Impact of Directly Assimilating Radar Reflectivity Using a Reflectivity Operator Based on a Double-Moment Microphysics Scheme on the Analysis and Forecast of Typhoon Lekima (1909)

Abstract

In previous studies, radar reflectivity is often directly assimilated using reflectivity operators based on a single-moment (SM) microphysics scheme, though the forecast model uses a double-moment (DM) microphysics scheme. With the fixed number concentrations, only the mixing ratios of hydrometeors are directly updated during the assimilation, which leads to a mismatch between the analyzed microphysical state variables and the microphysics scheme of the forecast model. In this study, the radar reflectivity is directly assimilated through an observation operator consistent with the DM Thompson microphysics scheme used in numerical integrations, and the impact of reflectivity operators based on SM and DM schemes on the analysis performance of the ensemble Kalman filter for typhoon Lekima on 9 August 2019 is evaluated. Reflectivity observations from a single operational weather radar in Wenzhou City, Zhejiang Province of China are assimilated. In addition, the dual-polarization observations from the same radar are used to evaluate the quality of the analysis. The analyzed reflectivity and dual-polarization characteristics obtained by different reflectivity operators are examined in detail. Compared with the experiments applying the reflectivity operator based on the SM Lin scheme, the use of a reflectivity operator consistent with the DM Thompson scheme adopted in the forecast model results in analyzed reflectivity and polarization characteristics that are more consistent with the observed characteristics in terms of general structure, location, and intensity. Forecasted reflectivity, 3 h accumulated precipitation, and typhoon intensity and track are also evaluated. The application of the reflectivity operator based on the DM scheme makes better forecasts of typhoon intensity, precipitation, and reflectivity, which also improves the forecast skills on typhoon tracks to a certain extent.

1. Introduction

Landing typhoons are among the most disastrous weather systems across the world. They may cause heavy rain and flood disasters during landfall, resulting in serious damage to coastal areas. Such disastrous impacts highlight the importance of accurate forecasts on landing typhoons and the accompanying precipitation. Therein, the microphysical processes within clouds have a strong influence on the evolution of typhoons. However, the current understanding of the complex microphysical processes and the associated impacts is not yet complete. Successful numerical prediction of typhoons requires accurate initial conditions and numerical weather prediction (NWP) models that can precisely simulate deep moist convection with microphysical processes. NWP models often utilize bulk microphysical parameterization (MP) schemes for cloud and precipitation processes such as the formation, growth, breakup, evaporation, and sedimentation of precipitation particles. In these schemes, semi-empirical functions are employed for the particle size distributions (PSDs) of each type of hydrometeor, with one well-known functional form being the gamma distribution [1,2],

$$N_x\left(D\right)=N_{0x}{D}^{{\alpha }_x}{e}^{-{\lambda }_{x}D},$$

(1)

where there are three free parameters: the intercept parameter $N_{0x}$, the shape parameter ${\alpha }_x$, and the slope parameter $\lambda$. In this formula, the number concentration $N\left(D\right)$ is a function of particle diameter $D$, and the subscript $x$ refers to the type of hydrometeor. Using a fixed $N_0$ and $\alpha =0$, Single-Moment (SM) MP schemes predict $\lambda$, which is a function related to the directly predicted mixing ratio of hydrometeors [3,4]. Double-moment (DM) schemes generally predict the total number concentration of hydrometeors in addition to the mixing ratios, allowing $N_0$ and $\lambda$ to change while maintaining $\alpha$ constancy [5,6,7]. With the rapid growth of computing power, the MP schemes are becoming widely applied. By independently predicting the mixing ratio and total number concentration of hydrometeors, the DM schemes allow for greater flexibility in MP processes, such as altering the number concentration while maintaining a constant mixing ratio when aggregation or breakup occurs. Additionally, the DM schemes have the capability to simulate particle size sorting, resulting in a more realistic vertical distribution of hydrometeor sizes [2]. Research shows that the DM MP schemes can reproduce the structure and evolution of convective precipitation more realistically, such as dual polarization characteristics and hailstorm forecasts [8]. The Thompson scheme [9], as a semi-DM MP scheme, predicts two parameters of the PSDs for rain and cloud ice but only one parameter for snow and hail/graupel. This scheme is currently widely used in various operational regional models, including the Rapid Refresh with a 13 km horizontal grid spacing [10], the High-Resolution Rapid Refresh with a 3 km grid spacing [11,12,13], and the Typhoon Ensemble Data Assimilation and Prediction System [14].

Radar is one of the few observation systems capable of observing the inner core of tropical cyclones (TCs), and it has a resolution comparable to that of the convective-scale models. Using dense radar data in initialization for convective-scale prediction is presently the main approach adopted by high-resolution numerical models [15,16,17,18,19,20,21,22,23,24]. Compared with radar radial wind, there are still many issues to be addressed in terms of the reflectivity data assimilation due to their direct relation to cloud microphysical processes, such as the correlations between hydrometeors and large-scale variables or vertical velocities, the strong non-linearity in model and observation operators, and non-Gaussian errors.

When a forecast model utilizes the DM MP schemes, it is necessary to initialize the corresponding model state variables, including both mixing ratios and number concentrations. Most studies on the direct assimilation of reflectivity adopt the observation operator based on the Lin SM scheme [3]. This operator calculates reflectivity based on the Rayleigh scattering assumption with fixed number concentrations. For rainwater, the reflectivity is calculated based on Smith et al. (1975) [25], from

$$Z_r={\displaystyle \frac{{10}^{18}\times 720{\left(\rho q_r\right)}^{1.75}}{{\pi }^{1.75}{N}_{0r}^{0.75}{\rho }_r^{1.75}}},$$

(2)

where ${\rho }_r=1000 \mathrm{k}\mathrm{g}{\mathrm{m}}^{-3}$ is the density of rainwater and $N_{0r}=8.0\times {10}^6 {\mathrm{m}}^{-4}$ is the intercept parameter, and $Z_r$ can be written as:

$$Z_r=3.63\times {10}^9{{(\rho q}_r)}^{1.75},$$

(3)

where $\rho$ is the air density and $q_r$ is the rainwater mixing ratio. In this equation, the reflectivity is not related to rainwater number concentration, inconsistent with that in the forecast model adopting a DM MP scheme. Therefore, the number concentrations cannot be directly updated when using this operator to assimilate reflectivity. Tong et al. [26] employed a reflectivity operator based on the Lin scheme in the Gridpoint Statistical Interpolation (GSI) ensemble variational (EnVAR) framework while the forecast model adopted the Thompson scheme. It was found that this inconsistency would introduce additional initial error.

Recently, a reflectivity operator based on the Thompson scheme developed by Jung et al. [27] was implemented in a GSI ensemble Kalman filter (EnKF) framework. This operator computes the scattering amplitudes of rain using the T-matrix method and utilizes the Rayleigh scattering approximation for snow and graupel particles. The EnKF reflectivity assimilation framework has been successfully examined with typhoon Lekima in our previous study [28]. As the first attempt to directly assimilate reflectivity in typhoon prediction using an observation operator based on the Thompson scheme, this study indicated that the assimilation of reflectivity improves both intensity and precipitation forecast skills for typhoon Lekima. However, in the previous study, we only used DM Thompson as the observation operator. The comparison of the results of EnKF reflectivity assimilation using SM and DM observation operators needs to be further evaluated to demonstrate the benefits of one over the other during typhoon analysis and forecasts. In this study, we select the same case of super typhoon Lekima that made landfall in Wenling, Zhejiang Province in east China on 9 August 2019. Analyses and forecasts using the SM Lin operator and DM Thompson operator are compared. The reflectivity observations from single coastal WSR-88D radar at Wenzhou station are assimilated, and the polarimetric radar observations from the same station are used for verification.

The remainder of this study is organized as follows: Section 2 provides a brief overview of typhoon Lekima and a description of data assimilation (DA) experiments. In Section 3, the assimilation results obtained by using Lin and Thompson reflectivity operators are discussed and verified against radar observations. Section 4 summarizes the results and discusses potential future work.

2. Observation Operators and Data Assimilation Procedure

2.1. Observation Operators

The forward observation operator used in this study is developed in Jung et al. [26] and modified by Xue et al. [29] to accommodate the use of the DM scheme. Both the mixing ratios and total number concentrations are input variables of the forward observation operators. Reflectivities at horizontal ($Z_h$) and vertical ($Z_v$) are derived by integrating over the PSDs weighted by the scattering cross section depending on density, shape, and PSDs. Briefly, for rain, the scattering amplitudes calculated with T-matrix methods [30,31] at uniform drop size intervals are fitted to a power-law function of the drop size for reflectivity. For ice, the Rayleigh scattering approximation is employed. The presence of wet snow and wet hail/graupel by specifying a water fraction in the melting layer is incorporated to account for wet snow and wet hail/graupel. This melting ice model accounts for continuous variations in density and dielectric constants throughout the melting process.

For rain, reflectivity at horizontal and vertical polarizations can be calculated as follows:

$$Z_{h,r}={\displaystyle \frac{4{\lambda }^4{\alpha }_{ra}^2{N}_{0r}}{{\pi }^4{\left|K_w\right|}^2}}{\Lambda }_r^{-\left(2{\beta }_{ra}+1\right)}\Gamma \left(2{\beta }_{ra}+1\right)\left(\mathrm{m}{\mathrm{m}}^6{\mathrm{m}}^{-3}\right),$$

(4)

and

$$Z_{v,r}={\displaystyle \frac{4{\lambda }^4{\alpha }_{rb}^2{N}_{0r}}{{\pi }^4{\left|K_w\right|}^2}}{\Lambda }_r^{-\left(2{\beta }_{rb}+1\right)}\Gamma \left(2{\beta }_{rb}+1\right)\left(\mathrm{m}{\mathrm{m}}^6{\mathrm{m}}^{-3}\right),$$

(5)

where $\lambda \approx 10.7 \mathrm{c}\mathrm{m}$ is the radar wavelength for the WSR-88D radars. ${\alpha }_{ra}={\alpha }_{rb}=4.28\times {10}^{-4}$, ${\beta }_{ra}=3.04$, and ${\beta }_{rb}=2.77$ are adopted from the T-matrix calculation and fitting results. The value for the intercept parameter for rain in the Lin SM scheme is $N_{0r}=8\times {10}^6 {\mathrm{m}}^{-4}$, but a wide range of values within predicted total number concentrations can be used for the Thompson DM scheme. The slope parameter ${\Lambda }_r$ can be derived from the rain mixing ratio once the intercept parameter is specified. $K_w=0.93$ is the dielectric factor for water and $\mathsf{\Gamma }$ is the gamma function.

For other ice species, the reflectivities are given by:

$$Z_{h,x}={\displaystyle \frac{2880{\lambda }^4{N}_{0x}}{{\pi }^4{\left|K_w\right|}^2}}{\Lambda }_x^{-7}\left(A{\alpha }_{xa}^2+B{\alpha }_{xb}^2+2C{\alpha }_{xa}{\alpha }_{xb}\right),$$

(6)

$$Z_{v,x}={\displaystyle \frac{2880{\lambda }^4{N}_{0x}}{{\pi }^4{\left|K_w\right|}^2}}{\Lambda }_x^{-7}\left(B{\alpha }_{xa}^2+A{\alpha }_{xb}^2+2C{\alpha }_{xa}{\alpha }_{xb}\right),$$

(7)

where

$A={\displaystyle \frac{1}{8}}\left(3+4\mathit{cos}2\overline{\varphi }{e}^{-2{\sigma }^2}+\mathit{cos}4\overline{\varphi }{e}^{-8{\sigma }^2}\right)$,

$B={\displaystyle \frac{1}{8}}\left(3-4\mathit{cos}2\overline{\varphi }{e}^{-2{\sigma }^2}+\mathit{cos}4\overline{\varphi }{e}^{-8{\sigma }^2}\right)$,

and

$C={\displaystyle \frac{1}{8}}\left(1-\mathit{cos}4\overline{\varphi }{e}^{-8{\sigma }^2}\right)$,

Here, $x$ can be rs (rain–snow mixture), ds (dry snow), rh/g (rain–hail/graupel mixture), or dh/g (dry hail/graupel) and ${\mathrm{N}}_{0\mathrm{x}}$ is the intercept parameter for each species. $\overline{\varphi }=0°$ is the mean canting angle assumed for all hydrometeor spices, and the standard deviation of the canting angle $\sigma =20°$ for snow and $\sigma =60°\left(1-c{f}_w\right)$ for hail. Here, the water fraction in the melting snow or hail $f_w$ is accounted for the presence of wet snow and wet hail in the melting layer. For the water–snow mixtures, $f_w=q_r/\left(q_r+q_s\right)$, within rain mixing ratios ${(q}_r)$ and snow mixing ratios $\left(q_s\right)$. For the water–hail mixtures, $f_w=q_r\left(q_r+q_h\right)$, within rain mixing ratios ($q_r$) and hail mixing ratios ($q_h$). $c=0.8$, when the mixing ratios of rain–hail/graupel mixture $q_{rh/g}\ge 0.2 \mathrm{g}·{\mathrm{k}\mathrm{g}}^{-1}$, and otherwise, $c=4q_{rh/g}$.

The resultant ${\alpha }_{xa}$ and ${\alpha }_{xb}$ for snow and hail are obtained based on the Rayleigh scattering approximation for oblate spheroids, and fitted to polynomial functions of ${\mathrm{f}}_{\mathrm{w}}$:

${\alpha }_{rsa}=(0.194+7.094f_w+2.135{f_w}^2-5.225{f_w}^3)\times {10}^{-4}$,

${\alpha }_{rsb}=(0.191+6.916f_w-2.841{f_w}^2-1.160{f_w}^3)\times {10}^{-4}$,

${\alpha }_{rh/ga}=(0.191+2.39f_w-12.57{f_w}^2+38.71{f_w}^3-65.53{f_w}^4+56.16{f_w}^5-{{18.98f}_w}^6){10}^{-3}$,

${\alpha }_{rh/gb}=(0.165+1.72f_w-9.92{f_w}^2+32.15{f_w}^3-56.0{f_w}^4+48.83{f_w}^5-16.69{f_w}^6)\times {10}^{-3}$,

${\alpha }_{dsa}=0.194\times {10}^{-4}$,

${\alpha }_{dsb}=0.191\times {10}^{-4}$,

${\alpha }_{dh/ga}=0.191\times {10}^{-3}$, and

$${\alpha }_{dh/gb}=0.165\times {10}^{-3}.$$

(8)

The logarithmic reflectivity at the horizontal and vertical polarizations (${\mathrm{Z}}_{\mathrm{H}}$, ${\mathrm{Z}}_{\mathrm{V}}$, respectively) and differential reflectivity ($\mathrm{Z}\mathrm{D}\mathrm{R}$) are given by the reflectivities for different hydrometeor species:

$$Z_H=10{\log }_{10}\left(Z_{h,r}+Z_{h,rs}+Z_{h,ds}+Z_{h,rh/g}+Z_{h,dh/g}\right)\left(\mathrm{d}\mathrm{B}\mathrm{Z}\right),$$

(9)

$$Z_V=10{\log }_{10}\left(Z_{v,r}+Z_{v,rs}+Z_{v,ds}+Z_{v,rh/g}+Z_{v,dh/g}\right)\left(\mathrm{d}\mathrm{B}\mathrm{Z}\right),$$

(10)

$$Z_{DR}=10{\log }_{10}\left({\displaystyle \frac{Z_h}{Z_v}}\right)=10{\log }_{10}\left({\displaystyle \frac{Z_{h,r}+Z_{h,rs}+Z_{h,ds}+Z_{h,rh/g}+Z_{h,dh/g}}{Z_{v,r}+Z_{v,rs}+Z_{v,ds}+Z_{v,rh/g}+Z_{v,dh/g}}}\right)(\mathrm{d}\mathrm{B}).$$

(11)

The specific differential phases for the rain, rain–snow aggregate mixture, dry snow aggregate, rain–hail/graupel mixture, and dry hail/graupel are calculated from

$$K_{DP,x}={\displaystyle \frac{180\lambda }{\pi }}{N}_{0r}{\alpha }_{xk}{\Lambda }_r^{-\left({\beta }_{rx}+1\right)}\Gamma \left({\beta }_{xk}+1\right)\left(°{\mathrm{k}\mathrm{m}}^{-1}\right).$$

(12)

where ${\alpha }_{rk}=1.30\times {10}^{-5}$ and ${\beta }_{rk}=4.63$ for rain, ${\alpha }_{xk}$ for $K_{DP}$ from Equation (7) to be ${\mathsf{\alpha }}_{\mathrm{x}\mathrm{a}}-{\mathsf{\alpha }}_{\mathrm{x}\mathrm{b}}$ for the rain–snow aggregate and rain–hail/graupel mixture. Here, ${\alpha }_{dsk}=0.3\times {10}^{-6}$ for dry snow and ${\alpha }_{dh/gk}=0.26\times {10}^{-4}$ for dry hail/graupel. ${\beta }_{rk}=3$ for both ice species and water–ice mixtures.

The total $K_{DP}$ is given by the combination of the specific differential phases for different species:

$$K_{DP}=K_{DP,r}+K_{DP,rs}+K_{DP,ds}+K_{DP,rh}+K_{DP,dh}.$$

(13)

2.2. The EnKF Data Assimilation Procedure

In this study, the Gridpoint Statistical Interpolation (GSI) [32] EnKF DA system is applied for directly assimilating reflectivity data. This EnKF system uses the EnSRF method, following Whitaker and Hamill [33]. EnSRF assimilates each observation sequentially, which means updating the ensemble with one observation at a time. By treating observations individually, the analysis equations of the serial EnSRF algorithm for ensemble mean state $\overline{x}$ and the ensemble deviations from the mean $x_i^{\prime }$ are, respectively,

$${\overline{x}}^a={\overline{x}}^b+\mathbf{K}\left[y^o-H\left({\overline{x}}^b\right)\right],$$

(14)

$$x_i^{\prime a}=\left(\mathbf{I}-\alpha \mathbf{K}\mathbf{H}\right)x_i^{\prime b},$$

(15)

where

$$\mathbf{K}={\mathbf{P}}^b{\mathbf{H}}^{\mathrm{T}}{\left(\mathbf{H}{\mathbf{P}}^b{\mathbf{H}}^{\mathrm{T}}+\mathbf{R}\right)}^{-1},$$

(16)

is the Kalman gain matrix. Subscript $i$ is the index of ensemble member; superscripts $a$, $b$, and $o$ denote analysis, background, and observation, respectively; ${\mathbf{P}}^b$ is the background error covariance matrix; $\mathbf{H}$ is the linearized version of observation operator $H$ that project state vector $\mathrm{x}$ to observation vector ${\mathrm{y}}^{\mathrm{o}}$; $\mathbf{R}$ is the observation error covariance. $\alpha$ is a coefficient specific to the square-root algorithm, given by

$$\mathsf{\alpha }={\left(1+\sqrt{{\displaystyle \frac{\mathbf{R}}{\mathbf{H}{\mathbf{P}}^b{\mathbf{H}}^{\mathrm{T}}+\mathbf{R}}}}\right)}^{-1}$$

(17)

the background error covariances ${\mathbf{P}}^b{\mathbf{H}}^{\mathrm{T}}$ and $\mathbf{H}{\mathbf{P}}^b{\mathbf{H}}^{\mathrm{T}}$ in Equation (16) are estimated from the background ensemble, according to

$${\mathbf{P}}^b{\mathbf{H}}^{\mathrm{T}}={\displaystyle \frac{1}{N-1}}{\sum }_{i=1}^N\left(x_i^{\prime b}\right){\left[H\left(x_i^{\prime b}\right)\right]}^{\mathrm{T}},$$

(18)

$$\mathbf{H}{\mathbf{P}}^{\mathrm{b}}{\mathbf{H}}^{\mathrm{T}}={\displaystyle \frac{1}{N-1}}{\sum }_{i=1}^N\left[H\left(x_i^{\prime b}\right)\right]{\left[H\left(x_i^{\prime b}\right)\right]}^{\mathrm{T}}.$$

(19)

where $N$ is the ensemble size, and $H$ is the observation operator, which can be nonlinear.

Repeat the above update steps for each observation sequentially until all observations at the current time step have been assimilated.

In this study, the analysis variables contained in state vector $\mathrm{x}$ include the gridpoint values of zonal wind ($u$), meridional wind ($\mathrm{v}$), vertical wind ($w$), potential temperature ($\theta$), dry air mass in column ($MU$), mixing ratios of water vapor ($q_v$), cloud water ($q_c$), rain water ($q_r$), ice ($q_i$), snow ($q_s$), and graupel ($q_g$), number concentrations of ice ($N_i$), and rain ($N_r$). The observation vector $y^o$ is radar reflectivity $\mathrm{Z}$. The observation operator $\mathrm{H}$ is defined by Equations (3), (5), and (8).

3. Overview of Typhoon Lekima Case and Experimental Design

As a high-impact case studied by many previous studies [28,34,35], typhoon Lekima was generated on 4 August 2019 and upgraded to a super typhoon in the afternoon of 7 August. It made landfall along the coast of Wenling City, Zhejiang Province of east China at around 1745 UTC (Universal Time Coordinated, the same below) on 10 August, with the maximum central wind reaching the scale of force 16 (52 m s⁻¹). Afterwards, it continued to move northwards, successively passing through Zhejiang, Jiangsu, and Shandong provinces, and made its second landfall in Qingdao of Shandong Province with the maximum wind reaching force 9 (23 m s⁻¹). The intensity of typhoon Lekima ranks fifth among the typhoons that made landfall on the mainland of China since 1949. After landfall, it moved slowly and lingered over the land for up to 44 h, ranking sixth among the over-land duration since records began in 1949. Under its influence, extreme heavy rainfall occurred in Zhejiang, Shandong, and Jiangsu. Specifically, the rainfall in Kuocang Mountain in Linhai City reached 831 mm, acting as the second heaviest rainstorm induced by the typhoons that made landfall in Zhejiang Province.

In this study, forecast experiments are performed using the Weather Research and Forecasting (WRF) model [36] version 3.9.1. The model domain has 548 × 452 grid points with a 3 km horizontal resolution and 51 vertical levels. The Thompson MP scheme is used for all model forecasts. Correspondingly, the forecast state variables of model consist of horizontal wind field ($u$ and $v$), vertical wind field ($w$), potential temperature ($\theta$), dry air mass of the entire atmospheric column ($MU$), water vapor mixing ratio ($q_v$), and mixing ratios of cloudwater, rainwater, ice, snow, and graupel ($q_c$, $q_r$, $q_i$, $q_s$, and $q_g$), as well as the number concentration of ice ($N_i$) and rainwater ($N_r$). Other physical parametrizations include the Yonsei University (YSU) planetary boundary layer scheme [37], the unified Noah land surface model [38], and the rapid radiative transfer model for general circulation models (RRTMG) shortwave and longwave schemes [39].

The workflow of cycled DA and forecast experiments is shown in Figure 1, aligning with Luo et al. [28]. The initial condition for ensemble member 41 is taken from the Global Forecast System (GFS) analysis initialized at 0600 UTC on 9 August, and ensemble perturbations generated from the WRFDA 3DVAR using cv3 background error covariance option [40] are added to the GFS analysis and expanded to another 40 ensemble members. A two-dimensional (2D) recursive filter is applied horizontally with a de-correlation length scale of 6 km, and a homogeneous Gaussian filter with a length scale of 3 km is applied vertically to three-dimensional (3D) fields with random Gaussian distributed perturbations to generate smoothed, spatially correlated initial perturbations. The standard deviations of the perturbations added to each variable are 1 m s⁻¹ for $u$, $v$, and $w$; 1 K for $\theta$; and 0.2 g kg⁻¹ for the mixing ratios of hydrometeors ($q_c$, and $q_v$). The initial fields for member 41 were taken directly from the GFS analysis. Subsequently, a 5 h ensemble forecasts before 1100 UTC are conducted for spin-up. Six cycled DAs are run from 1100 UTC to 1200 UTC on 9 August. Radar reflectivity observations are assimilated every 12 min. Free 12 h forecasts initialized from the final analysis of member 41 at 1200 UTC are conducted.

Two sets of experiments using SM Lin and DM Thompson microphysics operators (short for LIN and TM experiments hereafter, respectively) are conducted for comparison (Table 1). The background and analysis reflectivity are calculated using the Lin operator for the LIN experiment, and correspondingly, the Thompson operator is used for the TM experiment. In LIN experiment, the MP scheme used for DA is inconsistent with that for model integration. Furthermore, we applied the Thompson operator specifically to calculate the background and LIN-analyzed reflectivity for the LIN_TM experiment, in which the other mismatch is introduced between the DA and the post-process. In the six cycles, reflectivity operators are based on Lin or Thompson MP schemes in the DA process, while the same model using the Thompson scheme is employed in the forecast process. Thus, the MP schemes used in forecast and DA processes are the same in TM experiment but different in LIN experiment. Ensemble member 41 is selected to reveal the differences between LIN and TM experiments. Radar reflectivity observations by the WSR-88D radar at Wenzhou are processed by a quality control and processing procedure from the Py-ART software version 2.0 [41]. The raw reflectivity data are processed to remove ground clutter, speckles, and other artefacts, and interpolated onto the locations of the model-grid columns horizontally with a horizontal resolution of 3 km and 33 vertical levels, where the vertical heights are 0.5, 0.75, 1.0, 1.25, 1.5, 1.75, 2.0, 2.25, 2.5, 2.75, 3.0, 3.5, 4.0, 4.5, 5.0, 5.5, 6.0, 6.5, 7.0, 7.5, 8.0, 8.5, 9.0, 10.0, 11.0, 12.0, 13.0, 14.0, 15.0, 16.0, 17.0, 18.0, and 19.0 km. Similar to Luo et al. [28], no further data thinning on the model grid is performed. Our earlier sensitive covariance localization experiments varied the localization radius for radar observations either horizontally (3, 12, 24 km) or vertically (0.1, 0.2, 0.4 scale height) during DA. It was found that using a moderate horizontal covariance localization radius and shorter vertical scale height for radar data had a positive impact on forecast skills. Hence, in our DA configurations, the radius used in the horizontal covariance localization function [42] is set to 12 km, and the vertical scale height is set to 0.1 in unit of $-\log \left({\displaystyle \frac{P}{Pref}}\right)$. Observation errors are assumed as 5 dBZ. In order to maintain the ensemble spread during DA, the relaxation to prior spread (RTPS) [43] multiplicative inflation method is applied with an inflation factor of 0.95.

Table 1. List of assimilation experiments.

Experiment	Microphysics Scheme for Model Integration	Microphysics Scheme for Observation Operator	Analysis Variables Updated by EnKF
TM	Thompson	Thompson	$u$$,v$, $w$, $\theta$, $MU$, $q_v$, $q_c$, $q_r$, $q_i$, $q_s$, $q_g$, $N_i$, $\mathrm{and}{N}_r$
LIN	As in TM	Lin	As in TM
LIN_TM	As in TM	Same as LIN for whole DA cycles, but the background and analysis reflectivity shown in Figure 2, Figure 3 and Figure 4 is calculated by Thompson operator.	As in TM

Table 1. List of assimilation experiments.

Experiment	Microphysics Scheme for Model Integration	Microphysics Scheme for Observation Operator	Analysis Variables Updated by EnKF
TM	Thompson	Thompson	$u$$,v$, $w$, $\theta$, $MU$, $q_v$, $q_c$, $q_r$, $q_i$, $q_s$, $q_g$, $N_i$, $\mathrm{and}{N}_r$
LIN	As in TM	Lin	As in TM
LIN_TM	As in TM	Same as LIN for whole DA cycles, but the background and analysis reflectivity shown in Figure 2, Figure 3 and Figure 4 is calculated by Thompson operator.	As in TM

Figure 2. Root mean square innovations (unit: dBZ) of radar reflectivity of the background and the analysis of LIN and TM experiments. LIN_TM indicates that the reflectivity is calculated using the Thompson operator for LIN experiment.

Figure 2. Root mean square innovations (unit: dBZ) of radar reflectivity of the background and the analysis of LIN and TM experiments. LIN_TM indicates that the reflectivity is calculated using the Thompson operator for LIN experiment.

Figure 3. Composite reflectivity (unit: dBZ) by (a) the observation, the background of (b) LIN and (c) TM experiments, and the analysis fields of (d) LIN_TM (LIN analysis with the Thompson operator), (e) LIN, and (f) TM experiments at 1100 UTC on 9 August. The black dashed line in (a) represents the location of the vertical cross-section in Figure 4 and Figure 5.

Figure 3. Composite reflectivity (unit: dBZ) by (a) the observation, the background of (b) LIN and (c) TM experiments, and the analysis fields of (d) LIN_TM (LIN analysis with the Thompson operator), (e) LIN, and (f) TM experiments at 1100 UTC on 9 August. The black dashed line in (a) represents the location of the vertical cross-section in Figure 4 and Figure 5.

Figure 4. Vertical cross-sections of reflectivity (unit: dBZ) by (a) the observation, the backgrounds of (b) LIN, and (c) TM experiments, and the analysis fields of (d) LIN_TM, (e) LIN, and (f) TM experiments along the line shown in Figure 3a.

Figure 4. Vertical cross-sections of reflectivity (unit: dBZ) by (a) the observation, the backgrounds of (b) LIN, and (c) TM experiments, and the analysis fields of (d) LIN_TM, (e) LIN, and (f) TM experiments along the line shown in Figure 3a.

Figure 5. Cross-sections of reflectivity components (shaded, unit: dBZ) and mixing ratios (black contour, unit: g kg⁻¹) of (a–d) rain, (e–h) graupel, and (i–l) snow by the background of (a,e,i) LIN and (b,f,j) TM experiments, and the analysis fields of (c,g,k) LIN, and (d,h,l) TM experiments along the line illustrated in Figure 3a. The starting values of the contours are 0.5 g kg⁻¹, 0.01 g kg⁻¹, and 0.1 g kg⁻¹ and the intervals are 0.8 g kg⁻¹, 0.3 g kg⁻¹, and 1.0 g kg⁻¹ for the mixing ratios of rain, graupel, and snow, respectively. The hot-pink contours in (a–d) represent the number concentration of rainwater with the starting value of 1.25 m³ and an interval of 1.0 m³.

Figure 5. Cross-sections of reflectivity components (shaded, unit: dBZ) and mixing ratios (black contour, unit: g kg⁻¹) of (a–d) rain, (e–h) graupel, and (i–l) snow by the background of (a,e,i) LIN and (b,f,j) TM experiments, and the analysis fields of (c,g,k) LIN, and (d,h,l) TM experiments along the line illustrated in Figure 3a. The starting values of the contours are 0.5 g kg⁻¹, 0.01 g kg⁻¹, and 0.1 g kg⁻¹ and the intervals are 0.8 g kg⁻¹, 0.3 g kg⁻¹, and 1.0 g kg⁻¹ for the mixing ratios of rain, graupel, and snow, respectively. The hot-pink contours in (a–d) represent the number concentration of rainwater with the starting value of 1.25 m³ and an interval of 1.0 m³.

4. Results

4.1. Results of First-Time Analyses

To clearly illustrate the impact of reflectivity observation operators based on Lin and Thompson schemes on DA, we assess the performance of DA in the first analysis cycle at 1100 UTC on 9 August 2019, using the same background field generated by the 5 h forecasts of WRF model integrated with the Thompson scheme. We calculated the root mean square innovations (RMSIs) for the background and analyzed reflectivity averaged over those grid points with the observed reflectivity exceeding 15 dBZ, as shown in Figure 2. In both TM and LIN experiments, the RMSIs of the analysis are significantly lower than those in the background field, indicating that both observation operators are able to force the analysis field closer to the observations. Compared with the TM experiment, the RMSIs of the LIN experiment are obviously larger in both background and analysis, indicating that the inconsistency between reflectivity operator and model prediction in LIN experiment may introduce additional errors in the DA process. Eventually, the two mismatches among forecasts, DA, and post-process in LIN_TM result in extremely large RMSIs (approximately 16 dBZ) of the analysis field, which are even higher than that (15 dBZ) in the background field.

The composite reflectivity of the background and analysis in the TM and LIN experiments after the first analysis cycle are verified against the observations, and the results are shown in Figure 3. The observed reflectivity shows that Lekima is characterized by distinct double eyewalls, with the inner rainband stronger in the west and weaker in the east. The outer spiral rainband structure is clear, leading to the unevenly distributed and local heavy precipitation in the eastern coastal areas of Zhejiang Province, China. Convection is vigorous near Taizhou city, which is the center of heavy precipitation (Figure 3a). Compared with observations, the background reflectivity obtained through the observation operators of TM and LIN is stronger, whereas the bias by LIN is even more significant. After DA, the results by both experiments tend to approach the observations, and the errors of overestimation are corrected. Moreover, the analysis field obtained from the TM experiment is closer to the observations compared with that by the LIN experiment, and the region of heavy precipitation near Taizhou becomes more apparent (Figure 3b,c,e,f). In the LIN_TM experiment, there are unreasonably strong echoes within the inner and outer rainbands due to the application of the TM operator to calculate the reflectivity of the analysis field obtained from the LIN experiment (Figure 3d). In a sense, the reflectivity by the LIN_TM experiment is equivalent to the reflectivity output directly by the WRF model at the initial time, indicating that the precipitation pattern reflected by the analyzed reflectivity may be inaccurate because of the inconsistency of the MP schemes between assimilation and model integration.

To further investigate the impact of the Thompson and Lin operators during the assimilation process, a group of cross-sections along the dashed line in Figure 3a are displayed (Figure 4). Compared with observations, the background reflectivity calculated using Thompson and Lin operators both display more uneven spatial distributions and stronger intensities of severe convective regions, with the overestimation by the LIN experiment being greater than that by the TM experiment (Figure 4a–c). After DA, the reflectivity by the two experiments below the altitude of 6 km becomes closer to the observation at low-middle levels, but it still remains unchanged in the background field at high-level areas (above 10 km). These phenomena are due to the available height of observation (below 10 km) and a shorter vertical localization radius (0.1 × lnP) in DA. Below 8 km, the analyzed reflectivity of the TM experiment is greatly improved compared with that of LIN experiment, even though the reflectivity cores of TM experiment are stronger than the observations. The reflectivity calculated using the Thompson operator in the LIN_TM experiment exhibits significant differences with that in the LIN analysis state using the Thompson operator in the near-surface layer (below 4 km).

Figure 5 shows the analysis and background values of the mixing ratios of rain, graupel, and snow and the number concentrations of rainwater at 1100 UTC, as well as the reflectivity of their relative contributions. In terms of the background field, the reflectivity is overestimated by the LIN operator for rainwater, graupel, and snow. Similarly, the analysis values of the LIN experiment are also overestimated, and the overestimation in the reflectivity of ice-phase hydrometeors (graupel and snow) is more significant than that of the liquid phase (rainwater). The results suggest that if the background field is integrated using the Thompson MP scheme and the analysis updates apply the observation operator based on the SM Lin scheme, there may be more hydrometeors produced compared with that by using the same Thompson operator.

Since the number concentration of rainwater ($N_r$) is a model state variable, it is suggested to be updated during the analysis process. Utilizing the ensemble-based covariance of EnKF, $N_r$ can be easily updated. It is found that the analyzed $N_r$ in the TM experiment is enhanced more significantly above the altitude of 6 km compared with that in the LIN experiment (Figure 5c,d). In view of the mixing ratio of rainwater ($q_r$), the analyzed value obtained by the TM experiment is slightly higher than that by the LIN experiment at low levels. From the aspect of graupel and snow, the mixing ratios of snow and graupel ($q_s$ and $q_g$) analyzed by the TM experiment are slightly higher than those by the LIN experiment, but the spurious reflectivity contributed by graupel and snow ($Z_g$ and $Z_s$) existing in the LIN experiment is apparently reduced in the TM experiment (Figure 5e–l). This is related to the fact that the LIN experiment utilizes hail rather than graupel. The intercept parameter of hail is larger than that of graupel, and therefore the reflectivity is overestimated.

From the perspective of the typhoon numerical simulation, the structure, dynamics, and evolution of the typhoon circulation are affected by the PSDs of hydrometeors. The size distribution of hydrometeors (raindrops, snowflakes, ice particles) affects the rate of latent heat release during phase changes (e.g., freezing, condensation). This release of latent heat is crucial for driving the convection within typhoons, impacting storm structure. Therefore, proper initialization of PSDs is crucial for successful typhoon forecasting. Due to the lack of direct three-dimensional PSD observations, it is difficult to directly examine the PSDs in models. Previous studies have shown that dual-polarization radar observations can be used to evaluate the impact of MP schemes on the simulation of hydrometeor state variables [44,45]. The dual-polarization observations from Wenzhou radar station, which have not been assimilated, are used to evaluate the analysis variables. In order to directly compare the observed and analyzed dual-polarization variables, the dual-polarization observation operator proposed by Jung et al. [26] is used to convert the model state variables into observed variables (see Equations (10)–(12)). The observed reflectivity illustrates that asymmetric double eyewalls are found in typhoon Lekima with the inner rainband being stronger in the west and weaker in the east at the height of 5.5 km (Figure 6a). The results of the LIN experiment demonstrate that the precipitation of the outer rainband of Lekima after assimilation is stronger than that of the observation. Additionally, the horizontal reflectivity simulated by the TM experiment is significantly weaker than that by the LIN experiment, and the pattern is slightly closer to that of the observation (Figure 6b,c). Overall, the distributions of specific differential phases (KDP) and the differential reflectivity (ZDR) obtained from the analysis field of the LIN experiment differ significantly from the observations (Figure 6e,h). Moreover, the polarization characteristics from the TM experiment are relatively closer to the observations compared with that by the LIN experiment (Figure 6f,i). In the LIN experiment, the ZDR of the inner rainband on the southwest side of the typhoon inner core is large, which may be due to an excessively strong size-sorting mechanism [34,46,47] that leads to the accumulation of excessive large-sized hydrometeors in that region (Figure 6e). Meanwhile, in the TM experiment, the size-sorting mechanism can be better simulated, thereby resulting in a ZDR value that is closer to the observed value on the southwest side of the typhoon (Figure 6f). The excessive size-sorting in the LIN experiment may be caused by the application of fixed intercept parameters for rainwater in PSDs, thus causing an overestimation in the ZDR [13]. Furthermore, the particle size in the outer rainband analyzed by the LIN experiment is significantly smaller than that in the observation, while the TM experiment can effectively reduce this underestimation to a certain extent. The observed KDP is generally weak and evenly distributed throughout the typhoon circulation, with high values in local areas on the northeast side of the inner rainband and on the southwest side of the outer rainband, corresponding to the distribution of the reflectivity intensity within the typhoon circulation (Figure 6g). Both the LIN and TM analyses show a good correspondence between KDP and reflectivity, with high reflectivity corresponding to large KDP values. However, the excessively high KDP in the spiral rainband on the west side of the typhoon analyzed by the LIN experiment is partly due to the reduced intercept parameter for rainwater in the LIN experiment. This reduced intercept parameter increases the median volume diameter of raindrops, and larger particles lead to a greater differential reflectivity (Figure 6h).

Since the EnKF can utilize cross-covariance to update the model state variables of non-hydrometeors, we investigated the impact of reflectivity observation operators based on different MP schemes on the dynamic and thermodynamic characteristics of the analysis field. Figure 7 shows the analysis increments of potential temperature and horizontal wind speed near surface (at the lowest level of model). The differences in the analysis increments of horizontal wind between the two experiments are not significant. Compared with the TM experiment, the adjustment in the potential temperature increment by the LIN experiment is larger, resulting in a larger negative value in the negative increment region at the northwest of the typhoon. This is related to the higher reflectivity analyzed by the LIN experiment (Figure 3e). The higher reflectivity indicates more hydrometeors and more precipitation, which lead to a stronger cooling effect, and the decrease in temperature is unfavorable for maintaining the typhoon intensity in model forecasts.

4.2. Results of 1H-CYCLED Analyses

During the 1 h DA window from 1100 UTC to 1200 UTC, reflectivity is assimilated directly every 12 min by using reflectivity observation operators based on different MP schemes. Figure 8 shows the reflectivity at different heights from the observation and the two sets of experiments at the final analysis time after six DA cycles. To a certain extent, both the LIN and TM experiments are able to capture the characteristics of observed reflectivity at the altitudes of 3 km and 5.5 km. However, there is an overestimation of the echo intensity in the typhoon’s inner rainband at the altitude of 3 km, as well as an underestimation of the stratiform precipitation in the outer rainband by the LIN experiment. Additionally, many scattered and spurious convective cells are produced at the altitude of 5.5 km compared with few by the TM experiment (Figure 8b,e). The reflectivity intensity and coverage analyzed by the TM experiment are closer to those of the observations (Figure 8c,f). Despite the similarity in the final analyzed reflectivity, the morphological differences in microphysical variables between the LIN and TM experiments are significant. Figure 9 shows the average mass diameters and mixing ratios of raindrops at the height of 3 km and graupel at the height of 5.5 km. The formula to compute the average mass diameter ($D_{nr}$) refers to Equation (8) in Jung et al. [48], where the $D_{nx}$ is calculated for the exponential distribution as

$$D_{nx}={\left({\displaystyle \frac{q_x{\rho }_{air}}{\pi {\rho }_x{Nt}_x}}\right)}^{1/3},$$

(20)

where ${\rho }_{air}$ is the density of air, subscript $x$ can be rain ($r$), snow ($s$), or graupel/hail ($g/h$). $q$ is hydrometeor mixing ratio, $Nt$ is the total number concentration, and $\mathsf{\rho }$ is the density of particles.

In the LIN experiment based on an SM scheme, the average particle size is a monotonic function of the mixing ratio. Therefore, hydrometeors with large particle sizes only exist in the regions with high mixing ratios, as shown in Figure 9a,c. Compared with the LIN experiment, the raindrops produced in the high reflectivity regions at lower levels in the TM experiment have slightly larger diameters (Figure 9b). Moreover, the TM experiment produces more graupel particles with larger diameters at higher levels, while the increase in mixing ratio is not significant (Figure 9d). This mismatch between mixing ratio and particle size indicates that there are more graupel particles with large diameters near the updraft region in the TM experiment. Graupel particles with large diameters may enhance updrafts primarily through the release of latent heat during the riming process, which warms the surrounding air and increases its buoyancy. Therefore, the updraft in the TM experiment may be stronger. This may lead to an enhanced typhoon intensity prediction.

Figure 10 exhibits the east–west cross-section of potential temperature and horizontal wind speed passing through the center of Lekima. Compared with the LIN experiment (Figure 10a), the near-surface wind speeds near the typhoon center are stronger in simulations by the TM experiment. Particularly, the wind speeds exceed 60 m s⁻¹ at a height of approximately 50 m above the ground on the western side of Lekima. The area with the wind speed greater than 48 m s⁻¹ on the western side extends to a height of over 2 km. The range of low-wind-speed area at the typhoon center is broader, and the wind speed at the middle level (4–9 km) is lower, indicating that the typhoon eye area in the TM experiment is clearer. The distributions of potential temperature are characterized by two valley areas within the entire layer from 0 to 9 km in the typhoon center, suggesting that there are two warm areas throughout the entire layer in the typhoon center. These are known as double warm cores, corresponding to the double-eyewall structure of the typhoon (Figure 10b).

4.3. Results of 12-h Forecasts

To quantitatively evaluate the forecasts of the two experiments, Figure 11 examines the hourly composite reflectivity forecast errors relative to the reflectivity observations. The root mean square errors (RMS) of the forecasted reflectivity are calculated for all grid points where the observed reflectivity is greater than 15 dBZ. Compared with the LIN experiment, the forecast skills of the TM experiment within the first 9 h are better, especially during the first 3 h when the root mean squares are significantly lower. The advantage of the TM reflectivity operator gradually disappears, and the forecasting performance becomes comparable to that of the LIN experiment after 10 h.

Figure 12 displays the 12 h intensity and track forecasts initiated at 1200 UTC on 9 August after six DA cycles by the LIN and TM experiments. The Tropical Cyclone Best Track Dataset issued by Shanghai Typhoon Institute of the China Meteorological Administration are utilized for comparison. In terms of intensity, both the LIN and TM experiments underestimate the maximum wind speed within the first 9 h, but the forecast of the TM experiment shows significant improvement compared with that by the LIN experiment (Figure 12a). From the perspective of track forecast, the initial positions and tracks are forecasted to be more westward by both experiments, but the forecast performance on tracks by the TM experiment is slightly better than that by the LIN experiment. As for the reason for the significant DA impact on the TC position, EnKF ensemble background error covariance includes cross correlation between hydrometeors and large-scale variables. Therefore, assimilating radar reflectivity can make obvious adjustments not only for hydrometeors but also for Ps and temperature, which changes the sea level pressure (SLP) field correspondingly. For the positive DA impact on the initial position in the TM experiment, we believe the possible reason is the consistency of MP scheme between model integration and observation operator, resulting in the balance among the analysis variables and SLP obtaining appropriate updates.

Compared with the observations, both TM and LIN experiments overestimate the precipitation intensity in the core region of the typhoon, with the forecasted precipitation location deviating from the observation, and the forecasted range of heavy precipitation in the core region is larger and located further northward (Figure 13). Due to the adjustments on the initial position and track forecast by the TM experiment, the location of heavy precipitation is also adjusted. Under this adjustment, the forecasted precipitation is closer to the observations in terms of intensity and location (Figure 13a,c). For precipitation in the outer rainbands, the TM experiment improves the forecast accuracy over the LIN experiment, resulting in a larger range of heavy precipitation near Taizhou. Additionally, the precipitation south of Hangzhou Bay is well captured, which is more consistent with the observations.

5. Conclusions and Discussion

In previous studies, reflectivity observation operators based on SM MP schemes (such as the Lin scheme) were commonly used, even when the forecasting model employed a DM MP scheme, such as the Thompson scheme used in operational models like the High-Resolution Rapid Refresh [11,12,13]. Since the SM scheme only predicts the mixing ratio of hydrometeors, previous studies have only utilized the reflectivity observation operator to update the mixing ratio, overlooking the number concentration variable predicted by the DM scheme. This study compares the performance of observation operators based on the Thompson DM and LIN SM MP schemes. Regarding the specific case of typhoon Lekima, assimilation and forecasting experiments are conducted by using the Lin operator and the Thompson operator. The results reveal that the EnKF assimilation applying the Lin operator overestimates the mixing ratios of rain, snow, and graupel. Moreover, the number concentration of rainwater can be updated through the ensemble cross-covariance, while its distribution differs slightly from the updates using the Thompson operator. Furthermore, since dual-polarization observations provide additional information about the hydrometeors, (including their PSDs, shape, and phase), they are highly useful in validating convective-scale simulations. Compared with the simulated polarization parameters by the LIN experiment, the dual-polarization features in the analysis fields of the TM experiment are closer to the observations in terms of general shape, location, and intensity. The mismatch issues in the LIN experiment led to worse performance on the forecasting of reflectivity and precipitation in the early stages compared with that by the TM experiment. Moreover, the forecast skills on typhoon intensity and track are also worse.

It is worth noting that, as the first attempt to evaluate the impact of reflectivity operators based on single- and double-moment microphysical schemes on the direct assimilation of radar reflectivity in typhoon numerical forecasts, this study is of great significance in exploring the potential of radar observations in typhoon forecasting. However, the results of this study are based on only one typical case of typhoon Lekima, and it is necessary to conduct more experiments and typhoon case studies to draw more reliable conclusions. Further improvements in assimilation effect can also be achieved by studying observation errors related to radar assimilation, adaptive vertical localization, and other aspects. In addition, assimilating other types of observations, such as surface observations, sounding, and satellite observations, is expected to help improve the larger-scale environment and thereby extend the forecast lead time. Combining all available multi-source observations should be the direction of future assimilation research.