The Impacts of Assimilating Radar Reflectivity for the Analysis and Forecast of “21.7” Henan Extreme Rainstorm Within the Gridpoint Statistical Interpolation–Ensemble Kalman Filter System: Issues with Updating Model State Variables

Abstract

Based on the “21.7” Henan extreme rainstorm case, this study investigates the influence of updating model state variables in the GSI-EnKF (Gridpoint Statistical Interpolation–ensemble Kalman filter) system with the Thompson microphysics scheme. Six sensitivity experiments are conducted to assess the impact of updating different model state variables on the EnKF analysis and subsequent forecast. The experiments include the Z_ALL experiment (updating all variables), the Z_NoEnv experiment (excluding dynamical and thermodynamical variables), the Z_NoNr experiment (excluding rainwater number concentration), and three additional experiments that examine the removal of updating horizontal wind (U, V), vertical wind (W), and perturbation potential temperature (T), which are marked as Z_NoUV, Z_NoW, and Z_NoT. The results indicate that updating different model state variables leads to various effects on dynamical, thermodynamical, and hydrometeor fields. Specifically, excluding the update of vertical wind or perturbation potential temperature has little effect on the rainwater mixing ratio, whereas excluding the update of the rainwater number concentration causes a significant increase in the rainwater mixing ratio, particularly in the northern region of Zhengzhou. Not updating horizontal wind or environmental variables shifts the rainwater mixing ratio northward, deviating from the observed rainfall center. The analysis of near-surface divergence and vertical wind also reveals that not updating certain variables could result in weaker or less detailed wind structures. Although radar reflectivity, which is mainly influenced by the mixing ratios of hydrometeors, shows consistent spatial distribution across experiments, their intensity varies, with the Z_ALL experiment showing the most accurate prediction. The 4 h deterministic forecasts based on the ensemble mean analysis demonstrate that updating all variables provides the best improvement in predicting the “21.7” Henan extreme rainstorm. These results emphasize the importance of updating all relevant model variables for improving predictions of extreme rainstorms.

1. Introduction

Extreme rainfall events, marked by their short duration, high intensity, and strong local variability, pose significant challenges for meteorological and hydrological predictions. The accurate prediction of such events is crucial not only for forecasting but also for issuing timely warnings, especially in countries like China, which is highly vulnerable to the devastating effects of extreme rainfall [1]. So far, numerical weather prediction (NWP) has still shown suboptimal performance in the forecast of extreme rainfall events. The primary reason is the high sensitivity of numerical models to initial conditions [2]. One promising solution is data assimilation (DA), which combines model outputs with real-time observational data to provide a more precise estimate of the atmosphere’s current state [3]. Therefore, the forecast skill of extreme rainfall events can be enhanced with more precise initial conditions for NWP models. Currently, the initial conditions for mesoscale NWP models rely primarily on conventional observational data and large-scale model background fields. However, due to the limited spatiotemporal resolution of these data, it is challenging to effectively capture the occurrence and development of extreme rainfall. In contrast, Doppler weather radars serve as useful tools for storm-scale meteorological sounding. They have high temporal resolution (6 min) and spatial resolution (250 m), making them an essential platform used in DA to improve the prediction of extreme rainfall events [4].

The assimilation of radar reflectivity and radial velocity into NWP models requires specialized observation operators. While the operator for radial velocity is relatively straightforward, involving the spatial transformation of the model’s background wind field [5], reflectivity is more complex due to its association with hydrometeors and the intricate cloud microphysical processes. Assimilating reflectivity data, therefore, remains a challenging task, as it requires aligning the model’s microphysics parameterization with the observed reflectivity [6]. Currently, variational assimilation offers advantages in dynamical consistency, computational efficiency, and flexibility in handling diverse observations, making it particularly effective in the assimilation of radar reflectivity [7,8,9]. Utilizing the variational method for assimilating radar reflectivity includes both direct and indirect methods. In the early stages, Sun and Crook (1997) [10] retrieved rainwater from radar reflectivity based on the Z-q_r (reflectivity–rainwater) relationship under the assumption of the Marshall–Palmer drop size distribution and then used the four-dimensional variational (4DVAR) system to assimilate the retrieved rainwater. Xiao et al. (2005) [11] developed a direct assimilation scheme for radar reflectivity in the Weather Research and Forecasting Model Data Assimilation (WRFDA) system with the model total water mixing ratio used as a control variable in a warm rain model and then computed the simulated reflectivity by using the Z-q_r relation in Sun and Crook (1997) to realize the assimilation of reflectivity data. To effectively assimilate radar reflectivity, microphysical variables for both liquid (water) and frozen (snow, hail, etc.) particles should be considered in the analysis variables. For this purpose, Gao and Stensrud (2012) [12] proposed a direct assimilation scheme for reflectivity that includes both warm rain and ice phase microphysics by adding model variables related to the ice phase microphysical processes as control variables.

The background error covariance in the variational method remains homogeneous and does not adapt to the real-time evolution of the weather system. In contrast, the ensemble Kalman filter (EnKF) eliminates the need for tangent linear and adjoint models of the observation operator, which makes it especially effective for handling nonlinear observation operators [13]. Moreover, the EnKF provides a background error covariance with flow dependency, enabling a better representation of correlations between hydrometeors and large-scale variables [14]. This feature makes the EnKF method particularly promising and advantageous for assimilating radar reflectivity compared to traditional variational methods. Numerous studies have demonstrated the potential of the EnKF method to assimilate radar data [15,16,17,18,19]. Current research on EnKF-based radar reflectivity DA primarily focuses on single-moment microphysics schemes. For example, Dong and Xue (2013) [20] directly assimilated radar reflectivity and effectively improved the forecast skill of precipitation associated with Hurricane Ike. In their study, only hydrometeors and air pressure, instead of other large-scale variables, were updated during the assimilation, and the observation operator for reflectivity was based on a single-moment microphysics scheme, which means that the hydrometeor number concentration was not updated during the assimilation. Numerous studies have suggested that the double-moment microphysical parameterization scheme, which predicts both the mixing ratio and number concentration of hydrometeors, offers greater accuracy in representing microphysics processes compared to single-moment schemes [21]. To fully harness the potential of radar reflectivity, employing a double-moment microphysics scheme for direct EnKF DA is essential. By the selection of the Henan extreme rainstorm case on 20 July 2021 (hereafter referred to as “21.7” Henan extreme rainstorm), sensitivity experiments on the update of hydrometeor variables and other large-scale model variables are performed during the EnKF analysis to investigate their impacts on the analysis and subsequent forecast when radar reflectivity is assimilated.

This study is organized as follows: Section 2 provides an overview of the “21.7” Henan extreme rainstorm case, detailing the observation operator for radar reflectivity, the GSI-EnKF (Gridpoint Statistical Interpolation–ensemble Kalman filter) algorithm, and the experimental design. The impact of the sensitivity experiments on the model state variable updates when assimilating reflectivity data is discussed in Section 3. Section 4 provides conclusions and discussions on this study.

2. Data and Methodologies

2.1. Overview of the “21.7” Henan Extreme Rainstorm

Henan experienced an extremely rare and severe rainstorm on 20 July 2021, with the heaviest precipitation occurring in Zhengzhou. The 850 hPa weather chart of this event at 0000 UTC 20 July is shown in Figure 1a. Two typhoons named “In-Fa” and “Cempaka” coexisted during this event and conveyed plenty of water vapor from the northwest Pacific Ocean to Henan Province [22]. It can be seen in Figure 1b that the Zhengzhou surface automatic meteorological station recorded a 24 h rainfall of 612.9 mm, and the maximum hourly rainfall reached 201.9 mm (from 0800 UTC to 0900 UTC on 20 July), breaking the historical record for the highest hourly rainfall in mainland China. The extreme rainstorm caused severe economic losses and safety threats to the local government and residents, resulting in more than 300 deaths and about CNY 100 billion in direct economic losses [23].

2.2. Observation Operators for Radar Reflectivity

In this study, observation operators for radar reflectivity proposed by Jung et al. (2010) [24] are adopted with a full T-matrix scattering method for the calculation of scattering amplitudes. Look-up tables are established to store the scattering amplitudes of hydrometers with specific diameters. The formulas for the radar horizontal reflectivity factor are presented as follows:

$$Z_{h,x}={\displaystyle \frac{4{\lambda }^4}{{\pi }^4|K_w{|}^2}}{\displaystyle {\int }_0^{D_{\max ,x}}n(D)(A|f_{a,x}(\pi ){|}^2+B|f_{b,x}(\pi ){|}^2+2C|f_{a,x}(\pi )||f_{b,x}(\pi )|)dD}({\mathrm{mm}}^6{\mathrm{m}}^{-3})$$

(1)

where

$$\begin{gathered} A={\displaystyle \frac{1}{8}}(3+4\cos 2\overline{\varphi }{e}^{-2{\sigma }^2}+\cos 4\overline{\varphi }{e}^{-8{\sigma }^2}), \\ B={\displaystyle \frac{1}{8}}(3-4\cos 2\overline{\varphi }{e}^{-2{\sigma }^2}+\cos 4\overline{\varphi }{e}^{-8{\sigma }^2}), \\ C={\displaystyle \frac{1}{8}}(1-\cos 4\overline{\varphi }{e}^{-8{\sigma }^2}). \end{gathered}$$

The subscript x can be hydrometeors, including rain (r), rain–snow mixture (rs), and dry snow (ds). f_a(π) and f_b(π) are back scattering amplitudes along the major and minor axes in complex forms, which vary with diameters. The symbol * represents the conjugate. Re[…] denotes the real part of a complex number, |…| means the absolute value, and <…> represents the ensemble average of canting angles. D is the diameter of a given hydrometeor and D_max is the maximal diameter of each hydrometeor. n(D) is the number concentration of the hydrometeor, which is consistent with the microphysics scheme used in the prognostic model. $\overline{\varphi }$ is the mean canting angle, σ is the standard deviation of the canting angle, λ is the wavelength of the radar, and K_w is the dielectric factor for water, which is set as 0.93.

2.3. The GSI-EnKF Algorithm

The EnSRF (Ensemble Square Root Filter) [25] method is adopted for the assimilation in the GSI-EnKF system. In the EnSRF method, the update equations for the ensemble mean (${\overline{\mathbf{x}}}^{\mathrm{a}}$) and the deviation of each member from the ensemble mean (${\mathbf{x}}^{\prime \mathrm{a}}$) are presented as follows:

$${\overline{\mathbf{x}}}^{\mathrm{a}}={\overline{\mathbf{x}}}^{\mathrm{b}}+\mathbf{K}(\mathbf{y}-\mathbf{H}{\overline{\mathbf{x}}}^{\mathrm{b}})$$

(2)

$${\mathbf{x}}^{\prime a}={\mathbf{x}}^{\prime b}-\tilde{\mathbf{K}}\mathbf{H}{\mathbf{x}}^{\prime b}$$

(3)

$$\tilde{\mathbf{K}}=\alpha \mathbf{K}$$

(4)

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

(5)

where $\mathbf{K}$ is the Kalman gain, which is defined as $\mathbf{K}=\mathbf{B}{\mathbf{H}}^{\mathrm{T}}(\mathbf{H}\mathbf{B}{\mathbf{H}}^{\mathrm{T}}+\mathbf{R}{)}^{-1}$. $\alpha$ is a constant ranging from 0 to 1 for each analysis time. By multiplying $\mathbf{K}$ by $\alpha$, $\tilde{\mathbf{K}}$ is the gain used to update ensemble deviations from the ensemble mean. $\mathbf{B}$ is the background error covariance matrix; $\mathbf{R}$ is the observation error covariance matrix; and $\mathbf{H}$ is the observation operator. The superscript ‘T’ and ‘$-1$’ represent the transposition and the inversion of a matrix, respectively.

To overcome the insufficient spread of the first guess ensemble in the EnKF, the multiplicative inflation is adopted to adjust the spread of the analyses/posterior ensemble back to the backgrounds/prior ensemble [26]. The inflation given at each analysis gridpoint is formulated as follows:

$${\sigma }^b=\sqrt{\sum _{i=1}^n{({\mathbf{x}}_i^{\prime b})}^2/(n-1)}$$

(6)

$${\sigma }^a=\sqrt{{\sum }_{i=1}^n{({\mathbf{x}}_i^{\prime a})}^2/(n-1)}$$

(7)

$$r=(\beta {\displaystyle \frac{{{\sigma }^b-\sigma }^a}{{\sigma }^a}}+1)$$

(8)

$$r{\mathbf{x}}_i^{\prime a}\to {\mathbf{x}}_i^{\prime a}(\mathrm{i}\mathrm{n}\mathrm{f}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{d})$$

(9)

where ${\sigma }^b$ is the standard deviation of the prior ensemble, ${\sigma }^a$ is the standard deviation of the posterior ensemble before the inflation, $r$ is the inflation factor that each ensemble member deviates from the ensemble mean, and $\beta$ is the inflation parameter that is tunable. In this study, $\beta$ is set as 0.99.

2.4. Experimental Design

Figure 2 shows the domain of the WRF model. The domain is centered over Henan Province, consisting of 800 × 700 grids in the latitudinal and longitudinal directions, respectively. To better depict the structure of the heavy rainfall in the model, the horizontal grid distance is set to 3 km. There are 51 layers in the vertical direction from the surface to 50 hPa. The physical schemes employed in the experiments include the Thompson microphysics scheme [27], the YSU (Yonsei University) boundary layer scheme [28], the RRTM (Rapid Radiative Transfer Model) longwave radiation scheme [29], and the Dudhia shortwave radiation scheme [30]. No cumulus scheme was used because the horizontal grid distance satisfies convective-allowing resolution.

Figure 3 illustrates the detailed experimental flow chart. The initial and lateral conditions used for the deterministic forecast in the WRF model are derived from the 0.25° × 0.25° ERA5 (ECMWF Reanalysis v5) data. To generate the initial ensemble perturbations for the EnKF analysis, the mean of the 0.5°*0.5° GEFS (Global Ensemble Forecast System) ensemble members is subtracted from each individual member, and the resulting perturbations are then added to the deterministic forecast, creating 30 ensemble members. Initially, a 13 h ensemble forecast is conducted from 1800 UTC 19 July to 0700 UTC 20 July. Subsequently, EnKF analysis is performed every 6 min by assimilating reflectivity from the Zhengzhou radar for the following one hour. The Zhengzhou radar operates on the S-band with a wavelength of about 10 cm. It has 9 elevation angles: 0.5°, 1.5°, 2.4°, 3.4°, 4.3°, 6.0°, 9.9°, 14.6°, and 19.5°. A full-volume scan takes roughly 6 min to complete. The radar beam has a horizontal and vertical width of approximately 0.9°, and the range gate spacing is set at 250 m. The coverage of the Zhengzhou radar used in the EnKF analysis is shown in Figure 2. The following steps are included for the quality control of the radar observations: performing the hydrometeor classification [31] to identify and remove non-meteorological echoes; discarding echoes with a signal-to-noise ratio of less than 10 dB [32]; and applying the median filter to smooth the observations [33]. After quality control, filtered radar observations are interpolated to the ‘tilt’ form with bilinear interpolation [16]. When using the Thompson microphysics scheme, the model variables, which can be updated by the EnKF analysis, include the three-dimensional wind components (U, V, and W), perturbation geopotential (P_H), perturbation potential temperature (T), water vapor mixing ratio (q_v), mixing ratios of cloud water (q_c), rainwater (q_r), ice (q_i), snow (q_s), and graupel (q_g), and the number concentrations of ice (N_i) and rainwater (N_r). Some parameters in the GSI-EnKF system are set as follows: the horizontal covariance localization is set to 18 km, the vertical covariance localization is set to 0.7 lnP [34], and the observation error of Z is set to 5 dBZ [35]. Finally, the ensemble mean of the final analysis fields is used for the 4 h deterministic forecast from 0800 UTC to 1200 UTC 20 July.

As shown in

Table 1. Updated variables of all experiments.

Name of Experiments	Updated Model Variables
Z_ALL	U, V, W, T, PH, qv, qc, qi, qr, qs, qg, Ni, Nr
Z_NoEnv	PH, qv, qc, qi, qr, qs, qg, Ni, Nr
Z_NoNr	U, V, W, T, PH, qv, qc, qi, qr, qs, qg, Ni
Z_NoUV	W, T, PH, qv, qc, qi, qr, qs, qg, Ni, Nr
Z_NoW	U, V, T, PH, qv, qc, qi, qr, qs, qg, Ni, Nr
Z_NoT	U, V, W, PH, qv, qc, qi, qr, qs, qg, Ni, Nr

, six experiments are designed to investigate the impacts of updating different model state variables in the GSI-EnKF system on the analysis and prediction of the “21.7” Henan extreme rainstorm when assimilating radar reflectivity data. The Z_ALL experiment, which updates all model variables, is used as a benchmark. The other five experiments partially remove the updates of certain model state variables to examine the impacts of these removals on the analysis and prediction of the heavy rainfall when assimilating reflectivity in the GSI-EnKF system. The update of the dynamic and thermodynamic environmental variables (U, V, W, T) is dismissed in the Z_NoEnv experiment to investigate the impacts of merely updating hydrometeor variables. Considering the double-moment characteristic of the Thompson microphysics scheme, the update of the number concentration of rainwater (N_r) is not included in the Z_NoNr experiment to test the impacts of updating only the hydrometeor mixing ratio variable. For the four environmental variables, three additional experiments are set up to examine the impacts of removing the updates of horizontal winds (U, V), vertical wind (W), and perturbation potential temperature (T) on the EnKF analysis and subsequent forecast, respectively. These experiments are denoted as Z_NoUV, Z_NoW, and Z_NoT.

3. Results

Figure 4 shows the accumulated q_r at all model levels from the analysis at 0800 UTC on 20 July 2021. Since radar reflectivity reflects information on both the number concentration and mixing ratio of hydrometeors, all experiments show a maximum accumulated q_r at the center of Zhengzhou City, with values exceeding 100 g/kg, though their distribution patterns are different. In the Z_ALL experiment (Figure 4a), the maximum accumulated q_r is 100.2 g/kg when all variables are updated. In the Z_NoNr experiment (Figure 4b), because radar reflectivity directly reflects information on both the number concentration and mixing ratio of hydrometeors, when N_r is not updated, the maximum accumulated q_r reaches 117 g/kg after assimilating radar reflectivity, causing an excessive increase in q_r, which leads to some forecast biases of precipitation, as discussed later. In the Z_NoEnv experiment (Figure 4c), when the dynamic and thermodynamic environmental variables are not updated, the accumulated q_r is slightly higher than that in the Z_ALL experiment, with a maximum value of 106.9 g/kg, which causes some inconsistency in dynamic or thermal aspects. Specifically, in the Z_NoUV experiment (Figure 4d), the distribution pattern of accumulated q_r is similar to that in the Z_NoEnv experiment, whereas in the Z_NoW experiment (Figure 4e) and the Z_NoT experiment (Figure 4f), the distribution pattern of accumulated q_r is similar to that in the Z_ALL experiment. Therefore, the update of the horizontal wind field has a greater impact on the q_r analysis among the updates of all the dynamic and thermodynamic variables.

Figure 5 shows the q_r profiles along the black dashed line in Figure 4a which traverses the maximum precipitation observed by the surface automatic weather station from 0800 UTC to 0900 UTC on 20 July 2021 (Zhengzhou National Station, 34.71°N, 113.66°E). In the Z_ALL experiment (Figure 5a), the area where q_r exceeds 5.5 g/kg spans from 34.7°N to 34.8°N. In the Z_NoNr experiment (Figure 5b), the area where q_r exceeds 5.5 g/kg spans from 34.68°N to 34.83°N, with a significant increase of q_r to the north of the Zhengzhou National Station, indicating a northward extension trend of precipitation. In the Z_NoEnv experiment (Figure 5c), the area where q_r exceeds 5.5 g/kg spans from 34.71°N to 34.84°N, with the Zhengzhou National Station almost at the southern edge of the high-q_r area, indicating an overall northward bias in precipitation, which can be verified by the subsequent precipitation forecast results. For the Z_NoUV experiment (Figure 5d), its q_r profile is similar to that of the Z_NoEnv experiment. The q_r profiles in the Z_NoW experiment (Figure 5e) and the Z_NoT experiment (Figure 5f) are similar to that in the Z_ALL experiment. It is noteworthy that in the Z_NoEnv and Z_NoT experiments, since the perturbation potential temperature variable is not updated, the height fluctuation of the 0 °C isotherm is negligible along the section line.

Figure 6 shows the observed precipitation from 0800 UTC to 0900 UTC on 20 July 2021 and the divergence at 10 m surface height of all experiments from the analysis at 0800 UTC. The solid black dot in the figure marks the location of the Zhengzhou National Station. According to the observations (Figure 6a), there are high precipitation centers in the center and southwest of Zhengzhou City, with the 1 h accumulated precipitation exceeding 50 mm in central Zhengzhou and over 25 mm in southwest Zhengzhou. In the Z_ALL experiment (Figure 6b), the area around the Zhengzhou National Station shows negative divergence, indicating low-level convergence in this area. Due to the continuity of atmospheric mass, the Zhengzhou National Station is in a region of positive divergence, but the values are not large, indicating weak divergence. In the Z_NoNr experiment (Figure 6c), the Zhengzhou National Station is also surrounded by a region of negative divergence, but the positive divergence region to the west is significantly stronger than in the Z_ALL experiment, weakening the intensity of the heavy rainfall center. In the Z_NoEnv experiment (Figure 6d) and the Z_NoUV experiment (Figure 6e), although the area to the west of the Zhengzhou National Station shows negative divergence, the divergence is flawed due to the lack of detailed description of the horizontal wind, as the horizontal wind variables are not updated. Among all dynamic and thermodynamic variables, updating vertical wind and perturbation potential temperature has little impact on the near-surface divergence. The distribution of divergence in the Z_NoW experiment (Figure 6f) and the Z_NoT experiment (Figure 6g) is similar to that in the Z_ALL experiment. For all experiments, the divergence located to the southwest of Zhengzhou City is negative. However, in the experiments where horizontal wind variables are not updated (i.e., the Z_NoEnv experiment and the Z_NoUV experiment), the divergence values in this region are significantly smaller than those in the other experiments.

Figure 7 shows the profiles of reflectivity and the vertical wind vector from the 0800 UTC analysis on 20 July 2021. The section line is along the black dashed line in Figure 4a. In the Z_ALL experiment (Figure 7a), the maximum vertical wind speed appears above the region where reflectivity exceeds 55 dBZ. The thickness of the region with reflectivity greater than 55 dBZ is higher on the southern side compared to the northern side. In the Z_NoNr experiment (Figure 7b), due to the lack of N_r updates, the assimilation of radar reflectivity results in an excessive increase in q_r, raising the thickness of the region with reflectivity exceeding 55 dBZ on the northern side to above 2 km. In addition, the thickness of the echo’s southern side increases, as well as the vertical wind speed. In the Z_NoEnv experiment (Figure 7c), due to the absence of updates of environmental variables, the wind vectors above the echo center are relatively uniform and consistent, failing to reflect the detailed structure of the heavy rainfall system. In the Z_NoUV experiment (Figure 7d) and the Z_NoW experiment (Figure 7e), due to the lack of updates of the complete three-dimensional wind vector variables, the vertical wind speed is significantly greater than that in the Z_ALL experiment when horizontal wind speed variables are not updated, and significantly less than that in the Z_ALL experiment when vertical wind speed variables are not updated. Such a vertical wind field for the heavy rainfall system is unreasonable. In the Z_NoT experiment (Figure 7f), the lack of updates of perturbation potential temperature has a minimal impact on wind vectors and reflectivity, with the profile structure remaining basically consistent with that in the Z_ALL experiment.

Figure 8 shows the profiles of pseudo-equivalent potential temperature and temperature from the 0800 UTC analysis on 20 July 2021, along the black dashed line in Figure 4a. In the Z_ALL experiment (Figure 8a), when all variables are updated, the center of the pseudo-equivalent potential temperature is located at approximately 2 km height. From 2 km to 4 km height, the pseudo-equivalent potential temperature decreases with height, indicating convective instability near the heavy rainfall center, which provides dynamic lifting conditions for the initiation of heavy rain. Additionally, the 15 °C and 20 °C temperature contour lines protrude upward in this area, indicating a warm center associated with heavy rain. In the Z_NoNr experiment (Figure 8b), the area with a pseudo-equivalent potential temperature greater than 360 K is significantly smaller than that in the Z_ALL experiment, indicating that the thermodynamic or moisture conditions in the analysis are less favorable when N_r is not updated. In the Z_NoEnv experiment (Figure 8c), the lack of updates of environmental variables result in the disappearance of the pseudo-equivalent potential temperature center, and the temperature contour lines become flatter, indicating an unreasonable thermodynamic and moisture structure in the analysis. In the Z_NoUV experiment (Figure 8d), the pseudo-equivalent potential temperature center also disappears due to the lack of updates to the horizontal wind field, although the temperature contour lines still exhibit an upward protrusion. In the Z_NoW experiment (Figure 8e), the profile structure is basically consistent with the Z_ALL experiment, indicating that updating the vertical wind variables has little impact on the analysis of pseudo-equivalent potential temperature and temperature. In the Z_NoT experiment (Figure 8f), although the pseudo-equivalent potential temperature center exists and the temperature contour lines exhibit an upward protrusion, both centers are slightly northward, deviating from the area above the heavy rainfall center from 0800 UTC to 0900 UTC, and the structure is more regular, failing to reflect the subtle differences in spatial distribution.

Figure 9 shows the comparison of the composite reflectivity from the analysis of all experiments against observations at 0800 UTC on 20 July 2021. According to the observations (Figure 9a), the maximum composite reflectivity in central Zhengzhou is 55.5 dBZ. For all experiments, the spatial distribution of composite reflectivity is relatively consistent, with the main difference being the intensity of the maximum composite reflectivity in central Zhengzhou. As the figure shows, updating vertical wind and perturbation potential temperature has little impact on the composite reflectivity. The maximum composite reflectivity in the analysis of the Z_ALL (Figure 9b), Z_NoW (Figure 9f), and Z_NoT (Figure 9g) experiments is 60.5 dBZ. In the Z_NoNr experiment (Figure 9c), the lack of N_r updates results in an excessive increase in q_r, leading to a maximum composite reflectivity of 60.8 dBZ in the analysis. In the Z_NoEnv (Figure 9d) and Z_NoUV (Figure 9e) experiments, the lack of updates of horizontal wind results in the weakest echo intensity in central Zhengzhou among these experiments, with a maximum composite reflectivity of 60.0 dBZ.

Figure 10 shows the comparison of the composite reflectivity from the forecast of all experiments against observations at 0900 UTC on 20 July 2021. According to the observations (Figure 10a), the maximum composite reflectivity in central Zhengzhou is 54.9 dBZ, slightly weaker than that at 0800 UTC, with the echo structure becoming slightly more scattered. In all experiments, the echo intensity in central Zhengzhou is weaker than that in the 0800 UTC analysis, and the area with echo intensity exceeding 45 dBZ significantly decreases, with the echo structure becoming gradually more scattered. Similarly to the characteristics of the 0800 UTC analysis, the spatial distribution patterns of the 0900 UTC composite reflectivity forecast fields can be divided into three categories. The Z_ALL (Figure 10b), Z_NoW (Figure 10f), and Z_NoT (Figure 10g) experiments fall into one category, each with a maximum composite reflectivity of 55.7 dBZ. The Z_NoEnv (Figure 10d) and Z_NoUV (Figure 10e) experiments form another category, each with a maximum composite reflectivity of 54.4 dBZ. The Z_NoNr experiment (Figure 10c) stands alone in the third category, with a maximum composite reflectivity of 56.5 dBZ. In summary, updating the N_r variable can help weaken overestimated echoes by more accurately adjusting q_r, while updating the horizontal wind variables among all the environmental variables enhances the echo intensity.

Figure 11 shows the 4 h accumulated precipitation from 0800 UTC to 1200 UTC on 20 July 2021. The dashed box represents the location of Zhengzhou, and the blue solid line is the reference line for comparing precipitation areas. According to the observations (Figure 11a), the center of the accumulated precipitation is in Zhengzhou, which is located to the east of the reference line. Since only radar reflectivity is assimilated, lacking constraints from other observations, the precipitation centers in all experiments are located on or slightly to the east of the reference line, showing some deviation from the observations. The distribution of accumulated precipitation is closely related to q_r and is influenced by the vertical distribution of q_r. In the Z_ALL experiment (Figure 11b), precipitation exceeding 100 mm is mostly located to the north of Zhengzhou, with an area in central Zhengzhou where precipitation exceeds 75 mm. In the Z_NoNr experiment (Figure 11c), the lack of N_r updates results in an imbalance or excessive q_r increment before and after the analysis, leading to the disappearance of the area with precipitation exceeding 75 mm in central Zhengzhou and the appearance of an incorrect forecast area exceeding 75 mm to the west of the reference line, around 113°E. In the experiments related to environmental variable updates, the Z_NoEnv (Figure 11d) and Z_NoUV (Figure 11e) experiments show that the precipitation center significantly shifts north to around 35°N. The Z_NoW (Figure 11f) and Z_NoT (Figure 11g) experiments have a precipitation distribution similar to the Z_ALL experiment, indicating that updating horizontal wind variables provides a more accurate horizontal dynamical field. This significantly affects the location and intensity of the low-pressure center associated with the precipitation system, thereby influencing the forecast of the rainband distribution.

4. Conclusions and Discussion

Based on the GSI-EnKF assimilation system, this study selects the “21.7” Henan extreme rainstorm case to conduct sensitivity experiments on the model state variable updates, focusing on the Thompson double-moment microphysics scheme. The experiments investigate the impact of updating model state variables on EnKF analysis and subsequent forecasts from the perspectives of dynamics, thermodynamics, and hydrometeor components. A total of six experiments are set up: the Z_ALL experiment, which updates all variables as a baseline; the Z_NoEnv experiment, which does not update dynamical and thermodynamical environmental variables (U, V, W, T); and the Z_NoNr experiment, which does not update the rainwater number concentration (N_r). Additionally, three experiments are conducted to examine the effects of removing updates of horizontal wind (U, V), vertical wind (W), and perturbation potential temperature (T) variables on the EnKF analysis and subsequent forecast, labeled as the Z_NoUV, Z_NoW, and Z_NoT experiments.

In the EnKF analysis, using different updated variables has different effects on the analysis of dynamical, thermodynamical, and hydrometeor fields. For the rainwater mixing ratio, not updating the vertical wind or perturbation potential temperature variables has minimal impact on the analysis, with the field structure remaining similar to when all the variables are updated. However, not updating the number concentration variable causes a significant increase in q_r in the north of Zhengzhou, resulting in larger q_r increments. Not updating horizontal wind variables or dynamical and thermodynamical environmental variables shifts q_r generally northward, with areas exceeding 5.5 g/kg deviating from the heavy rainfall center observed at the Zhengzhou National Station. Regarding near-surface divergence, not updating vertical wind or perturbation potential temperature variables has little impact, showing strong convergence around the observed rainfall center and a divergence field consistent with the update of all variables. Not updating the number concentration variable leads to strong divergence to the west of the heavy rainfall center, weakening rainfall intensity. Not updating horizontal wind variables or dynamical and thermodynamical environmental variables results in weaker convergence at the rainfall center, with divergence values less than 6 × 10⁻⁵ s⁻¹, lacking detailed descriptions of the horizontal dynamical field. For vertical wind, not updating perturbation potential temperature variables produces a vertical wind field structure similar to when all variables are updated, while not updating the number concentration variable shows slightly stronger updrafts at the rainfall center. Not updating dynamical and thermodynamical environment variables results in uniform and consistent wind vectors above the rainfall center, failing to reflect the detailed vertical wind structure of the rainstorm system. When the update of three-dimensional wind is incomplete, the analyzed vertical wind is also unreasonable. Specifically, not updating horizontal wind variables results in excessively high vertical wind speeds, while not updating vertical wind variables results in excessively low vertical wind speeds. For pseudo-equivalent potential temperature and temperature, the profile structure is consistent between not updating vertical wind variables and updating all variables, with the warm center corresponding to the rainfall center and a shallow convective instability region above the rainstorm center, where ${\displaystyle \frac{\partial {\theta }_{se}}{\partial z}}<0$. Not updating the number concentration variable slightly weakens the pseudo-equivalent potential temperature at the rainfall center, indicating deteriorated thermodynamic or moisture conditions in the analysis. Not updating horizontal wind variables or dynamical and thermodynamical environmental variables results in the disappearance of the pseudo-equivalent potential temperature center and a flattening of temperature contour lines due to the lack of horizontal momentum updates, leading to the disappearance of the warm center associated with the rainstorm. Not updating perturbation potential temperature variables displaces the pseudo-equivalent potential temperature center and warm center northward, away from the rainfall center, which fails to reflect subtle spatial distribution differences. In summary, the update of all model variables in the EnKF analysis can result in reasonable analyses of the dynamical, thermodynamical, and hydrometeor fields.

Although updating different model variables in the EnKF analysis significantly impacts the analysis of divergence, vertical wind, pseudo-equivalent potential temperature, and temperature, radar reflectivity only contains information on hydrometeor mixing ratios and number concentrations, which have little relation with each other in double-moment microphysics. Since the mixing ratios of all hydrometeors are updated in all sensitivity experiments, the spatial distribution of composite reflectivity is fairly consistent across both the analysis and forecast, with only slight differences in echo intensity in central Zhengzhou. Specifically, the Z_ALL, Z_NoW, and Z_NoT experiments show consistent maximum composite reflectivity with moderate intensity. The Z_NoEnv and Z_NoUV experiments have consistent maximum composite reflectivity but with slightly weaker intensity. The Z_NoNr experiment has the highest maximum composite reflectivity. The 4 h deterministic forecasts based on the ensemble mean analysis also exhibit similar characteristics. The rainband distribution is generally consistent among the Z_ALL, Z_NoW, and Z_NoT experiments. The Z_NoEnv and Z_NoUV experiments show that the precipitation center significantly shifts northward. In the Z_NoNr experiment, the area with precipitation exceeding 75 mm in Zhengzhou’s central region almost disappears, and there is an erroneous forecast of precipitation exceeding 75 mm at around 113°E. When all variables are updated, the maximum composite reflectivity in the analysis and forecast after assimilating radar reflectivity is higher than the observations. In addition, the analysis for dynamical, thermodynamical, and hydrometeor fields is the most reasonable, indicating that the experiment with all variables updated provides the best improvement for predicting the “21.7” Henan extreme rainstorm.

Despite the assimilation of radar reflectivity data yielding positive results when all model variables are updated, this study only focuses on an extreme rainfall case. Thus, whether updating all model variables has the same results in different synoptic systems, such as typhoons and squall lines, needs to be further investigated. Additionally, the radar operator used in this study can simulate polarimetric measurements, including differential reflectivity (Z_DR) and specific differential phase (K_DP), which contains microphysical information on the hydrometeors and their particle size distributions. We plan to address the assimilation of these polarimetric observations and their impacts on the EnKF analysis and subsequent forecast in our future study.