Polarimetric measurements are sensitive to the sizes, concentrations,
orientations, and shapes of raindrops. Thus, rainfall rates calculated from
polarimetric radar are influenced by the raindrop shapes and canting. The
mean raindrop shape can be obtained from long-term raindrop size distribution
(DSD) observations, and the shapes of raindrops can play an important role in
polarimetric rainfall algorithms based on differential reflectivity
(

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 (

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

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

Radar measurements often suffer from the system biases of

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

In this study we used the compact 2DVD version deployed on the campus of
Kyungpook National University, Daegu, Korea (35.9

Specifications for dual-polarization radar in Bislsan.

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

The Ministry of Land, Infrastructure, and Transport (MLIT) operates the
Bislsan (BSL) dual-polarization radar in Bislsan, Korea (35.7

The BSL S-band dual-polarization radar was located about 22.3 km
(17

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

The locations of the Bislsan polarimetric radar and the 2DVD at the rain gauge site.

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:

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).

Distribution of fall velocity and oblateness according to
drop diameter.

Time series of accumulated rainfall measured from the
rain gauge and estimated from the 2DVD:

Summary of the date, type of precipitation, and accumulated rainfall comparison values between 2DVD and rain gauge measurements for the 33 rainfall events.

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

One-hour (left panel) and total accumulated rainfall (right panel) from the 2DVD and rain gauge for the 33 rainfall cases.

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 (

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 (

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.

In order to produce the polarimetric rainfall algorithms, the theoretical
polarimetric variables (e.g.,

Different raindrop axis-ratio relations for the oblate raindrop model. The upper right subfigure illustrates the axis ratio of an oblate raindrop.

Polarimetric rainfall relations between

The radar measurements are affected by various observational errors, such as
ground echoes, beam broadening, anomalous propagation echoes, and
calibration biases of radar

The calibration biases of

Scatterplot of

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.

We compared the new axis-ratio experimental fit with existing mean
axis-ratio relations such as those of Pruppacher and Beard (1970), Beard and
Chuang (1987), and Brandes et al. (2002) (see Fig. 5). Consisting in the
following polynomial formulas:

The differences in the mean axis-ratio relations seemed small, and dependence of the raindrop axis ratio on climatic regimes was not clearly observed, although raindrop shapes can be influenced by the temperature and pressure (Beard and Chuang, 1987). Differences of raindrop shape can also be caused by measurement errors, drop oscillation, event selection criterion, and the fitting method used (Thurai and Bringi, 2005). A small error in the mean axis ratio can lead to significant errors in the estimated DSD and rainfall rates (Bringi and Chandrasekar, 2001). Therefore, the consideration of the accurate raindrop shapes based on long-term DSD data is necessary to improve the polarimetric rainfall estimations.

To investigate the variability of the DSD in rainfall estimations from
polarimetric parameters, the rain rate

The reflectivity factor is affected by the absolute calibration error, and
it requires accurate knowledge of the radar constant. The differential
reflectivity is a relative power measurement of any rainfall algorithm.
Therefore, it can be measured without being affected by absolute calibration
errors. However, the

In order to evaluate radar rainfall estimations according to different
rainfall relations and raindrop shapes, we compared the 1 h rain rate from
the BSL S-band radar with the hourly rain rate obtained by the use of the
rain gauge in Daegu, Korea. Furthermore, the rainfall estimate from the 2DVD
data was included for comparison. Here, the time of observations was short
and unstable rainfall events in regard to the continuity and stability of
measurement data were excluded from the analysis. Therefore, Statistical
validation of the radar and 2DVD rainfall estimates for the different
rainfall relations were performed for 18 rainfall events among the 33
rainfall cases. The MAE and RMSE are given by

Scatter plot of the 1 h rain rate from rain gauge
(

Scatter plots of the 1 h rain rates from rain gauge
(

Time series of the

Same as Fig. 9, except that the data are for 16 September 2012.

Comparison of the 1 h rain rate (left ordinate) and
accumulated rainfall (right ordinate) obtained by the BSL S-band radar and
rain gauge. The

Mean absolute error (MAE) and root-mean-square error (RMSE) of rainfall estimates before and after applying bias correction.

*BC: bias correction.

Radar measurements can suffer from

The application of absolute calibration biases is the most effective way to
reduce radar rainfall errors, in particular, for rainfall estimators with
both

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

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,

To perform radar calibration measured

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

This research was supported by the “Development and application of cross governmental dual-pol radar harmonization (WRC-2013-A-1)” project of the Weather Radar Center, Korea Meteorological Administration. Edited by: G. Vulpiani Reviewed by: S. Sebastianelli and four anonymous referees