Implementing an Indirect Radar Assimilation Scheme with a 1D Bayesian Retrieval in the Numerical Prediction Model

Highlights

What are the main findings?

• The use of a 1D Bayesian method to retrieve and constrain water vapor from radar reflectivity for assimilation improves the balance between observations and the background field.
• The optimized assimilation scheme effectively corrects systematic positive biases in water vapor, reducing overforecasting, particularly within the first 6 h.

What is the implication of the main finding?

• The study provides a robust method for radar reflectivity data assimilation, offering a significant advancement in short-term precipitation forecasting.
• This approach to assimilation could serve as a model for other forecasting systems looking to integrate radar data effectively, potentially improving their predictive capabilities.

Abstract

To enhance the operational efficiency of the CMA-BJ3.0 regional numerical model and address the issue of short-term precipitation overforecasting caused by assimilating estimated saturated water vapor, this study investigates the assimilation of radar reflectivity mosaic data by optimizing the configuration of retrieved water vapor in the indirect assimilation scheme. A 1D (one-dimensional) Bayesian method was employed to retrieve and constrain water vapor from reflectivity observations, generating retrieved water vapor for assimilation to mitigate overforecasting biases. A case study of precipitation on 1 August 2022 was analyzed, with particular focus on comparing the innovation vector statistics, spatial patterns of analysis increments, and physical mechanisms underlying forecast differences across multiple data assimilation configurations. Results showed that an observation-background (O-B) statistical distribution closer to a Gaussian unbiased state indicated a better balance between observations and the background field. The optimized scheme corrected systematic positive biases in water vapor, curbed excessive increments, and effectively resolved the overforecasting issue by refining the initial water vapor field. Batch experiments quantitatively demonstrated that assimilating 1D Bayesian-retrieved water vapor significantly improved precipitation forecast scores, particularly for higher magnitudes (≥25.0 mm/3 h), and reduced the over-forecast within the first 6 h. While the study focused on improving short-term precipitation accuracy without considering hydrometeor impacts or convective dynamics, the 1D Bayesian method, despite its background-dependency, proved effective in correcting water vapor biases, making it a promising assimilation scheme.

1. Introduction

Data assimilation is a critical process in numerical weather prediction, integrating a diverse range of observational data to enhance the accuracy of forecast models [1,2]. Doppler weather radar data assimilation is particularly crucial for bolstering the precision of regional high-resolution numerical weather forecasts [3]. Extensive research has been conducted over the past decades, focusing on the initialization of convective-scale numerical weather forecast models with radar data. The methodologies employed include physical initialization techniques [4], which leverage the relationship between radar reflectivity and precipitation to adjust model profiles, and complex cloud analysis methods that utilize radar reflectivity to infer cloud water content and vertical motion [5]. Additionally, 3D/4D variational assimilation methods have been widely adopted to optimize model states by minimizing the difference between model predictions and observational data over a given time window [6,7,8]. Ensemble Kalman filters have also been utilized to assimilate data by updating model states based on the departure from observations, providing a sample of analysis uncertainties [9,10,11]. Moreover, hybrid data assimilation methods, which combine variational and ensemble techniques, have logically emerged to capitalize on the strengths of both approaches [8,12,13,14].

The assimilation of weather radar data in convective-scale numerical prediction models has been shown to be beneficial for the analysis and short-term (6 h) forecasting of severe convective weather events. The reflectivity, which signals the water content in clouds, is a vital source of observational data for high-resolution variational assimilation systems. However, direct assimilation of radar reflectivity has its limitations, including the exclusion of ice-phase processes and sensitivity to the humidity of the background field, which can introduce significant errors when the background field is too dry [15].

To mitigate these limitations, a retrieval algorithm has been employed to derive hydrometeor profiles (including rain, dry snow, wet snow, and ice water) from radar reflectivity measurements prior to data assimilation. Alternatively, water vapor fields have been estimated through reflectivity-derived parameters before assimilation. This methodology effectively circumvents errors inherent in the linear observation operator [15,16]. This has been shown to improve precipitation forecasts, with the effect of estimating water vapor on the forecast accuracy being more pronounced. However, such an approach primarily updates phase-related variables of hydrometeors and has limited impact on perturbations of water vapor and potential temperature, which are crucial for convective system development. This can result in less effective forecasts in many situations. Thus, improving the means of retrieving water vapor from radar reflectivity and the assimilation strategies within rapid update cycling systems is of significant practical importance.

There is a scarcity of research on water vapor retrieval assimilation based on radar reflectivity. Among the work that has been conducted, Caumont et al. (2010) and Wattrelot et al. (2013) implemented a 1D Bayesian+3DVAR radar reflectivity assimilation method in the mesoscale model developed by the Météo-France [17,18]. Using radar reflectivity observations, the relative humidity profile was obtained based on Bayesian theory as a “retrieved observation”. The 3DVAR assimilation and retrieved relative humidity were studied in a numerical model at the cloud-resolving scale, and the results showed that assimilating “retrieved water vapor” observations can significantly improve short-term precipitation forecasts. Zhang et al. (2014) developed a 1DVAR (one-dimensional variational) assimilation system to retrieve the precipitation rate from radar reflectivity observations [19]. In their approach, a linearized large-scale condensation scheme and a simplified convection parameterization scheme were employed as the precipitation observation operator. The retrieved water vapor profiles were subsequently assimilated into the GRAPES (Global and Regional Assimilation and Prediction System) model using 3DVAR (three-dimensional variational) initialization. This methodology significantly enhanced the accuracy of precipitation forecasts [19]. Building on the method of identifying convective regions through radar-based vertically integrated liquid water content, Lai et al. (2019) further retrieved water vapor from the background field, operating on the premise that these deep convective columns are saturated [20]. For two tornado weather processes, the assimilation of radar radial wind, radar reflectivity, and retrieved water vapor observation data was carried out based on the 3DVAR method. The results showed that the convective system path after assimilating retrieved water vapor has a better correspondence with the tornado occurrence location, and the equitable threat score of the reflectivity factor forecast within 0–3 h is improved. Wang et al. (2013.a) designed a scheme to estimate cloud water vapor and cloud water using radar reflectivity based on the WRF (Weather Research and Forecasting model) assimilation system (WRFDA), and assimilated the retrieved observations into the WRF model [15]. Subsequent studies have further demonstrated the value of assimilating radar observations for improving numerical weather prediction. Specifically, Chen et al. (2024) successfully assimilated differential reflectivity (ZDR) column-retrieved water vapor using a 3DVar method, which effectively enhanced the short-term forecast skill of convective storms [21]. In a related approach, Liu et al. (2021) assimilated the retrieved water vapor into a dual-resolution hybrid 3DEnVAR system by combining radar data and lightning data, leading to significant improvements in the prediction of a high-impact convective event [22]. The results showed that the assimilated retrieved water vapor makes a significant positive contribution to the short-term forecasting of the precipitation generated by severe convective events in summer.

Within the China Meteorological Administration Beijing Short-term numerical assimilation and prediction system (CMA-BJ3.0), radar reflectivity is assimilated via an indirect variational framework that hydrometeor and water vapor fields are retrieved from reflectivity data and subsequently assimilated. However, a significant drawback of this retrieval method is its inherent assumption that all observations exceeding 30 dBZ indicate saturated atmospheric conditions (RH = 100%) [15], resulting in the assimilation of only saturated water vapor data. Additionally, the exclusive use of positively biased water vapor innovation frequently contributes to overforecasting of short-term precipitation. In the operational mode of rapid successive assimilation cycles, the impact on the atmospheric thermal profile becomes further pronounced. Consequently, the predictive capability of precipitation exhibits a marked decline after multiple cycles.

In order to address the shortcomings of saturated water vapor assimilation in the current operation of CMA-BJ3.0, and with the purpose of incorporating more retrieved water vapor pseudo-observations to improve the quality of the initial water vapor field, this study used a 1D Bayesian approach to retrieve water vapor from reflectivity based on a version of the preliminary study by Caumont et al. (2010) [17] and constrained the approach in the assimilation operation to verify its improvement over the operational retrieved water vapor assimilation scheme. Following this introduction, Section 2 provides a description of the radar products used for assimilation purposes, as well as the configuration of the assimilation and forecast models. The 1D Bayesian approach is also presented in detail, including a description of the reflectivity observation operator and the 1D approach, and the necessary screening decisions that were made for it. Section 3 examines the assimilation experimental results, mainly to study the impact on the analysis and to assess the forecasting of precipitation on the basis of evaluation metrics/scores. Finally, Section 4 summarizes and discusses the results, emphasizing the advantages and disadvantages of this assimilation approach.

2. Data and Methods

2.1. Models and Data

The short-term, rapid-refresh, multi-scale analysis and prediction system (CMA-BJ3.0) was employed in this study. The forecasting and data assimilation modules of this system are based on version 4.1.2 of the WRF and WRFDA model, with further in-depth development.

CMA-BJ3.0 utilizes a single-domain grid with a resolution of 3 km, encompassing a total of 1945 × 1498 grid points. The specific model domain is shown in Figure 1. In the vertical dimension, the model consists of 61 layers, with the model’s top-level set at 10 hPa. The system is driven by the global forecast of the European Centre for Medium-Range Weather Forecasts (ECMWF) as the lateral boundary condition. The data assimilation process employs the U/V control variable and multi-scale three-dimensional variational data assimilation techniques [23].

The radar reflectivity data employed in this study were synthesized from reflectivity observations derived from 135 radars (shown in Figure 2), processed by the IUMRADAR reflectivity mosaic system. The horizontal span of the radar reflectivity mosaic data extends from 12.2°N to 54.2°N in latitude and from 73.0°E to 135°E in longitude. The radar reflectivity mosaic data are vertically stratified into 30 layers, with a horizontal resolution of 0.5 km at altitudes between 1 and 8 km, and 1 km at altitudes between 9 and 16 km.

2.2. Assimilation Method

The 3DVAR assimilation system of CMA-BJ3.0 generates an analysis $x_a$ by minimizing the 3DVAR cost function $J(x)$ [24] as follows:

$$\begin{array}{lll}J(x)& =& J_b+J_o\\ & =& {\displaystyle \frac{1}{2}}{(x-x_b)}^T{B}^{-1}(x-x_b)+{\displaystyle \frac{1}{2}}{(H(x)-y_o)}^T{R}^{-1}(H(x)-y_o)\end{array}$$

(1)

where $J_b$ and $J_o$ are the background term and observation term, respectively; $x_b$ is the first estimate from a previous forecast (background); $y_o$ is the observation vector; $H$ is a nonlinear observation operator that relates the model space to the observation space; $B$ is the background error covariance matrix; and $R$ is the observational error covariance, which is a diagonal matrix.

In the CMA-BJ3.0 operational variational assimilation system, an indirect assimilation method for radar reflectivity is implemented. This approach involves augmenting the control variables with hydrometeor variables, which encompass rain ($q_r$), snow ($q_s$), and hail ($q_h$), and designing an observation operator for radar reflectivity that classifies hydrometeors based on the background field temperature [16].

The empirical relationships between the radar equivalent reflectivity factor ($Z_e$) and the equivalent water contents for rain ($q_r$), snow ($q_s$), and hail ($q_h$) are as follows [25,26]:

$$\begin{array}{l}{Z}_e\left(q_r\right)=3.63\times {10}^9{\left(\rho q_r\right)}^{1.75}\hspace{1em}\\ Z_e\left(q_s\right)=9.80\times {10}^8{\left(\rho q_s\right)}^{1.75}\\ Z_e\left(q_h\right)=4.33\times {10}^{10}{\left(\rho q_h\right)}^{1.75}\end{array}$$

(2)

where ρ is the air density. The relationships between reflectivity and equivalent reflectivity factor are: $Z=10{\log }_{10}{Z}_e$.

Reflectivity is directly determined by the hydrometeors. However, the initialization of these hydrometeor species is not anticipated to have a significant impact on short-range forecasts due to their limited role in convection and their inherent unpredictability [27], since adjusting the humidity variable is considered more effective. Within the CMA-BJ3.0 assimilation system, the assimilation of water vapor estimated from reflectivity is also used as another indirect assimilation method. This assimilation technique is activated when the radar reflectivity exceeds a certain threshold (set at 30 dBZ), indicating a saturation condition with a relative humidity of 100%. The corresponding saturation water vapor value is then calculated and assimilated as a retrieved observation, based on the background field temperature and pressure.

However, the selective assimilation of exclusively saturated water vapor produces innovation vectors that violate the unbiased Gaussian distribution assumption (Figure 3), resulting in excessive water vapor analysis increments and false alarms in short-term heavy rainfall forecasts.

2.3. Bayesian Retrieval of Water Vapor

A 1D Bayesian retrieval method has been developed to estimate relative humidity profiles from radar reflectivity data prior to the 3DVAR assimilation. This Bayesian approach enables the retrieval of the most likely vertical profiles of relative humidity based on observed reflectivity profiles and a database of consistent reflectivity vertical profiles, utilizing the model state near the observation site [17].

The methodology described in detail [17] is summarized hereafter. Let the vector x represent a model vertical profile to retrieve, x_true denotes the true state vector, and the vector y_o represents a set of available observations. The best estimate of x given the set of observations y_o is (see, e.g., Lorenc, 1986) [28]:

$$E(x)=\int xP\left(x=x_{true}\mid y=y_o\right)\mathrm{d}x$$

(3)

Using Bayes’ theorem, it can be rewritten as

$$E(x)=\int xP(y=y_{\mathrm{o}}\mid x=x_{true})P(x=x_{true}) dx$$

(4)

A first approximation replaces the integral expression with a finite, discretized sum. If we assume that the errors of the observations y_o and of the simulated observations y are Gaussian and uncorrelated, we have

$$\begin{array}{l}P(y=y_{\mathrm{o}}\mid x=x_{true})\\ \propto exp\{-{\displaystyle \frac{1}{2}}{[y_{\mathrm{o}}-h(x)]}^T{(O+S)}^{-1}[y_{\mathrm{o}}-h(x)]\}\end{array}$$

(5)

where O and S are the observation and simulation error covariance matrices, respectively, and h is the observation operator that simulates observations from the model. Equation (4) can be simplified as

$$E(x)={\displaystyle \sum _i{x}_i}{\displaystyle \frac{W_i}{{\displaystyle \sum _j{W}_j}}}$$

(6)

with $W_i\equiv exp\{-{\displaystyle \frac{1}{2}}{[y_o-h(x_i)]}^T{R}^{-1}[y_o-h(x_i)]\}$ where $x_i$ is a profile taken from the model background files.

For each observed column of reflectivity ($y_Z$), a column of retrieved qv observations ${\mathit{y}}_{\mathrm{po}}^{q_v}$ can be computed by a linear combination of simulated columns taken from the model background state weighted by a function of the difference between observed and simulated reflectivities:

$${\mathit{y}}_{\mathrm{po}}^{q_{\mathrm{v}}}={\displaystyle \sum _i{x}_i^{q_v}}{\displaystyle \frac{\exp \left[-\frac{1}{2}{J}_{po}(x_i)\right]}{{\displaystyle \sum _j\exp \left[-\frac{1}{2}{J}_{po}(x_j)\right]}}}$$

(7)

with

$$J_{po}(x)={\left[y_Z-H_Z(x)\right]}^T{R}_Z^{-1}\left[y_Z-H_Z(x)\right].$$

(8)

where $x_i^{q_v}$ are columns of model relative humidity taken from the background state in the vicinity of the observation, $H_Z(x)$ is the simulated reflectivity by the radar simulator, and ${\mathbf{R}}_Z$ is the observation error covariance matrix.

In order to eliminate negative effects of the assimilation of estimated saturated water vapor observations in CMA-BJ3.0, the water vapor retrieved from reflectivity via the 1D Bayesian method was assimilated in this study. One limitation of the 1D statistical method is that the retrieved vertical profiles depend on what the model is able to simulate at the time of analysis. For instance, if precipitation is observed in an area where no rain is triggered by the model, the method will not be able to find neighboring columns with significant reflectivity [18]. Therefore, a two-step assimilation method was adopted, in which the analysis field after assimilating conventional data was used as the background field for retrieving water vapor assimilation. To further avoid the possibility that the dry background field may lead to an underestimation of the retrieved saturated water vapor, the 1D Bayesian method was enabled only if the value of reflectivity was less than 30 dBZ. These execution conditions and water vapor retrieval processes using the 1D Bayesian method adopted in this study are summarized in Figure 4.

3. Results

To quantify how 1D Bayesian-derived water vapor assimilation affects analysis and forecasting, a further analysis was conducted between the estimated saturated water vapor assimilation scheme and the 1D Bayesian scheme, aimed at validating the effectiveness of the 1D Bayesian scheme in addressing the issue of precipitation overforecasting. Heavy precipitation events in North China, East China, and South China that occurred on 6 August 2022 were selected as a case study. During the precipitation events, the operational forecast based on the estimated saturated water vapor assimilation scheme systematically overestimated both precipitation intensity and coverage. Two parallel experiments were conducted, including a control experiment (CTRL) and a contrast experiment (NEW_QV). The default assimilation settings of saturated water vapor estimated from reflectivity were employed in the CTRL experiment, while the water vapor retrievals using the 1D Bayesian method were assimilated in the NEW_QV experiment. The model configuration of CMA-BJ3.0 used in the case study is summarized in

Table 1. Overview of the CMA-BJ3.0 configuration used in the present study.

Parameter	Model Configuration
Horizontal resolution	1945 × 1498
Number of layers	61
Top layer	10 hPa
Vertical Coordinate system	terrain-following vertical coordinate
Area coverage	13.5°–57.8°N, 60.5°–149.5°E
Explicit microphysical scheme	Thompson
Longwave radiation scheme	Rapid Radiative Transfer Model (RRTM)
Shortwave radiation scheme	Rapid Radiative Transfer Model for General Circulation Models (RRTMG)
Boundary layer scheme	Yonsei University scheme (YSU)
Surface scheme	Noah land surface scheme

. In all experiments, a two-step assimilation approach was adopted. First, conventional observations (including ships, drifting buoys, land stations, airports, radiosonde, pilot balloon, aircraft, and wind profile) were assimilated to produce an analysis field, which then served as the initial condition for the subsequent water vapor retrieval. Both experiments initiated their simulations at 0000 UTC on 6 August 2022. Additional details regarding the experimental configurations are summarized in

Table 2. Settings of the assimilation experiments.

Abbreviation	Experiment Name	Observation for First Step Assimilation	Observation for Second Step Assimilation
CTRL	Control experiment	Conventional observation data	Retrieved hydrometeors and estimated saturated water vapor from reflectivity
NEW_QV	contrast experiment	Conventional observation data	Retrieved hydrometeors and retrieved water vapor via the 1D Bayesian method from reflectivity

.

3.1. Innovation Vector

Figure 5 shows the distribution of the vertically integrated water vapor observations assimilated at 00:00 UTC on 20 August 2022, comprising (a) the estimated saturated water vapor (red dots) and (b) the values retrieved by the 1D Bayesian method (blue dots). The retrieved radar water vapor observations via the 1D Bayesian method demonstrate a significantly broader spatial coverage and a higher resolution relative to the limited saturated water vapor observations denoted by the red dots in Figure 5a. In the context of data assimilation, such comprehensive and high-resolution observational data are crucial as they can more accurately constrain the initial conditions of numerical models, thereby potentially enhancing the precision of the assimilation process.

The first step of an assimilation analysis is to analyze the difference between the observation, background and analysis, that is, the innovation vector (O-B) and the observation minus analysis (O-A). Under ideal conditions, the O-B and O-A should follow an unbiased Gaussian distribution. Figure 6 presents the O-B and O-A frequency distributions with their fitted Gaussian distributions (red dashed lines) for the vertically integrated water vapor observations assimilated at 00:00 UTC on 20 August 2022. Panel (a) shows the O-B statistics for the CTRL experiment (using estimated saturated water vapor), panel (b) the O-B for the NEW_QV experiment (using 1D Bayesian-retrieved profiles), panel (c) the O-A for CTRL, and panel (d) the O-A for NEW_QV. In the NEW_QV experiment, the quantity of available observations increases by roughly fivefold compared to the limited saturated water vapor observations that are solely assimilated. In the NEW_QV experiment, after assimilating water vapor retrieved from reflectivity using the 1D Bayesian method, the O-B distribution of the assimilated water vapor more closely resembles a Gaussian unbiased distribution compared to the CTRL experiment. As illustrated in Figure 6b, the O-B mean deviation (The difference between the mean value of the fitted O-B normal distribution and the mean value of the standard O-B normal distribution) of NEW_QV was 0.449 g/kg. Although the O-B distribution of NEW_QV is slightly biased, it remained closer to zero compared to the O-B mean deviation (2.144 g/kg)_in the CTRL experiment. This demonstrates that assimilating water vapor retrieved by the 1D method is a more theoretical assimilation strategy. Similarly, the average deviation of O-A in NEW_QV (0.055 g/kg) was significantly lower than that of CTRL (0.497 g/kg). Moreover, the average value of O-A was smaller than that of O-B, which verified the correctness of the assimilation technique.

In the two sets of experiments, the horizontal O-B distribution of water vapor at different altitudes and the radar reflectivity distribution at corresponding altitudes were compared. A comparison of radar reflectivity data and the O-B distribution of the estimated water vapor across different altitudes is depicted in Figure 7. The left-hand column of this figure displays the horizontal distributions of radar reflectivity observations at the respective altitudes of 2000 m and 4000 m. In contrast, the right-hand column presents the O-B distributions of estimated water vapor at corresponding heights as simulated in the CTRL experiment. In the three regions of North China, East China, and South China, the estimated saturated water vapor distribution has a good correspondence with the strong radar reflectivity. However, in areas beyond the region characterized by strong radar reflectivity, a significant number of reflectivity observations corresponding to the assumed unsaturated water vapor are often disregarded, particularly at the altitude of 2000 m. Positive O-B deviations fill the entire field, which means that the humidity in the cloud area will definitely increase, thus enhancing the development of convective systems. In the hourly update cycle assimilation, the excessive positive deviation of water vapor observations relative to the background field is most likely one of the main reasons for the excessive precipitation forecast.

A comparative analysis of radar reflectivity data and water vapor retrieved by the 1D Bayesian method across different altitudes is presented in Figure 8. The left-hand column of this figure displays the horizontal distributions of radar reflectivity observations at the respective altitudes of 2000 m and 4000 m; the right-hand column presents the retrieved water vapor distributions at corresponding heights as simulated in the NEW_QV experiment. In the NEW_QV experiment, negative water vapor O-B appears in the weak reflectivity area in its scheme, and a large number of assumed unsaturated water vapor can be utilized. In the CTRL experiment, at the lower (2000 m) and upper (4000 m) bounds of the observational altitudes, the assimilation process incorporated a limited quantity of estimated water vapor, which exhibited positive skewness. Conversely, the NEW_QV experiment enriched the dataset by incorporating a substantial amount of assumed unsaturated water vapor, thereby offering a more comprehensive and precise depiction of the humidity field. Furthermore, within the NEW_QV experiment, the assimilation strategy for strong radar reflectivity observations (>30 dBZ) was aligned with that of the CTRL experiment. This consistency ensures that the water vapor field associated with severe convective systems is not underrepresented.

3.2. Impact of Data Assimilation on the Initial Field

To further understand the impact of the two different retrieved water vapor assimilation strategies on the analysis fields, a comparison of the initial field’s water vapor assimilation increments of the two experiments at multiple model layers is performed. Figure 9 shows the initial horizontal water vapor fields of the CTRL experiment at the 4th, 7th, 11th, and 15th layers of the model. Similarly to the O-B distribution characteristics of water vapor in the CTRL experiment, the positive water vapor increment covers the entire observation area, especially in East China, parts of North China, and parts of South China, with the maximum water vapor increment being approximately 8.7 g/kg. Although only the estimated saturated water vapor is incorporated into the assimilation system, the impact range of the positive water vapor increment causes far exceeds the distribution of its corresponding strong reflectivity observations.

The initial horizontal water vapor fields of the NEW_QV experiment at the 4th, 7th, 11th, and 15th layers of the model are shown in Figure 10. The coverage of positive water vapor increments in North China, East China, and South China is significantly reduced compared with that in the CTRL experiment, with the maximum value of the water vapor increment being approximately 6.2 g/kg. Meanwhile, negative water vapor increments appear around the area of strong reflectivity values, with the minimum water vapor increment being approximately −2.3 g/kg. The smaller scale of positive water vapor increments and the negative water vapor increments corresponding to the weak reflectivity observations suggest a more restrained adjustment of the water vapor field, which is expected to overcome the problem of short-term precipitation overforecasting in the assimilation of saturated water vapor scheme.

3.3. Impact of Data Assimilation on Precipitation

In order to verify the ability of the assimilation of water vapor retrieved by the 1D scheme to suppress false warnings of short-term precipitation forecasts after adjusting the initial water vapor field, a comparison of the 3 h cumulative precipitation forecasts of the two groups of experiments relative to the actual ground situation is presented. Figure 11 compares the 3 h cumulative precipitation (from 0600 UTC to 0900 UTC 6 August 2022, units: mm) of the NEW_QV experiment and the CTRL experiment with the actual 3 h cumulative precipitation observations. Specifically, Figure 11a shows the observed 3 h accumulated precipitation, Figure 11b depicts the 3 h accumulated precipitation predicted by the CTRL experiment, and Figure 11c presents the 3 h accumulated precipitation predicted by the NEW_QV experiment.

Compared with observations, both experiments successfully simulate the local precipitation in North China, East China, and South China. The precipitation intensity simulated by the CTRL experiment is overestimated, especially for the precipitation of the 50 mm threshold forecast, which is consistent with the range of the excess water vapor positive increment (Figure 11). The analytical inference presented in the previous section—that the too strong initial water vapor field due to the assimilation of estimated saturated water vapor would lead to overestimation of short-term precipitation—is thereby confirmed. The simulated local precipitation intensity and distribution in North China, East China, and South China are closer to observations in the NEW_QV experiment, compared with the precipitation in CTRL experiment, despite a persistent tendency toward precipitation overforecasting in the NEW_QV. This improvement in the NEW_QV precipitation forecast can be explained by the more accurate initial water vapor field, which is due to the water vapor retrieved by the 1D Bayesian method being able to more accurately describe the atmospheric humidity environment.

A comparison of the 6 h cumulative precipitation (from 0600 UTC to 1200 UTC 6 August 2022, units: mm) forecasts of the two groups of experiments relative to the actual ground situation are also presented (Figure 12). Specifically, Figure 12a shows the observed 6 h cumulative precipitation, while Figure 12b and Figure 12c depict that of the CTRL and NEW_QV experiment, respectively. When the forecast period is extended to 6 h, the over-enhanced water vapor increment still has a positive effect on the overestimation of precipitation in the CTRL experiment. Larger areas of overestimation appear in North China, East China, and South China in the CTRL experiment, as compared with their 3 h cumulative precipitation forecast performances. In North China and East China especially, the range of precipitation forecasts exceeding the 60 mm threshold is far beyond the actual observation. On the contrary, after assimilating the water vapor retrieved by the 1D method, the 6 h precipitation forecast still performs satisfactorily. While ensuring that precipitation above the threshold of 60 mm is not missed, it still effectively suppresses the overestimation of heavy precipitation forecasts.

In order to objectively evaluate the improvement in the short-term precipitation forecasting skill by assimilating the water vapor retrieved by the 1D Bayesian method compared with assimilating only the estimated saturated water vapor in the operational scheme, a 7-day hourly updated cycle assimilation batch experiment was implemented. The batch experiment started at 0000 UTC 1 August 2022 and ended on 7 August 2022, and also covered the study period of the case experiment. The results were tested and evaluated using the MET (Model Evaluation Tools) test toolkit. MET is a numerical weather forecast test tool developed by the Developmental Testbed Center of NCAR. In this paper, two test scores—the Threat Score (TS) and forecast bias (BIAS)—of the MET test were used for joint evaluation. TS represents the accuracy of the forecast, and the value range is 0–1. The closer to 1, the higher the forecast accuracy. BIAS measures the deviation between the predicted precipitation range and the actual observed range. The closer to 1, the closer the ranges of the predicted and observed precipitation. When it is greater than 1, this means that there is a false alarm in the forecast, and when it is less than 1, it means that there is an underestimate in the forecast. In addition to TS and BIAS, the Probability of Detection (POD) and Success Ratio (SR) were also calculated to provide a more complete assessment of forecast performance. POD measures the fraction of observed precipitation events that were correctly forecast, ranging from 0 to 1, with higher values indicating better detection of actual events. SR, on the other hand, measures the proportion of forecasted events that actually occurred, also ranging from 0 to 1, where values closer to 1 indicate fewer false alarms. Together, POD and SR help to distinguish between errors due to missed events and those due to false alarms, offering deeper insight into the sources of forecast inaccuracy.

A quantitative evaluation of the 3 h cumulative precipitation was first performed.

Figure 13 shows the TS values and BIAS scores for the 3 h cumulative precipitation forecasted at multiple initial moments in the CTRL and NEW_QV experiment. The NEW_QV scheme demonstrated a significant and consistent improvement in forecast skill. Across the 10 mm, 25 mm, and 50 mm precipitation thresholds, the Threat Score (TS) improved from (0.17, 0.08, 0.03) in the CTRL experiment to (0.18, 0.10, 0.04) in the NEW_QV experiment, corresponding to relative increases of 5.88%, 25.00%, and 33.33%, respectively. More notably, the NEW_QV scheme substantially mitigated the strong positive bias evident in CTRL, reducing the Bias score from (1.97, 2.58, 3.54) to (1.47, 1.72, 1.95)—a reduction of 25.31%, 33.32%, and 45.00%, respectively—thereby approaching the ideal value of 1. To provide a more complete verification, we supplement the original TS and BIAS assessment with two additional categorical metrics: the Probability of Detection (POD) and the Success Ratio (SR = 1 − false alarm). Both were computed for 3-hourly accumulated precipitation. Although the CTRL experiment demonstrates a slightly higher POD, which suggests a greater capacity to correctly identify observed precipitation events, this metric is accompanied by a lower SR. The lower SR in the CTRL experiment indicates a higher incidence of false alarms, which negatively influences the TS and contributes to an increased BIAS. In contrast, the NEW_QV experiment maintains a balance between POD and SR, focusing on reducing the occurrence of false alarms while preserving a satisfactory level of event detection. This balanced approach results in a forecast that is more accurate and reliable, as evidenced by the enhanced TS and the reduced BIAS across the various precipitation thresholds assessed in this study. Consistent with the 3 h forecast analysis, the 6 h forecast evaluation of Probability of Detection (POD) and Success Ratio (SR) reveals similar trends (shown in Figure 14). For the CTRL experiment, a higher POD is observed, suggesting an increased capacity to identify precipitation events. However, this is counterbalanced by a lower SR, indicating a higher incidence of false alarms. Importantly, the elevated POD in the CTRL experiment does not translate into improved overall precipitation forecast performance. Instead, the excessive number of false alarms, as reflected by the lower SR, detracts from the forecast’s reliability and utility.

All these positive results indicate that the simulation accuracy of the model for convective events has been improved by applying the 1D Bayesian scheme. It can be concluded that the assimilation of retrieved observations created by the 1D Bayesian approach avoids the systematic positive analysis bias and further addresses the problem of overforecasting of severe convective short-term precipitation.

4. Summary and Discussion

In order to improve the operational benefits of the CMA-BJ3.0 regional numerical model forecasting system, a study on the assimilation of radar reflectivity mosaic data in CMA-BJ3.0 was carried out. In this study, a 1D Bayesian method was adopted for water vapor retrieved from reflectivity observations, which was further optimized and constrained. Then, the retrieved water vapor was assimilated to mitigate the issue of excessive short-term precipitation overforecasting attributed to the assimilation of estimated saturated water vapor in current operational systems.

We then analyzed a case of precipitation overforecasting on 1 August 2022 to examine the characteristics of the innovation vector across different assimilation schemes, its effect on analysis increments, and the mechanisms influencing precipitation forecast performance. Our case study revealed that an O-B statistical outcome closer to a Gaussian unbiased distribution in the NEW_QV experiment signified more balance between observations and the background. The NEW_QV experiment effectively corrected the systematic positive bias of water vapor, and the excessive increment of water vapor was curbed. The more precise adjustment of the water vapor analysis field in the analysis experiment led to an effective resolution of the excessive precipitation overforecasting problem.

Subsequently, batch experiments were conducted to quantitatively evaluate the enhancement effect brought about by the assimilation of water vapor retrieved by the 1D Bayesian method on precipitation forecasting. The evaluations indicated that the precipitation forecast score of the model was significantly improved following the assimilation of water vapor retrieved by the 1D Bayesian method, particularly for heavy precipitation (25.0 and 50.0 mm/3 h), and the false alarm rate within the initial 6 h was markedly reduced, thereby substantially enhancing the model’s precipitation forecast performance.

This study was dedicated to the enhancement of a radar-reflectivity-based water vapor assimilation scheme aimed at improving the short-term precipitation forecasting accuracy, without considering the impact of retrieved hydrometeors on precipitation forecast outcomes. The bulk verification results indicate that the assimilation of water vapor retrieved by the 1D Bayesian method ameliorates the operational issue of excessive precipitation forecasting associated with the assimilation of estimated saturated water vapor in reflectivity, and that this improvement can primarily be attributed to a more accurate initial water vapor field. It is important to note, however, that the dynamical influences that trigger strong convective precipitation were not considered in this study. Nonetheless, although the 1D Bayesian method is background-field-dependent and does not strictly meet the assumption of independence between the background and observations, its role in correcting systematic positive biases in water vapor makes it a preferred assimilation scheme for water vapor. The application and assessment of this scheme in more advanced assimilation techniques, such as 4DVAR and Ensemble Kalman Filter assimilation, will be the focus of future research in radar data assimilation. The performance of our proposed assimilation scheme during non-summer periods will be investigated in our future studies.