Radar dataset and rainfall cases
In this study, the performance of the bias correction methods has been
evaluated by comparing the observed rainfall data from rain gauges
operated by the KMA (Korea Meteorological Administration). The
observed rainfall data were collected from 642 ground rain gauges
(called AWS, Automatic Weather Station) located in the Korean
Peninsula, 321 of which were for calibration, and 321 for validation
in Fig. 1. The Bislsan S-band dual-polarimetric radar, which was
installed and operated by the Ministry of Land, Infrastructure and
Transport (MLIT) in 2009, was selected to be the absolute reference
radar to estimate the Z bias (described in Sect. 2.2). Horizontal
and vertical reflectivity (ZH and ZV),
differential reflectivity (ZDR), differential phase
(ΦDP), specific differential phase (KDP),
correlation coefficient (ρHV), and spectrum width
(SW) were estimated with a gate size of 0.125 km. The scan
strategy has six elevation angles, with a 2.5 min update cycle. The
Accuracy of a reference radar shows that bias is
2.01 mmh-1, RMSE is 3.55 mmh-1, and
correlation coefficient is 0.89 in 10 rainfall cases from October 2011
to October 2012. Other studies also show a reference radar has more
than 80 % accuracy, on average, in both quantitative and
qualitative tests (You et al., 2014; Jeong et al., 2014; Kim et al.,
2015). The target radars that required Z bias correction were 11
single-polarimeric radars (Baegnyeondo, Kwanaksan, Oseonsan, Jindo,
Gosan, Seongsan, Gudeoksan, Myeonbongsan, Gangneung, Gwnagdeoksan,
Incheon) with a scan range of maximum 200 km (C-band) and
240 km (S-band), and a gate size of 0.250 km, operated
by the KMA, in Fig. 2. Table 1a shows the radars and rain-gauges used
for estimating the Z bias and the data period, and Table 1b shows
the 18 rainfall cases (in the summer season) used for the verification
of the Z bias and rainfall estimation bias correction methods.
Quantitative precipitation estimation model
This paper utilized the Radar-AWS Rainrate (RAR) calculation system
(Hereafter called the RAR system) for the QPE model. The RAR system,
which was developed by the KMA in 2006, is operated on site, based on
11 single-polarimetric radars. The RAR system produces a merged
rainfall field for the Korean Peninsula through a series of steps
(production of the radar reflectivity field, calculation of AWS
rainfalls, derivation of the Z–R relationship, etc.) (refer to
Fig. 3).
The RAR system estimates the parameters of the Z–R relationship,
in real-time, for real-time rainfall estimates (Weather Radar Center,
2011). The RAR system utilizes 10 min reflectivity and AWS rainfall,
in the Window Probability Matching Method (WPMM) (Rosenfeld et al.,
1993), to estimate the rainfalls in each radar site and the merged
rainfalls of radar sites for producing composite rainfall fields. The
used reflectivity, which are quality controlled (removal of
non-meteorological echoes), are averaged on 3×3 pixels with
a certain AWS as the centers are used. The WPMM method reproduces the
probability density functions (pdfs) of ground rainfall from the AWSs,
and radar reflectivity, and determines the Z–R relationship using
these pdfs (refer to Eqs. and ) (Rosenfeld et al.,
1993).
∫0∞f(Ze)Pc(Ze)dZe=∫0∞RPc(R)dRPc(R)=P(R|R>RT),Pc(Ze)=P(Ze|Ze>ZeT)
where Ze is the radar reflectivity (dBZ), Pc() is
the conditional probability function, R is the rainfall
(mmh-1), and T is the threshold.
The conditional probability functions in Eq. () are derived
from Eq. (), and the thresholds of rainfall and radar
reflectivity are 0.1 mmh-1 and 10 dBZ. The parameters of
the Z–R relationship have been estimated using radar reflectivity
and AWS rainfalls, from 1 prior, with the least square fit of the
power law. The number of radar reflectivity and AWS rainfalls over
a certain threshold are required in order to estimate the parameters
accurately. If there is not enough data, the estimated rainfalls from
that Z–R relationship are inaccurate. To overcome this
limitation, if the number of available AWSs is more than 30 % of
those available in each radar site, the parameters of the Z–R
relationship can be estimated. If it is less than 30 %, Z=200R1.6 (Marshall and Palmer, 1948) is applied for the rainfall
estimates (Korea Meteorological Administration, 2012b).
Secondly, the composite rainfall field for the whole country may be
produced using each radar rainfall estimate; however, appropriate
merging methods (including maximum value, average value, minimum
value, and distance weighting methods) must be conducted because the
scan ranges of the radar sites overlap. Because the maximum value
method is applied to merge radar rainfalls by the KMA (Korea
Meteorological Administration, 2012b), the identical method is also
utilized in this paper.
Bias correction methods
Reflectivity measurement bias correction method
Weather radars continuously carry out measurement cycles, which
include sending signals into the atmosphere and receiving and
analyzing the return signals for meteorological observation. The
measurement of the reflectivity itself suffers from hardware
malfunctions (e.g. electronic miscalibration, signal misprocessing)
and radar characteristics (e.g. attenuation). When converting radar
reflectivity into rainrates (Z–R relationship) leads to an
additional bias that can lower the accuracy of rainfall estimation. To
estimate the Z bias of the target weather radars, a reference
weather radar that has been absolutely corrected is required. The
Z bias is defined as the difference between the measured
reflectivity of the reference radar and the target radar, under the
same spatial and temporal conditions (Weather Radar Center, 2012). The
procedure of estimating the Z bias is described as follows.
Calibration of the reference weather radar
This paper selected a Bislsan S-band dual-polarimeric radar (hereafter
Bislsan dual-pol radar), which can be self-calibrated and is more
accurate than the reference weather radar. To calibrate the Bislsan
dual-pol radar, a self-consistency constraint method that uses the
relationship between the reflectivity (Z), varied by the radar beam
power and the specific differential phase (KDP) and
affected by only the particle size or the concentration and not the
radar beam power, was utilized. The procedure of the self-consistency
constraint method is as follows (Weather Radar Center, 2012).
Derive the ZH–KDP relationship,
theoretically, from the Drop Size Distributions (DSDs).
Calculate the KDP for each radar pixel from the
observed ZH, using the derived
ZH–KDP relationship and the
ΦDP as the integrating calculated KDP
along each radial.
Calculate the difference angle (θ) using a scatter plot
between the calculated ΦDP, from (2) and observed
from the Bislsan dual-pol radar, and calculate the Z bias
(ε) by inputting the difference angle (θ) into
Eqs. () and () (Lee et al., 2006) (refer to
Fig. 4).
tanθ=∑i=1n(ΦDP_cal-ΦDP_obs)∑i=1nΦDP_obs2ε(dB)=10blog(tanθ)
where, ΦDP_cal is the theoretical ΦDP
from the DSDs, ΦDP_cal is the observed ΦDP from the dual-pol radar, θ is the difference
angle, b is the empirical constant, and ε is the
estimated Z bias.
Calculation of <inline-formula><mml:math display="inline"><mml:mi>Z</mml:mi></mml:math></inline-formula> bias for the target weather radars
After calibration of the Bislsan dual-pol radar for the Z bias was
completed, the target single-pol radars that are located adjacent to
the reference radar were calibrated according to the reflectivity of
the reference radar. The procedure for calculating the Z bias of the
target radars is as follows (Korea Meteorological Administration,
2011).
Remove the beam-blockage area using the beam-blockage
information (penetration ratio more than 90 %).
Reflect the accumulated attenuation effects, due to the
rainfall, in the observed reflectivity (attenuation ratio less than
10 %).
Generate the 3-dimensional CAPPI for the reflectivity.
Set up equidistant pairs between the reference and target
radars, within 200 km from the center of the reference
radar; however, whenever a Bislsan dual-pol radar was the reference
radar, the distance was within 100 km.
Compare the reflectivity of the reference and target radars, within a ±5 km reflectivity overlap area.
Calculate the reflectivity differences, at intervals of
0.5 km from 1.5–3.5 km altitude, with
consideration to the ground clutter and the bright band, and average
the reflectivity differences for the Z bias of the target radar.
Figure 5 shows the concept of the Z bias for the target radar, which
has been calculated from the reflectivity differences in the overlap
area, between the reference and the target radars. After the
calibration of the target radar#1 for the Z bias was completed,
target radar #1 was the reference radar for target radar #2
(adjacent to target radar #1). The procedure mentioned above was
equally applied for target radar #1 and #2, to calculate the
Z bias of target radar #2.
Rainfall estimation bias correction methods
The estimated rainfall, based on the radars, has the QPE model bias
(parameters of Z–R relationship, parameters of QPE model, QPE
model structures, etc.) even if calibrated reflectivity is inputted
into the QPE model. In this paper, the Mean Field Bias Correction
(MFBC) method and the Local Gauge Correction (LGC) method have been
applied to the outcomes from the QPE model, in order to correct the
rainfall estimation bias.
Mean field bias correction method
The fundamental concept of the MFBC method is that the bias correct
factor (G/R ratio factor) is calculated using the
ratio of the spatial average (mean), between the rainfalls, estimated
using radars and observed rainfall at a corresponding field (or point,
pixel). Then corrected rainfall is calculated by multiplying the
G/R ratio factor, and the radar rainfall
estimates. The equation of the MFBC method is as follows.
G/Rratio factor=∑i=1nGi/∑i=1nRi
where, Gi is the rainfall of the ith rain gauge, Ri is
the radar rainfall estimates of the ith point (or pixel), and n
is the total number of the ground rain gauge. In the case of utilizing
the MFBC method in a certain area (or for a certain period), the
identical G/R ratio factor is uniformly applied to
radar rainfall estimates all over the area.
Local Gauge Correction method
This study dealt with the Local Gauge Correction (LGC) method, which
has been employed in the NMQ (National Mosaic and QPE) of the NOAA
(National Oceanic and Atmospheric Administration) and NSSL (National
Severe Storms Laboratory) (Zhang et al., 2011). The LGC method, which
assigns the weights to a bias between the ground rainfall detected by
AWSs and the radar rainfall estimates, is a modified version of the
Inverse Distance Weighting (IDW) method. The LGC method is able to
correct the rainfall cases that occur locally by modifying the
rainfall estimates in each pixel. The procedure of the LGC method is
as follows (refer to Fig. 6):
This paper defined that rLGC,i is the corrected rainfall
estimates in a certain point i, ri is the radar rainfall
estimates in a certain radar pixel i, and Re,i is the
expected error estimates. This relationship is expressed as following
equation:
STEP 1:rLGC,i=ri-Re,i=rLGC,i(b,D)
where D is the effective radius for calculating the radar rainfall
bias, b is the weight of the variable d, and d is the distance
between the AWSs and the pixels in the radars. The estimated weights,
according to Eq. (), are applied to Eq. (6) (Zhang et al.,
2011).
Re,i=∑j=1mejwj/∑j=1mwj
If general, wj=1/djb (if dj≤D) or 0 (if dj>D)
If the numbers of AWS in the region are sparse,
α=∑j=1mexp-dj2/(D/2)2;wj=α×1/djb(ifdj≤D)or0(ifdj>D)
where ej is the error between the rainfalls observed from the
AWSs (gj) and the radar rainfall estimates (rj), w is the
weight of the error (=rj-gj), j is the jth AWS, m is
the number of AWSs within the effective radius, and α is the
impact factor. If the α is more than one, the number of AWSs
is enough for the rainfall-bias correction. Otherwise, if it is less
than one, if the number of AWSs is sparse (the α is less than
one), the revised weights have been calculated by multiplying α
with the original weights (wj=α×1/dj2).
Ei is defined as the difference between the rLGC from STEP 1
and the ground rainfall, gi, and it depends on b and D.
STEP 2:Ei=rLGC-gi=Ei(b,D)
The Mean Square Error (MSE) for Ei is expressed as Eq. (10), and
it also depends on parameters b and D. The parameters of the LGC
method (b and D) have been determined using the stepwise method
for minimizing the MSE value, and applied to Eq. (8) to calculate the
radar rainfall estimates, rLGC.
STEP 3:MSE=∑i=1nEi2/n=MSE(b,D)
This paper has assumed that the scan range of the radars (D) is the
maximum range (240 km) used by all AWSs on the Korean
Peninsula. Although it takes a long time to carry out the LGC
algorithm under this assumption, it is considered to be appropriate to
verify the improvement of the radar rainfall estimates using the LGC
method.
In sequence, because the LGC method is highly dependent on the number
of AWSs that are available and accurate, a quality control algorithm
for the AWSs has been conducted to remove lower-quality AWSs that have
larger expected errors than the others. The conditions of the quality
control are as follows: (i) in a certain AWS, if the number of pixels
that have a DR,E less than 5 mm are less than 25 % of
the total pixels, a certain AWS is designated as an “abnormal AWS”
and is thus removed. DR,E are the differences between
Re,i and Ei, within 10 km radius from the
center of a certain AWS. (ii) The LGC method has been conducted until
the number of available AWSs was more than 90 % of all the
filtered AWSs. If this procedure is stopped, a calculated
rLGC at the present stage is used for the corrected
rainfall estimates. (iii) The procedure of the LGC method is finally
finished after repeating the routine more than approximately four
times. Furthermore, if the ratio of the abnormal AWSs is more than
7 %, the procedure of the LGC method is also finished (Korea
Meteorological Administration, 2012). The thresholds were decided
using the stepwise method, and are appropriate for the LGC method
applied to the RAR calculation system. However, since the thresholds
are somewhat subjective, it is considered that future studies should
be conducted that deal with this limitation.