements. We thank the two anonymous reviewers fortheir
constructive comments. The research of Jussi Leinonen,Matthew D.
Lebsock, Simone Tanelli and Ousmane O. Sy wascarried out at the Jet
Propulsion Laboratory (JPL), CaliforniaInstitute of Technology,
under contract with NASA. The workof Jussi Leinonen and Matthew D.
Lebsock was supported bythe NASA Aerosol-Cloud-Ecosystem and
CloudSat missionsunder RTOP WBS 103930/6.1 and 103428/8.A.1.6,
respectively.Jussi Leinonen was partly funded under subcontract
1559252from JPL to UCLA. Simone Tanelli and Ousmane O. Sy
ac-knowledge support from the GPM GV program and the ACEScience
Working Group funding for the acquisition and initialprocessing of
APR-3 data, and support from the Earth ScienceU.S. Participating
Investigator program for the detailed analysis ofW-band Doppler
data. Funding for the research of Brenda Dolan,Randy J. Chase and
Joseph A. Finlon was provided by NASAPrecipitation Measurement
Missions grants NNX16AI11G (BD)and NNX16AD80G (Randy J. Chase and
Joseph A. Finlon)under Ramesh Kakar. Dmitri Moisseev acknowledges
the fundingreceived through ERA-PLANET, trans-national project
iCUPE(grant agreement 689443), funded under the EU Horizon
2020Framework Programme, and the Academy of Finland (grant
nos.307331 and 305175). The research work of Annakaisa von
Lerberwas funded by EU’s Horizon 2020 research and innovation
program(EC-HORIZON2020-PR700099-ANYWHERE).
Edited by: Mark KulieReviewed by: two anonymous referees
References
Bailey, M. P. and Hallett, J.: A Comprehensive Habit Diagram
forAtmospheric Ice Crystals: Confirmation from the Laboratory,AIRS
II, and Other Field Studies, J. Atmos. Sci., 66,
2888–2899,https://doi.org/10.1175/2009JAS2883.1, 2009.
Beyer, W. H.: CRC Handbook of Mathematical Sciences, CRCPress,
Boca Raton, Florida, USA, 1987.
Bohren, C. F. and Huffman, D. R.: Absorption and Scattering
ofLight by Small Particles, John Wiley & Sons, Inc., New
York,USA, 1983.
Botta, G., Aydin, K., Verlinde, J., Avramov, A. E., Ackerman,A.
S., Fridlind, A. M., McFarquhar, G. M., and Wolde, M.:Millimeter
wave scattering from ice crystals and their aggre-gates: Comparing
cloud model simulations with X-and Ka-band radar measurements, J.
Geophys. Res., 116, D00T04,https://doi.org/10.1029/2011JD015909,
2011.
Delanoë, J. M. E., Heymsfield, A. J., Protat, A., Bansemer, A.,
andHogan, R. J.: Normalized particle size distribution for
remotesensing application, J. Geophys. Res.-Atmos., 119,
4204–4227,https://doi.org/10.1002/2013JD020700, 2014.
Dolan, B. and Rutledge, S. A.: A theory-based hydrom-eteor
identification algorithm for X-band polarimet-ric radars, J. Atmos.
Ocean. Tech., 46,
1196–1213,https://doi.org/10.1175/2009JTECHA1208.1, 2009.
Durden, S. L. and Tanelli, S.: GPM Ground ValidationAirborne
Precipitation Radar 3rd Generation (APR-3) OLYMPEX V2, Dataset
available online from theNASA EOSDIS Global Hydrology Resource
Center Dis-tributed Active Archive Center, Huntsville, Alabama,
USA,https://doi.org/10.5067/GPMGV/OLYMPEX/APR3/DATA201,2018.
Erfani, E. and Mitchell, D. L.: Growth of ice particle mass and
pro-jected area during riming, Atmos. Chem. Phys., 17,
1241–1257,https://doi.org/10.5194/acp-17-1241-2017, 2017.
Field, P. R. and Heymsfield, A. J.: Importance of snow toglobal
precipitation, Geophys. Res. Lett., 42,
9512–9520,https://doi.org/10.1002/2015GL065497, 2015.
Gergely, M., Cooper, S. J., and Garrett, T. J.: Using
snowflakesurface-area-to-volume ratio to model and interpret
snow-fall triple-frequency radar signatures, Atmos. Chem. Phys.,17,
12011–12030, https://doi.org/10.5194/acp-17-12011-2017,2017.
Harrington, J. Y., Sulia, K., and Morrison, H.: A Method
forAdaptive Habit Prediction in Bulk Microphysical Models. PartI:
Theoretical Development, J. Atmos. Sci., 70,
349–364,https://doi.org/10.1175/JAS-D-12-040.1, 2013.
Helmus, J. J. and Collis, S. M.: The Python ARM Radar
Toolkit(Py-ART), a Library for Working with Weather Radar Data
inthe Python Programming Language, J. Open Res. Software, 4,e25,
https://doi.org/10.5334/jors.119, 2016.
Heymsfield, A. J. and Kajikawa, M.: An Improved Approach
toCalculating Terminal Velocities of Plate-like Crystals and
Grau-pel, J. Atmos. Sci., 44, 1088–1099,
https://doi.org/10.1175/1520-0469(1987)0442.0.CO;2, 1987.
Heymsfield, A. J., Field, P., and Bansemer, A.: Exponentialsize
distributions for snow, J. Atmos. Sci., 65,
4017–4031,https://doi.org/10.1175/2008JAS2583.1, 2008.
Hitschfeld, W. and Bordan, J.: Errors Inherent in the
RadarMeasurement of Rainfall at Attenuating Wavelenghts,J.
Meteorol., 11, 58–67,
https://doi.org/10.1175/1520-0469(1954)0112.0.CO;2, 1954.
Hogan, R. J., Illingworth, A. J., and Sauvageot, H.:
Measuringcrystal size in cirrus using 35- and 94-GHz radars, J.
At-
Atmos. Meas. Tech., 11, 5471–5488, 2018
www.atmos-meas-tech.net/11/5471/2018/
https://doi.org/10.5194/amt-11-5471-2018-supplementhttps://doi.org/10.1175/2009JAS2883.1https://doi.org/10.1029/2011JD015909https://doi.org/10.1002/2013JD020700https://doi.org/10.1175/2009JTECHA1208.1https://doi.org/10.5067/GPMGV/OLYMPEX/APR3/DATA201https://doi.org/10.1002/2015GL065497https://doi.org/10.1175/JAS-D-12-040.1https://doi.org/10.5334/jors.119https://doi.org/10.1175/1520-0469(1987)0442.0.CO;2https://doi.org/10.1175/1520-0469(1987)0442.0.CO;2https://doi.org/10.1175/2008JAS2583.1https://doi.org/10.1175/1520-0469(1954)0112.0.CO;2https://doi.org/10.1175/1520-0469(1954)0112.0.CO;2
-
J. Leinonen et al.: Retrieval of snowflake microphysical
properties 5487
mos. Ocean. Tech., 17, 27–37,
https://doi.org/10.1175/1520-0426(2000)0172.0.CO;2, 2000.
Houze Jr., R. A., McMurdie, L., Tanelli, S., Mace, J., and
Nes-bitt, S.: OLYMPEX Science Summary for 3 December 2015,available
at:
http://olympex.atmos.washington.edu/archive/reports/20151203/20151203Science_summary.html
(last access:2 February 2018), 2015a.
Houze Jr., R. A., McMurdie, L., Zagrodnik, J., Duffy, G.,
Dur-den, S., and Funk, A.: OLYMPEX Science Summary for 4December
2015, available at:
http://olympex.atmos.washington.edu/archive/reports/20151204/20151204Science_summary.html(last
access: 2 February 2018), 2015b.
Houze Jr., R. A., McMurdie, L. A., Petersen, W. A., Schwaller,M.
R., Baccus, W., Lundquist, J. D., Mass, C. F., Nijssen,
B.,Rutledge, S. A., Hudak, D. R., Tanelli, S., Mace, G. G.,
Poel-lot, M. R., Lettenmaier, D. P., Zagrodnik, J. P., Rowe, A.
K.,DeHart, J. C., Madaus, L. E., and Barnes, H. C.: The
OlympicMountains Experiment (OLYMPEX), B. Am. Meteorol. Soc.,
98,2167–2188, https://doi.org/10.1175/BAMS-D-16-0182.1, 2017.
ITU: Recommendation ITU-R P.676-11: Attenuation by atmo-spheric
gases, International Telecommunications Union, 2016.
Jackson, R. C., McFarquhar, G. M., Stith, J., Beals, M., Shaw,R.
A., Jensen, J., Fugal, J., and Korolev, A.: An Assess-ment of the
Impact of Antishattering Tips and Artifact Re-moval Techniques on
Cloud Ice Size Distributions Measured bythe 2D Cloud Probe, J.
Atmos. Ocean. Tech., 31,
2567–2590,https://doi.org/10.1175/JTECH-D-13-00239.1, 2014.
Jaynes, E. T.: Probability Theory: The Logic of Science,
CambridgeUniversity Press, Cambridge, UK, 2003.
Kedem, B. and Chiu, L.: On the lognormality of rain rate, P.
Natl.Acad. Sci. USA, 84, 901–905, 1987.
Kneifel, S., Kulie, M. S., and Bennartz, R.: A triplefrequency
approach to retrieve microphysical snow-fall parameters, J.
Geophys. Res., 116, D11203,https://doi.org/10.1029/2010JD015430,
2011.
Kneifel, S., von Lerber, A., Tiira, J., Moisseev, D., Kol-lias,
P., and Leinonen, J.: Observed relations betweensnowfall
microphysics and triple-frequency radar mea-surements, J. Geophys.
Res.-Atmos., 120, 6034–6055,https://doi.org/10.1002/2015JD023156,
2015.
Korolev, A., Strapp, J. W., Isaac, G. A., and Emery, E.:
Im-proved Airborne Hot-Wire Measurements of Ice Water Con-tent in
Clouds, J. Atmos. Ocean. Tech., 30,
2121–2131,https://doi.org/10.1175/JTECH-D-13-00007.1, 2013.
Korolev, A. V., Strapp, J. W., Isaac, G. A., and Nevzorov, A.
N.:The Nevzorov Airborne Hot-Wire LWC-TWC Probe: Princi-ple of
Operation and Performance Characteristics, J. Atmos.Ocean. Tech.,
15, 1495–1510, https://doi.org/10.1175/1520-0426(1998)0152.0.CO;2,
1998.
Kulie, M. S., Hiley, M. J., Bennartz, R., Kneifel, S.,
andTanelli, S.: Triple frequency radar reflectivity signatures
ofsnow: Observations and comparisons to theoretical ice parti-cle
scattering models, J. Appl. Meteorol. Clim., 53,
1080–1098,https://doi.org/10.1175/JAMC-D-13-066.1, 2014.
Kuo, K.-S., Olson, W. S., Johnson, B. T., Grecu, M., Tian,
L.,Clune, T. L., van Aartsen, B. H., Heymsfield, A. J., Liao, L.,
andMeneghini, R.: The Microwave Radiative Properties of FallingSnow
Derived from Nonspherical Ice Particle Models. Part I:An Extensive
Database of Simulated Pristine Crystals and Ag-
gregate Particles, and Their Scattering Properties, J. Appl.
Me-teorol. Clim., 55, 691–708,
https://doi.org/10.1175/JAMC-D-15-0130.1, 2016.
Lamb, D. and Verlinde, J.: Physics and Chemistry of Clouds,
Cam-bridge University Press, Cambridge, UK, 2011.
Lawson, R. P., O’Connor, D., Zmarzly, P., Weaver, K., Baker,
B.,Mo, Q., and Jonsson, H.: The 2D-S (Stereo) Probe: Designand
Preliminary Tests of a New Airborne, High-Speed, High-Resolution
Particle Imaging Probe, J. Atmos. Ocean. Tech., 23,1462–1477,
https://doi.org/10.1175/JTECH1927.1, 2006.
Leinonen, J. and Moisseev, D.: What do triple-frequency radar
sig-natures reveal about aggregate snowflakes?, J. Geophys.
Res.,120, 229–239, https://doi.org/10.1002/2014JD022072, 2015.
Leinonen, J. and Szyrmer, W.: Radar signatures of
snowflakeriming: A modeling study, Earth Space Sci., 2,
346–358,https://doi.org/10.1002/2015EA000102, 2015.
Leinonen, J., Kneifel, S., Moisseev, D., Tyynelä, J.,
Tanelli,S., and Nousiainen, T.: Evidence of NonspheroidalBehavior
in Millimeter-Wavelength Radar Observa-tions of Snowfall, J.
Geophys. Res., 117, D18205,https://doi.org/10.1029/2012JD017680,
2012a.
Leinonen, J., Moisseev, D., Leskinen, M., and Petersen, W.:A
Climatology of Disdrometer Measurements of Rainfallin Finland over
Five Years with Implications for GlobalRadar Observations, J. Appl.
Meteorol. Clim., 51,
392–404,https://doi.org/10.1175/JAMC-D-11-056.1, 2012b.
Leinonen, J., Lebsock, M. D., Tanelli, S., Suzuki, K.,
Yashiro,H., and Miyamoto, Y.: Performance assessment of a
triple-frequency spaceborne cloud-precipitation radar concept
usinga global cloud-resolving model, Atmos. Meas. Tech., 8,
3493–3517, https://doi.org/10.5194/amt-8-3493-2015, 2015.
Leinonen, J., Lebsock, M. D., Stephens, G. L., and Suzuki,K.:
Improved Retrieval of Cloud Liquid Water from Cloud-Sat and MODIS,
J. Appl. Meteorol. Clim., 55,
1831–1844,https://doi.org/10.1175/JAMC-D-16-0077.1, 2016.
Liao, L., Meneghini, R., Iguchi, T., and Detwiler, A.: Use of
dual-wavelength radar for snow parameter estimates, J. Atmos.
Ocean.Tech., 22, 1494–1506,
https://doi.org/10.1175/JTECH1808.1,2005.
Locatelli, J. D. and Hobbs, P. V.: Fall speeds and masses
ofsolid precipitation particles, J. Geophys. Res., 79,
2185–2197,https://doi.org/10.1029/JC079i015p02185, 1974.
Lu, Y., Jiang, Z., Aydin, K., Verlinde, J., Clothiaux, E. E.,
and Botta,G.: A polarimetric scattering database for non-spherical
ice par-ticles at microwave wavelengths, Atmos. Meas. Tech., 9,
5119–5134, https://doi.org/10.5194/amt-9-5119-2016, 2016.
Mascio, J. and Mace, G. G.: Quantifying uncertainties in radar
for-ward models through a comparison between CloudSat and
SPar-tICus reflectivity factors, J. Geophys. Res.-Atmos., 122,
1665–1684, https://doi.org/10.1002/2016JD025183, 2017.
Mascio, J., Xu, Z., and Mace, G. G.: The Mass-Dimensional
Proper-ties of Cirrus Clouds During TC4, J. Geophys. Res.-Atmos.,
122,10402–10417, https://doi.org/10.1002/2017JD026787, 2017.
Matrosov, S. Y.: Possibilities of cirrus particle sizing from
dual-frequency radar measurements, J. Geophys. Res., 98,
20675–20683, https://doi.org/10.1029/93JD02335, 1993.
Matrosov, S. Y.: A dual-wavelength radar methodto measure
snowfall rate, J. Appl. Meteo-
www.atmos-meas-tech.net/11/5471/2018/ Atmos. Meas. Tech., 11,
5471–5488, 2018
https://doi.org/10.1175/1520-0426(2000)0172.0.CO;2https://doi.org/10.1175/1520-0426(2000)0172.0.CO;2http://olympex.atmos.washington.edu/archive/reports/20151203/20151203Science_summary.htmlhttp://olympex.atmos.washington.edu/archive/reports/20151203/20151203Science_summary.htmlhttp://olympex.atmos.washington.edu/archive/reports/20151204/20151204Science_summary.htmlhttp://olympex.atmos.washington.edu/archive/reports/20151204/20151204Science_summary.htmlhttps://doi.org/10.1175/BAMS-D-16-0182.1https://doi.org/10.1175/JTECH-D-13-00239.1https://doi.org/10.1029/2010JD015430https://doi.org/10.1002/2015JD023156https://doi.org/10.1175/JTECH-D-13-00007.1https://doi.org/10.1175/1520-0426(1998)0152.0.CO;2https://doi.org/10.1175/1520-0426(1998)0152.0.CO;2https://doi.org/10.1175/JAMC-D-13-066.1https://doi.org/10.1175/JAMC-D-15-0130.1https://doi.org/10.1175/JAMC-D-15-0130.1https://doi.org/10.1175/JTECH1927.1https://doi.org/10.1002/2014JD022072https://doi.org/10.1002/2015EA000102https://doi.org/10.1029/2012JD017680https://doi.org/10.1175/JAMC-D-11-056.1h