Introduction
Radar is a very useful monitoring tool for extreme weather forecasting,
flood forecasting, and rainfall estimations because of its high spatial and
temporal resolution. In particular, dual-polarization radar that provides
information on the reflectivity (ZH), differential reflectivity
(ZDR), differential phase (ΦDP), specific differential phase
(KDP), and cross-correlation coefficient (ρhv) can
distinguish precipitation types by means of backscatter and the differential
propagation phase of hydrometeors. Dual-polarization radar can also be used
to obtain more information about the raindrop size distribution (DSD), and
this in turn can help to reduce the impact of DSD variability on rainfall
estimations (Cifelli et al., 2011). The DSD can be characterized by
parameters such as the diameter, concentration, orientation, and shape.
Disdrometers and aircraft imaging investigations have been widely used to
study the DSD variability especially as a function of the rainfall rate
(Bringi et al., 2003). Polarimetric parameters are sensitive to the DSD
properties. Rainfall rates estimated from polarimetric radar measurements
are affected by the mean shape of raindrops and canting (Brandes et al.,
2002).
The average shape of a raindrop can be inferred from its size through
application of a shape–size relationship for a raindrop. Some researchers
have attempted to produce the mean shape of raindrops. Keenan et al. (2001);
Brandes et al. (2002); Thurai and Bringi (2005); and Marzuki et al. (2013)
derived empirical relations from observational data, and Pruppacher and
Beard (1970); Green (1975), and Beard and Chuang (1987) investigated the
shape of raindrops falling under the influence of gravity. These raindrop
axis-ratio relations play an important role in the derivation of
polarimetric radar rainfall algorithms that use ZDR and KDP
(Jameson, 1983, 1985; Gorgucci et al., 2001). Polarimetric rainfall
algorithm can be derived from long-term DSD measurements. However, the
derivation of new empirical algorithms based on long-term DSD data is still
challenging for different climatological environments.
Several different polarimetric rainfall algorithms have been developed by
assuming raindrop shapes (Sachidananda and Zrnić, 1987; Chandrasekar et
al., 1990; Ryzhkov and Zrnić, 1995; Gorgucci et al., 2001). However,
radar rainfall estimations are affected by the following two different
sources of errors: (i) errors in radar measurements such as from attenuation,
bright bands, ground clutter, and calibration bias of ZH and ZDR (Zawadzki, 1984; Villarini and Krajewski, 2010; Sebastianelli et al.,
2013) and (ii) errors in the conversion of the radar measurements into
rainfall rates at the ground level. In addition, the error is also related
to the gamma assumption on the retrieve of the rain rate from
dual-polarization radar measurements (Adirosi et al., 2014). The DSDs
variability affects the accuracy of radar-derived rainfall (Maki et al.,
2005). Many earlier studies have explained the variability in the DSD by
evoking both different storm types and climatic regimes, and variations of
the DSD are known to be caused by climatological and physical factors (e.g.,
Ulbrich, 1983; Tokay and Short, 1996; Bringi et al., 2003). Variations in
time and space of the DSD are associated with changes in microphysical
processes such as evaporation, break-up, coalescence, and condensation. They
can be also due to the variation of vertical air motion (Marzuki et al.,
2013).
Radar measurements often suffer from the system biases of ZH and
ZDR, and thus, accurate measurement and calibration of ZH and
ZDR values are necessary to achieve accurate radar rainfall estimations
(Park and Lee, 2010). An assessment of the calibration bias of polarimetric
radar is possible by monitoring the hardware stability, and ZH and
ZDR measurements can be corrected by using ground validation equipment
such as a disdrometer. Joss et al. (1968) calibrated radar reflectivity by
using the vertical profile of reflectivity and disdrometer-inferred ZH.
The radar reflectivity was calibrated by comparisons between the radar and
disdrometer reflectivity to check the calibration of the WSR-88D (weather
surveillance radars – 1988 Doppler) at Greer, South Carolina (Ulbrich and
Lee, 1999). Goddard et al. (1982) and Goddard and Cherry (1984) compared
radar results with disdrometer results by using the axis-ratio relations of
Pruppacher and Beard (1970) and Pruppacher and Pitter (1971), respectively;
they found that radar measures of ZDR were 0.3 and 0.1 dB lower than
the disdrometer estimates. In addition to disdrometers, there are various
other ways to correct biases in radar data, such as by using the
ZH–KDP implementation of the self-consistency principle,
vertically pointing measurements, and comparisons of measured data and the
mean ZH–ZDR relationship (Kwon et al., 2015). Moreover, a variety
of radar calibration methods were introduced in Atlas (2002).
In this study, we computed the mean axis-ratio relation and developed
several polarimetric rainfall algorithms by using two-dimensional video
disdrometer (2DVD) measurements collected from September 2011 to October
2012 in Daegu, Korea. Specifically, three raindrop shape assumptions
(Pruppacher and Beard, 1970; Beard and Chuang, 1987; Brandes et al., 2002)
and the newly derived axis-ratio relation from 2DVD data were used to derive
polarimetric rainfall retrieval algorithms. The ZH and ZDR biases
of Bislsan dual-polarization radar were calibrated by comparing them with
simulated ZH and ZDR values obtained from the 2DVD. Improvements
in the quantitative rainfall estimations were achieved by applying the
ZH and ZDR calibration biases. In Sect. 2, the data used in this
study are described. The methodology for 2DVD data quality control,
derivation of the raindrop-axis ratio from 2DVD data, and simulations of the
polarimetric parameters by the T-matrix scattering method are described in
Sect. 3. The results of the statistical validation of rainfall estimation
are presented in Sect. 4. Finally, the conclusions are given in Sect. 5.
Data and instruments
Disdrometer
In this study we used the compact 2DVD version deployed on the campus of
Kyungpook National University, Daegu, Korea (35.9∘ N,
128.5∘ E). The 2DVD was installed in an observation field away
from the buildings. Disdrometers are used to find the DSD characteristics at
a given location. Disdrometer data used in this study were collected by a
2DVD from September 2011 to October 2012.
Specifications for dual-polarization radar in Bislsan.
Parameters
Characteristics
Variables
ZH, Vr, SW, ZDR, ΦDP, KDP, ρhv
Altitude of radar antenna
1085 m
Transmitter type
Klystron
Transmitter peak power
750 kW
Antenna diameter
8.5 m
Beam width of radar
0.95∘
Observation
frequency
2.785 MHz (S-band)
range
150 km
gate size
125 m
elevations
-0.5∘ , 0∘ , 0.5∘ , 0.8∘ , 1.2∘ , 1.6∘ (6 elevation)
The 2DVD consists of two orthogonal light sheets (referred to as A and B
line-scan cameras). Line-scan cameras have single-line photo detectors. The
particle shadows are detected on the photo detectors, and the particle
images are recorded from two sides and at different heights when the
particles are falling through the measurement area (10 cm × 10 cm).
The 2DVD measures drop size, fall velocity, and the shape of individual
particles. From these data, one can calculate the DSD and all related
quantities such as the rain rate, total drop number concentration, and
liquid water content. A more detailed description of the 2DVD is given in
Kruger and Krajewski (2002).
Radar
The Ministry of Land, Infrastructure, and Transport (MLIT) operates the
Bislsan (BSL) dual-polarization radar in Bislsan, Korea (35.7∘ N,
128.5∘ E, 1085 m). The BSL S-band radar has observation range of
150 km and a frequency of 2.5 min because it is used primarily for
hydrological observations and flood forecasts. The BSL S-band radar measures
polarimetric variables such as ZH, ZDR, KDP, and ρhv in real time. Six elevation angles from -0.5 to
1.6∘ were available, with a gate size resolution of 125 m and
radar beam width of 0.95∘. The specifications of the BSL radar
are shown in Table 1.
The BSL S-band dual-polarization radar was located about 22.3 km
(17∘) away from the 2DVD location (Fig. 1). These geographical
locations were adopted to compare the two sets of observation data. We used
radar data from September 2011 to October 2012. During this period, rainfall
events were analyzed for ZH and ZDR calibration and for rainfall
estimation. In addition, the 0.0∘-elevation plan position
indicator (PPI) radar data were used to avoid effects due to beam blocking
and ground echoes on the measurements, whilst being as close as possible to
the 2DVD. The ZH and ZDR radar parameters were averaged over five
successive gate size resolutions and two adjacent azimuth angles, and
KDP was calculated from the filtered ΦDP as the slope of a
least squares fit.
Rain gauge
A tipping bucket rain gauge was used to validate the 2DVD rainfall
estimations. The rain gauge used in this study was a RG3-M tipping bucket
rain gauge from the Onset Computer Corporation. The maximum rainfall rate of
the rain gauge was 127 mm (5 in) per hour, and the operating temperature
range was from 0 to 50 ∘C. The bucket size of the rain
gauge was 0.2 mm and the time resolution was 0.5 s. The rain gauge
measurements were corrected to reduce instrumental uncertainties through
field inter-comparisons with a reference gauge. The rain gauge was installed
in the same location as the 2DVD.
The locations of the Bislsan polarimetric radar and the
2DVD at the rain gauge site.
Methodology
Quality control of 2DVD data
The 2DVD observation data were useful for investigating the characteristics
of rainfall. However, a number of particle outliers were measured, and these
anomalous data points were due to wind turbulence, splashing, break up of
drops, and mismatching between camera A and B (Raupach and Berne, 2015).
These results can lead to incorrect information about the particles.
Therefore, before using the 2DVD data, a quality control process was needed.
Figure 2a and b show the fall velocity and oblateness distribution
according to the raindrop diameter before the data quality control procedure
was performed. In Fig. 2b and c, we compare the axis-ratio–diameter
relation of Pruppacher and Beard (1970) with that found by the disdrometer
before and after the correction, respectively. Some particles had fall
velocities beyond the terminal velocity of large raindrops. In particular,
the outliers appeared prominently in the small raindrop ranges. To remove
these outliers, velocity-based filtering was applied to the 2DVD measurement
data (Thurai and Bringi, 2005). The equations used are the following:
VmeasuredD-VAD<0.4VADVAD=9.65-10.3exp-0.6D,
where D (mm) is the drop diameter, Vmeasured (m s-1) is the fall
velocity as measured by the 2DVD, and VA represents the Atlas velocity
formula (Atlas et al., 1973). The procedure removed about 17 % of the
values that did not correspond well with the expected normal distribution
(Fig. 2c). Despite the application of velocity-based filtering, significant
bias still remained in the small drop size area. This was due to
instrumental limitations such as the mismatch problems with the line-scan
cameras and the limited vertical resolution of the instrument. Therefore,
the oblateness data corresponding to raindrop diameters smaller than 0.5 mm
were removed when we calculated the new axis-ratio formula.
To analyze the reliability of the 2DVD data, we compared the rain rates
calculated from the 2DVD data (Eq. 2) to collocated rain gauge measurements;
the difference of accumulated rainfall represents the percent error (Eq. 3).
R=6×10-4π∑DminmaxDD3VDNDΔD[mm h-1]PE=|ARrain gauge-AR2DVD|ARrain gauge×100[%]
Here, Dmax and Dmin are the maximum and minimum diameters of the
observed drops in mm, N(D) is the drop number concentration in mm-1 m-3, V(D) is the drop fall velocity in m s-1, and D is the drop
interval (D= 0.2 mm). The drop fall velocity formula used was that
derived by Atlas et al. (1973); PE is the percent error and AR is the
accumulated rainfall in mm.
Distribution of fall velocity and oblateness according to
drop diameter. (a) Velocity-based filter for the drop measurements. The
color scale represents the drop number density (log scale). The dotted line
(orange) represents the results from the velocity formula of Atlas et al. (1973). (b) Drop axis ratios for all measured drops. (c) Drop axis ratios
after removing mismatched drops. The dotted line (black) represents the mean
axis-ratio results from the formula given in Pruppacher and Beard (1970).
Time series of accumulated rainfall measured from the
rain gauge and estimated from the 2DVD: (a) 14 October 2011, (b) 2 April
2012, (c) 21 April 2012, (d) 25 April 2012. (e) 23 August 2012, and (f) 27
August 2012.
Summary of the date, type of precipitation, and
accumulated rainfall comparison values between 2DVD and rain gauge
measurements for the 33 rainfall events.
Date
Time of
Accumulated rainfall (mm)
PE (%)
of observation (UTC)
Type
2DVD
rain gauge
09/05/11
01:00–15:00
C
7.07
6.86
3.16
09/09/11
15:20–21:20
S
4.28
4.31
0.72
09/10/11
00:00–23:59
C
19.48
17.83
9.28
09/29/11
00:00–17:00
S
3.81
3.72
2.46
10/13/11
00:00–23:59
S
3.93
4.11
4.59
10/14/11
00:00–09:00
S
13.20
13.52
2.40
10/21/11
06:00–23:59
S
53.33
65.83
18.99
04/02/12
14:00–23:59
M
17.85
16.26
9.78
04/21/12
00:00–23:59
S
32.17
32.13
0.12
04/25/12
00:00–08:00
S
18.63
17.83
4.48
05/01/12
08:00–21:00
S
4.08
3.53
15.62
05/08/12
07:00–11:00
C
8.94
9.60
6.89
05/14/12
00:00–15:00
S
22.16
19.79
10.88
05/28/12
06:00–07:00
C
15.19
14.50
4.79
06/08/12
03:00–23:59
C
17.07
19.40
11.98
06/23/12
00:00–08:00
C
13.43
14.50
4.79
07/06/12
00:00–18:00
C
22.43
20.18
11.13
07/12/12
17:00–21:00
M
7.51
7.45
0.88
07/13/12
01:00–12:00
C
25.22
25.08
0.55
07/15/12
00:00–12:00
C
8.22
7.64
7.54
07/16/12
15:00–23:59
M
16.40
18.42
10.97
07/21/12
09:00–10:30
C
5.86
5.68
3.15
08/12/12
01:00–18:00
C
20.25
18.42
9.95
08/13/12
00:00–15:00
C
37.27
34.09
9.31
08/23/12
00:00–23:59
M
90.88
83.86
8.38
08/24/12
00:00–23:59
S
7.37
7.45
1.01
08/27/12
16:00–23:59
S
13.62
12.54
8.66
08/29/12
19:00–23:59
S
6.26
5.29
18.39
09/09/12
00:00–23:59
S
21.56
18.65
15.61
09/16/12
00:00–23:59
S
83.12
69.88
18.95
09/17/12
00:00–07:00
M
63.64
58.55
8.69
10/22/12
06:00–11:00
M
13.63
14.92
8.64
10/27/12
00:00–09:00
S
8.77
8.20
6.94
We analyzed the rainfall cases that occurred from September 2011 to October
2012. Figure 3 shows the accumulated rainfall computed from the 2DVD and
rain gauge data for six of these cases. The six events occurred at (i) 00:00–09:00 UTC on 14 October
2011 (Fig. 3a), (ii) 14:00–23:59 UTC on 2
April 2012 (Fig. 3b), (iii) 00:00–23:59 UTC on 21 April 2012 (Fig. 3c),
(iv) 00:00–08:00 UTC on 25 April 2012 (Fig. 3d), (v) 00:00–23:59 UTC on 23
August 2012 (Fig. 3e), and (vi) 16:00–23:59 UTC on 27 August 2012 (Fig. 3f).
Figure 3a shows the accumulated rainfall computed from the 2DVD and
rain gauge data on 14 October 2011. As shown in Figs. 3a–f, the percent
errors from the six considered rainfall cases were 2.40, 9.78, 0.12, 4.48,
8.38 and 8.66 %, respectively. The overall distribution between the 2DVD
and rain gauge results was good. In general, earlier studies have found that
rainfall differences between disdrometer and rain gauge data were mostly in
the range of 10 to 20 % (McFarquhar and List, 1993; Sheppard and Joe,
1994; Hagen and Yuter, 2003; Tokay et al., 2003). These differences might
have been due to such issues as differences in instruments, effects due to
the measurement environment, and rainfall variability. Therefore, the
rainfall differences between the 2DVD and rain gauge results used in this
study were limited to a maximum of 20 % error, and the 2DVD data were
excluded from the analysis when the rainfall difference between the 2DVD and
rain gauge results exceeded 20 %.
After the quality control process, 33 rainfall cases were selected for
further investigations of the characteristics of rainfall over the Korean
Peninsula. The accuracy of the 33 rainfall cases was in the range of
0.12–18.99 % compared to in situ rain gauge data. The radar reflectivity
and 1 h rainfall rates measured by the rain gauge were used to classify the
data into different precipitation types. The criterion for the reflectivity
described by Chang et al. (2009) was applied in the present study, and
rainfall rates that had values of R > 5 mm h-1 (≤ 5 mm h-1)
were considered to be of the convective (stratiform) type. The
data set consisted of 15 stratiform rainfall cases, 12 convective rainfall
cases, and 6 mixed rainfall cases (total of 33 rainfall events) with
17 618 min DSD samples. The precipitation type, rainfall difference, and
accumulated rainfall for the 2DVD and rain gauge results are listed in Table 2. Figure 4 shows the hourly and total accumulated rainfall for the 2DVD and
rain gauge results. The overall agreement between the 2DVD and the rain
gauge results was good, and the total accumulated rainfall recorded by the
rain gauge was greater than that of the 2DVD by about 0.30 %.
One-hour (left panel) and total accumulated rainfall (right panel)
from the 2DVD and rain gauge for the 33 rainfall cases.
Raindrop axis ratio
A very small raindrop has an approximately spherical shape that becomes
oblate as its size increases. The shape of a raindrop according to the drop
size can be expressed as the mean axis-ratio relation. The mean raindrop
shape is associated with the measured DSD shape and diameter, which is
related to the variation of DSD. The DSD variations depend on different
storm types and climatic regimes (Marzuki et al, 2013), and they affects
rainfall rates derived from polarimetric radar measurements of reflectivity.
Hence, in order to produce rainfall estimation algorithms reflective of the
rainfall characteristic of the Korean Peninsula, a new mean axis-ratio
relation, using the 2DVD data listed in Table 2, was derived as a polynomial
function. The size of the diameter bin was 0.2 mm, and the oblateness data
corresponding to raindrop diameters smaller than 0.5 mm were removed when we
derived the new axis-ratio relation because oblateness in the small range (D < 0.5 mm) was significantly influenced by the calibration of the
instrument (Marzuki et al., 2013). In addition, we only displayed the
average values for the bins containing more than five drops in order to have
sufficient numbers of raindrops. Therefore, the measured maximum diameter
could reach to about 8 mm; however, the mean axis-ratio fitting was
established to be within 7 mm diameter because it does not have a sufficient
number of values in more than 7 mm diameter.
In order to produce the mean axis-ratio relation, various fitting methods
such as linear and polynomial (second-, third-, fourth-order) fits were
tried. The third-order polynomial relation was deemed the most suitable for
the observation data, as this, relation performed (i.e., goodness of the
fitting) better than others. The third-order polynomial new mean axis-ratio
relation (b/a) is as shown in Eq. (4), which can be reasonably extended to 7 mm:
b/a=0.997845-0.0208475D-0.0101085D2+6.4332×10-4D3(0.5≤D≤ 7mm),
where a and b are the major and minor axis, respectively, and D is the
equivalent volume diameter of the particle in mm. The statistical measures
corresponding to the correlation coefficient, root-mean-square error (RMSE),
and mean absolute error (MAE) were 0.989, 0.025, and 0.012, respectively.
List of different polarimetric rainfall relations used for
rainfall estimations and the mean absolute error (MAE), root-mean-square
error (RMSE), and correlation coefficient for estimated rain rates vs.
observations.
R(Zh)=α|Zh|β
Polarimetric rainfall relation
Scatterplot R-Re
Assumptions
α
β
MAE
RMSE
Corr.
1
0.0568
0.5876
0.96
2.40
0.93
Pruppacher and Beard (1970)
2
0.0587
0.5849
0.97
2.42
0.92
Beard and Chuang (1987)
3
0.0588
0.5851
0.97
2.42
0.92
Brandes et al. (2002)
4
0.0575
0.5870
0.97
2.41
0.92
New axis ratio (experimental fit)
R(KDP)=α|KDP|β
Polarimetric rainfall relation
Scatterplot R-Re
Assumptions
α
β
MAE
RMSE
Corr.
1
38.59
0.834
0.47
1.05
0.99
Pruppacher and Beard (1970)
2
43.66
0.765
0.67
1.43
0.97
Beard and Chuang (1987)
3
46.85
0.740
0.82
1.64
0.97
Brandes et al. (2002)
4
42.20
0.831
0.46
1.15
0.98
New axis ratio (experimental fit)
R(Zh, ZDR)=αZhβ100.1γZDR
Polarimetric rainfall relation
Scatterplot R-Re
Assumptions
α
β
γ
MAE
RMSE
Corr.
1
0.0112
0.89
-4.0964
0.45
0.77
0.99
Pruppacher and Beard (1970)
2
0.0094
0.88
-3.5321
0.46
0.84
0.99
Beard and Chuang (1987)
3
0.0090
0.88
-3.4908
0.47
0.86
0.99
Brandes et al. (2002)
4
0.0114
0.87
-3.7750
0.48
0.90
0.99
New axis ratio (experimental fit)
R(KDP, ZDR)=αKDPβ100.1γZDR
Polarimetric rainfall relation
Scatterplot R-Re
Assumptions
α
β
γ
MAE
RMSE
Corr.
1
66.56
0.96
-1.4041
0.29
0.45
1.00
Pruppacher and Beard (1970)
2
84.02
0.93
-1.6854
0.44
0.66
1.00
Beard and Chuang (1987)
3
96.57
0.92
-1.9085
0.59
0.86
0.99
Brandes et al. (2002)
4
74.80
0.97
-1.5489
0.23
0.36
1.00
New axis ratio (experimental fit)
Disdrometer-rainfall algorithms
In order to produce the polarimetric rainfall algorithms, the theoretical
polarimetric variables (e.g., ZH, ZDR, and KDP) were
simulated from the 2DVD data by using the T-matrix (transition) method
(Zhang et al., 2001). The polarimetric variables depend on the shape of
raindrops. The polarimetric rainfall algorithms were derived by making
assumptions about different axis-ratio relations. First, we calculated the
complex scattering amplitudes of raindrops at the S-band of the 10.7 cm
wavelength by using the mean axis-ratio relations. Second, we calculated the
scattering amplitudes for the different axis-ratio relations that were used
for the production of the polarimetric variables. The dual-polarimetric
variables were calculated by using Eqs. (5–7) (Jung et al., 2010):
Zh=4λ4π4|Kw|2∫0Dmax,xAfaπ|2+Bfbπ|2+2CRefaπfb∗πNDdD[mm6m-3],
Zv=4λ4π4|Kw|2∫0Dmax,xBfaπ|2+Afbπ|2+2CRefaπfb∗πNDdD[mm6m-3],
where
A=<cos4Φ>=18(3+4cos2ϕ¯e-2σ2+cos4ϕ¯e-8σ2)B=<sin4Φ>=18(3-4cos2ϕ¯e-2σ2+cos4ϕ¯e-8σ2)
and
C=<sin2Φcos2Φ>=18(1-cos4ϕ¯e-8σ2)KDP=180λπ∫0DmaxCkRefa0-fb0NDdD[∘km-1].
Here, Ck=<cos2Φ>=cos2Φe-2σ2.
Different raindrop axis-ratio relations for the oblate
raindrop model. The upper right subfigure illustrates the axis ratio of an
oblate raindrop.
fa(0) and fb(0) are complex forward-scattering amplitudes and
fa(π) and fb(π) are complex backscattering amplitudes
for polarization along the major and minor axes, respectively. Additionally,
fa∗ and fb∗ are their respective conjugates,
ϕ¯ is the mean canting angle, and σ is the standard
deviation of the canting angle. The terms ϕ¯ and σ
were assumed to be 0 and 7∘, respectively (Huang et
al., 2008). The maximum size of the observed particles is Dmax= 8 mm,
the radar wavelength is λ= 10.7 cm (S-band), the dielectric
factor for water is Kw= 0.93, and N(D) was calculated by using the
2DVD measurements.
Polarimetric rainfall relations between R and dual-polarimetric variables
were derived when the rain rate was greater than 0.1 mm h-1. The
derived new polarimetric rainfall relations according to different
axis-ratio relations are presented in Table 3.
Calibration of the radar
The radar measurements are affected by various observational errors, such as
ground echoes, beam broadening, anomalous propagation echoes, and
calibration biases of radar ZH and ZDR. These errors can lead to
significant uncertainty in precipitation estimations. Therefore,
accommodation of the calibration bias of radar is necessary to improve
quantitative rainfall estimations involving ZH and/or ZDR. The
radar calibration was done for light rainfall events, and the simulated
theoretical ZH and ZDR variables based on the new axis-ratio
relation (Eq. 4) were used.
The calibration biases of ZH and ZDR were calculated from the
comparison of measured ZH and ZDR with the simulated ZH and
ZDR from the 2DVD measurements. To compare polarimetric radar
parameters, the cross-match point must first be determined. This is because
2DVD data consist of point measurements, whereas radar data are measured in
a sampling volume. The BSL S-band radar data were averaged over five
successive gates and two adjacent azimuth angles centered on the 2DVD
location. The elevation angle of 0.0∘ PPI was used. The radar
rainfall estimation reliability was assessed before and after the
calibration to test the effectiveness of the calibration process.
Scatterplot of R derived from observed DSDs (17 618 min samples) and Re estimated from combinations of polarimetric parameters.
Re was then obtained from the same data set.
Mean absolute error (MAE) and root-mean-square error
(RMSE) of the radar estimates of hourly rain rates for the different radar
rainfall algorithms listed in Table 3.
R(ZH)=α|ZH|β
MAE
RMSE
Assumptions
RADAR
2DVD
RADAR
2DVD
1
1.02
0.96
1.39
1.24
Pruppacher and Beard (1970)
2
1.03
0.96
1.39
1.25
Beard and Chuang (1987)
3
1.03
0.96
1.39
1.25
Brandes et al. (2002)
4
1.02
0.96
1.39
1.24
New axis ratio (experimental fit)
R(KDP)=α|KDP|β
MAE
RMSE
Assumptions
RADAR
2DVD
RADAR
2DVD
1
6.04
0.69
6.99
0.93
Pruppacher and Beard (1970)
2
7.69
0.75
8.63
0.99
Beard and Chuang (1987)
3
8.67
0.76
9.62
1.00
Brandes et al. (2002)
4
6.80
0.71
7.78
0.93
New axis ratio (experimental fit)
R(ZH, ZDR)=αZHβ100.1γZDR
MAE
RMSE
Assumptions
RADAR
2DVD
RADAR
2DVD
1
0.89
0.66
1.22
0.92
Pruppacher and Beard (1970)
2
0.85
0.69
1.18
0.96
Beard and Chuang (1987)
3
0.87
0.73
1.20
1.02
Brandes et al. (2002)
4
0.85
0.72
1.17
0.99
New axis ratio (experimental fit)
R(KDP, ZDR)=αKDPβ100.1γZDR
MAE
RMSE
Assumptions
RADAR
2DVD
RADAR
2DVD
1
8.19
0.58
10.05
0.88
Pruppacher and Beard (1970)
2
10.92
0.61
12.98
0.91
Beard and Chuang (1987)
3
12.71
0.64
14.96
0.94
Brandes et al. (2002)
4
9.19
0.58
11.23
0.86
New axis ratio (experimental fit)
Conclusions
The purpose of this study was to find an optimal polarimetric rainfall
algorithm by using 2DVD measurements in Korea, and to improve the radar
rainfall estimations by correcting the ZH and ZDR biases. First,
we derived a new raindrop axis-ratio relation reflecting the rainfall
characteristics on the Korean Peninsula by using data from 33 rainfall
events, and this was done after checking the accuracy and performing a
quality control procedure for the 2DVD measurements. The derived raindrop
axis-ratio relation was compared with existing relations. The derived new
mean axis-ratio relation was very similar to existing axis-ratio relations
except for both small particles (≤ 2 mm) and large particles (≥ 5.5 mm). The dependence of the raindrop axis ratio on climatic regimes was
not clearly observed.
The polarimetric rainfall algorithms were derived based on various
assumptions about the shape of raindrops. The accuracy validation of the 1 h
rainfall rate obtained through rainfall algorithms was assessed by comparing
2DVD and BSL radar data with rain gauge measurements. As a result,
R(KDP, ZDR) based on the new axis-ratio relation was deemed
suitable for rainfall estimations according to the DSD statistics when
compared with others. This occurs because the effect of the DSD variability
declined in rainfall estimations obtained with the R(KDP) or
R(KDP, ZDR) compared to those obtained with the R(Zh).
However, if actual radar measurements were used, at lower rain rates
(< 10 mm h-1), the KDP-based algorithms displayed large
statistical errors, while R(Zh, ZDR) based on the new axis-ratio
relation showed the best performance. This occurs because the measured
KDP parameter was relatively noisy at lower rain rates. However, the
R(KDP, ZDR) algorithm based on the new axis-ratio relation
performed better than the others at higher rain rates (≥ 10 mm h-1). Therefore, in order to produce more accurate rainfall
estimations, the R(Zh, ZDR) and R(KDP, ZDR) algorithm
should be classified according to rainfall intensities.
To perform radar calibration measured ZH and ZDR were compared
with simulated ZH and ZDR. The calculated ZH and ZDR
bias was used to reduce radar bias, and to produce more accurate rainfall
estimations. After bias correction, radar rainfall estimations were closer
to rain gauge measurements, meaning an improvement of the first ones.
In this paper, different raindrops axis ratios were used to derive new
polarimetric rainfall relations, and the new polarimetric rainfall
algorithms were assessed with respect to their ability to produce accurate
point radar rainfall estimations. The new polarimetric rainfall algorithms
performed better than existing rainfall algorithms, and no large differences
were observed in regard to climatic regimes. In particular, the use of the
R(Zh, ZDR) algorithm lead to an improvement of radar rainfall
estimations in the Korean Peninsula since in this region extreme
precipitation systems such as tornados, supercells, and hail storms do not
often occur. We are now working to improve the KDP quality because it is
a very useful parameter for high rainfall rates estimation. A classification
of rain rates based on these results will also be performed in future work.
In addition, polarimetric rainfall algorithms will be developed to obtain
areal rainfall estimations through long-term DSD collection efforts and
several rainfall-cases-based analyses.