the Creative Commons Attribution 4.0 License.

the Creative Commons Attribution 4.0 License.

# Microphysical processes of super typhoon Lekima (2019) and their impacts on polarimetric radar remote sensing of precipitation

### Yabin Gou

### Hong Zhu

### Lulin Xue

The complex precipitation microphysics associated with super
typhoon Lekima (2019) and its potential impacts on the consistency of
multi-source datasets and radar quantitative precipitation estimation were
disentangled using a suite of in situ and remote sensing observations around
the waterlogged area in the groove windward slope (GWS) of Yandang Mountain (YDM)
and Kuocang Mountain, China. The main findings include the following: (i) the quality control processing for radar and disdrometers, which collect raindrop size distribution (DSD) data, effectively enhances the self-consistency between radar measurements, such as radar
reflectivity (*Z*_{H}), differential reflectivity (*Z*_{DR}), and the specific
differential phase (*K*_{DP}), as well as the consistency between radar, disdrometers,
and gauges. (ii) The microphysical processes, in which breakup overwhelms
coalescence in the coalescence–breakup balance of precipitation particles,
noticeably make radar measurements prone to be breakup-dominated in radar
volume gates, which accounts for the phenomenon where the high number
concentration rather than the large size of drops contributes more to a given
attenuation-corrected *Z*_{H} (${Z}_{\mathrm{H}}^{\mathrm{C}}$) and the significant
deviation of attenuation-corrected *Z*_{DR} (${Z}_{\mathrm{DR}}^{\mathrm{C}}$) from
its expected values (${\widehat{Z}}_{\mathrm{DR}}$) estimated by DSD-simulated
*Z*_{DR}–*Z*_{H} relationships. (iii) The twin-parameter radar rainfall estimates
based on measured *Z*_{H} (${Z}_{\mathrm{H}}^{\mathrm{M}}$) and *Z*_{DR}
(${Z}_{\mathrm{DR}}^{\mathrm{M}}$), and their corrected counterparts
${Z}_{\mathrm{H}}^{\mathrm{C}}$ and ${Z}_{\mathrm{DR}}^{\mathrm{C}}$, i.e.,
*R*(${Z}_{\mathrm{H}}^{\mathrm{M}}$, ${Z}_{\mathrm{DR}}^{\mathrm{M}}$) and
*R*(${Z}_{\mathrm{H}}^{\mathrm{C}}$, ${Z}_{\mathrm{DR}}^{\mathrm{C}}$), both tend
to overestimate rainfall around the GWS of YDM, mainly ascribed to the
unique microphysical process in which the breakup-dominated small-sized
drops above transition to the coalescence-dominated large-sized drops
falling near the surface. (iv) The improved performance of
*R*(${Z}_{\mathrm{H}}^{\mathrm{C}}$, ${\widehat{Z}}_{\mathrm{DR}}$) is attributed to
the utilization of ${\widehat{Z}}_{\mathrm{DR}}$, which equals physically
converting breakup-dominated measurements in radar volume gates to their
coalescence-dominated counterparts, and this also benefits from the better
self-consistency between ${Z}_{\mathrm{H}}^{\mathrm{C}}$, ${\widehat{Z}}_{\mathrm{DR}}$, and *K*_{DP},
as well as their consistency with the surface counterparts.

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Weather radars form the cornerstone of national weather warnings and
forecast infrastructure in many countries. Doppler radar networks play an
indispensable role in modern meteorological and hydrological applications,
such as quantitative precipitation estimation (QPE), in support of the
application of some hydrological models for water resource management,
especially during high-impact weather events in urban environments
(Chandrasekar et al., 2018; Cifelli et al., 2018; Chen and Chandrasekar, 2018).
Although technological advances such as dual-polarization have tremendously
improved weather radar applications in hydrometeorology remote sensing, it
is still a challenge to incorporate complex precipitation dynamics and
microphysics in an adaptive manner to optimize the quantitative applications
of polarimetric radar measurements, including horizontal reflectivity *Z*_{H},
differential reflectivity *Z*_{DR}, copolar correlation coefficient *ρ*_{HV},
differential propagation phase Φ_{DP}, and its range derivative *K*_{DP}
(specific differential phase). Traditional utilization of these measurements
has only been able to extract some information on complex spatiotemporal
precipitation variability.

In general, three main factors contribute to radar QPE uncertainties: radar
measurement error, parameterization error of various radar–rain rate (*R*)
relationships, and random error. In practical applications, it is crucial to
consider these three factors as a whole to ensure radar rainfall estimates
approximate the surface rainfall truth as much as possible. Among
conventional radar QPE algorithms, those developed based on *Z*_{H} measurements
are typical and are still in use today. For instance, an earlier version of
the radar QPE algorithm in the National Oceanic and Atmospheric
Administration (NOAA) Multi-Radar/Multi-Sensor System (MRMS) and its refined
version both utilize multi-radar hybrid *Z*_{H} to derive the radar-based
rainfall field (Zhang et al., 2011, 2016). The recent update of MRMS further
incorporated specific attenuation (*A*_{H}) and *K*_{DP} to enhance the *Z*_{H}-based
algorithm (Wang et al., 2019; Ryzhkov et al., 2022), and such an update can
benefit from (i) the insensitivity of *A*_{H} to raindrop size distribution (DSD)
variability (Ryzhkov et al., 2014); (ii) *K*_{DP} is a better indicator of rain
rate and liquid water content (LWC, g m^{−3}) than *Z*_{H}, since *K*_{DP} connects more
tightly to the precipitation particle size distribution; and
(iii) *R*(*K*_{DP}) and
*R*(*A*_{H}) inherit the immunity of Φ_{DP} to miscalibration, attenuation,
partial beam blockage, and wet radome effects (Park et al., 2005; Ryzhkov et
al., 2014, 2022), which are hard to address when using *Z*_{H} for radar QPE,
especially at higher frequencies such as C- and X-bands (Park et al., 2005;
Matrosov, 2010; Frasier et al., 2013). However, since *A*_{H} and *α* are
simultaneously derived, *R*(*A*_{H}) partly inherits the sensitivity of *α*
to temperature (Ryzhkov et al., 2014), which occurs with the ascending
altitude of the propagation of one radar beam. Multi-parameter radar QPE
algorithms further integrate *Z*_{DR} with *Z*_{H}, *K*_{DP}, or *A*_{H} to infer more
information about raindrop shape, such as the double-measurement algorithm
*R*(*Z*_{H}, *Z*_{DR}), *R*(*K*_{DP}, *Z*_{DR}), and *R*(*A*_{H}, *Z*_{DR}) and the triple-measurement radar QPE
algorithm as *R*(*Z*_{H}, *Z*_{DR}, *K*_{DP}) (Matrosov, 2010; Gosset et al., 2010; Schneebeli
and Berne, 2012; Keenan et al., 2001; Chen et al., 2017; Gou et al., 2019b),
but these algorithms all assume that *Z*_{DR} measurements are well calibrated
and attenuation-corrected (Ryzhkov et al., 2005; Bringi et al., 2010).

In addition to radar measurements, disdrometer and rain gauge data are often
used to determine the optimal parameters of radar-based QPE algorithms (Lee
and Zawadzki, 2005; Tokay et al., 2005). For example, the MRMS system
utilizes long-term *Z*_{H} and gauge rainfall measurements to obtain
climatological *Z*–*R* relationships for each precipitation type (Zhang et al.,
2011, 2016). In Gou et al. (2018, 2020), rain gauge measurements are used to
dynamically adjust *Z*–*R* relationships to reflect the microphysical evolutions
of precipitation systems. Nevertheless, the accuracy of meteorological gauge
rainfall recordings is usually configured as 0.1 mm, and rain gauges may
record less rainfall than reality due to debris blockage (tree leaves,
insects, etc.) and the quick spinning of tipping buckets in a heavy shower
situation. In addition, the surface wind may hinder some raindrops from
falling into the tipping bucket, and the mechanical failures of the tipping
bucket will record abnormally high or low rainfall, which introduces
significant errors to the gauge network. Similarly, disdrometer measurements
can be affected by strong winds and mixed-phase hydrometeors falling through
the laser sampling area of the disdrometer, resulting in degraded quality of
the DSD recordings (Tokay and Bashor, 2010). Since the DSD data collected by
disdrometers are indispensable and sometimes are the only resources that can
be used for precipitation microphysical analysis and the establishment of
polarimetric radar rainfall relationships, meticulous quality control (QC)
must be conducted on the disdrometer measurements (Friedrich et al., 2013).

Another issue that is important but rarely considered in radar QPE is the
changing microphysics that occurs during the falling processes of
precipitation particles between radar volume gates and surface ground, which
is often indicated by inconsistent radar observations with their surface
counterparts. The *Z*_{H} measurements in the melting layer (ML) of a stratiform
rain system, which features falling melting snowflakes or ice crystals,
usually need to be corrected for subsequent rainfall
retrievals, especially when little rain is reported on the ground (Chen et
al., 2020). A severe updraft may introduce a large *Z*_{H} and *Z*_{DR} column (Snyder
et al., 2015; Carlin et al., 2017), while the surface rain gauge may record
little or time-lagged rainfall, which is frequently perceived in the front
of a squall line system or wind gust system. In addition, the contamination
of mixed-phase hydrometeor particles on *K*_{DP} and *A*_{H} may lead to *R*(*K*_{DP}) and
*R*(*A*_{H}) being overestimated (Gou et al., 2019b), and the falling wet
hailstones may also contaminate radar-measured *Z*_{H}, *K*_{DP}, and *A*_{H} (Donavon and
Jungbluth, 2007; Ryzhkov et al., 2014), leading to an overestimated hotspot
on the derived rainfall field if such contaminations are not well addressed.

The complex microphysical variations mentioned above may coexist in a large-scale precipitation system such as a typhoon.

Before the polarimetric update, the impacts of the coexisting precipitation
types on the radar QPE can be exploited through the vertical profile of
reflectivity (VPR, Xu et al., 2008; Zhang et al., 2011, 2016). During the
landfall of typhoon Hakui (2012), the VPR characteristics of coexisting
tropical, convective, and stratiform rain account for the spatial
precipitation variability (Gou et al., 2014). Super typhoon Lekima (2019)
was the first super typhoon that landed on the eastern coast of Zhejiang
after the polarimetric radar update, which provided an opportunity to
exploit more microphysical signatures of the typhoon. Lekima landed on the
coastal area of Chengnan town in Wen Ling (WL) city at 17:45 UTC, 9 August 2019, and the
maximum wind near its center was about 52 m s^{−1}, which made it the strongest
typhoon landing on the mainland of China in 2019. According to the
statistics of the Chinese Meteorological Administration, Lekima was detained
on land for 44 h; the affected area with rainfall measurements over 100 mm was about 361 000 km^{2} during this period, and 19 national
meteorological stations broke their historical daily rainfall recordings.
During landfall, high waves were stirred up along the coastline, as depicted
in Fig. 1a, and the landslide in Fig. 1b blocked the river and temporarily
formed a dike with a sudden rise of the water level of the river before the
collapse of the landslide dike, resulting in 22 casualties around this area.
Waterlogging submerged the road network and many buildings in the urban area
of Wen Ling (WL), Lin Hai (LH), Yu Huan (YH), and Xian Ju (XJ) in Taizhou (TZ) city (see Fig. 1c–f). Millions of people
were evacuated from TZ city or were trapped in the disaster area. A total of 57
casualties were reported due to the landslides, floods, and waterlogging
during the landfall of Lekima.

This paper investigates the microphysical characteristics of the typhoon-induced storm after its landfall, using observations from an S-band polarimetric radar deployed at Wenzhou (hereafter referred to as WZ-SPOL), six Thies disdrometers, and a local rain gauge network around the disaster area. So far, the reason for the significant convective asymmetries in the concentric eyewalls before its landfall has been ascribed to the phase locking of vortex Rossby waves (VRW), and the cloud and precipitation microphysics caused by this phase-locking VRW-triggered asymmetric convection have been revealed (Dai et al., 2021; Huang et al., 2022), mainly based on the WZ-SPOL radar and another Doppler weather radar in TZ city. The DSD differences in the eyewall and spiral rainbands based on surface disdrometer measurements have also been demonstrated (Bao et al., 2020). However, the microphysical processes inherent in Lekima after its landfall have not been thoroughly investigated.

The novel contributions of this paper are summarized as follows: (1) an
enhanced QC procedure for disdrometer measurement is developed and analyzed
through cross-comparison with rain gauge and WZ-SPOL radar measurements. (2) The microphysical process with overwhelming breakup over coalescence during
the landfall of Lekima is revealed based on radar and surface disdrometers.
(3) The impacts of dominant breakup and coalescence on radar QPE are investigated
through an *R*(*Z*_{H}, *Z*_{DR}) estimator, and this algorithm integrates the expected
*Z*_{DR} (i.e., ${\widehat{Z}}_{\mathrm{DR}}$) estimated from attenuation-corrected *Z*_{H}
(i.e., ${Z}_{\mathrm{H}}^{\mathrm{C}}$) to mitigate the negative effects of
the unique microphysical process, in which dominant breakup in the air
transitioned to dominant coalescence near the surface around the GWS of YDM.

The remainder of this article is organized as follows: Sect. 2 introduces the study domain, hardware configuration, and data processing methodologies. Section 3 details the precipitation microphysics associated with Lekima (2019). The impacts of dominant collision–breakup or collision–coalescence on radar QPE performance are also quantified in Sect. 3. Section 4 summarizes the main findings of this study and suggests future directions in implementing this work in an operational environment.

## 2.1 Study domain

As shown in Fig. 2a, this paper focused on the north side of WZ city and the
south side of TZ city. These two cities are both regional central cities of
eastern China: WZ is an important trade city with more than nine million
residents and an urban popularity density of 2900 km^{−2}. TZ is an important
seaport city in southeastern China with six million residents and an urban
popularity density of 688 km^{−2}. Historical typhoons have landed on the
coastlines of these two cities, indicating the necessity and importance of
monitoring typhoons coming into this area. With this aim, the S-band weather
radar in WZ was upgraded to a polarimetric radar system in 2019 to enhance
its precipitation-monitoring capability. The WZ-SPOL radar is deployed on a hill
(735 m) near the coastline, as depicted in Fig. 2a. It sufficiently covers
the flood and waterlogging disaster area caused by the landfall of Lekima.
Two mountains lie between WZ and TZ, Kuocang Mountain (KCM) and Yandang
Mountain (YDM). Although the mountainous terrain causes no serious beam
blockage issues, the vertical gap between the radar beam center and the
surface enlarges with ascending volume gates, as depicted in Fig. 2c. In
addition, KCM and YDM both feature a typical groove topography, as indicated
by the dashed lines in Fig. 2a, which benefits the assembling and uplifting
of water vapor on the lower atmospheric layers.

Six Thies laser-optical disdrometers have been deployed at the national meteorological stations around the target area since 2017 (see Figs. 2a and 1b). These include Xian Ju (XJ), Lin Hai (LH), Wen Ling (WL), Hong Jia (HJ), Yu Huan (YH), and Dong Tou (DT), and they provide particle size and terminal velocity (size–velocity) pairs with a 1 min time resolution. These size–velocity pairs are utilized to calculate rainfall intensity and to simulate dual-polarization radar measurements near the surface.

In addition, 356 tipping-bucket rain gauge stations (see Fig. 2b) are uniformly deployed around 10 towns that have suffered from landslide and waterlogging disasters within the coverage of a radius of 135 km from the WZ-SPOL radar. The time resolution of the gauge measurements is also configured as 1 min; if hourly gauge measurements are temporarily interrupted due to network issues, such as transmission congestion, these interrupted recordings will not be utilized. If we suppose that a gauge rainfall recording exceeds 1 mm, but the ratio between hourly gauge rainfall and any hourly radar estimates exceeds 10 (or less than 0.1 for the intercomparison), then this gauge measurement is suspected to be falsely reported and will not be used. This ratio (10, suggested in Marzen, 2004) is large enough to eliminate significant outliers but keep most other valuable gauge rainfall recordings.

## 2.2 Radar configuration and data processing

The WZ-SPOL radar adopts the simultaneous horizontal and vertical
polarization mode. For the routine operations, the standard volume coverage
pattern (VCP21) is configured, which has elevation angles including
0.5, 1.5, 2.4, 3.3,
4.3, 6.0, 9.9, 14.5, and
19.5^{∘}. The azimuthal radial resolution is set as 0.95^{∘},
and the range gate resolution is configured as 250 m for all elevation
angles. Radar-measured *Z*_{H}, *Z*_{DR}, *ρ*_{HV}, as well as radial velocity (*V*_{R}) and Ψ_{DP}, are archived in the radar data acquisition (RDA) system and then
transferred to the radar products generation system to produce some
predefined standard radar products. QC processing for WZ-SPOL radar data is
performed using the following steps:

- i.
*Ground clutter (GC) identification and mitigation.*Two parts are included in this step. The clutter mitigation decision (CMD) algorithm (Hubbert et al., 2009) has been integrated into the RDA software to filter the ground clutters in real-time, but some residual static ground clutters (RSGC) still exist in the WZ-SPOL radar measurements at the 0.5

^{∘}elevation angle. To further eliminate the RSGC, the WZ-SPOL radar*Z*_{H}measurements on the 0.5^{∘}elevation angle from August 2019 are utilized. The max number (*N*_{max}) of the pixel with*Z*_{H}*>*0 dBZ within 55 km from the WZ-SPOL radar is 6981, and the observation number (*N*_{obs}) of each pixel within this range is normalized by dividing*N*_{max}. Then, an RSGC statistical map is derived, as shown in Fig. 3a, representing the relative frequency (freq. % of*Z*_{H}*>*0 dBZ) within the coverage of the WZ-SPOL radar. In this map, the pixels with freq.*>*50 % are deemed to be contaminated by the RSGC, and they form an RSGC mask in Fig. 3b to eliminate RSGC-contaminated*Z*_{H}and*Z*_{DR}at the 0.5^{∘}elevation angle of the WZ-SPOL radar. - ii.
Ψ

_{DP}*processing.*A nine-gate smoothing is first carried out to suppress the noise signals along the Ψ

_{DP}range profile. Then, a procedure is executed to correct the aliased Ψ_{DP}based on the standard deviation of Ψ_{DP}in nine consecutive range gates (Wang and Chandrasekar, 2009), and 360^{∘}are added to the aliased Ψ_{DP}to guarantee a monotonically increasing Ψ_{DP}range profile. In addition, the iterative filtering method in Hubbert and Bringi (1995) is used to filter the backscatter differential phase, and a zero-started filtered Φ_{DP}(${\mathrm{\Phi}}_{\mathrm{DP}}^{\mathrm{filter}}$) range profile is obtained by removing the initial phase of Φ_{DP}. The ${\mathrm{\Phi}}_{\mathrm{DP}}^{\mathrm{filter}}$ range profile is utilized to estimate*K*_{DP}through a linear fitting approach (Wang and Chandrasekar, 2009) with an additional non-negative constraint on*K*_{DP}. - iii.
*Attenuation correction for**Z*_{H}.The ZPHI approach proposed by Bringi et al. (2001) is extended for correcting S-band

*Z*_{H}measurements:$$\begin{array}{}\text{(1a)}& {\displaystyle}{A}_{\mathrm{H}}\left(r\right)={\displaystyle \frac{{\left[{Z}_{\mathrm{H}}^{\mathrm{M}}\right]}^{b}\left[{\mathrm{10}}^{\mathrm{0.1}b\mathit{\alpha}\mathrm{\Delta}\mathrm{\Phi}\left({r}_{\mathrm{0}},{r}_{m}\right)}-\mathrm{1}\right]}{I\left({r}_{\mathrm{0}},{r}_{m}\right)+\left[{\mathrm{10}}^{\mathrm{0.1}b\mathit{\alpha}\mathrm{\Delta}\mathrm{\Phi}\left({r}_{\mathrm{0}},{r}_{m}\right)}-\mathrm{1}\right]I\left(r,{r}_{m}\right),}}\text{(1b)}& {\displaystyle}\mathrm{\Delta}{\mathrm{\Phi}}_{\mathrm{DP}}\left({r}_{\mathrm{0}},{r}_{m}\right)={\mathrm{\Phi}}_{\mathrm{DP}}\left({r}_{m}\right)-{\mathrm{\Phi}}_{\mathrm{DP}}\left({r}_{\mathrm{0}}\right),\text{(1c)}& {\displaystyle}I\left({r}_{\mathrm{0}},{r}_{m}\right)=\mathrm{0.46}b{\int}_{{r}_{\mathrm{0}}}^{{r}_{m}}\left[{Z}_{\mathrm{H}}^{\mathrm{M}}\right(r){]}^{b}\mathrm{d}s,\text{(1d)}& {\displaystyle}I\left(r,{r}_{m}\right)=\mathrm{0.46}b{\int}_{r}^{{r}_{m}}\left[{Z}_{\mathrm{H}}^{\mathrm{M}}\right(r){]}^{b}\mathrm{d}s,\text{(1e)}& {\displaystyle}{\mathrm{\Phi}}_{\mathrm{DP}}^{\mathrm{rec}}\left({r}_{\mathrm{0}},{r}_{m}\right)=\mathrm{2}{\int}_{{r}_{\mathrm{0}}}^{{r}_{m}}{\displaystyle \frac{{A}_{\mathrm{H}}\left(s,\mathit{\alpha}\right)}{\mathit{\alpha}}}\mathrm{d}s,\text{(1f)}& {\displaystyle}C\left({r}_{\mathrm{0}},{r}_{m}\right)={\int}_{{r}_{\mathrm{0}}}^{{r}_{m}}\left|{\mathrm{\Phi}}_{\mathrm{DP}}^{\mathrm{rec}}\left(s,\mathit{\alpha}\right)-{\mathrm{\Phi}}_{\mathrm{DP}}\right|\mathrm{d}s,\text{(1g)}& {\displaystyle}{Z}_{\mathrm{H}}^{\mathrm{C}}\left(r\right)={Z}_{\mathrm{H}}^{\mathrm{M}}\left(r\right)+\mathrm{2}\underset{\mathrm{0}}{\overset{r}{\int}}{A}_{\mathrm{H}}\left(s,\mathit{\alpha}\right)\mathrm{d}s,\end{array}$$where ${Z}_{\mathrm{H}}^{\mathrm{M}}$ and ${Z}_{\mathrm{H}}^{\mathrm{C}}$ denote the measured and attenuation-corrected reflectivity, respectively; Φ

_{DP}refers to the filtered differential phase; ${\mathrm{\Phi}}_{\mathrm{DP}}^{\mathrm{rec}}$ is a reconstructed differential phase through the ZPHI processing chain with an optimal coefficient*α*iteratively searched in the range [0.01, 0.12] by step 0.01 until the cost function*C*(*r*_{0},*r*_{m}) of the difference between Φ_{DP}and ${\mathrm{\Phi}}_{\mathrm{DP}}^{\mathrm{rec}}$ in Eq. (1f) is minimized. The coefficient*b*is assumed to be 0.62 for the S-band (Ryzhkov et al., 2014).The ZPHI approach utilizes ${Z}_{\mathrm{H}}^{\mathrm{M}}$ and ΔΦ

_{DP}in Eq. (1b) to calculate attenuation*A*_{H}. Here, it should be noted that three constraints are imposed on the ZPHI processing chain to ensure its practical performance, including a non-negative constraint on*A*_{H},*ρ*_{HV}constraint on the range gate partitioning, and convergence constraint to avoid incorrect calculation termination (Gou et al., 2019a). Finally, ${Z}_{\mathrm{H}}^{\mathrm{M}}$ is corrected to ${Z}_{\mathrm{H}}^{\mathrm{C}}$ according to Eq. (1g). - iv.
*Z*_{DR}*processing.*The

*Z*_{DR}offset is usually routinely obtained in zenith mode, with which near-zero*Z*_{DR}is anticipated in light rain scenarios, and then this offset is fed back to the RDA system to ensure slight*Z*_{DR}bias. Bringi et al. (2001) showed that all*Z*_{DR}values at the far side of one radial profile are expected to approximate 0 dB if the “intrinsic”*Z*_{H}is small enough (i.e., ${Z}_{\mathrm{H}}^{\mathrm{C}}$*<*20 dBZ) and attenuation-corrected*Z*_{DR}(${Z}_{\mathrm{DR}}^{\mathrm{C}}$) should approximate to their ${\widehat{Z}}_{\mathrm{DR}}$ along the whole radial profile; thus, appropriate*Z*_{DR}bias adjustment may effectively help in such a*Z*_{DR}approximation. In this process, near-zero ${\widehat{Z}}_{\mathrm{DR}}$ is also anticipated for far-side volume gates containing ice crystals with ${Z}_{\mathrm{H}}^{\mathrm{C}}\phantom{\rule{0.125em}{0ex}}\mathit{<}\phantom{\rule{0.125em}{0ex}}\mathrm{20}$ dBZ. Here, the exponential*Z*_{DR}–*Z*_{H}relationship is established as Eq. (2a) based on the quality-controlled DSD datasets from all national meteorological stations (denoted as*S*_{0}) detailed in Sect. 2.3 and the analysis in Sect. 3.1. Therein,*Z*_{H},*Z*_{DR}, and*K*_{DP}are simulated using the T-matrix method, assuming the raindrop aspect ratio in Brandes et al. (2002) at a temperature of 20^{∘}C. Then, the differential attenuation factor (*A*_{DP}) in Eq. (2b) is calculated by adjusting*β*to obtain ${Z}_{\mathrm{DR}}^{\mathrm{C}}$ according to Eq. (2c). The optimal*β*can be iteratively determined for*A*_{DP}by minimizing the differences between ${Z}_{\mathrm{DR}}^{\mathrm{C}}$ and ${\widehat{Z}}_{\mathrm{DR}}$ in Eq. (2d), along the whole radial range profile. Additional Δ*Z*_{DR}is also iteratively imposed on the whole range profile with a step of 0.1 dB to mitigate the residual*Z*_{DR}bias caused by miscalibration or wet radome effects. Then, ${Z}_{\mathrm{DR}}^{\mathrm{M}}$ is corrected by Eq. (2c) to ${Z}_{\mathrm{DR}}^{\mathrm{C}}$ through*A*_{DP}calculated by the optimal*β*. ${Z}_{\mathrm{DR}}^{\mathrm{C}}$ is utilized for the subsequent analysis and radar rainfall estimation:$$\begin{array}{}\text{(2a)}& {\displaystyle}{\widehat{Z}}_{\mathrm{DR}}\left(r\right)=\mathrm{1.3038}\times {\mathrm{10}}^{-\mathrm{4}}{Z}_{\mathrm{H}}(r{)}^{\mathrm{2.4508}},\text{(2b)}& {\displaystyle}{A}_{\mathrm{DP}}(r;\mathit{\beta})={\displaystyle \frac{\mathit{\beta}}{{\mathit{\alpha}}_{\mathrm{opt}}}}{A}_{\mathrm{H}}(r;{\mathit{\alpha}}_{\mathrm{opt}}),\text{(2c)}& {\displaystyle}{Z}_{\mathrm{DR}}^{\mathrm{C}}\left(r;\mathit{\beta}\right)=\mathrm{\Delta}{Z}_{\mathrm{DR}}+{Z}_{\mathrm{DR}}^{\mathrm{M}}\left(r\right)+\mathrm{2}{\int}_{\mathrm{0}}^{r}{A}_{\mathrm{DP}}\left(s,\mathit{\beta}\right)\mathrm{d}s,\text{(2d)}& {\displaystyle}{C}_{\mathrm{DR}}={\int}_{\mathrm{0}}^{r}\left|{Z}_{\mathrm{DR}}^{\mathrm{C}}\left(r;\mathit{\beta}\right)-{\widehat{Z}}_{\mathrm{DR}}\left(r\right)\right|\mathrm{d}r.\end{array}$$

## 2.3 DSD data processing

The Thies disdrometer measurements configured with 1 min sampling intervals
collected between 00:00 UTC, 9 August 2019, and 00:00 UTC, 11 August 2019,
are utilized. These measurements were variously affected by the strong
winds, with the hourly maximum wind speed exceeding 20 m s^{−1}, as depicted in
Fig. 4. Particularly, YH, WL, and DT suffered more seriously (*>* 40 m s^{−1}) after 16:00 UTC, 9 August 2019. Theoretically, the size–velocity
measurements of raindrops, which are recorded by disdrometers in pairs,
should be uniformly distributed as in the drop velocity model in Beard (1977), which can be represented as

where *D*_{i} is the diameter of the *i*th size class (diameter interval) and *V*_{B} is
estimated by *D*_{i}. However, real velocity measurement (*V*_{M}) of disdrometers may
deviate seriously from *V*_{B} due to the strong wind effects. For instance, many
size–velocity pairs at all six stations are biased with *V*_{M} *<* 0.5 *V*_{B}
and distributed in all predefined size classes; more deviated size–velocity
pairs of WL, YH, and DT are featured with *V*_{M} *<* 0.5 *V*_{B} in Fig. 5d–f
than in XJ, LH, and HJ in Fig. 5a–c, which can also be ascribed to high
wind speeds. Consequently, these size–velocity pairs need to be
preprocessed, and the QC procedure utilized hereafter includes the following
three steps:

- i.
For wind-contaminated size–velocity pairs, if the

*V*_{M}of the*i*th size class is located inside [0.5*V*_{B}, 1.5*V*_{B}] (enclosed by the blue lines in Fig. 5), the size–velocity pairs are deemed to agree well with Eq. (3) and will be kept; the other outliers will be eliminated. - ii.
For the potential hail (

*D*_{i}*>*5 mm) and graupel (*D*_{i}in [2 mm, 5 mm]), two size–velocity relationships listed in Friedrich et al. (2013) as$$\begin{array}{}\text{(4a)}& {\displaystyle}{V}_{\mathrm{H}}\left({D}_{i}\right)=\mathrm{10.58}\times (\mathrm{0.1}{D}_{i}{)}^{\mathrm{0.267}},\text{(4b)}& {\displaystyle}{V}_{\mathrm{G}}\left({D}_{i}\right)=\mathrm{1.37}\times (\mathrm{0.1}{D}_{i}{)}^{\mathrm{0.66}}\end{array}$$are selected to estimate the velocity of potential hail (

*V*_{H}) and graupel (*V*_{G}) corresponding to*D*_{i}. The size–velocity pairs that fulfilled $\left|{V}_{\mathrm{B}}-{V}_{\mathrm{M}}\right|<\left|{V}_{\mathrm{H}}-{V}_{\mathrm{M}}\right|$ or $\left|{V}_{\mathrm{B}}-{V}_{\mathrm{M}}\right|<\left|{V}_{\mathrm{G}}-{V}_{\mathrm{M}}\right|$ will be kept, because they are more prone to raindrops; otherwise, these measurements are eliminated from the original dataset depicted in Fig. 5. - iii.
The residual contaminations, which the above-mentioned processing cannot directly eliminate due to their similar size–velocity characteristics to raindrops, need another analysis based on DSD-derived median volume diameter (

*D*_{0}) and*Z*_{DR}. Larger*Z*_{DR}values are anticipated for melting solid particles than raindrops with similar diameters. The final QC processing result of the DSD dataset is presented in Sect. 3.1.

## 3.1 The consistency between multi-source data

### 3.1.1 The surface consistency between disdrometer and rain gauge

A DSD dataset is critical for establishing relationships between
polarimetric radar variables for radar QPE algorithms. Disdrometers and rain
gauges are usually deployed at the same meteorological site; although they
sample the precipitation differently, their rainfall measurements in the
same area should agree with each other. However, DSD-derived rainfall at six
stations, directly calculated from the size–velocity pairs in Fig. 5
without any QC processing (denoted as *R*_{M}), all presented unrealistically
large values: maximum *R*_{M} at LH, XJ, and HJ exceeded 200 mm that at DT
exceeded 400 mm and that at WL and YH unbelievably exceeded 3×10^{3} and 10^{4} mm during typhoon Lekima. For convenient comparison of
disdrometers with gauge rainfall series, *R*_{M} is rewritten as

where *R*_{TM} stands for the transformed rainfall value and *R*_{T}
stands for a rainfall threshold that is set a little larger than the maximum
hourly gauge rainfall. *C*_{T} is also manually set for each station, and *C*_{T}
partly indicates that *R*_{M} is at least *C*_{T} times higher than gauge rainfall.
The *R*_{M} part exceeding *R*_{T} can shrink into a limited range interval, and *R*_{T}
and *C*_{T} serve for comparing *R*_{M} and DSD-derived rainfall after QC processing
(denoted as *R*_{QC}) in the same figure, as depicted in Fig. 6. Accordingly,
*C*_{T} of YH and WL in Fig. 6 is huge (800 and 500, ≥20 at the other
stations). Meanwhile, DSD-derived maximum *Z*_{H}, *Z*_{DR}, *K*_{DP}, and *R*
exceeded 85 dBZ, 5.5 dB, 1500 ^{∘} km^{−1}, and 15000 mm h^{−1}, respectively (see Fig. 7a–c),
and they are also abnormally larger than the final QC-processed counterparts
(rectangles in Fig. 7a–c). If these unrealistic DSD-derived radar
variables were directly utilized to establish the parameters of any radar
QPE algorithm, an unrealistically overestimated radar rainfall field would
be obtained. Afterward, the QC procedure in Sect. 2.3 is first imposed on
the size–velocity pairs, and its performance and effectiveness are
investigated through comparison with gauge rainfall recordings.

According to a visual comparison in Fig. 6, the severe overestimation of *R*_{M}
at all six stations is reduced after processing wind effects, and a better
approximation is noticeable at XJ, HJ, LH, and DT in Fig. 6a–c and e,
where the extra hail and graupel processing hardly change the residual
differences. In contrast, the *R*_{QC} time series at WL agrees well with its
gauge rainfall recordings after the hail processing but is underestimated
after extra graupel processing (see Fig. 6d). This implies that WL suffers
from some solid particle contaminations. Still, these solid particles may melt
and have similar size–velocity characteristics to raindrops, and their
removal is responsible for the final underestimation of *R*_{QC} at WL after QC
processing. YH also suffered from solid particle contaminations. During its peak
rainfall recording period between 16:00 and 22:00 UTC, 9 August 2019, *R*_{QC}
in Fig. 6e changes relatively less after the hail processing and still
deviates largely from gauge rainfall recordings; conversely, *R*_{QC} better
approximates gauge rainfall after the graupel processing. This indicates
that the terminal velocity of these filtered particles is more prone to
graupel (not deduced by size). Section 3.2.1 further verifies the falling
solid particles.

These residual solid particles could result in a false relationship between
*D*_{0} and *Z*_{DR}. As shown in Fig. 8a, the fitted curve uniformly passed through
the scattergram, representing an excellent fitting relationship between *D*_{0}
and *Z*_{DR}. However, as mentioned above, these DSD-derived *D*_{0} and *Z*_{DR} still
suffer from some solid particle contaminations after processing the wind effects.
Even after hail and graupel processing, the scattergram in Fig. 8b still
presents a significant overfitted relationship between *D*_{0} and *Z*_{DR}. The
scatters with *Z*_{DR} *>* 2.5 dB are related to melting solid particles
with *D*_{0} ranging from 1.5 to 4 mm, and some have raindrop-like sizes
(*<* 2 mm). Finally, DSD-derived radar variables constrained by
*Z*_{DR} *<* 2.5 dB are assumed to be contributed by pure raindrops, and they
are utilized to fit the *D*_{0}–*Z*_{DR}, LWC–*K*_{DP}, and *K*_{DP}–*Z*_{H} relationships in Fig. 8c–e and the *Z*_{DR}–*Z*_{H} relationship in Eq. (2a) (see Fig. 8f):

Combining these relationships and another relationship between the
normalized concentration of raindrops (*N*_{w}, in mm^{−1} m^{−3}), LWC, and the mean volume
diameter of the drop size distribution (*D*_{m}, in mm) in Eqs. (9) and (10),

where *ρ*_{w} is the water density (1 g cm^{−3}), high-resolution DSD parameter fields can be derived from WZ-SPOL radar
measurements.

### 3.1.2 The self-consistency between radar measurements

The self-consistency can demonstrate the credibility of polarimetric radar
measurements through scattergrams (Fig. 9). The scattergrams in Fig. 9b and
d are obtained from all ${Z}_{\mathrm{H}}^{\mathrm{C}}$,
${Z}_{\mathrm{DR}}^{\mathrm{C}}$, and *K*_{DP} measurements described in Fig. 11.
The ZHPI approach (Bringi et al., 2001) with more constraints described in Gou
et al. (2019a) effectively mitigates the attenuation effects on *Z*_{H} and *Z*_{DR}
of the WZ-SPOL radar. The spatial fields of ${Z}_{\mathrm{H}}^{\mathrm{M}}$
and ${Z}_{\mathrm{DR}}^{\mathrm{M}}$ are not presented (they will not be used
for the subsequent analysis), but it is noticeable that radar-measured
${Z}_{\mathrm{H}}^{\mathrm{M}}$, ${Z}_{\mathrm{DR}}^{\mathrm{M}}$, and *K*_{DP} are
not self-consistent before attenuation correction processing: it is obvious
for ${Z}_{\mathrm{H}}^{\mathrm{M}}\phantom{\rule{0.125em}{0ex}}\mathit{>}\phantom{\rule{0.125em}{0ex}}\mathrm{40}$ dBZ and *K*_{DP} *>* 1 ^{∘} km^{−1} that *K*_{DP}–${Z}_{\mathrm{H}}^{\mathrm{M}}$ scatters deviates
positively from the theoretical *K*_{DP}–*Z*_{H} curve (Eq. 8 as depicted in Fig. 8e),
indicating that larger reflectivity values are anticipated for these *K*_{DP}
measurements. In addition, an overall deviation of
${Z}_{\mathrm{DR}}^{\mathrm{M}}$–${Z}_{\mathrm{H}}^{\mathrm{M}}$ distribution in
Fig. 9c from the theoretical *Z*_{DR}–*Z*_{H} curve (the black curve stands for Eq. 2a
as depicted in Fig. 8f) addresses a non-negligible negative *Z*_{DR} bias before
the differential attenuation correction. In contrast, the scattergram core
areas in Fig. 9b and d (defined as log_{10}(*N*) *>* 1.6) exhibit more
compact distribution along theoretical *K*_{DP}–*Z*_{H} and *Z*_{DR}–*Z*_{H} curves,
demonstrating the effectiveness of the attenuation correction to enhance the
self-consistency between ${Z}_{\mathrm{H}}^{\mathrm{C}}$,
${Z}_{\mathrm{DR}}^{\mathrm{C}}$, and *K*_{DP}.

Radar measurements are feedback from drops in the air, but disdrometers
collect DSD near the surface. In this sense, the comparison above also means
that radar measurements tend to be more consistent with their surface
counterparts after the correction. However, this does not mean that they
completely agree; conversely, ${Z}_{\mathrm{DR}}^{\mathrm{C}}$ still deviates
largely from ${\widehat{Z}}_{\mathrm{DR}}$ when reflectivity exceeds 35 dBZ in
Fig. 9d. In addition, the time series in Fig. 10 shows that extremely large
DSD-derived *Z*_{H}, *Z*_{DR}, and *K*_{DP} in Fig. 7 (time series not presented) have
diminished, and they begin to approximate their radar-measured counterparts.
The hail and graupel processing effectively improves the consistency between the
gauge and disdrometer, as mentioned above; furthermore, DSD-derived *Z*_{H} and
*K*_{DP} also simultaneously tend to better approximate radar-measured
${Z}_{\mathrm{H}}^{\mathrm{C}}$ and *K*_{DP}. Meanwhile, the residual differences
between radar and DSD are still prominent in terms of *Z*_{DR}, and larger
DSD-derived *Z*_{DR} than radar-measured ${Z}_{\mathrm{DR}}^{\mathrm{C}}$ occurs at
WL and YH, indicating that larger-sized drops are collected by WL and YH
than the radar volume gates above.

Considering that Eq. (2a) is fitted based on *S*_{0}, and *R*_{QC} at WL agrees better
with gauge rainfall if no graupel processing occurs, *S*_{0} can be refined: *S*_{I} excludes
large-sized drops by removing WL, *S*_{II} further excludes large-sized drops
from WL and YH, and *S*_{III} re-includes more large-sized drops by adding the
size–velocity pairs removed by graupel processing at WL. In this way, three
new *Z*_{DR}–*Z*_{H} relationships are re-established as

The further removal of the DT dataset from *S*_{II} will change the *Z*_{DR}–*Z*_{H}
relationship in Eq. (11b) very little (data not presented). Although there is
an uncertainty that large-sized drops may source either from melting solid
particles or the collision–coalescence, more large-sized drops in *S*_{0} and
*S*_{III} make Eqs. (2a) and (11c) (higher ${\widehat{Z}}_{\mathrm{DR}}$ estimates) prone
to the outcome of the dominant collision–coalescence process; conversely,
more small-sized drops in *S*_{II} and *S*_{III} make Eqs. (11a) and (11b) prone to
dominant collision–breakup. Resultantly, Eqs. (11a) and (11b) exhibit smaller
*Z*_{DR} than that of Eqs. (2a) and (11c) for a given
${Z}_{\mathrm{H}}^{\mathrm{C}}$, which agrees well with the simulation result
in Kumjian and Prat (2014). In Fig. 9d, radar-measured
${Z}_{\mathrm{DR}}^{\mathrm{C}}$ tends to be more consistent with Eqs. (11a) and
(11b) for a given ${Z}_{\mathrm{H}}^{\mathrm{C}}$ than Eqs. (2a) and (11c) in the
scattergram core area, and this
${Z}_{\mathrm{DR}}^{\mathrm{C}}$–${Z}_{\mathrm{H}}^{\mathrm{C}}$ scattergram
reflects that the governing collision–breakup processes in radar volume
gates restrain the drop size increase due to the coalescence–breakup
balance, which means ${Z}_{\mathrm{DR}}^{\mathrm{C}}$ does not grow similarly
to coalescence-dominated volume gates.

## 3.2 Microphysics of the landfall of Lekima (2019)

When super typhoon Lekima landed on the eastern coast of China, several
beneficial conditions for its evolution were perceived: (i) the severe
interaction between the mountain and the typhoon caused terrain-enhanced
precipitation, (ii) the wind speed shear (the bold black curves in Fig. 11a–d) with noticeable *V*_{R} differences benefited the strengthening
development of convective storms, and (iii) the typhoon carried abundant warm
moisture which can condensate if confronted with cold air. The
characteristics of Lekima can be described based on
${Z}_{\mathrm{H}}^{\mathrm{C}}$: the outer and inner eyewalls were both
featured with ${Z}_{\mathrm{H}}^{\mathrm{C}}\phantom{\rule{0.125em}{0ex}}\mathit{>}\phantom{\rule{0.125em}{0ex}}\mathrm{55}$ dBZ before
landfall in Fig. 11e, indicating the enhanced convective development of the
concentric eyewalls before its landfall; afterward, the inner eyewall was
destroyed and merged with the outer eyewall into a convective storm with an
enlarged area, with ${Z}_{\mathrm{H}}^{\mathrm{C}}\phantom{\rule{0.125em}{0ex}}\mathit{>}\phantom{\rule{0.125em}{0ex}}\mathrm{55}$ dBZ dwelling
around the GWS of YDM (in Fig. 11f), and then the storm area with
${Z}_{\mathrm{H}}^{\mathrm{C}}\phantom{\rule{0.125em}{0ex}}\mathit{>}\phantom{\rule{0.125em}{0ex}}\mathrm{55}$ dBZ transitioned to the north
GWS of YDM (in Fig. 11g) but strongly weakened when it passed over the
mountain ridge between YDM and KCM (as depicted in Fig. 11h). More complex
microphysical processes than these described also occurred during the
landfall of Lekima.

### 3.2.1 Polarimetric signatures of solid particles

The time series of vertical polarimetric radar measurement (Figs. 12–17), which is constructed with an altitude resolution of 100 m based on the technique in Zhang et al. (2005), is chosen to describe the microphysical evolutions upon each station; DSD-derived radar measurements in Sect. 3.1 assist in interpreting what occurred near the surface. The combination of radar and DSD can effectively explain the potential microphysical processes in the vertical gap between the air and the surface.

The freezing level (FL) is significant in the vertical measurements (see
Figs. 12, 14, and 17), and its altitude is about 7 km: the layers with
near-zero ${Z}_{\mathrm{DR}}^{\mathrm{C}}$ measurements dominate above the FL,
indicating the dominant dry snow aggregates
(${Z}_{\mathrm{H}}^{\mathrm{C}}\phantom{\rule{0.125em}{0ex}}\mathit{<}\phantom{\rule{0.125em}{0ex}}\mathrm{30}$ dBZ); *ρ*_{HV} is relatively
weaker (*<* 0.98) below the FL, indicating the dominant mix-phase
particles in the ML (near 6 km). In addition, the sustaining large *K*_{DP}
(*>*1 ^{∘} km^{−1}) upon WL and HJ (Figs. 12 and 14) after 18:00 UTC, 9 August 2019, (after landfall) indicates the high concentration of solid
particles above the FL. In addition, the significant upward extension of
${Z}_{\mathrm{H}}^{\mathrm{C}}$ (*>* 40 dBZ) and
${Z}_{\mathrm{DR}}^{\mathrm{C}}$ (*>* 1 dB) columns marked with black
rectangles indicate the developing convective storms; the black ellipses
indicate potential updrafts coupled with the storm; the blue ellipses
indicate subsiding signatures of falling solid particles deducing from
gradual decreasing heights of *ρ*_{HV} *<* 0.98 over time. The
convective storms are accompanied by abundant water content, as indicated by
significant *K*_{DP} (*>* 0.5^{∘} km^{−1}) columns extending upwards, which
benefited the size increases of the falling solid particles. The
microphysical processes of the solid particles differed at each station.

The WZ-SPOL radar initially measured similar *Z*_{DR} but larger *Z*_{H} and *K*_{DP} compared
with DSD at the WL station (rectangle 1 in Fig. 10) before the landfall of
Lekima, and more concentrated hydrometeors aloft accompanying the updrafts
compared to the surface in this process account for this phenomenon, which
is verified in the first rectangle of Fig. 12a and c. Furthermore, two
consecutive severe updrafts passed over WL, one from the outer eyewall and
the other from the inner eyewall, causing the significant upward extension
of ${Z}_{\mathrm{H}}^{\mathrm{C}}$, ${Z}_{\mathrm{DR}}^{\mathrm{C}}$, and *K*_{DP}
columns below the FL, as depicted in two black rectangles in Fig. 12. As
illustrated in two black ellipses, some ice particles might ascend with the
first updraft, then fall and melt in the time gap between two updrafts, with
the signature of *ρ*_{HV} *<* 0.98 reaching the lowest layer of 1.8 km; they instantly suffered from another size increase process confronting
the second updraft (in the second ellipse) and then fell with the subsiding
signals of *ρ*_{HV} and ${Z}_{\mathrm{DR}}^{\mathrm{C}}$ (in the blue
ellipse): ${Z}_{\mathrm{DR}}^{\mathrm{C}}\phantom{\rule{0.125em}{0ex}}\mathit{<}\phantom{\rule{0.125em}{0ex}}\mathrm{0.5}$ dB was sustained when
*ρ*_{HV} gradually transitioned from *ρ*_{HV} *<* 0.84 around the FL
to *ρ*_{HV} *<* 0.98 on the lowest layer, indicating the existence of
some near-spherical but mixed-phase particles during this falling process.
These solid particles partly account for the larger DSD-derived *Z*_{DR} near the
surface than the WZ-SPOL radar (rectangle 2 in Fig. 10), but the coalescence of
raindrops might also partly account for this DSD-derived larger *Z*_{DR}.

Similar updrafts occurred upon the YH station (rectangle 3 in Fig. 10), and
the WZ-SPOL radar measured similar *K*_{DP} but weaker *Z*_{H} and *Z*_{DR} compared with
DSD before the hail/graupel processing. Featuring with similar
${Z}_{\mathrm{H}}^{\mathrm{C}}$ extending upwards upon the YH station, large
${Z}_{\mathrm{DR}}^{\mathrm{C}}$ (*>* 1.2 dB) and weak *K*_{DP} (*<* 0.2 ^{∘} km^{−1}) accompanied the updrafts with *ρ*_{HV} *<* 0.98 in the
black ellipse of Fig. 13, indicating that dominant large-sized mixed-phase
particles were developing around the ML. Then, in the blue ellipse, the
subsiding signals of *ρ*_{HV} *<* 0.84 formed in Fig. 13d after 16:30 UTC and tended to decrease their heights over time; finally, they
transitioned to *ρ*_{HV} *>* 0.98 on the top of the
${Z}_{\mathrm{DR}}^{\mathrm{C}}$ (*>* 2 dB) columns, attributing to the
transformation of melting solid particles into big raindrops. Compared with
surface DSD, the decrease in radar-measured ${Z}_{\mathrm{H}}^{\mathrm{C}}$
and *K*_{DP} reflects the reduction of LWC in the vertical gap; this LWC
reduction did not contribute to the size increase of drops, because radar and
DSD presented similar *Z*_{DR}. Another possible explanation is that some LWC is
absorbed by the falling solid particles, contributing to the filtered *Z*_{DR}
part in the hail/graupel processing.

Another solid particle falling occurred upon HJ, which is to the north of
the landfall positions of Lekima. Even with the unnoticeable upward
${Z}_{\mathrm{H}}^{\mathrm{C}}$ enhancement between 17:00 and 18:00 UTC, 9 August 2019, as depicted in Fig. 14a, the large
${Z}_{\mathrm{DR}}^{\mathrm{C}}$ signals of the ML in Fig. 14b diminished due
to the updraft, ${Z}_{\mathrm{DR}}^{\mathrm{C}}$ and *K*_{DP} both increased, and
*ρ*_{HV} reduced steadily after 18:00 UTC above the FL in the black ellipses
of Fig. 13b–d. Subsiding signals of *ρ*_{HV} *<* 0.84 also emerged
after 18:00 UTC, resulting in the *ρ*_{HV} reduction from 0.98 to 0.96 on
the lowest layer. Conditioning *V*_{M} by [0.5*V*_{B}, 1.5*V*_{B}] eliminated some size–velocity pairs of the solid particles at HJ, because solid precipitation particles have smaller terminal velocities than liquid particles.
Conversely, the rising overestimation of *R*_{QC} by reconditioning *V*_{M} by [0.4 *V*_{B},
1.5 *V*_{B}] in Fig. 6b (the dotted green line) further verified this possibility.

These common characteristics feature in HJ, DT, LH, and XJ in Figs. 14–17:
*K*_{DP} (*<* 0.5 ^{∘} km^{−1}) above the FL indicated a lower concentration of
ice particles upon DT, LH, and XJ than upon the other three sites, which
refrains the size increase of falling solid particles through the
aggregation process; the insignificant ${Z}_{\mathrm{H}}^{\mathrm{C}}$
(*<* 45 dBZ) and *K*_{DP} (*<* 0.2 ^{∘} km^{−1}) extending upwards reflect
the relatively low concentration of hydrometeors below the ML upon HJ, LH,
and XJ, which refrains the further size increases of melting ice particles
in the warm rain environment. The exceptions in
${Z}_{\mathrm{DR}}^{\mathrm{C}}$ columns upon DT between 18:00 and 19:00 UTC
in Fig. 15b were attributed to the falling melting ice particles upon an
updraft with high LWC (*K*_{DP} *>* 1^{∘} in Fig. 15c); those in LH
between 18:00 and 19:00 UTC were attributed to the sustaining weak updrafts
(${Z}_{\mathrm{H}}^{\mathrm{C}}$ <45dBZ) but more concentrated ice
particles above the FL. The deep ML (*ρ*_{HV} *<* 0.98) also features
these stations, and this signature even extends down to the lowest layer of
LH and HJ with ${Z}_{\mathrm{DR}}^{\mathrm{C}}\phantom{\rule{0.125em}{0ex}}\mathit{>}\phantom{\rule{0.125em}{0ex}}\mathrm{2}$ dB dwelling below
the FL. In addition, most ice particles upon these four stations might have
melted in the air before being collected by disdrometers near the surface,
which effectively accounts for the small rainfall differences between
disdrometers and rain gauges. However, the residual differences between
radar and DSD are mainly related to the warm process of raindrops below the
ML.

### 3.2.2 Polarimetric signatures of raindrops

The deviation of ${Z}_{\mathrm{DR}}^{\mathrm{C}}$ from ${\widehat{Z}}_{\mathrm{DR}}$
is a non-negligible phenomenon during landfall of Lekima: underestimated
${Z}_{\mathrm{DR}}^{\mathrm{C}}$ in Fig. 11i–l compared with
${\widehat{Z}}_{\mathrm{DR}}$ in Fig. 11m–p emerged in areas with significant
*K*_{DP} in Fig. 11q–t, which simultaneously emerged around the GWS of YDM.
Apparently, ${Z}_{\mathrm{DR}}^{\mathrm{C}}$ cannot completely approximate
${\widehat{Z}}_{\mathrm{DR}}$ after correction; intrinsically, the microphysical
composition issue, either dominant large-sized or small-sized raindrops
filling in radar volume gates, resultantly determines final
${Z}_{\mathrm{DR}}^{\mathrm{C}}$–${Z}_{\mathrm{H}}^{\mathrm{C}}$ distribution.
One typical radial range profile in Fig. 18 is detailed to clarify this
phenomenon. The ellipse-surrounded storm area contributes the most
attenuation and differential attenuation with maximum Δ*Z*_{H} = 7.9 dBZ
and Δ*Z*_{DR} = 0.645 dB, respectively, in Fig. 18a and b. Although the
correction can result in enhanced consistency between *Z*_{H} and *K*_{DP} (see
Sect. 3.1.2) and some ${Z}_{\mathrm{DR}}^{\mathrm{C}}$ have indeed partly
approximated well to ${\widehat{Z}}_{\mathrm{DR}}$ (outside the ellipse in Fig. 18b), the other ${Z}_{\mathrm{DR}}^{\mathrm{C}}$ within the storm (in the
ellipse) still have a residual *Z*_{DR} bias of about −1 dB. Additionally, *ρ*_{HV} ranging from 0.99 to 1 (in Fig. 15c) further indicates the dominance of
pure liquid precipitation; high LWC and *N*_{w} can be deduced from Eqs. (8) and (9)
(*K*_{DP} ≈ 3.5 ^{∘} km^{−1}; ΔΦ_{DP} ≈ 68.5^{∘} in Fig. 12c). *Z*_{H} is a composite integral of hydrometeors with different sizes and
number concentrations, and *Z*_{DR} is sensitive to hydrometeor size; therefore,
high concentrations of small-sized drops rather than large-sized drops
contribute more to radar-measured ${Z}_{\mathrm{H}}^{\mathrm{C}}$ in radar
volume gates. This unique composition resultantly causes an overestimated
${\widehat{Z}}_{\mathrm{DR}}$ estimated by ${Z}_{\mathrm{H}}^{\mathrm{C}}$, or
conversely, underestimated ${Z}_{\mathrm{DR}}^{\mathrm{C}}$ compared with
${\widehat{Z}}_{\mathrm{DR}}$.

The hydrometeor size sorting (HSS) partly accounts for the position
inconsistency between ${Z}_{\mathrm{H}}^{\mathrm{C}}$ and
${Z}_{\mathrm{DR}}^{\mathrm{C}}$, and it is significant in the
rectangle-surrounded area of the inner eyewall, characterized by a maximum
of ${Z}_{\mathrm{DR}}^{\mathrm{C}}$ in Fig. 12i on the significant upwind
gradients of *K*_{DP} in Fig. 12q (Homeyer et al., 2021; Hu et al., 2020). Since
${Z}_{\mathrm{H}}^{\mathrm{C}}$ in Fig. 12e and *K*_{DP} in Fig. 12q are consistent
with each other, the large ${\widehat{Z}}_{\mathrm{DR}}$ estimated by
${Z}_{\mathrm{H}}^{\mathrm{C}}$ also horizontally deviates from the area with
large ${Z}_{\mathrm{DR}}^{\mathrm{C}}$. Differential sedimentation of
hydrometeors of various sizes is the intrinsic reason for HSS (Feng and
Bell, 2019), which is significant in the outer eyewall. The higher LWC
(*>* 3 g m^{−3}) features the outer eyewall as depicted in Fig. 16e;
the area with large ${Z}_{\mathrm{DR}}^{\mathrm{C}}$ (*>* 2 dB)
consists of dominant larger-sized drops with *D*_{0} *>* 1.8 mm in Fig. 16a, but relatively lower concentration with log_{10}(*N*_{w}) *>* 4.4 in
Fig. 16a than in its downwind area. Meanwhile, lower LWC (*<* 2 g m^{−3})
features a cyclonical downwind area, but this area consists of dominant
higher concentrated (log_{10}(*N*_{w}) *>* 4.4) small-sized drops
(*D*_{0} *<* 1.625 mm). However, HSS cannot account for the overall
underestimation of ${Z}_{\mathrm{DR}}^{\mathrm{C}}$ when pixels with large
${Z}_{\mathrm{H}}^{\mathrm{C}}$, ${Z}_{\mathrm{DR}}^{\mathrm{C}}$, and *K*_{DP}
coincide.

The collision process in warm rain has three probable colliding outcomes:
bounce, coalescence, and breakup. In one volume gate, bounce cannot change
raindrop size and concentration; coalescence boosts the size increase, but
breakup increases the concentration. The existence of large raindrops with
*D*_{0} *>* 1.8 mm around the GWS of YDM (in Fig. 19b and c) indeed
back the occurrences of collision–coalescence processes, which corresponds
to ${Z}_{\mathrm{DR}}^{\mathrm{C}}$ (*>* 1.8 dB in Fig. 11j and
k). However, if the size increases contribute enough in one volume gate,
${Z}_{\mathrm{DR}}^{\mathrm{C}}$ might have well-approximated
${\widehat{Z}}_{\mathrm{DR}}$ in the storm area and agree better with
${Z}_{\mathrm{H}}^{\mathrm{C}}$. In addition, raindrops cannot continue
increasing their size; spontaneous breakup (Srivastava, 1971) or
collision–breakup due to vertical wind shear (i.e., Deng et al., 2019)
co-occurs during the falling process of drops:

- i.
The first evidence comes from the radar-measured ${Z}_{\mathrm{DR}}^{\mathrm{C}}$–${Z}_{\mathrm{H}}^{\mathrm{C}}$ scattergram in Fig. 11d, and it tends to be more consistent with

*Z*_{DR}–*Z*_{H}relationships dominated by small-sized drops related to the breakup, not large-sized drops related to the coalescence. This also agrees with the simulation results in Kumjian and Prat (2014). - ii.
The second natural phenomenon is the decreasing

*Z*_{DR}downward in the lower atmospheric layers. Although some ${Z}_{\mathrm{DR}}^{\mathrm{C}}$ columns were indeed enhancing downward in Figs. 12–17, particularly in the time frames with significant updrafts with ${Z}_{\mathrm{H}}^{\mathrm{C}}$ extending upwards upon WL and YH, more time frames presented a dominant decreasing ${Z}_{\mathrm{DR}}^{\mathrm{C}}$ toward the ground, such as at DT, HJ, LH, and XJ. - iii.
The residual differences between radar and DSD are evident for the possible process in the vertical gap between radar volume gates and the surface. If dominant collision–coalescence occurred, DSD-derived

*Z*_{DR}should be more significant than their radar counterparts in the air. However, the opposite is true at XJ, HJ, and LH, as depicted in Fig. 10. Meanwhile, DT exhibits similar*Z*_{DR},*Z*_{H}, and*K*_{DP}to its radar counterparts after the landfall of Lekima, which is also evidence against the contribution from coalescence.

The collision–coalescence indeed occurs, but the breakup balances the size
increase. This is evident in the evolutions of *D*_{0} and *N*_{w} constrained by a
given LWC, which is typical around the GWS of YDM. In Fig. 19c, g, and
k, the identical LWC fill in the rectangle-surrounded and
ellipse-surrounded regions; the latter exhibits larger *D*_{0} (*>* 1.75 mm) but lower *N*_{w} with log_{10}(*N*_{w}) *<* 4.4; conversely, the
former shows smaller *D*_{0} (*<* 1.75 mm) but higher *N*_{w} with
log_{10} (*N*_{w}) *>* 4.4. Similar situations occurred in the two
left columns in Fig. 19, and sparse large-sized *D*_{0} is only prominent in a
small area (in ellipse and rectangle); high *N*_{w} but small *D*_{0} are features of
the other parts of the typhoon. The LWC in one range gate will contribute
not only to the size increase but also to the concentration, attributing to
the balance between coalescence and breakup.

Combining the abovementioned observations, the overwhelming breakup of
large-sized drops over coalescence firmly restrains the magnitudes of
radar-measured ${Z}_{\mathrm{DR}}^{\mathrm{C}}$ for a given
${Z}_{\mathrm{H}}^{\mathrm{C}}$, accounting for the noticeable deviation of
${Z}_{\mathrm{DR}}^{\mathrm{C}}$ from ${\widehat{Z}}_{\mathrm{DR}}$ (in Fig. 11).
Despite all this, collision–coalescence accompanied by the terrain-enhanced
precipitation occurred when Lekima took high LWC (*>* 2 g m^{−3}) and
passed over YDM, as depicted in Fig. 19f and g, resulting in an overall
LWC reduction around the GWS of KCM (i.e., Fig. 19g to h). During
this period, *D*_{0} and *N*_{w} simultaneously increased: *D*_{0} increased by about 0.5 mm from Fig. 19a to *D*_{0} *>* 1.5 mm in Fig. 19c; log_{10} (*N*_{w}) increased
about 0.4–0.8 from Fig. 19i to k, and these
enhancements coincided well with the GWS of YDM. The gradual but
insignificant enhancement persisted around the GWS of KCM, including an LWC
increase by about 1 g m^{−3} (i.e., Fig. 19e–h), a diameter transition from
*D*_{0} *<* 1.25 mm to *D*_{0} *>* 1.5 mm (i.e., Fig. 19a–d), and
growth of log_{10} (*N*_{w}) about 0.4 in sparse pixels (i.e., Fig. 19i–l), but this enhancement was relatively weaker than that around the
GWS of YDM. This comparison indicates that extensive large-sized drops had
formed and fallen around the GWS of YDM before Lekima moved to the north,
which effectively accounts for the flood disasters. However, the utilization
of radar-measured ${Z}_{\mathrm{DR}}^{\mathrm{C}}$ may not derive accurate
radar rainfall fields.

## 3.3 Radar QPE analysis

### 3.3.1 The performances of radar QPE

Utilizing the DSD dataset from *S*_{0}, three primary radar rainfall rate
relationships for *R*(*Z*_{H}), *R*(*K*_{DP}), and *R*(*Z*_{H}, *Z*_{DR}) are respectively established
as

based on the standard weighted least squares nonlinear fitting method and
DSD-derived radar variables (depicted in Fig. 20). In addition,
${Z}_{\mathrm{DR}}^{\mathrm{M}}$, ${Z}_{\mathrm{DR}}^{\mathrm{C}}$, and
${\widehat{Z}}_{\mathrm{DR}}$ are integrated with *Z*_{H} to exploit the
impacts of the above-mentioned microphysical process on radar QPE algorithms.
The pixel-to-pixel linear average accumulation scheme is utilized to
retrieve radar 6 h rainfall fields for these radar QPE estimators and
is then evaluated independently by comparing gauge 6 h rainfall
measurements through the absolute normalized mean error (*E*_{NMA}),
root mean square error (*E*_{RMS}), and correlation coefficient (*E*_{CC}) as

where *r*_{i} and *g*_{i} refer to radar rainfall estimates and gauge rainfall.
The 6 h radar rainfall fields retrieved by
*R*(${Z}_{\mathrm{H}}^{\mathrm{M}}$), *R*(${Z}_{\mathrm{H}}^{\mathrm{C}}$), *R*(*K*_{DP}),
*R*(${Z}_{\mathrm{H}}^{\mathrm{M}}$, ${Z}_{\mathrm{DR}}^{\mathrm{M}}$),
*R*(${Z}_{\mathrm{H}}^{\mathrm{C}}$, ${Z}_{\mathrm{DR}}^{\mathrm{C}}$), and
*R*(${Z}_{\mathrm{H}}^{\mathrm{C}}$, ${\widehat{Z}}_{\mathrm{DR}}$) are derived in
Fig. 21, as well as the scattergram between radar rainfall estimates and
gauge rainfall measurements, depicted in Fig. 22, to reveal their practical
performances around the disaster area.

*R*(${Z}_{\mathrm{H}}^{\mathrm{M}}$) presents lower rainfall estimates in Fig. 21a than the other radar rainfall estimators in Fig. 21b–f, although they
have similar rainfall center shapes. In terms of statistical scores in Table 1, *R*(${Z}_{\mathrm{H}}^{\mathrm{M}}$) does not perform the worst among all radar
rainfall estimators. Its *E*_{RMS}, *E*_{NMA}, and *E*_{CC} even outperform
*R*(${Z}_{\mathrm{H}}^{\mathrm{M}}$, ${Z}_{\mathrm{DR}}^{\mathrm{M}}$) by 57 %,
31.6 % and 7.9 %, and outperform *R*(${Z}_{\mathrm{H}}^{\mathrm{C}}$,
${Z}_{\mathrm{DR}}^{\mathrm{C}}$) by 63.8 %, 34.9 % and 6 %,
respectively. However, its underestimation can easily be perceived from the
scatters in Fig. 22a when rainfall recordings exceed 100 mm in the center
rainfall area. This phenomenon can be ascribed to the attenuation on
${Z}_{\mathrm{H}}^{\mathrm{M}}$ caused by the highly concentrated hydrometeors
in the storm during the landfall of Lekima.

In contrast, *R*(${Z}_{\mathrm{H}}^{\mathrm{C}}$) in Fig. 21b presents higher
rainfall estimates and *R*(${Z}_{\mathrm{H}}^{\mathrm{C}}$) mainly overestimates,
since more scatters are distributed above the diagonal line (*y*=*x*) as
depicted in Fig. 22b, and its *E*_{CC} outperforms that of
*R*(${Z}_{\mathrm{H}}^{\mathrm{M}}$) by 4.2 %, even with larger *E*_{NMA} and *E*_{NMA}
scores. The overestimation of *R*(${Z}_{\mathrm{H}}^{\mathrm{C}}$) in the
rainfall center area conversely demonstrates the effectiveness of the
attenuation correction based on the ZPHI approach, because the same *R*(*Z*_{H})
relationship is utilized for the rainfall retrieval; the only difference is
the replacement of ${Z}_{\mathrm{H}}^{\mathrm{M}}$ with
${Z}_{\mathrm{H}}^{\mathrm{C}}$.

*R*(*K*_{DP}) in Fig. 21c presents a similar rainfall field structure to
*R*(${Z}_{\mathrm{H}}^{\mathrm{C}}$). The scores of *R*(*K*_{DP}) are just a little
superior to that of *R*(${Z}_{\mathrm{H}}^{\mathrm{C}}$) in Table 1, with its
*E*_{RMS}, *E*_{NMA}, and *E*_{CC} outperforming that of *R*(${Z}_{\mathrm{H}}^{\mathrm{C}}$)
by 3.1 %, 3.2 %, and 0.5 %, respectively. The scattergrams in Fig. 22b
and c are also similar to each other, indicating that *R*(*K*_{DP}) and
*R*(${Z}_{\mathrm{H}}^{\mathrm{C}}$) both overestimate, although *R*(*K*_{DP}) is less
overestimated when rainfall recordings are less than 100 mm. Their similar
performances can be attributed to the consistency between radar-measured *K*_{DP}
and ${Z}_{\mathrm{H}}^{\mathrm{C}}$ measurements as described in Sect. 3.1.2.

*R*(${Z}_{\mathrm{H}}^{\mathrm{M}}$, ${Z}_{\mathrm{DR}}^{\mathrm{M}}$) and
*R*(${Z}_{\mathrm{H}}^{\mathrm{C}}$, ${Z}_{\mathrm{DR}}^{\mathrm{C}}$) in Fig. 21d and e both present significantly higher estimates in the rainfall
center area than the others, which results in severe overestimation
according to the scattergrams in Fig. 22d and e. Furthermore,
*R*(${Z}_{\mathrm{H}}^{\mathrm{C}}$, ${Z}_{\mathrm{DR}}^{\mathrm{C}}$) obtains the
worst *E*_{RMS} and *E*_{NMA} scores of all radar rainfall estimators, and this can be
explained based on the *Z*_{H}-related and *Z*_{DR}-related calculation items as
demonstrated in Fig. 23: ${Z}_{\mathrm{H}}^{\mathrm{C}}$ obtains much higher
rainfall estimates through *Z*_{H}-related items than
${Z}_{\mathrm{H}}^{\mathrm{M}}$. However, the calculation needs to be further
adjusted through the *Z*_{DR}-related item: the larger *Z*_{DR} measurements
correspond to fewer final rainfall estimates. A −0.5 dB *Z*_{DR} bias could result
in relatively less rainfall adjustment, according to Fig. 23. The
attenuation effects on ${Z}_{\mathrm{DR}}^{\mathrm{M}}$ make the corresponding
rainfall calculation less adjusted, which can effectively account for the
overestimation of *R*(${Z}_{\mathrm{H}}^{\mathrm{M}}$,
${Z}_{\mathrm{DR}}^{\mathrm{M}}$). However, the correction cannot make
${Z}_{\mathrm{DR}}^{\mathrm{C}}$ completely consistent with
${Z}_{\mathrm{H}}^{\mathrm{C}}$, but it is underestimated, as demonstrated in
Sect. 3.1.2, which is related to the dynamic microphysical process
described in Sect. 3.2.

The spatial texture of *R*(${Z}_{\mathrm{H}}^{\mathrm{C}}$,
${\widehat{Z}}_{\mathrm{DR}}$) in Fig. 21f presents slightly fewer rainfall
estimates than *R*(${Z}_{\mathrm{H}}^{\mathrm{C}}$) and *R*(*K*_{DP}) in Fig. 21b and
c, and the scattergram in Fig. 22f shows that
*R*(${Z}_{\mathrm{H}}^{\mathrm{C}}$, ${\widehat{Z}}_{\mathrm{DR}}$) agrees better with
the gauge rainfall than in Fig. 22b and c.
*R*(${Z}_{\mathrm{H}}^{\mathrm{C}}$, ${\widehat{Z}}_{\mathrm{DR}}$) effectively
reduces the overestimates and is obviously superior to
*R*(${Z}_{\mathrm{H}}^{\mathrm{M}}$, ${Z}_{\mathrm{DR}}^{\mathrm{M}}$) and
*R*(${Z}_{\mathrm{H}}^{\mathrm{C}}$, ${Z}_{\mathrm{DR}}^{\mathrm{C}}$). The
*E*_{RMS}/*E*_{NMA} score of *R*(${Z}_{\mathrm{H}}^{\mathrm{C}}$, ${\widehat{Z}}_{\mathrm{DR}}$)
is better than *R*(${Z}_{\mathrm{H}}^{\mathrm{C}}$) and *R*(*K*_{DP}), by $\mathrm{8.6}\phantom{\rule{0.125em}{0ex}}\mathit{\%}/\mathrm{5}\phantom{\rule{0.125em}{0ex}}\mathit{\%}$ and $\mathrm{5.7}\phantom{\rule{0.125em}{0ex}}\mathit{\%}/\mathrm{1.8}\phantom{\rule{0.125em}{0ex}}\mathit{\%}$,
respectively, although its *E*_{CC} score is
slightly worse by 0.2 % and 0.3 %. The superiority of
*R*(${Z}_{\mathrm{H}}^{\mathrm{C}}$, ${\widehat{Z}}_{\mathrm{DR}}$) can also be
apparently attributed to the incorporation of ${\widehat{Z}}_{\mathrm{DR}}$.
${\widehat{Z}}_{\mathrm{DR}}$ is not a real radar measurement; it is directly
estimated from ${Z}_{\mathrm{H}}^{\mathrm{C}}$ from the theoretical
DSD-derived *Z*_{DR}–*Z*_{H} relationship in Eq. (2a). ${\widehat{Z}}_{\mathrm{DR}}$ is
naturally self-consistent with ${Z}_{\mathrm{H}}^{\mathrm{C}}$ and *K*_{DP}, since
${Z}_{\mathrm{H}}^{\mathrm{C}}$ and *K*_{DP} have agreed well with their
DSD-derived counterparts regarding the *K*_{DP}–*Z*_{H} distributions and
pixel-to-pixel comparisons in Sect. 3.1. The utilization of the
DSD-derived *Z*_{DR}–*Z*_{H} relationship intrinsically assumes that composition in
radar volume gates has a similar size and concentration to its surface
counterparts; therefore, ${\widehat{Z}}_{\mathrm{DR}}$ can be seen as an
equivalent radar variable. The replacement of ${Z}_{\mathrm{DR}}^{\mathrm{C}}$
with ${\widehat{Z}}_{\mathrm{DR}}$ is also equivalent to imposing the surface raindrop size
and concentration on radar measurements. The relatively larger
${\widehat{Z}}_{\mathrm{DR}}$ than ${Z}_{\mathrm{DR}}^{\mathrm{C}}$ means a more
significant adjustment can be performed for rainfall estimation using
*R*(${Z}_{\mathrm{H}}^{\mathrm{C}}$, ${\widehat{Z}}_{\mathrm{DR}}$), according to Fig. 23, and this also indicates that the anticipated giant raindrops had fallen
around the GWS of YDM. Except for the simultaneous *D*_{0} and *N*_{w} increases, the
following alternative ${\widehat{Z}}_{\mathrm{DR}}$ indirectly verifies the
dominant collision–coalescence around this area.

### 3.3.2 The impacts of microphysical processes on radar QPE

The consistency between radar and surface measurements is critical for radar
QPE algorithms, but the microphysical process in the vertical gap between
air and surface may worsen the practical performances of radar QPE. This is
the case around the GWS of YDM: the primary outcome of the collision process
transitions from a dominant breakup in the air to dominant coalescence near
the surface due to the topographical enhancement. Using radar measurements
on the lowest elevation angle to retrieve radar QPE implicitly assumes that
they are representative of surface precipitation, but they are not in this
situation; only *R*(*Z*_{H}), *R*(*K*_{DP}), and *R*(*Z*_{H}, *Z*_{DR}) relationships established
based on the DSD dataset represent the feedback near the surface. Although
*R*(${Z}_{\mathrm{H}}^{\mathrm{C}}$, ${\widehat{Z}}_{\mathrm{DR}}$) performs best, ${\widehat{Z}}_{\mathrm{DR}}$ can also be estimated by
Eqs. (11a)–(11c). However, ${Z}_{\mathrm{DR}}^{\mathrm{C}}$ changes little if a
smaller or larger ${\widehat{Z}}_{\mathrm{DR}}$ estimated by Eqs. (11a)–(11c) is imposed
in the correction procedure, as
${Z}_{\mathrm{DR}}^{\mathrm{C}}$–${Z}_{\mathrm{H}}^{\mathrm{C}}$ scattergrams
shown in Fig. 24a–c. Furthermore, the corresponding three *R*(*Z*_{H}, *Z*_{DR})
relationships based on *S*_{I}–*S*_{III} can be established as

The alternative utilization of *S*_{I}–*S*_{III} slightly changes the parameters of
*R*(*Z*_{H}, *Z*_{DR}) with minor rainfall rate differences estimated by Eqs. (12c),
(14a)–(14c). However, the impacts on ${\widehat{Z}}_{\mathrm{DR}}$ are non-negligible,
particularly for a given ${Z}_{\mathrm{H}}^{\mathrm{C}}$ exceeding 35 dBZ, and
smaller ${\widehat{Z}}_{\mathrm{DR}}$ means weaker adjustment for the *Z*_{HL}-related
item, as depicted in Fig. 23.

As in the analysis in Sect. 3.1.2, radar-measured
${Z}_{\mathrm{DR}}^{\mathrm{C}}$–${Z}_{\mathrm{H}}^{\mathrm{C}}$ in volume gates
tend to be more consistent with *S*_{I} and *S*_{II}, because breakup overwhelms in the
coalescence–breakup balance, so if breakup still dominates when these drops
further fall on the ground, *R*(${Z}_{\mathrm{H}}^{\mathrm{C}}$,
${\widehat{Z}}_{\mathrm{DR}})$ estimated by Eqs. (14a) and (14b) should
perform better than that estimated by Eq. (12c). However, in reality, their
spatial fields in Fig. 25a and b and scattergrams in Fig. 26a and b
conversely present a similar overestimation as
*R*(${Z}_{\mathrm{H}}^{\mathrm{M}}$, ${Z}_{\mathrm{DR}}^{\mathrm{M}}$) and
*R*(${Z}_{\mathrm{H}}^{\mathrm{C}}$, ${Z}_{\mathrm{DR}}^{\mathrm{C}}$), which
contradict the anticipated results. Such a contradiction means
${\widehat{Z}}_{\mathrm{DR}}$ estimated by Eqs. (11a) and (11b) is not representative
enough for surface precipitation. In contrast,
*R*(${Z}_{\mathrm{H}}^{\mathrm{C}}$, ${\widehat{Z}}_{\mathrm{DR}}$) in Fig. 25c shows even lower rainfall estimates than that in Fig. 21f (obtained
through Eq. 12c based on *S*_{0}), which can also be seen by comparing the
scattergrams in Figs. 26c and 22f. In addition, when large-sized drops
are gradually excluded from the DSD dataset for ${\widehat{Z}}_{\mathrm{DR}}$ and
*R*(${Z}_{\mathrm{H}}^{\mathrm{C}}$, ${\widehat{Z}}_{\mathrm{DR}})$, *E*_{CC}
changes little in Table 2, whereas *E*_{RMS} and *E*_{NMA} both exhibit a monotonic
increasing tendency, implying the non-negligible contribution of large-sized
drops around the GWS of YDM.

The dominant breakup in the air but dominant coalescence around the GWS of YDM can be ascribed to the overshooting of radar beams and the topographical
enhancement. In this sense, the utilization of ${\widehat{Z}}_{\mathrm{DR}}$
instead of ${Z}_{\mathrm{DR}}^{\mathrm{C}}$ equals a physical conversion of
breakup-dominated outcome in one volume gate for a given
${Z}_{\mathrm{H}}^{\mathrm{C}}$ into their coalescence-dominated counterparts
in an average sense. In this conversion process, consistency between
radar-measured ${Z}_{\mathrm{H}}^{\mathrm{C}}$ and *K*_{DP} in the air and the
surface counterparts (DSD-derived *K*_{DP} and *Z*_{H}) has been achieved, as
indicated in Sect. 3.1.2, demonstrating the mass conservation
characteristics of falling drops. Therefore, radar-measured
${Z}_{\mathrm{H}}^{\mathrm{C}}$ and *K*_{DP} around the GWS of YDM may change
insignificantly, which makes it conducive for
*R*(${Z}_{\mathrm{H}}^{\mathrm{C}}$, ${\widehat{Z}}_{\mathrm{DR}})$ to obtain
a better radar rainfall field.

## 3.4 Discussion

The microphysical processes during the landfall of typhoon Lekima have been revealed based on the analysis of consistency between measurements from radar, disdrometers, and rain gauge networks. The cause of the flood disaster around the GWS of YDM, and its impacts on the practical performance of radar QPE algorithms have been investigated. Several critical issues should be considered for radar quantitative applications in future:

- i.
High-quality DSD datasets could lay a solid foundation for microphysical analysis and polarimetric radar applications, but selecting representative datasets for different microphysical processes is critical to determine parameters for quantitative applications, such as the construction of relationships between

*Z*_{H},*Z*_{DR},*K*_{DP}, and*R*. The size–velocity QC procedure could be deeply refined for radar QPE in cold seasons. So far, one-dimensional disdrometers (OTT or Thies) are the main facilities to collect DSD measurements in the national meteorological stations over China. However, both GWS areas in this article have no DSD measurements for directly revealing and validating the critical precipitation process in the typhoon center area. Furthermore, there are more similar GWS areas in south China, thus deploying some two-dimensional disdrometers in these vital target locations could be beneficial for future research. - ii.
The polarimetric radar measurements are indispensable for microphysical analysis and quantitative applications. In particular,

*Z*_{DR}provides critical signatures for analyzing the collision process in this super typhoon event. Currently, more X-band polarimetric radar systems have been planned and/or deployed to fill the gap of operational S-band radar networks. Although*Z*_{DR}of S-,C-, and X-band radars is sensitive to drop size in different degrees,*Z*_{DR}biases in X-band radar measurements can be more serious in a super typhoon case due to radome attenuation. The correction methods of*Z*_{H}and*Z*_{DR}in this article could potentially be further refined for X-band applications. - iii.
The spatial variability of precipitation could be far more complex, and it is oversimplified to assert that convective or stratiform rainfall always exhibits breakup or coalescence (Kumjian and Prat, 2014). It is noticed that the practical performances of

*R*(${Z}_{\mathrm{H}}^{\mathrm{C}}$, ${\widehat{Z}}_{\mathrm{DR}}$) rely on determining optimal ${\widehat{Z}}_{\mathrm{DR}}$ based on the representative DSD dataset of the microphysical process, which is the main limitation of*R*(${Z}_{\mathrm{H}}^{\mathrm{C}}$, ${\widehat{Z}}_{\mathrm{DR}}$).*R*(*K*_{DP}) or*R*(*A*_{H}) are insensitive to such uncertainty, and they can outperform*R*(${Z}_{\mathrm{H}}^{\mathrm{C}}$, ${\widehat{Z}}_{DR}$) if they are further optimized. In addition, a single relationship between*R*and radar measurements might not be applicable to all range gates within the radar coverage, for example,*R*(*Z*_{H}),*R*(*K*_{DP}), and*R*(*Z*_{H},*Z*_{DR}) relationships listed in Table 3 are different; therefore, the residual differences between radar estimates and gauge measurements are still significant for*R*(${Z}_{\mathrm{H}}^{\mathrm{C}}$),*R*(*K*_{DP}), and*R*(${Z}_{\mathrm{H}}^{\mathrm{C}}$, ${\widehat{Z}}_{\mathrm{DR}}$). Merging radar with gauge measurements may partly reduce such differences if surface gauge rainfall bias caused by strong wind can be mitigated effectively. - iv.
The vertical gap between radar measurements and surface hinders deriving more optimal relationships and the complete vertical view of the microphysical processes, which are critical in precipitation events such as this super typhoon case. Sophisticated correction models are necessary to mitigate uncertainty caused by the vertical gap, such as the classical models for vertical extrapolation if only radar measurements on higher altitudes are available, either caused by complete beam blockage of mountainous terrain or the high altitudes of radar sites. Efficient implementation of the correction models requires prior knowledge of vertical microphysical precipitation variations. Still, the precipitation process should be determined to effectively match the model with radar measurements. In this typhoon case, the microphysical process is much more complicated, but if the coalescence–breakup balance of the collision process can be measured quantitatively and incorporated into radar QPE algorithms in the future, a more reasonable model can be established to enhance radar QPE performance.

This paper utilized a range of data, including observations from the WZ-SPOL radar, disdrometers, and gauge rainfall measurements, to analyze the microphysical processes during the landfall of Lekima (2019). The investigation focused on demonstrating the impacts of precipitation microphysics on the consistency of multi-source measurements and radar QPE performance. The main findings are summarized as follows:

- i.
Measurements from radar, disdrometers, and rain gauges are more consistent after the QC processing, including attenuation correction of radar observations and wind and hail/graupel processing of size–velocity measurements from disdrometers.

- ii.
The breakup overwhelms coalescence as the primary outcome of the collision process of raindrops, noticeably making radar-measured ${Z}_{\mathrm{DR}}^{\mathrm{C}}$–${Z}_{\mathrm{H}}^{\mathrm{C}}$ be breakup-dominated, which accounts for that high drop concentration rather than large drop size contributes more to a given ${Z}_{\mathrm{H}}^{\mathrm{C}}$ and the residual deviation of ${Z}_{\mathrm{DR}}^{\mathrm{C}}$ from ${\widehat{Z}}_{\mathrm{DR}}$.

- iii.
*R*(${Z}_{\mathrm{H}}^{\mathrm{C}}$) performs comparably well with*R*(*K*_{DP}) owing to attenuation correction, but*R*(${Z}_{\mathrm{H}}^{\mathrm{C}}$, ${Z}_{\mathrm{DR}}^{\mathrm{C}}$) performs worse with serious overestimation. This is related to the unique microphysical process around the GWS of YDM, in which the breakup-dominated small-sized drops in radar sampling volumes were located above the surface but coalescence-dominated large-sized drops were near the surface. - iv.
*R*(${Z}_{\mathrm{H}}^{\mathrm{C}}$, ${\widehat{Z}}_{\mathrm{DR}}$) outperforms*R*(${Z}_{\mathrm{H}}^{\mathrm{C}}$) and*R*(*K*_{DP}) in terms of the*E*_{RMS}and*E*_{NMA}scores, and the utilization of ${\widehat{Z}}_{\mathrm{DR}}$ instead of ${Z}_{\mathrm{DR}}^{\mathrm{C}}$ is close to physically converting breakup-dominated measurements in radar range gates to coalescence-dominated counterparts, which boosts better self-consistency between ${Z}_{\mathrm{H}}^{\mathrm{C}}$, ${\widehat{Z}}_{\mathrm{DR}}$, and*K*_{DP}and their consistency with the surface counterparts derived from disdrometer measurements.

The complex precipitation microphysics may have other unknown impacts on the self-consistency of radar measurements and the consistency between multi-source datasets, which is still a challenge for future research. An in-depth understanding of such microphysical processes is critical for improving radar quantitative remote sensing of precipitation. Deployment of cost-effective zenith radar (X- or Ka-band) networks may be an effective complement of operational weather radar networks. Collaborative observations of various remote sensing facilities such as these can not only help to resolve more microphysical processes in the vertical gaps currently missed by scanning radars but also support the development of more reasonable models to mitigate the resulting application uncertainty, especially in complex terrain regions.

The code and data that support the findings of this article are available on request from the first author (Yabin Gou) or corresponding author (Haonan Chen).

YG carried out the data collection and detailed analysis. He was also part of the polarimetric radar data processing and product generation team. HC supervised the work and provided critical comments. YG and HC wrote the manuscript. HZ contributed to critical comments and revisions. LX reviewed and edited the manuscript.

The contact author has declared that none of the authors has any competing interests.

Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

This research is primarily supported by the National Natural Science Foundation of China under grant no. 41375038 and the Zhejiang Provincial Natural Science fund through award LY17D050001. The work of Haonan Chen is supported by the Colorado State University and the National Oceanic and Atmospheric Administration (NOAA) through Cooperative Agreement NA19OAR4320073. The authors acknowledge the anonymous reviewers for their careful review and comments on this article. They also thank Lin Deng at the Shanghai Typhoon Institute of China Meteorological Administration for the discussion on typhoon microphysical processes, Yuanyuan Zheng and Fen Xu at the Jiangsu Institute of Meteorological Sciences for the discussion on radar measurements during this particular event, and Bo Si and Xiaolong Huang for double-checking the locations and measurement quality of meteorological stations. The S-band polarimetric radar, disdrometer, and rain gauge data are provided by the Chinese Meteorological Administration and are available upon request.

This paper was edited by Yuan Wang and reviewed by two anonymous referees.

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