quantitative precipitation estimation (QPE) of snowfall has generally been
expressed in power-law form between equivalent radar reflectivity factor
(

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

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

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

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

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.

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

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 (

One source of uncertainty in applying the Böhm or Heymsfield and
Westbrook (HW) method is calculating the area ratio (

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,

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 (

In our application of the HW method, the

The two optic planes of the 2DVD are separated by around 6

Illustration of the matching procedure. In the situation shown, it
is assumed that camera A observed a particle at time

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

Fall speed vs.

Hanesch 2DVD scan line criteria.

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

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

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

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:

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

The 00:00 UTC, 31 January 2012, 850

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

Some D3R parameters relevant for this study. Full D3R specifications can be found in Vega et al. (2014).

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

D3R scan strategies on 31 January 2012. The

The time series of averaged raw

Figure 8 shows the time profile of the averaged

The averaged raw

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,

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

Use Joanneum matching and filtering method as in (2) but compute mass using
Heymsfield–Westbrook equations as well as the revised

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

Comparison of the 2DVD-derived

From 00:45 to 01:30 UTC on 31 January 2012, the three 2DVD-derived

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

Comparison of the 2DVD-derived DWR using HB, LM, and
HW methods with the D3R-measured DWR. Panel

We also refer to airborne (Ku, Ka) band radar data at 00:30 UTC which showed
DWR measurements of 3–6

To obtain radar–SR relationships, we use the 2DVD data and simulations. Since
we employ a constant PSD adjustment factor, it will scale both

2DVD-derived

Coefficients and exponents of the power-law

By using dual-wavelength radar, we can estimate SR using

Coefficients and exponents of the SR(

Estimated SR using

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

Comparison of the radar-derived accumulated SR using HB, LM,
and HW methods with Pluvio gauge measurement.

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

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

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

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 (

Two scattering models are used to compute the

The case study chosen is a large-scale synoptic snow event that occurred
over the instrumented site of CARE during GCPEx. The

The direct comparison of DWR (ratio of

The retrieval of SR was formulated as

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.

The data used in this study can be made available upon request to the corresponding author.

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

The authors declare that they have no conflict of interest.

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