quantitative precipitation estimation (QPE) of snowfall has generally been
expressed in power-law form between equivalent radar reflectivity factor
(Ze) and liquid equivalent snow rate (SR). It is known that
there is large variability in the prefactor of the power law due to changes
in particle size distribution (PSD), density, and fall velocity, whereas the
variability of the exponent is considerably smaller. The dual-wavelength
radar reflectivity ratio (DWR) technique can improve SR
accuracy by estimating one of the PSD parameters (characteristic diameter),
thus reducing the variability due to the prefactor. The two frequencies
commonly used in dual-wavelength techniques are Ku- and Ka-bands. The basic
idea of DWR is that the snow particle size-to-wavelength ratio is
falls in the Rayleigh region at Ku-band but in the Mie region at
Ka-band.
We propose a method for snow rate estimation by using NASA D3R radar DWR and
Ka-band reflectivity observations collected during a long-duration synoptic
snow event on 30–31 January 2012 during the GCPEx (GPM Cold-season
Precipitation Experiment). Since the particle mass can be estimated using
2-D video disdrometer (2DVD) fall speed data and hydrodynamic theory, we
simulate the DWR and compare it directly with D3R radar measurements. We also use
the 2DVD-based mass to compute the 2DVD-based SR. Using three different mass
estimation methods, we arrive at three respective sets of Z–SR and
SR(Zh, DWR) relationships. We then use these relationships with D3R
measurements to compute radar-based SR. Finally, we validate our method by
comparing the D3R radar-retrieved SR with accumulated SR directly measured by a
well-shielded Pluvio gauge for the entire synoptic event.
Introduction
A detailed understanding of the geometric, microphysical, and scattering
properties of ice hydrometeors is a vital prerequisite for the development of
radar-based quantitative precipitation estimation (QPE) algorithms. Recent
advances in surface and airborne optical imaging instruments and the wide
proliferation of dual-polarization and multi-wavelength radar systems
(ground based, airborne or satellite) have allowed for observations of the
complexity inherent in winter precipitation via dedicated field programs
(e.g., Skofronick-Jackson et al., 2015; Petäjä et al., 2016). These
large field programs are vital given that the retrieval problem is severely
underconstrained due to large number of geometrical and microphysical
parameters of natural snowfall, their extreme sensitivity to subtle changes
in environmental conditions, and co-existence of different populations of
particle types within the sample volume (e.g., Szyrmer and Zawadzki, 2014).
The surface imaging instruments that give complementary measurements and are
used in a number of recent studies include (i) 2-D video disdrometer (2DVD;
Schönhuber et al., 2008), (ii) precipitation imaging package (PIP; von
Lerber et al., 2017), (iii) Multi-Angle Snowflake Camera (MASC; Garrett et
al., 2012). When these instruments are used in conjunction with a
well-shielded GEONOR or PLUVIO gauge, it is shown that a physically
consistent representation of the geometric, microphysical, and scattering
properties needed for radar-based QPE can be achieved (Szyrmer and Zawadzki,
2010; Huang et al., 2015; von Lerber et al., 2017; Bukovčić et al.,
2018). In this study, we use the 2DVD and PLUVIO gauge located within a
double fence international reference (DFIR) wind shield to reduce wind
effects.
Radar-based QPE has generally been based on Ze–SR (Ze is reflectivity;
SR is liquid equivalent snow rate) power laws of the form Ze=α(SR)β,
where the prefactor and exponent are estimated based on (i) direct correlation
of radar-measured Ze with snow gauges (Rasmussen et
al., 2003; Fujiyoshi et al., 1990; Wolfe and Snider, 2012) or (ii) using
imaging disdrometers such as 2DVD or PIP (Huang et al., 2015; von Lerber et
al., 2017). Recently, Falconi et al. (2018) developed Ze–SR power laws at
three frequencies (X-, Ka-, and W-band) by direct correlation of radar and PIP
observations. These studies have highlighted the large variability of
α due to particle size distribution (PSD), density, fall velocity,
and dominant snow type, whereas the variability in β is considerably
smaller. Similarly, both methods, (i) and (ii), have been used to estimate ice
water content (IWC) from Ze using power laws of the form Ze=a(IWC)b
based on airborne particle probe data, direct measurements of IWC, and
airborne measurements of Ze (principally at X-, Ka-, and W-bands)
(e.g., Heymsfield et al., 2005, 2016; Hogan et al., 2006).
The advantage of airborne data is that a wide variety of temperatures and
cloud types can be sampled (Heymsfield et al., 2016).
The dual-wavelength reflectivity ratio (DWR, the ratio of reflectivity from two
different bands) radar-based QPE was proposed by Matrosov (1998), Matrosov et al. (2005) to
improve SR accuracy by estimating the PSD parameter (median volume diameter
D0) with relatively low dependence on density if assumed constant. There
has been limited use of dual-λ techniques for snowfall estimation,
mainly using vertical-pointing ground radars or nadir-pointing airborne
radars (Liao et al., 2005, 2008, 2016; Szyrmer and Zawadzki, 2014; Falconi et
al., 2018). The dual-λ method is of interest to us due to the
availability of the NASA D3R scanning radar (Vega et al., 2014), which, to
the best of our knowledge, has not been exploited for snow QPE to date.
The DWR is defined as the ratio of the equivalent radar reflectivity factors at
two different frequency bands. The main principle in DWR is that the particle's
size-to-wavelength ratio falls in the Rayleigh region at a low-frequency band
(e.g., Ku-band) but in the Mie region at a high-frequency band (e.g., Ka-band)
(Matrosov, 1998; Matrosov et al., 2005; Liao et al., 2016). Previous studies
have shown that the DWR can be used to estimate Dm, where Dm is defined
as the ratio of the fourth moment to the third moment of the PSD expressed in
terms of liquid-equivalent size or mass (Liao et al., 2016). In this sense
the DWR is similar to differential reflectivity (Zdr) in dual-polarization
radar technique, where Zdr is used to estimate Dm (but the physical
principles are, of course, different; Meneghini and Liao, 2007). The SR is
obtained by “adjusting” the coefficient α in the Ze–SR power law
based on the estimation of Dm provided by the DWR. The prefactor α
depends on the intercept parameter of the PSD (von Lerber et al., 2017) and not
on Dm directly. However, because of the apparent negative correlation between Dm and
PSD intercept parameter for a snowfall of a given intensity (Delanoë et
al., 2005; Tiira et al., 2016), measurements of Dm can be used to
adjust the Ze–SR power law.
This paper is organized as follows. In Sect. 2, we introduce the approach
and methodologies proposed and used in this study, which may be considered
technique development. We briefly explain how to estimate the mass of ice
particles using a set of aerodynamic equations based on Böhm (1989) and
Heymsfield and Westbrook (2010). We also give a brief introduction of the
scattering model based on particle mass. Section 3 provides a brief
overview of instruments installed at the test site and the dual-wavelength
radar used in this study (D3R: Vega et al., 2014). We analyze surface and D3R
radar data from one synoptic snowfall event during GCPEx and compare SR retrieved
from DWR-based relations with SR measured by a snow gauge. The conclusions and
possibilities for further improvement of the proposed techniques are
discussed in Sect. 4. The acronyms and symbols are listed in Appendix.
MethodologyEstimation of particle mass
The direct estimation of the mass of an ice particle is difficult and at present
there is no instrument available to do this automatically. The conventional
method is to use a power-law relation between the mass and the maximum dimension
of the particle of the form m=aDb, where the prefactor a and exponent b
are computed via measurements of particle size distribution N(D) from aircraft
probes and independent measurements of the total ice water content as an
integral constraint (Heymsfield and Westbrook, 2010). A similar method was used by
Brandes et al. (2007), who used 2DVD data for N(D) and a snow gage for the liquid
equivalent snow accumulation over periods of 5 min. These methods are more
representative of an average relation when one particle type (e.g., snow
aggregates) dominates the snowfall with large deviations possible for
individual events with differing particle types (e.g., graupel).
To overcome these difficulties a more general method was proposed by
Böhm (1989) based on estimating mass from fall velocity measurements,
geometry, and environmental data if the measured fall velocity is in fact the
terminal velocity (i.e., in the absence of vertical air motion or turbulence
and in more or less uniform precipitation). The methodology has been
described in detail by Szyrmer and Zawadzki (2010), Huang et al. (2015), and von
Lerber et al. (2017), and we refer to these articles for details. The
essential feature is the unique nonlinear relation between the Davies
(1945) number (X) and the Reynolds number (Re), where X is the ratio of mass to
area or m/Ar0.25 (Ar=Ae/A is the area ratio, where
Ae is the effective projected area normal to the flow and A is the area
of the minimum circumscribing circle or ellipse that completely contains
Ae) and the Re is the product of terminal fall speed and the characteristic
dimension of the particle. We have neglected the environmental parameters
(air density, viscosity) as well as boundary layer depth of Abraham (1970)
and the inviscid drag coefficient. The procedure is to (i) compute Re from
fall velocity measurements and characteristic dimension of the particle
(usually the maximum dimension), (ii) compute the Davies number X, which is
expressed as a nonlinear function of Re, and boundary layer parameters
(C0=0.6 and δ0=5.83; Böhm, 1989) and (iii) estimate
particle mass from X and Ar. Heymsfield and Westbrook (2010) proposed a
simple adjustment (based on field and tank experiments) by defining a
modified Davies number as proportional to m/Ar0.5 along with
different boundary layer constants (C0=0.292; δ0=9.06)
from Böhm. Their adjustment was shown to be in very good agreement with
recent tank experiments by Westbrook and Sephton (2017), especially for
particles like pristine dendrites with low Ar and at low Re. Note that the
difference of C0 and δ0 in Böhm and
Heymsfield–Westbrook equations is mainly due to differences in the shape-correcting factor (Ar) to find the optimal relation between drag
coefficient (or Davies number, X) and Reynolds number (Re). This
is the main parameterization error in this set of equations.
Geometric and fall speed measurements
One source of uncertainty in applying the Böhm or Heymsfield and
Westbrook (HW) method is calculating the area ratio (Ar) using
instruments such as 2DVD or precipitation instrument package (PIP) as they
do not give the projected area normal to the flow (i.e., they do not give
the needed top view, but rather the 2DVD gives two side views on orthogonal
planes as illustrated in Fig. 1). This is reasonable for snow aggregates
which are expected to be randomly oriented. The other source of uncertainty
is in the definition of characteristic dimension used in Re, which in the HW
method is taken to be the diameter of the circumscribing circle that
completely encloses the projected area, the maximum dimension (Dmax;
this is what we use for the 2DVD in our application of the HW method). For
the Böhm method we use the procedure in Huang et al. (2015), which used
Dapp defined as the equal-volume spherical diameter.
A snowflake observed by a 2DVD from two views. The thick black
line is the contour of the snowflake and the thin black lines show the holes
inside the snowflake. The effective area, Ae, equals the area enclosed
by the thick black curve minus the area enclosed by thin lines. The blue
line represents the minimum circumscribed ellipse, the enclosed area of which is
denoted by A.
The two-dimensional video disdrometer (2DVD) used herein is described in
Schönhuber et al. (2000), and calibration and accuracy of the instrument
are detailed in Bernauer et al. (2015). The 2DVD is equipped with two
line-scan cameras (referred to as cameras A and B) which can capture the
particle image projection in two orthogonal planes (two side views). As
mentioned earlier the area ratio (Ar) should be obtained from the
projected image in the plane normal to the flow (i.e., top or bottom view).
However, to the best of our knowledge, there are no ground-based instruments
that can automatically and continuously capture the horizontal projected
views (i.e., in the plane orthogonal to the flow) of precipitation particles
(however, 3-D-reconstruction based on multiple views can give this
information; Kleinkort et al., 2017). Compared with other optical-based
instruments, such as HVSD (hydrometeor velocity size detector; Barthazy et
al., 2004) or SVI (snow video imager; Newman et al., 2009), which only captures
the projected view in one plane, the 2DVD offers views in two orthogonal
planes, giving more geometric information. Figure 1 shows a snowflake
observed by a 2DVD from two cameras. The thick black line is the contour of
the particle and the thin black lines show the holes inside the particle.
The effective projected area Ae in the definition of area ratio is easy
to compute by counting total pixels from the particle's image, and then
multiplying by horizontal and vertical pixel width. The blue line is the
minimum circumscribed ellipse. The area of the ellipse is A in the definition
of area ratio. The size of particle measured by 2DVD is called the apparent
diameter (Dapp) which is defined as the diameter of the equivalent
volume sphere (Schönhuber et al., 2000; Huang et al., 2015). The
Dapp is used when computing Re, as mentioned earlier. The area ratio and
Dapp are the geometric parameters that are used in our implementation of
the Böhm method.
In our application of the HW method, the A is based on the diameter of the
circumscribed circle that completely encloses the projected pixel area
(Ae), which is easy to calculate from the contours in Fig. 1. Thus the
area ratio is Ae/A, while the characteristic dimension in Re is the diameter
of the circumscribing circle. Note that the area ratio and characteristic
dimension in Re depend on the type of instrument used (e.g., advanced version
of snow video imager by von Lerber et al., 2017; the HVSD by Szyrmer and
Zawadzki, 2010). These instruments give a projected view in one plane only and
thus geometric corrections are used as detailed in the two references.
The two optic planes of the 2DVD are separated by around 6 mm and the
accurate distance is based on calibration by dropping 10 mm steel balls at
three corners of the sensing area (details of the calibration as well as
accuracy of size, fall speed, and other geometric measures are given in
Bernauer et al., 2015). During certain time periods, more than one
precipitation particle falls in the 2DVD observation area. Since the two cameras
look in different directions, the particles observed by camera A and camera B
need to be paired. This pairing procedure is called “matching”, and it
is illustrated in Fig. 2. The time period [t1, t2] is dependent on
the assumed reasonable fall speed range. Assuming that the minimum and
maximum reasonable fall speeds are vmin and vmax, respectively, the
distance between two optic planes is Dd, and camera A observed a
particle at t0, we have t1=t0+Dd/vmax and
t2=t0+Dd/vmin. After matching, the fall speed can
be calculated as Dd/Δt, where Δt is the time difference
between two cameras observing the same particle. Because the fall speed of
the 2DVD is dependent on matching, the geometric features and fall speeds
will be in error when mismatch occurs. Huang et al. (2010) analyzed snow
data from the 2DVD and found that the 2DVD manufacturer's matching algorithm
for snow resulted in a significant mismatching problem (see also Bernauer
et al., 2015). In the Appendix of Huang et al. (2010), they showed that the
mismatch will cause the volume, vertical dimension, and fall speed of
particles to be overestimated. Subsequently, the mass of particles will
also be overestimated, mainly because of fall speed. To get the best
estimation of mass, they used 2DVD single-camera data and re-did the
matching based on a weighted Hanesch criteria (Hanesch, 1999). If the match
criteria are not satisfied, then that particle is rejected; it follows that
the concentration will tend to be underestimated. To readjust the
measured concentration for this underestimate (assumed to be a constant
factor), the procedure described in Huang et al. (2015) is used, which only
involves the ratio of the total number of particles counted in the scan area
of the single camera to the number of successfully matched particles in the
virtual measurement area. For the event analyzed here (using method 1 in
Sect. 3.3), this adjustment factor is between 1.1 and 1.5. The Pluvio
gauge accumulation is not used as a constraint in method 1. The disadvantage
of using single-camera data, as described in Huang et al. (2015), is that
the particle contour data are not available (i.e., the manufacturer's code
does not provide line scan data from single camera). Without contour data,
both Dapp and A can only be estimated by the maximum width of the scan line
and height of the particle as detailed in Huang et al. (2015). Moreover, the
diameter of the circumscribing circle or ellipse cannot be obtained without
contour data. The only quantity included in single-camera data is Ae in
terms of number of pixels. The Huang and Bringi approach (Huang et al., 2015)
is referred to as HB, because both PSD (particle size distribution) and
reflectivity (Ze) are computed using Dapp as the measure of
particle size.
Illustration of the matching procedure. In the situation shown, it
is assumed that camera A observed a particle at time t0, and afterwards
during a certain time period, t1 to t2, camera B observed two
particles. The matching procedure decides which particle observed by camera B
is the same particle observed by camera A.
For methods 2 and 3 in Sect. 3.3, we used the manufacturer's matching
algorithm, which gives the contour data. To avoid overestimating mass due to
mismatch, we need to filter out those particles with unreasonable fall
speeds. The vertical dimension of the particle's image before match is
expressed as a number of scan lines (i.e., how many scan lines are masked by
the particle). After match (so vt is known), the vertical pixel width is
vt/fs, where fs is the scan frequency of a camera
(∼55kHz), and the vertical size of the particle is the
vertical pixel width multiplied by the number of scan lines. Because two
optical planes of the 2DVD are parallel, theoretically, the number of scan
lines from cameras A and B should be the same. Considering the distance from
the particle to the two cameras (projective effect of a camera), the digital
error of a camera and particle rotation in two planes, the difference in the
number of scan lines between two cameras may not always be the same but
should be very close. Hanesch (1999) gave a set of matching criteria,
the most important being the tolerance of the number of scan lines between
the two cameras (see Table 1). To obtain reliable fall speeds, we examined
all matched particles (given by the manufacturer's matching algorithm,
numbering 507 833 for the event and marked as green in Fig. 3) and removed
those particles which did not satisfy the Hanesch scan line criteria,
resulting in 175 199 (34.5 %) of particles that did satisfy the match
criteria (magenta marks in Fig. 3). We used the fall speeds of these filtered
particles to compute their mass for both Böhm and Heymsfield–Westbrook
methods, and then divided the mass by apparent volume (=πDapp3/6) to get the particle density. Since the maximum density
of ice particles is around 0.9 gcm-3, we further remove particles
with density larger than 1 gcm-3. After this two-step
filtering, the particles we use for further analysis (numbering 128 063) are
shown in Fig. 3 as blue points. The filtering will eliminate particles,
which will reduce the liquid equivalent snow accumulation. Hence, the Pluvio
gauge accumulation is used as an integral constraint, i.e., the
concentration in each bin is increased by a constant factor to match the
2DVD accumulation to the Pluvio accumulation. This constraint is only used
in methods 2 and 3 in Sect. 3.3.
Fall speed vs. Dapp for the synoptic case on 31 January 2012
at the CARE site. The green circles represent the results of the
manufacturer's matching algorithm, which is known to allow mismatched
particles with unrealistic fall speeds. The first filtering step is the
selection of matched particles which satisfy Hanesch scan line criteria
(magenta). The second filter step is shown as blue crosses, which are based on
particles with density (from mass computed by Böhm's or
Heymsfield–Westbrook method) lower than 1 gcm-3.
Hanesch 2DVD scan line criteria.
Max of totalDifference ofscan linesscan lines≤20<321–4415 %–11 %45–18111 %≥18220Scattering model
The scattering computation of ice particles is difficult because of their
irregular shapes with large natural variability (e.g., snow
aggregates or rimed crystals). The most common scattering method used in the
meteorological community is the discrete dipole approximation (DDA; Draine
and Flatau, 1994). However, DDA is very time consuming and not suitable for
large numbers of particles, especially at W-band (e.g., Chobanyan et al.,
2015). On the other hand, the T-matrix method (Mishchenko et al., 2002) is
more time efficient and commonly used in radar meteorology but it requires
that the irregular particle shape be simplified to an axis-symmetric shape
(e.g., spheroid). Ryzhkov et al. (1998) have shown that, in the Rayleigh region,
the radar cross section is mainly related to particle's mass squared and
less to the shape. For Mie scattering, however, the irregular snow shape
plays a more significant role. Westbrook et al. (2006, 2008) used the
Rayleigh–Gans approximation to develop an analytical equation for the
scattering cross sections of simulated snow aggregates of bullet rosettes
using an empirical fit to the form factor that accounts for deviations from
the Rayleigh limit. Here, we use two scattering models, one based on the
soft spheroid (Huang et al., 2015) with a fixed axis ratio and quasi-random
orientation. The apparent density is calculated as the ratio of mass to
apparent volume. There is considerable controversy in the literature on the
applicability of the soft spheroid model with a fixed axis ratio, especially at
Ka and higher frequencies such as W-band (e.g., Petty and Huang, 2010; Botta
et al., 2010; Leinonen et al., 2012; Kneifel et al., 2015). However, Falconi
et al. (2018) used the soft spheroid scattering model using T-matrix to
compute Ze (at X-, Ka-, and W-bands) and showed that an effective optimized
axis ratio of (oblate) spheroid could be selected that directly matches
measured Ze by radar (their optimal axis ratio, however, varied with the
frequency band, i.e., 1 for X-band, 0.8 for Ka, and 0.6 for W). They also
found some differences in the optimal axis ratios for fluffy snow vs.
rimed snow. Nevertheless, they compared DDA calculations of complex-shaped
aggregates to the soft spheroid model at W-band and concluded that the axis
ratio can be used as a tuning parameter. They also showed the importance
of size integration to compute Ze, i.e., the product of N(D) and the radar
cross section for the soft spheroid vs. complex-shape aggregates. Their
result implied that smaller particles had a larger value for the product
when using a soft spheroid of 0.6 axis ratio relative to complex aggregates
and vice versa for larger particles, leading to compensation when Ze is
computed by size integration over all sizes. Thus, the soft spheroid model
with axis ratio at 0.8 used by Huang et al. (2015), and which is used herein
at Ku- and Ka-bands, is a reasonable approximation.
The second scattering model we used herein is from Liao et al. (2013), who
use an effective fixed density approach to justify the oblate spheroid
model. To compare the scattering properties of a snow aggregate with its
simplified equal-mass spheroid, Liao et al. (2013) used six-branch bullet
rosette snow crystals with maximum dimensions of 200 and 400 µm as two basic elements that simulate snow aggregation. They
computed the backscattering coefficient, extinction coefficient, and
asymmetry factor for simulated snowflakes, using the DDA and for the
corresponding spheres and spheroids with the same mass but density fixed at
0.2 or 0.3 gcm-3, and hence the apparent sphere volume equals the
mass divided by the assumed fixed density. They showed that, when the
frequency was lower than 35 GHz (Ka-band), the Mie scattering properties of
spheres with a fixed density equal to 0.2 gcm-3 were in a good
agreement with the scattering results for the simulated complex-shaped
aggregate model with the same mass using the DDA (see also Kuo et al.,
2016). They also showed this agreement with a spheroid model with a fixed
axis ratio of 0.6 and random orientation. Here, we use the Liao et al. (2013)
equivalent spheroid model with a fixed effective density of 0.2 gcm-3
at Ku- and Ka-bands (note that we estimate the mass of each
particle from 2DVD measurements as described in Sect. 2.1). Note that this
fixed-density spheroid scattering model is not based on microphysics (where
the density would fall off inversely with increasing size) but on scattering
equivalence with a simulated (same-mass) complex-shaped aggregate snowflake
(Liao et al., 2016).
Case analysisTest site instrumentation and the synoptic event
The GPM Cold-season Precipitation Experiment (GCPEx) was conducted by the
National Aeronautics and Space Administration (NASA), USA, in cooperation
with Environment Canada in Ontario, Canada from 17 January to 29 February 2012.
The goal of GCPEx was “… to characterize the ability of
multi-frequency active and passive microwave sensors to detect and estimate
falling snow…” (Skofronick-Jackson et al., 2015). The field
experiment sites were located north of Toronto, Canada between Lake Huron
and Lake Ontario. The GCPEx had five test sites, namely CARE (Centre for
Atmospheric Research Experiments), Sky Dive, Steam Show, Bob Morton, and
Huronia. The locations of five sites are shown in Fig. 4. The CARE site was
the main test site for the experiment, located at 44∘13′58.44′′ N,
79∘46′53.28′′ W and equipped with an extensive suite of ground
instruments. The 2DVD (SN37) and OTT Pluvio2 400 used for observations
and analyses in this paper were installed inside a DFIR (double fence
intercomparison reference) wind shield. The dual-frequency dual-polarized
doppler radar (D3R) was also located at the CARE site (Vega et al., 2014)
near the 2DVD. The instruments used in this paper are depicted in Fig. 5.
Because the radar and the instrumented site were nearly collocated, we can
effectively view the set-up as similar to a vertical-pointing radar as
described in more detail in Sect. 3.2.
A map of the GCPEx field campaign. The five test sites are CARE,
Sky Dive, Steam Show, Bob Morton, and Huronia. The ground observation
instruments, namely 2DVD, D3R, and Pluvio, used in this research, were
located at CARE.
Instruments used in this study: (a) 2DVD (SN37),
(b) D3R (dual-wavelength dual-polarized doppler radar), and (c) OTT Pluvio2 400
precipitation gauge.
We examine a snowfall event on 30–31 January 2012 that occurred across the
GCPEx study area between roughly 22:00 UTC, 30 January and 04:00 UTC, 31 January.
Details of this case using King City radar and aircraft spiral
descent over the CARE site is given in Skofronick-Jackson et al. (2015).
This event resulted in liquid accumulations of roughly 1–4 mm across the
GCPEx domain with fairly uniform snowfall rates throughout the event. At the
CARE site the accumulations over an 8 h period were <3.5mm. Echo
tops as measured by high-altitude airborne radar were 7–8 km. The
precipitation was driven by a shortwave trough moving from southwest to
northeast across the domain. Figure 6 displays the 850 hPa geopotential
heights (m), temperature (K), relative humidity (%), and winds (ms-1)
at 00:00 UTC, 31 January, during the middle of the accumulating
snowfall. A trough axis is apparent just to the west of the GCPEx domain
(green star in Fig. 6). Low-level warm-air advection forcing upward motion
is coincident with high relative humidity on the leading edge of the trough,
over the GCPEx domain (Fig. 6). Temperatures in this layer were around -10
to -15∘C throughout the event, supporting efficient crystal
growth, aggregation, and potentially less dense snowfall as this is in the
dendritic crystal temperature zone (e.g., Magono and Lee, 1966). Aircraft
probe data during a descent over the CARE site between 23:15 and 23:43 UTC
showed the median volume diameter (D0) of 3 mm, with particles up
to a maximum of 8 mm (aggregates of dendrites) at 2.2 km m.s.l. with a large
concentration of smaller sizes < 0.5 mm (dendritic and irregular
shapes; Skofronick-Jackson et al., 2015). At the surface, photographs of the
precipitation types by the University of Manitoba showed small irregular
particles and aggregates (<3mm) at 23:30 UTC on 30 January.
The 00:00 UTC, 31 January 2012, 850 hPa geopotential heights (m, black
solid contours), temperature (K, red: above freezing, blue: below
freezing), relative humidity (%, green shaded contours), and wind (ms-1,
wind barbs). The red dot in the center right portion of the figure
denotes the general location of the GCPEx field instruments.
D3R radar data
The D3R is a Ku- and Ka-band dual-wavelength polarimetric scanning radar.
It was designed for ground validation of rain and falling snow from GPM
satellite-borne DPR (dual-frequency precipitation radar). The two
frequencies used in the D3R are 13.91 GHz (Ku) and 35.56 GHz (Ka). These two
frequencies were used for scattering computations in this research as well.
Some parameters of the D3R radar relevant for this paper are shown in Table 2.
The range resolution of the radar is adjustable but usually set to
150 m
and the near-field distance is ∼300m; the practical minimum
operational range is around 450 m. The minimum detectable signal of the D3R
is -10dBZ at 15 km. This means that when Zh is -10dBZ at 15 km,
the signal-to-noise ratio (SNR) is 0 dB. Therefore, the SNR at any range,
r, can be computed as follows:
SNRr=Zhr+10+20log1015r[dB].
The SNR is a very important indicator for radar data quality control (QC),
the other important parameter for QC (in terms of detecting “meteo” vs.
“nonmeteo” echoes) being the texture of the standard deviation (SD) of the
differential propagation phase (φdp). We randomly selected 20
out of 85 RHI sweeps from 31 January 2012 and computed the SD of Ku-band
φdp for each beam over 10 consecutive gates where SNR ≥10dB.
According to the histogram of the SD of φdp, 90 % of
the values were less than around 8∘. Radar data at a range gate m
are identified as “good” data (i.e., meteorological echoes) only if the
standard deviation of φdp from the (m-5)th gate to the
(m+4)th gate is less than 8∘. This criterion sets a good data
mask for each beam at Ku-band. On the other hand, the φdp at
Ka-band was determined to be too noisy and hence not used herein. The
good data mask for the Ka-band beam is set by the mask determined by the Ku-band
criteria, with the additional requirement that the Ka-band SNR >3dB for the range gate to be considered good. Note that both radars
are mounted on a common pedestal so that the Ku and Ka-band beams are
perfectly aligned.
Some D3R parameters relevant for this study. Full D3R
specifications can be found in Vega et al. (2014).
KuKaFrequency (GHz)13.9135.56Min detectable signal-10dBZ at 15 kmRange (km)0.45–30 Range resolution (m)150 Anterior beam width∼1∘
There are four scan types that can be performed by the D3R, namely PPI
(plan position indicator), RHI (range height indicator), surveillance, and
vertical pointing. Figure 7 shows the scan strategies of the D3R on
31 January 2012, which consisted of a fast PPI scan (surveillance
scan; 10∘ per second) followed by four RHI scans (1∘ per
second),
except from 01:00 to 02:00 UTC. The RHI scans with an azimuth angle of
139.9∘ point to the Steam Show site and those at 87.8∘ point to
the Sky Dive site. There were no RHI scans pointing to the Bob Morton site,
and Huronia (52 km) was beyond the operational range (maximum 30 km) of the
D3R. During the most intense snowfall the D3R scans did not cover the
instrument clusters at the Sky Dive and Steam Show sites. So we were left with
the analysis of the D3R radar data at close proximity to the 2DVD or effectively
vertical-pointing equivalent using RHI data from 75 to 90∘ at the
nearest practical range of 600 m. PPI scan data at low elevation angle
(3∘) were also used from range gate at 600 m. The assumption is that
there is little evolution of particle microphysics from about 600 m height
to the surface and that the synoptic-scale snowfall was uniform in azimuth
(confirmed by Skofronick-Jackson et al., 2015). The snowfall was spatially
uniform around the CARE site so we selected data at 600 m range to be
compared with the 2DVD and Pluvio observations (this range was selected based on the
minimum operational range of 450 m; see Table 2) to which 150 m was added
based on close examination of data quality. For RHI scans, the Zh at
each band was averaged over the beams from 75 to 90∘. The
75∘ is obtained from 600⋅cos(75∘)≈155m which is close
to the range resolution. For the fast PPI scan, Zh was averaged over
all azimuthal beams at 600 m range.
D3R scan strategies on 31 January 2012. The y axis is azimuth
angle (RHI; red x) or elevation angle (PPI; blue o). The scan rate of
RHI was 1∘s-1 and 10∘s-1 for PPI.
The time series of averaged raw Zh at the CARE site. There are
two problems indicated in this figure: (i) the Ku-band Zh is smaller
than the Ka-band Zh on average. (ii) Compared with the Ka-band, there
are many too small values of the Ku-band Zh.
Figure 8 shows the time profile of the averaged Ze at Ku- and
Ka-bands. There are two problems indicated in this figure. First,
theoretically, the Ku-band Ze should be greater than or equal to the
Ka-band Ze. The smaller Ku-band Zh indicates that a Z offset exists
at both bands. The other problem is that, compared with the Ka-band, there
are many dips in the Ku-band Zh. By comparing Fig. 8 with Fig. 7, we found
that these dips occur only at RHI scans with azimuth angle larger than
300∘. We examined those RHI scans beam by beam from 90 to
75∘. We further found that when the elevation angle is smaller than
78∘, the unreasonably low Zh disappears. Therefore, the RHI scans
with azimuth angles larger than 300∘ were averaged over the 75 to
78∘ elevation angles. To compute the DWR, we need to know the Z offset
between the two bands. The measured Zh includes three components
(neglecting attenuation):
Zhmeas=Zhtrue±errorZh+Zoffset,
where “error” refers to measurement fluctuations (typically with standard deviation
of ∼1dB). The DWR is obtained as the difference between Ku-band
Zh and Ka-band Zh, with Zh being in units of dBZ. The measured
DWR is as follows:
DWRmeas=DWRtrue∓errorDWR+ΔZoffset,
where error (DWR) is now increased, since the Ku- and Ka-band measurement
fluctuations are uncorrelated (standard deviation of around 1.4 dB). The
ΔZoffset is determined by selecting data where the scatterers
(snow particles) are sufficiently small in size so that Rayleigh scattering
is satisfied at both bands, i.e., DWRtrue=0dB. The criteria are used
here to select gates where Ku-band Zh<0dBZ along with
spatial averaging, which reduces the measurement fluctuations in DWR to estimate
ΔZoffset in Eq. (3). Figure 9 shows the averaged Zh for
the two bands from 20 RHI scans which satisfy the conditions above. After
removing three extreme values (outliers) from Fig. 9, ΔZoffset was estimated as -1.5dB, which is used in the subsequent data
processing.
The averaged raw Zh for Ku- and Ka-bands. The Zh was
randomly selected from 20 of 85 RHI scans with Ku-band Zh<0dBZ,
range <1km, and Ka-band SNR >3dB.
2DVD data analysis
The 2DVD used in this study was also located at the CARE site. The
particle-by-particle mass estimation is based on three methods as follows:
Following the procedure in Huang et al. (2015) we use 2DVD single-camera
data and apply the weighted Hanesch-matching algorithm (Hanesch, 1999) to
rematch snowflakes. A PSD adjustment factor is computed as in Huang et al. (2015)
without using the Pluvio gauge as a constraint. Mass is computed from
fall speed, Dapp and environmental conditions using Böhm (1989). The
apparent density of the snow (ρ) is defined as 6m/πDapp3. A mean power-law relation of the form ρ=αDappβ is derived for the entire event as in Huang et al. (2015)
as well as 1 min averaged N(Dapp) is calculated. Note that the
scattering model is based on the soft spheroid model with fixed axis
ratio =0.8 and apparent density ρ. The results obtained by this method
are denoted HB in the figures and in the rest of the paper.
Use the manufacturer's (Joanneum Research, Graz, Austria) matching algorithm
and filter-mismatched snowflakes as described in Sect. 2.2. The mass is
computed from Böhm's equations. The PSD adjustment factor is based on
using the Pluvio gauge accumulation as a constraint. Following Liao et al. (2013)
as far as the scattering model is concerned, the density is fixed at
0.2 gcc-1
and the volume is computed from mass=density⋅volume. The
effective equal-volume diameter is Deff and the corresponding PSD is
denoted N(Deff), which is different from N(Dapp) in (1) above.
Henceforth, this method is denoted LM.
Use Joanneum matching and filtering method as in (2) but compute mass using
Heymsfield–Westbrook equations as well as the revised Deff and
N(Deff). This method is denoted HW. Thus, the only difference with
(2) is in the estimation of mass and the difference in Deff and
N(Deff). The PSD adjustment factor is based on using the Pluvio gauge
accumulation as a constraint. The scattering model follows Liao et al. (2013).
The 2DVD measured liquid equivalent snow rate (SR) can be computed directly
from mass as follows:
SR=3600Δt∑i=1N∑j=1MVjAj;mmh-1,
where Δt is the integral time (typically 60 s), N is the number of
size bins (typically 101 for the 2DVD), M is the number of snowflakes in the
ith size bin, and Aj is the measured area of the jth snowflake.
Further, Vj is the liquid equivalent volume of the jth snowflake, so
it is directly related to the mass. Figure 10 compares the liquid equivalent
accumulation computed using the three methods above based on 2DVD
measurements with the accumulation directly measured by the collocated
Pluvio snow gauge. The Pluvio-based accumulation at the end of the event
(03:30 Z) was 1.9 mm while the 2DVD-measured accumulations using the three
methods are 1.27 mm (HB), 1.45 mm (LM), and 1.24 mm (HW). It
is expected that the PSDs of LM and HW should be underestimated because of
eliminating mismatched particles which, in principle, could be rematched.
Rematching mismatched particles is a research topic on its own and is
beyond the scope of this paper. We used a simple way to adjust the PSD for
methods 2 and 3 by scaling the PSD by a constant so that the final
accumulation matches the Pluvio gauge accumulation. Specifically, the PSD
adjustment factors are 1.3 for LM and 1.52 for HW. Note that PSD adjustment
of HB (method 1) is not done by forcing 2DVD accumulation to agree with
Pluvio, rather the method described in Huang et al. (2015) is used giving
the adjustment factor of 1.54 for 00:00–00:45 UTC and 1.11 for 00:45–04:00 UTC.
From the Pluvio accumulation data in Fig. 10 the SR is nearly constant at
0.7 mmh-1 between relative times of 1.5 and 3 h (or actual time from 01:00 on
30 January to 02:30 UTC).
Comparison of liquid equivalent accumulations computed using HB,
LM, and HW methods based on 2DVD measurements and that were
directly measured by the collocated Pluvio snow gauge. We used the total
accumulation to estimate the PSD adjustment factor for the LM and HW
methods.
The radar reflectivities at the two bands are simulated by using the
T-matrix method assuming a spheroid shape with an axis ratio of 0.8,
consistently with Falconi et al. (2018). The PSD is adjusted for methods 1, 2, and 3 as
described above. The orientation angle distribution is assumed to be
quasi-random with Gaussian distribution for the zenith angle
[mean=0∘,σ=45∘] and uniform distribution
for the azimuth angle. However, other studies have assumed σ=10∘ (Falconi et al., 2018). The recent observations of
snowflake orientation by Garrett et al. (2015) indicate that substantial
broadening of the snow orientation distribution can occur due to turbulence.
Figure 11 compares the time series of D3R-measured Zh with the
2DVD-derived Ze for the entire event (20:00–03:30 UTC at (a) Ku- and
(b) Ka-band). The Ze for both bands computed by the three methods
generally agree with the D3R measurements to within 3–4 dB. Overall, LM
gives the highest Ze and HB gives the lowest, which is especially evident at
Ka-band. This is consistent with scattering calculations by Kuo et al. (2016)
of single spherical snow aggregates using constant density (0.3 gcc-1)
giving higher radar cross sections and size-dependent density, i.e., density
falls off as inverse size (giving lower cross sections). This feature is
consistent with the scattering models referred to herein as LM and HB.
Comparison of the 2DVD-derived Zh with D3R measurements for
the entire event, Ku-band (a), and Ka-band (b). This synoptic system
started at around 21:00 Z on 30 January and ended at around 03:30 Z on 31 January 2012.
Ze by LM is close to HW and slightly higher, whereas the
HB method gives the lowest Ze. Ze results computed by all
methods generally agree with D3R measured Zh.
From 00:45 to 01:30 UTC on 31 January 2012, the three 2DVD-derived
Ze simulations deviate systematically from the D3R results for both
bands. The other period is from 23:00 to 23:30 UTC on 30 January 2012,
when the Ku-band Ze has significant deviation from the D3R observations
but the Ka-band Ze generally agrees with the D3R. Note that this
synoptic event started at around 21:00 UTC on 30 January and
stopped at 03:30 UTC. We checked the D3R data and found that, before 22:30 UTC,
the RHI scans were from 0 to 60∘, so there were no usable
data available for comparison with the 2DVD and Pluvio at the CARE site. We
note that at 00:30 UTC the King City C-band radar recorded Zh in the
range 15–20 dBZ around the CARE site, which is in reasonable agreement with
the D3R radar observations (Skofronick-Jackson et al., 2015).
Figure 12a compares the time series of DWR simulated from 2DVD observations
with the D3R measurements, whereas Fig. 12b shows the scatterplot In general,
HB appears in qualitatively better agreement (better correlated and with
significantly less bias) with D3R measurements relative to both LM and HW
(significant underestimation relative to D3R). The scatterplot in Fig. 12b
is an important result since in the HB method the soft spheroid scattering
model is used with density varying approximately inverse with Dapp
(density-Dapp power law where the larger snow particles have lower
density). Hence for a given mass the Dapp is larger (relative to Ka-band
wavelength) and enters the Mie regime, which lowers the radar cross section
at Ka-band (relative to same mass but constant density radar cross section
in LM and HW). Whereas at Ku-band the difference in radar cross sections is
less between the two methods (Rayleigh regime). The significant DWR bias in LM
and HW relative to DWR observations is somewhat puzzling in that the Liao et
al. (2013) scattering model radar cross sections agree with the synthetic
complex shaped snow aggregates of the same mass at Ka-band, whereas the HB
model underestimates the radar cross section relative to the synthetic
complex shaped aggregates. On the other hand, Falconi et al. (2018)
demonstrate that the soft spheroid model is adequate at X (close to Ku-band)
and Ka-band and by inference adequate for DWR calculations with the caveat that
different effective axis ratios may need to be used at Ka- and W-bands.
Comparison of the 2DVD-derived DWR using HB, LM, and
HW methods with the D3R-measured DWR. Panel (a) shows the time
profile of the D3R, and (b) shows the scatterplot.
We also refer to airborne (Ku, Ka) band radar data at 00:30 UTC which showed
DWR measurements of 3–6 dB about 1 km height MSL around the CARE site but
nearly 0 dB above that all the way to the echo top (Skofronick-Jackson et
al.,
2015). The latter is not consistent with aircraft spirals over the CARE site
about an hour earlier where maximum snow sizes reach ∼8mm.
In spite of the difficulty in reconciling the observations from the
different sensors, the appropriate scattering model in this particular event
appears to favor the soft spheroid model used in HB based on better
agreement with DWR observations. The other factor to be considered is the PSD
adjustment factor, which is assumed constant and independent of size, which
may not be the case, especially for the LM and HW methods as considerable
filtering is involved due to mismatch (as discussed in Sect. 2.2). Note
that a constant PSD adjustment factor will not affect DWR but it will affect
Ze. For the HB method Huang et al. (2015) determined the PSD adjustment
factor for four events by comparing the 2DVD PSD to that measured by a
collocated SVI (snow video imager which was assumed to be the “truth”) for each
size bin. The PSD adjustment was found to not be size dependent for the HB
method. On the other hand, because of the filtering of mismatched particles
by the LM and HW methods, the PSD adjustment factor may be size dependent in
which case the DWR will also change. More case studies are clearly needed to
understand the applicability of the LM and HW methods of simulating DWR.
Snow rate estimation
To obtain radar–SR relationships, we use the 2DVD data and simulations. Since
we employ a constant PSD adjustment factor, it will scale both Ze and
SR similarly. Figure 13 shows the scatterplot of the 2DVD-derived Ze
vs. 2DVD-measured SR along with a power-law fit as Z=aSRb. The fitting
method used is based on weighted total least square (WTLS) so the power law
can be inverted without any change. The coefficients and exponents of the
power-law Z–SR relationship for both bands and three methods are given in Table 3.
It is obvious from Fig. 13 that there is considerable scatter at Ku-band
for all three methods with the normalized standard deviation (NSD), ranging
from 55 % to 70 %. Whereas at Ka-band the scatter is significantly lower
with NSD from 40 % to 45 %. The errors in Table 3 are generally termed
parameterization errors.
2DVD-derived Zh vs. 2DVD-measured SR scatterplots, with
Z–SR power-law fits, for Ku- and Ka-bands and the HB method (a), LM
method (b), and HW method (c).
Coefficients and exponents of the power-law Z–SR relationship
for HB, LM, and HW methods and Ku- and Ka-bands, respectively.
By using dual-wavelength radar, we can estimate SR using Ze at two bands
as follows:
SRKu=a1′⋅ZKub1′SRKa=a2′⋅ZKab2′,
where a′=(1/a)b′ and b′=1/b. To reduce error, we may take the
geometric mean of these two estimators as follows:
SR‾=SRKu⋅SRKa1/2=c⋅ZKud⋅DWRe,
where c=(a1′a2′)1/2, d=(b1′+b2′)/2, and e=-b2′/2. Note that the DWR in Eq. (6) is on a linear scale, i.e., expressed
as a ratio of reflectivity in units of mm6m-3. Using Table 3 to
set the initial guess of (c, d, e), nonlinear least squares fitting was used to
determine the optimized (c, d, e) with the cost function being the squared
difference between the 2DVD-based measurements of SR and cZKudDWRe,
where ZKu and DWR are from 2DVD simulations. Figure 14 shows the SR computed
from the 2DVD simulations of Ku-band Ze and the DWR using Eq. (6) vs.
the 2DVD-measured SR. The (c, d, e) values for the three methods are given in Table 4.
As can also be seen from Fig. 14 and Table 4, the SR(ZKu,DWR) using the LM
method results in the lowest NSD of 28.49 %, but the other two methods
have similar values of NSD (≈30 %) and, as such, these
differences are not statistically significant. Although
SR(ZKu,DWR) has a smaller parameterization error than Ze–SR, the
SR(ZKu,DWR) estimation is biased high when SR<0.2mmh-1 (see Fig. 14).
When SR is small, the size of snowflakes is usually also small and falls in
the Rayleigh region at both frequencies, resulting in DWR very close to 1 (when
expressed as a ratio). This implies that there is no information content in
the DWR so including it just adds to the measurement error. Hence, for small
SR or when DWR ≈1, we use the Ze–SR power law.
Coefficients and exponents of the SR(ZKu,DWR) relation (see
Eq. 10) for three methods.
Estimated SR using Ze and DWR of the 2DVD and Eq. (10) vs.
2DVD SR scatterplot for the HB method (a), LM method (b), and HW method (c).
So far the single-frequency SR retrieval algorithms were based on 2DVD-based
simulations with a PSD adjustment factor using the total accumulation from
Pluvio as a constraint. The algorithm we propose for radar-based estimation
of SR is to use Eq. (6) when DWR >1 and SR >0.2mmh-1, else
we use the ZKa–SR power law (note that we do not use the ZKu-SR power law as
the measurement errors of ZKu seem to be on the high side, Fig. 9). The
precise thresholds used herein are ad hoc and may need to be optimized using a
much larger data set. Figure 15a shows the radar-derived accumulation using
ZKa–SR vs. the Pluvio accumulation vs. time. The total accumulation
from the Pluvio is 2.5 mm and the three radar-based total accumulations,
for HB, LM, and HW methods amount to [2.6, 1.8, 2.6 mm]. Except
for the underestimation in the LM method (-28 %), the other two methods
agree with the Pluvio accumulation in this event. Figure 15b is the same as
Fig. 15a, except the combination algorithm mentioned above is used. For this
case, ∼33 % of data used the ZKa–SR power law due to
threshold constraints given above. The event accumulations for
HB, LM, and HW methods amount to [2.4, 1.9, 2.2 mm], which are consistent with the
algorithm that uses only the ZKa–SR power law. However, the criteria of
relative bias error in the total accumulation (in events with low
accumulations such as this one) are not necessarily an indication that the
DWR-based algorithm is not adding value. Rather, the criteria should be snow
rate intercomparison, which could not be done due to the low resolution
(0.01 mmmin-1) of the Pluvio2 400 gauge along with the low event total
accumulation of only 2.5 mm. A close qualitative examination of Fig. 15b
shows that the HB method more closely “follows” the gauge
accumulation relative to HB in time in Fig. 15a. In Fig. 15, the time grid is
different for the radar-based data and the gauge data. It is common to
linearly interpolate the gauge data to the radar sampling time and if this
is done, the rms error for the HB method reduces from 0.1 mm (when using only
the ZKa–SR power law) to 0.045 mm for the DWR algorithm, which constitutes
a significant reduction by a factor of 2.
Comparison of the radar-derived accumulated SR using HB, LM,
and HW methods with Pluvio gauge measurement. (a) The
radar SR is computed by ZKa–SR relationships. The Pluvio-accumulated SR on
03:18 UTC is 2.48 mm. The radar-accumulated SRs for HB, LM, and HW
are 2.64, 1.81, and 2.66 mm. (b) The radar SR is computed by
combining SR(ZKu,DWR) and ZKa–SR as described in the text. The accumulated
SR derived from the radar using HB method is 2.38 mm, using LM it is 1.94 mm and using HW it is 2.24 mm.
The total error in the radar estimate of SR is composed of both
parameterization errors as well as measurement errors with measurement
errors dominating, since the DWR involves the ratio of two uncorrelated
variables. From Sect. 8.3 of Bringi and Chandrasekar (2001), the total
error of SR in Eq. (6) is around 50 % (ratio of standard deviation to the
mean). The assumptions are (a) the standard deviation of the measurement of
Ze is 0.8 dB, (b) the standard deviation of the DWR (in dB) measurement is
1.13 dB, and (c) the parameterization error is 30 % from Table 4. However,
considering the Ze fluctuations in Fig. 9, the measurement standard
deviation probably exceeds 0.8 dB, especially at Ku-band. Thus, sufficient
smoothing of DWR is needed to minimize the measurement
error as much as possible while maintaining sufficient spatial resolution.
Note that the error model used here is additive with the parameterization,
and measurement errors modeled as zero mean and uncorrelated with the
corresponding error variances estimated either from data or via simulations
(as described in Sect. 7 of Bringi and Chandrasekar, 2001). This is a
simplified error model since it assumes that radar Z and snow gage
measurements are unbiased based on accurate calibration. A more elaborate
approach of quantifying uncertainty in precipitation rates is described by
Kirstetter et al. (2015).
Summary and conclusions
The main objective of this paper is to develop a technique for snow
estimation using scanning dual-wavelength radar operating at Ku- and Ka-bands
(D3R radar operated by NASA). We use the 2-D video disdrometer and collocated
Pluvio gauge to derive an algorithm to retrieve snow rate from reflectivity
measurements at the two frequencies compared to the conventional
single-frequency Ze–SR power laws. The important microphysical information
needed is provided by the 2DVD to estimate the mass of each particle knowing
the fall speed, apparent volume, area ratio, and environmental factors from
which an average density-size relation is derived (e.g., Huang et al., 2015;
von Lerber et al., 2017; Böhm, 1989; Heymsfield and Westbrook, 2010).
We describe in detail the data processing of 2DVD camera images (in two
orthogonal planes) and the role of particle mismatches that give erroneous
fall speeds. We use the Huang et al. (2015) method of rematching using
single-camera data but also use the manufacturer's matching code with
substantial filtering of the mismatched particles since the apparent volume
and diameter (Dapp) are more accurate. To account for the filtering of
the mismatched particles, the particle size distribution (in methods 2 and
3 in Sect. 3.3) is adjusted by a constant factor using the total
accumulation from the Pluvio as a constraint.
Two scattering models are used to compute the ZKu and ZKa, termed
the soft spheroid model (Huang et al., 2015; HB method) and the
Liao–Meneghini (LM) model, which uses the concept of effective density.
In these two methods the particle mass is based on Böhm (1989). The
method of Heymsfield and Westbrook (2010) is also used to estimate mass
which is similar to Böhm (1989) but is expected to be more accurate
(Westbrook and Sephton, 2017); along with the LM model for scattering, this
method is termed HW.
The case study chosen is a large-scale synoptic snow event that occurred
over the instrumented site of CARE during GCPEx. The ZKu and ZKa
were simulated based on 2DVD data and the three methods, i.e., HB, LM, and HW
yielded similar values within ±3dB. When compared with D3R radar
measurements extracted as a time series over the instrumented site, the LM
and HW methods were closer to the radar measurements with the HB method being
lower by ≈3dB. Some systematic deviations of simulated
reflectivities by the three methods from the radar measurements were
explained by a possible size dependence of the PSD adjustment factor.
The direct comparison of DWR (ratio of ZKu to ZKa) from simulations
with DWR measured by radar showed that the HB method gave the lowest bias
with the data points more or less evenly distributed along the 1:1 line. The
simulation of DWR by LM and HW methods underestimated the radar measurements of
DWR quite substantially, even though the correlation appeared to be reasonable.
The reason for this discrepancy is difficult to explain since a constant PSD
adjustment factor (different for method 1 relative to methods 2 and 3 in
Sect. 3.3) would not affect the DWR. From the scattering model viewpoint, the
LM method takes into account the complex shapes of snow aggregates via an
effective density approach, whereas the HB method uses soft spheroid model
with density varying approximately inversely with size. We did not attempt
to classify the particle types in this study.
The retrieval of SR was formulated as SR=c⋅ZKud⋅DWRe, where
[c,d,e] were obtained via nonlinear least squares for the three methods. The
total accumulation from the three methods using radar-measured ZKu and
DWR were compared with the total accumulation from the Pluvio (2.5 mm) to
demonstrate closure. The closest to Pluvio was the HB method (2.4 mm), next
was the HW method (2.24 mm) and then there was LM (1.94 mm). At such low total
accumulations, the three methods show good agreement with each other as well
as with the Pluvio gauge. The poor resolution of the gauge combined with the
relatively low total accumulation in this event precluded direct comparison
of snow rates. The combined estimate of parameterization and measurement
errors for snow rate estimation was around 50 %. From variance
decomposition, the measurement error variance as a fraction of the total
error variance was 58 %, and the parameterization error variance fraction
was 42 %. Further, the DWR was responsible for 90 % of the measurement
error variance, which is not surprising since it is the ratio of two
uncorrelated reflectivities. Thus, the DWR radar data have to be smoothed
spatially (in range and azimuth) to reduce this error, which will degrade the
spatial resolution but is not expected to pose a problem in large-scale
synoptic snow events.
The snow rate estimation algorithms developed here are expected to be
applicable to similar synoptic-forced snowfall under similar environmental
conditions (e.g., temperature and relative humidity) but not, for example, to
lake effect snowfall as the microphysics are quite different. However,
analyses of more events are needed before any firm conclusions can be drawn
as to applicability to other regions or environmental conditions.
Data availability
The data used in this study can be made available upon request to the
corresponding author.
List of acronyms and symbols.
Acronyms andDescriptionRemarkssymbolsAMinimum circumscribing circle or ellipse that completely contains AeAeParticle's effective projected area normal to airflowArArea ratio. The ratio of Ae to A (Ae/A)C0Inviscid drag coefficientDappApparent diameter. It is equivalent-volume spherical diameter commonly used in 2DVD.DDADiscrete dipole approximationDdDistance between two optical planes of 2DVDDeffEffective diameterLiao et al. (2013)DFIRDouble fence international referenceDmMass-weighted mean diameterDmaxMaximum dimension of a particleDWRDual-wavelength ratioEq. (3)D0Median volume diameterD3RDual-wavelength dual-polarization doppler radarfsScanning frequency of 2DVD line-scan cameraGCPExGPM Cold-season Precipitation ExperimentHBHuang and Bringi methodHuang et al. (2015)HVSDHydrometeor velocity size detectorHWHeymsfield and Westbrook methodHeymsfield and Westbrook (2010)IWCIce water contentLMLiao and Meneghini methodLiao et al. (2013)N(D)Concentration of PSD function of sizePIPPrecipitation imaging packagePPIPlan position indicatorPSDParticle size distributionQPEQuantitative precipitation estimationReReynolds numberRHIRange height indicatorSNRSignal-to-noise ratioEq. (1)SRLiquid equivalent snow ratioEqs. (4) and (5)vmin or vmaxMinimum or maximum possible terminal fall speedvtTerminal fall speedXDavies number, also called best numberZdrDifferential reflectivityZeEquivalent reflectivity factor. In this paper, we refer to the reflectivity factor based on scattering computation.ZhRadar horizontal reflectivity factorEq. (1)ZKa or ZKuRadar reflectivity factor at Ka- or Ku-bandEq. (5)ZoffsetThe offset of radar reflectivity measurementδ0A dimensionless coefficient relate to boundary layer thickness.φdpDifferential propagation phase2DVD2-D video disdrometerAuthor contributions
GJH and VNB developed the main idea of this article. GJH analyzed 2DVD data,
processed D3R data, adapted the scattering models for the case considered, simulated
radar reflectivity factor, derived Ze–SR and SR(Z,DWR) relationships, and wrote most
of the article draft. AJN described the meteorological aspects of the studied case and
wrote Sect. 3.1. VNB, DM, and BMN validated the scattering model used in the article.
VNB and GL validated the D3R data. VNB and BMN supervised the NASA PMM Science research.
GL supervised Korea Brain Pool Program and KMA grant. BMN and VNB reviewed and edited
the article.
Competing interests
The authors declare that they have no conflict of interest.
Acknowledgements
Gwo-Jong Huang acknowledges support from the Brain Pool Program through the National
Research Foundation of Korea (NRF) funded by the Ministry of Science and ICT
(grant number 171S-5-3-1874). All authors except Gyuwon Lee acknowledge support
from NASA PMM Science grant NNX16AE43G. Authors Gwo-Jong Huang and Gyuwon Lee were funded by
the Korea Meteorological Administration Research and Development Program
under Grant KMI2018-06810.
Edited by: S. Joseph Munchak
Reviewed by: three anonymous referees
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