A New Post-Processing Method for Improving Track and Rainfall Ensemble Forecasts for Typhoons over Eastern China

Abstract

This paper proposes a new post-processing method for model data in order to improve typhoon track and rainfall forecasts. The model data used in the article include low-resolution ensemble forecasts and high-resolution forecasts. The entire improvement method contains the following three steps. The first step is to correct the typhoon track forecast: three ensemble member optimization methods are applied to the low-resolution ensemble forecasts, and then the best optimization method is selected with the principle of the smallest average distance error. The results of rainfall forecasts show that the corrected rainfall forecast performs better than the original forecasts. The second step is to derive the high-resolution probability rainfall forecast: the neighborhood method is applied to the deterministic high-resolution rainfall forecast. The last step is to correct the typhoon rainfall forecast: the low- and high-resolution forecasts are blended using the probability-matching method with two different schemes. The results show that the forecasts of the two schemes perform better than the original forecast under all rainfall thresholds and all forecast lead times. In terms of bias score, a rain forecast from one scheme corrects the rainfall deviation from observation better for light and moderate rainfall, whereas a rain forecast from another scheme corrects the rainfall deviation better for heavy and torrential rainfall. The better performance of corrected rain forecasts in the case of Typhoon Lekima and Rumbia over eastern China is demonstrated.

1. Introduction

China is strongly affected by typhoons, with an average of seven landings each year. In summer and autumn, the southeastern coastal area of China is highly vulnerable to typhoons and concomitant hazardous weather conditions, such as intense rain, strong winds, and storm surges, which can pose threats to lives, livelihoods, infrastructure, and property. Accurate forecasting of typhoon tracks and rainfall amount/intensity is the key to typhoon defense and disaster reduction strategies [1]. For example, 2005 was a year with a significant number of typhoons affecting China, with typhoons ‘Metsa’, ‘Talim’, and ‘Khanun’ hitting from August to September. In Anhui province alone, 5.75 million people were affected by the disaster, with nearly 100 deaths. The affected area of crops reached 6.45 million mu, resulting in indirect economic losses of 7.2 billion yuan. Among them, ‘Talim’ had the largest precipitation range and the strongest intensity, with a total rainfall of 573 mm in Yuexi and a 24 h rainfall of 493 mm, causing landslides, flash floods, and severe waterlogging. The large improvements in computer performance and numerical ensemble prediction systems (EPSs) have been rapidly developed over the last two decades [2] and then applied to typhoon track prediction.

Deterministic forecasting is generated through the use of all available computing power of the model at the highest possible resolution. While in the ensemble forecast, the ensemble is comprised of many forecast members. Since the late 1990s, various applications of ensemble forecasting have been studied with respect to typhoons [3]. Because of the nature of variation in atmospheric conditions, ensemble forecasting can yield better predictions than single deterministic forecasting. Ensemble forecasting can eliminate the random error associated with the evolution of the weather system that cannot be eliminated by statistical probability forecasting [4]. Aberson et al. [5,6] first demonstrated the feasibility of ensemble forecasting for tropical cyclone track and intensity prediction in the 1990s. An increasing number of studies [7,8,9] have applied ensemble forecasting to typhoon prediction.

Two main aspects are involved in the application of ensemble forecasting to the study of typhoons: one is the establishment of a typhoon ensemble forecasting system, and the other is the application of post-processing and correction of ensemble forecasts. For the first aspect, the major studies are the generation of initial fields and physical disturbances, data assimilation, and so on. Early studies [10,11,12] have shown that precipitation forecasting is sensitive to the initial fields of the model, and ensemble forecasting systems based on the initial fields can not only determine the forecast for a single precipitation forecast but also provide reliable probability forecasts. Later, Brooks et al. [13] and Mullen et al. [14] found that the divergence of ensemble member precipitation forecasts is also sensitive to different parameterization schemes and different assimilation systems. For example, Zhang et al. [10] implemented EOF (Empirical Orthogonal Function) analysis to generate a hurricane environment and structural perturbations and showed that the track ensemble forecasts of all test cases were better than deterministic forecasts. Zhang and Weng [11] used a cloud-resolving mesoscale ensemble forecasting model to simulate the heavy rainfall caused by Typhoon Morakot in Taiwan and obtained better forecast results through testing. Meanwhile, data assimilation technology is also crucial for accurately predicting typhoon precipitation. Shen F et al. [12,13,14,15,16] have performed a lot of research on assimilating radar and satellite data for typhoon prediction. In addition, Xu D et al. [17,18,19,20,21,22] also conducted research on assimilating satellite data to forecast hurricane tracks and intensities. These attempts have all yielded better forecast results.

For the second aspect, a method of applying ensemble forecasting to typhoon track prediction has been developed by Taiwan’s Central Meteorological Bureau by clustering the typhoon tracks of ensemble forecast members [23]. Qian et al. [24] proposed a real-time correction method using the European Centre for Medium-Range Weather Forecasts (hereafter ECMWF) ensemble prediction of typhoon tracks and operational positioning of the China Meteorological Administration (hereafter CMA) for operational track forecasting. Their results showed that the average track errors after correction were smaller than those of both the ensemble’s mean track and deterministic forecasting of ECMWF. With regard to post-processing for typhoon rainfall ensemble forecasting, many correction techniques that were applied to general rainfall could also be applied to typhoon rainfall, such as the probability-matching mean (PM), fuse matching average (FM) and frequency-matching method corrections (FMM). On the basis of typhoon track ensemble forecasts of ECMWF, Chen et al. [25] used ensemble member optimizations, FM and PM to correct typhoon rainfall amounts. Their results showed that the outcome of correction gave better performance than ECMWF deterministic forecasts. Fang and Kuo [26] proposed a dual-resolution ensemble forecasting system to establish ensemble forecasting for quantitative precipitation forecasting of typhoons. The system collects forecasts from large, low-resolution, and small, high-resolution ensembles.

In the daily operation of typhoon rainfall prediction, due to limitations imposed by computational resources, the requirement of timeliness, and different advantages of different resolution models, research into the post-processing and correction of typhoon tracks and rainfall forecasting have strong scientific significance and practical value. However, because of the strong influence of terrain on typhoon forecasts, a low-resolution global ensemble model does not have sufficient capability to forecast typhoon rainfall accurately. Therefore, based on previous research, we have conducted further research mainly on three methods to correct typhoon track forecast and the application of the neighborhood method for probability forecast. In this paper, we adopt a dual-resolution forecasting system to forecast typhoon rainfall. The theoretical basis of this method is that the ensemble forecasting members of the low-resolution model generally underestimate the amount of rainfall, while the high-resolution forecast can make up for this defect. But, because of limitations imposed by computational resources, it is hard to develop enough ensemble members of high-resolution models to capture track uncertainty. Therefore, low-resolution ensemble forecasting is used to estimate the optimal possible typhoon track, and then the spatial structure of rainfall distribution is estimated by the corresponding members. The forecast of rainfall amount is further adjusted by high-resolution probability forecasting. Considering the large amount of computation required to construct the high-resolution ensemble model in practical terms, we use the neighborhood method [27,28,29,30] to obtain the high-resolution probability forecast.

Here, to improve the forecasting of typhoon rainfall in eastern China, we first apply the ensemble member optimization method to low-resolution ensemble forecasting for better typhoon tracks and rainfall. Then, we derive a high-resolution probability rainfall forecast from the high-resolution deterministic forecast via the neighborhood method. Finally, using a probability-matching method, we develop a dual-resolution forecast that blends low- and high-resolution rainfall forecasts. The remainder of this paper is structured as follows: Section 2 presents the data information and methodology for typhoon post-processing methods and evaluation methods. Section 3 evaluates the QPF performance of the dual-resolution rainfall forecasts. Section 4 and Section 5 present the cases of Typhoon Lekima and Rumbia to illustrate the better performance of the correction applied to forecasting. Section 6 gives the main conclusions of the study.

2. Data and Methodology

2.1. Data

The experimental datum for low-resolution ensemble forecasting in this study is typhoon track and rainfall forecasts originating from ensemble prediction systems (EPSs), which are ECMWF and NCEP ensemble forecasts (hereafter as EC_EPS and NCEP_EPS, respectively) for 10 typhoons (

Table 1. 10 Typhoons during 2014–2019.

Typhoon Number	Rainfall Period Studied	Typhoon Name
201410	22–25 July 2014	MATMO
201513	7–11 August 2015	SOUDELOR
201521	28 September–2 October 2015	DUJUAN
201614	14–17 September 2016	MERANTI
201617	27 September–1 October 2016	MEGI
201622	20–22 October 2016	HAIMA
201710	29 July–4 August 2017	HAITANG
201814	11–17 August 2018	YAGI
201818	16–20 August 2018	RUMBIA
201909	9–11 August 2019	LEKIMA

) that occurred during 2014–2019 and made landfall in eastern China, bringing high amounts of rainfall. Among the 10 typhoon cases in Table 1, the first eight typhoons are used for method development, and the last two typhoon cases are used to test the forecast performance of the correction method. The ensemble forecasts from the EPSs (

Table 2. Specifications of the EPSs as of 2014.

	EC_EPS	NCEP_EPS
Model resolution	TL669L91	T254L28
Vertical levels	62	28
Initial time (UTC)	0000; 1200	0000; 0600; 1200; 1800
Ensemble size	51	21

) are decoded from the North Western Pacific Tropical Cyclone Ensemble forecasting project of THORPEX Interactive Grand Global Ensemble in Cyclone XML format. EC_EPS generates forecasts twice a day (00, 12 UTC). NCEP_EPS generates 4 forecasts every day (00, 06, 12, 18 UTC), which is consistent with the CMA forecast. The high-resolution deterministic forecast in the research is the Shanghai Meteorological Service WRF ADAS real-time modeling system (SMS-SWARMS; referred to hereafter as “WARMS”), which is from the Shanghai Typhoon Research Institute. In eastern China, the forecast of WARMS [31] has been widely applied and evaluated. The modeling domain consists of 760 by 600 horizontal grid points at a 9-km resolution, with 51 layers along the vertical direction. Rainfall observation data are retrieved from the Land Data Assimilation System (CLDAS) of CMA. Since 1998, these precipitation data have covered all of China, with a resolution of 6.25 km and a time interval of every hour. Then, the data have been widely applied to operational numerical weather forecasts, agriculture, ecological hydrology, and drought monitoring [32,33].

Verification is performed over the area strongly affected by typhoons (the heavily hit area). The post-processing and verification of typhoon tracks have been applied in the area (blue box shown in Figure 1) spanning from 25° N to 40° N and from 112° E to 124° E. Meanwhile, typhoon rainfall post-processing and verification have been applied in the area (red box shown in Figure 1) spanning from 27° N to 39° N and from 114° E to 123° E. That is determined by the location of the typhoons during the main precipitation period over eastern China. The rainfall data analyzed in this paper are 6 h cumulative precipitation. According to the standards of the Central Meteorological Observatory, rainfall data are grouped into four categories according to intensity, with the thresholds for light, moderate, heavy, and torrential rainfall set to 0.1, 5, 10, and 25 mm per 6 h, respectively.

2.2. Methodology

Correction of typhoon track and rainfall forecasts employs the following steps:

(1) Three ensemble member optimization methods (hereafter EMOMs) means the method to select the best ensemble members to constitute a new ensemble forecast for better performance. EMOMs are applied to EC_EPS, NCEP_EPS, and multi-model EPS (both EC_EPS and NCEP_EPS and ensemble members are not weighted) forecasts to construct a new ensemble forecast. The new low-resolution track and rainfall ensemble forecasts are obtained from the corresponding members selected by the best EMOM;

(2) Depending on WARMS performance within 6 h before the forecast time, the best range (which is detailed in Section 2.2.2) is determined for the neighborhood method in order to transform WARMS to WARMS_EPS. Then, the high-resolution rainfall probability forecast is obtained;

(3) Two schemes of the probability-matching methods are applied to blend low- and high-resolution rainfall forecasts.

2.2.1. Three EMOMs for Typhoon Track

To identify the best EPS members (i.e., those that provide results that most closely resemble observations), we adopt three EMOMs to correct the typhoon track forecast. According to the real-time typhoon position and the track forecast from CMA, we select N members with the smallest distance error in the latest received forecast (in the daily operation of typhoon rainfall prediction) of typhoon tracks. Such a selection method has been explored for ECMWF ensemble by Qian et al. [24], and the method is proven to have good potential in operational application. On the basis of the typhoon position from CMA and track forecasts from EC_EPS, NCEP_EPS, and multi-model EPS, three EMOMs are developed to select the track forecast members, allowing the new low-resolution track and rainfall ensemble forecasts to be obtained. As Figure 2 shows, the three EMOMs are defined as follows:

EMOM based on objective position (EMOM_OP): according to the objective real-time typhoon position (from CMA), N members predicting tracks with the smallest distance error in the latest ensemble forecast (from the typhoon positioning time) are selected. Based on historical statistical results, N is determined based on the minimum average track distance errors;

EMOM based on subjective forecast (EMOM_SF): according to the subjective track forecast (from CMA), the N members predicting tracks with the smallest distance error in the latest ensemble forecast are selected. N is determined using the same method as EMOM_OP;

EMOM based on both objective position and subjective forecast (EMOM_OPSF): according to the track constructed by objective real-time typhoon position and subjective track forecast (from CMA), the N members predicting tracks with the smallest distance error in the latest ensemble forecast are selected. N is determined using the same method as EMOM_OP.

2.2.2. Neighborhood Method for Rainfall Forecast

The high-resolution probability forecasts (WARMS_EPS) were processed using the deterministic forecast of WARMS using the neighborhood method. The neighborhood method is a method of converting a deterministic forecast into a probabilistic forecast using certain statistical methods at each grid point in the research area. As described by Theis [27], in the neighborhood method for post-processing model rainfall forecasts, at a given location (x₀, y₀) of the model grid, a “neighborhood” around this grid point is defined and extends into space (x, y). A circular (or square) area of influence is specified to define a neighborhood around each grid point. And the best radius (or a side length) of the neighborhood area is determined by the maximum area under the receiver operating characteristic curve. Assuming location (x₀, y₀) as the center point, we construct a probability density function using precipitation forecasts from the model grid points within the neighborhood. So, according to the probability density function within the neighborhood, the model precipitation forecasts are assumed to be independent and identically distributed. Over the model domain, the shape and size of the neighborhood are fixed. This probability of exceeding is just the number of model precipitation forecasts within the neighborhood that are greater than a given exceedance threshold, divided by the total number of grid points within the neighborhood [34]. To generate a fractional value at each point, the number of grid boxes with rainfall ≥q (with q in the present study equaling 0.1, 5, 10, or 25 mm per 6 h) within the neighborhood is divided by the total number of boxes within the neighborhood. The fractional value of each point equals the number of grid boxes with rainfall ≥ q (q equaling 0.1, 5, 10, or 25 mm per 6 h). When we choose the neighborhood with a radius or a square range, the fraction is the probability of the rainfall, which equals or exceeds q. Therefore, this method could recognize the inherent unpredictability and then pick up the probabilistic information from the deterministic forecast. Figure 3 shows the selection of the model grid range in the neighborhood method.

2.2.3. Typhoon Rainfall Correction

The new post-processing method for improving track and rainfall ensemble forecasts includes (1) the new track and rainfall ensemble forecast (low-resolution) obtained by EMOMs. The 6 h rainfall field of member iel of the low-resolution ensemble forecast at the time itl and the point ip can be represented by R_L(iel, itl, ip) with iel = 1, 2, …, ML, itl = 1, 2, …, T, and ip = 1, 2, …, P, where ML is the number of members of the new ensemble forecast (low resolution), T is the length of the time series (set to 12 for the total 72 h simulation in 6 h intervals), and P is the number of points in the studied area. (2) The new rainfall probability forecast (high resolution) was obtained using the neighborhood method from WARMS. Similarly, the rainfall field of WARMS, at the time ith and the point ip, can be represented by WRH(ith, ip) with ith= 1, 2, …, T. And the 6 h rainfall field of the high-resolution probability can be represented by R_H(ith, ip). (3) The use of probability matching based on the low- and high-resolution to construct a synthetic 6 h rainfall forecast. The reconstructed rainfall forecast developed by rainfall correction (probability-matching technique) is denoted as NEWEN.

Let R_NEWEN(it, ip) represent the 6 h rainfall field of the NEWEN to be constructed at the time it and the point ip; its construction is detailed in the following five steps below:

(1)

Step 1: Calculate the distance Dis(LE − L0) between typhoon track from CMA L0 and track from low-resolution ensemble forecast LE. L0 represents the objective real-time typhoon position in EMOM_OP, the subjective track forecast in EMOM_SF, or the track constructed by objective real-time typhoon position and subjective track forecast in EMOM_OPSF. LE represents track forecast from EC_EPS, NCEP_EPS, or multi-model EPS;

(2)

Step 2: Sort the distance Dis(LE − L0) by increasing order and average the leading N members to compose a new track forecast F (F = AVE{Min|Dis(LE − L0)|_N}). According to the calculation of F in 2014–2018 typhoons, N is chosen so that it provides the smallest distance error of F;

(3)

Step 3: Based on the selected number (N) of ensemble members, according to the best EMOM, the low-resolution rainfall ensemble forecast R_L(iel, itl, ip) is constructed;

(4)

Step 4: Depending on the WARMS performance within 6 h before the forecast time, the best range is determined for the neighborhood method in order to transform WARMS to WARMS_EPS. And then, the high-resolution rainfall probability forecast R_H(ith, ip) is obtained;

(5)

Step 5: Perform probability matching using the rainfall pattern and the rainfall frequency distribution. Thus, the probability-matching rainfall field R_NEWEN(it, ip) is constructed.

In the study of Ebert [34], the probability matching technique has the advantage that it can be used to blend two data sets, that one data type generally gives superior spatial representation, and the other usually has greater accuracy. According to the method, the PDF of less accurate data can be set to the PDF of more accurate data. In our case (as shown in

Table 3. Experimental design of the various schemes used for rainfall correction.

Scheme Name	New Forecast Type	Rainfall Pattern Adjustment	Rainfall Frequency Adjustment
S1	deterministic	AVE[RL(iel, itl, ip)]	RH(itl, ip)
S2	deterministic	AVE[0.5 RL(iel, itl, ip) + 0.5 WRH(ith, ip)]	RH(itl, ip)

), the most likely spatial representation of the rain field is given by rainfall pattern adjustment, while the best frequency of distribution of rain rates is given by rainfall frequency adjustment.

The NEWEN constructed by the above-described probability-matching technique, and for comparison, two schemes are constructed in Table 3: (1) S1, the rainfall pattern adjustment is average of R_L(iel, itl, ip) and the rainfall frequency adjustment is R_H(itl, ip); (2) S2, the rainfall pattern adjustment is average of 0.5 R_L(iel, itl, ip) + 0.5 WR_H(ith, ip) and the rainfall frequency adjustment is R_H(itl, ip).

2.2.4. Evaluation Method for Forecast Performance

The area under the Receiver Operating Characteristic curve (ROC area), ETS (Equitable Threat Score), Brier score, and Bias score were used in this study for the purpose of evaluating forecast performance. The ROC curve is a measuring tool to evaluate the performance of the forecast, distinguishing between events and non-events. In different probability thresholds, the hit rate ($HR$ is plotted as a function of the false alarm rate ($FAR$). The HR and FAR are defined as follows:

$$HR={\displaystyle \frac{a}{a+b}}$$

(1)

$$FAR={\displaystyle \frac{FA}{FA+CN}}$$

(2)

where a, b are the numbers of hits and false alarms, respectively, FA denotes the number of false alarms, and CN denotes the number of correct negatives. A ROC curve close to the upper-left corner is commonly accompanied by a large ROC area and indicates high performance.

The $ETS$ is often used to quantitatively evaluate the rainfall forecasting ability of a numerical model [35,36]. The $ETS$ is defined as follows:

$$ETS={\displaystyle \frac{a_r}{a+b+c-a_r}}$$

(3)

$$a_r={\displaystyle \frac{(a+b)\times (a+c)}{a+b+c+d}}$$

(4)

where $a_r$ is a correction factor of model hits expected under a random forecast, and $\mathrm{c}$ and $\mathrm{d}$ are the numbers of misses and correct no-rain forecasts, respectively. The $ETS$ value ranges from −1/3 to 1, with a perfect score of 1.

The Brier score is usually used to evaluate the accuracy of weather forecasts based on the Euclidean distance between the actual outcome and the predicted probability assigned to the outcome for each observation [37]. The Brier score could capture discrimination and calibration, with low values being desirable. The Brier score is defined as:

$$BS={\displaystyle \frac{1}{n}}{\sum }_{j=1}^n{(p_j-o_j)}^2$$

(5)

$\mathrm{n}$ represents the number of samples. $o_j$ represents observation, and when the value of observation is greater than a selected threshold, $o_j$ = 1; otherwise, $o_j$ = 0. $p_j$ is forecast probability.

The $Bias$ score is a traditional verification method to evaluate the deviation of the forecast model. The Bias is defined as:

$$Bias={\displaystyle \frac{a+b}{a+c}}$$

(6)

When the forecast is perfect, the bias equals 1, and the forecast frequency is equal to the observation frequency. When the bias is higher (lower) than 1, this indicates that the frequency of prediction is higher (lower) than that of observation.

3. Results

3.1. Ensemble Forecasting Performance Based on Ensemble Member Optimization Methods

Three EMOMs are applied to EC_EPS, NCEP_EPS, and multi-model EPS, respectively. Figure 4 shows the distance errors of tracks for different numbers of ensemble members selected using three EMOMs. The three EMOMs used are based on the typhoon statistics for 2014–2018. The curves have a minimum track distance error at some number of members N; thus, a new ensemble of N members can be constructed. In Figure 4a,d, the difference between minimum distance errors of EC_EPS (64 km) and NCEP_EPS (63 km) is very small in 24 h lead time but grows with the increase of lead time in Figure 4b,c,e,f. And the advantage of EC_EPS becomes more pronounced (the minimum value of the EC_EPS distance error is less than that of NCEP_EPS) in 48 and 72 h lead time. On the whole, the EC_EPS forecast performs better than the NCEP_EPS and multi-model EPS with respect to the track correction of EMOM_OPSF. This result means that for the case where one of the ensemble forecasts is clearly better than the other, the multi-model EPS (composed of the two forecasts) has no advantage in terms of performance. In addition, as shown in Figure 4a–c, when EMOM_OPSF is applied to the EC_EPS track forecast, the number of selected members is 20 for the minimum track distance error.

Figure 5 presents the EC_EPS forecast after correction by EMOM_OPSF with 20 members, allowing the rainfall Brier score of the new ensemble forecast and the original forecast (EC_EPS) for different rainfall thresholds to be compared. The results show that the Brier score of the new ensemble forecast is smaller than that of the original forecast for all rainfall thresholds. Therefore, the EMOM_OPSF method not only reduces the track distance error but also improves the ensemble rainfall forecast. It should be noted that precipitation samples with different forecast times are different, and the Brier scores for different forecast times are not comparable.

Figure 6 shows the spatial distribution of the rainfall Brier score difference between the original ensemble forecast and the new ensemble forecast. When the Brier score difference is greater than (less than) 0, the original ensemble forecast Brier score is greater than (less than) the new one, and the new forecast is better than (worse than) the original forecast. For the forecast lead time of 48 h, the Brier score difference in most areas of eastern China is greater than 0, and the effect of rainfall correction is appreciable. With the forecast lead time increasing to 72 h, the area of the Brier score difference greater than 0 is smaller than that of 48 h. Thus, the effect of the correction method on rainfall forecast performance decreases with the increase in forecast lead time. For all rainfall thresholds, the main area of correction encompasses the coastal area and Shandong Province, which are also the main areas affected by typhoon rainfall in eastern China.

3.2. Probability Forecast (WARMS_EPS) Based on the Neighborhood Method

In this paper, probability forecasts of WARMS_EPS are derived from the deterministic forecast WARMS using the neighborhood method. The key to this method is the determination of a reasonable range according to observations (i.e., the prediction ability of the model). Spatial neighborhoods in the present study are defined as square areas with a side length determined by the ROC area (the area under the ROC curve). Because the large ROC area indicates a high forecast performance (which has been mentioned in Section 2.2.4), the best range (side length) of the neighborhood area is determined by the maximum ROC area. To obtain the optimal probability forecast (WARMS_EPS) at a certain time, the range for the probability forecast is determined by the performance of WARMS during the 6 h before the identified time. The best spatial neighborhood is selected by the principle of maximum ROC area of the previous 6 h. For example, as shown in Figure 7a, to derive the range for the WARMS_EPS forecast with a starting time of 20:00 CST (China Standard Time, CST = UTC + 8) on 9 August, according to the ROC area from 14:00 CST to 20:00 CST on 9 August, the best range is selected. In addition, as shown in Figure 7b, we select the best range depending on the ROC area of the WARMS forecast from 02:00 to 08:00 CST on 10 August to determine the range for the WARMS_EPS forecast with a starting time of 08:00 CST on 10 August. Under different rainfall thresholds, the best range also varies.

3.3. Rainfall Forecast Performance after Application of Probability Matching

After blending the low-resolution ensemble forecast (EC_EPS) and the high-resolution probability forecast (WARMS_EPS) using the adopted probability-matching method, S1 and S2 quantitative rainfall forecasts are obtained according to different schemes. The forecasting performances of S1 and S2 are evaluated in comparison with the ensemble mean of EC_EPS and WARMS to reflect the advantages of the correction method based on the original forecast of high-resolution deterministic forecast and low-resolution ensemble forecast. Figure 8 compares the ETS values of the four forecasts for different rainfall thresholds. For all four rainfall thresholds, the ETS values of S1 and S2 are higher than those of EC_EPS ensemble mean and WARMS, meaning that the accuracy of rainfall forecasts after dual-resolution blending is higher than that of the original forecasts. And S2 values are higher than those of S1. The ETS values of S1 and S2 for the light, moderate, and heavy rainfall thresholds are substantially higher, especially those of S2. In torrential rainfall thresholds, the ETS values of S2 have more obvious advantages within 36 h lead time. With increasing lead time, ETS values gradually decrease under all rainfall thresholds. For the heavy and torrential rainfall thresholds, ETS values decrease markedly after a 36 h forecast lead time, and there is no obvious difference between the forecasts.

In addition to the comparison of ETS values, the bias scores of the rainfall forecasts before and after blending within the 72 h lead time forecast were also compared under all rainfall thresholds. Overall, S1 and S2 rainfall forecasts show better bias scores (closer to 1) compared with the EC_EPS ensemble mean and WARMS forecasts. For light and moderate rainfall thresholds, the bias of S2 is closer to 1 than the bias of S1, meaning that the scheme used for S2 is more effective than that used for S1 for correcting rainfall deviation from observation. In contrast, for heavy and torrential rainfall thresholds, the bias of S1 is superior. To sum up the results for bias correction, the rainfall forecast of S2 performs better for light and moderate rainfall thresholds, and that of S1 performs better for heavy and torrential rainfall thresholds.

4. Case Study: Typhoon Lekima (No. 1909)

4.1. Overview of Typhoon Lekima

Typhoon Lekima (No. 1909) was generated in the ocean east of the Philippines on 4 August 2019 (China Standard Time, hereafter CST). The Chinese Central Meteorological Observatory upgraded this event from a tropical depression to a tropical storm at 17:00 CST on 4 August. Lekima made landfall in the coastal area of Chengnan Town, Wenling City, Zhejiang Province, in the early morning of 10 August. After landfall, the track of Lekima gradually changed from northwest to north (Figure 8a). From 9 to 12 August 2019, Typhoon Lekima brought extremely high rainfall over eastern China and almost province-wide rainstorms in Zhejiang, Jiangsu, and Shandong provinces. As shown in Figure 8b, during this 4-day period, more than 60% of all rain gauge stations across eastern China registered accumulated rainfall amounts of >100 mm. Lekima was the third-strongest typhoon to make landfall in Zhejiang since 1949. More than 10 provinces were affected, and the direct economic loss ranks second for landfall typhoons since 2000.

4.2. Typhoon Track and Rainfall Performance Based on EMOM_OPSF

The track forecast of EC_EPS for Typhoon Lekima (Figure 9) is corrected using the EMOM_OPSF method, and based on the research above, the number of selected members is 20. A comparison of the distance errors before and after the correction (Figure 10) shows that the mean distance errors of the ensemble forecasts after correction are all smaller than those before correction for forecast lead times of 24, 48, and 72 h, meaning that EMOM_OPSF improved the EC_EPS track forecast in the case of Lekima.

Then, it is explored whether the new ensemble forecast has an effective correction to the rainfall forecast. Figure 11 shows a comparison of the rainfall Brier score between the ensemble forecast before and after correction for a forecast lead time of 72 h (6 h interval) for different rainfall thresholds. With increasing lead time, the Brier score of all ensemble rainfall forecasts gradually decreases for all rainfall thresholds. On the whole, the Brier score of the ensemble rainfall forecasts is smaller than that of the original ensemble forecasts. Therefore, the EMOM_OPSF method could correct the rainfall forecast for Typhoon Lekima.

4.3. Performance of the Probability-Matching Rainfall Forecasts

Because of the low resolution of the global model forecast, the typhoon rainfall forecast of EC_EPS is not sufficiently accurate, meaning that the high-resolution forecast needs correction. The neighborhood method is used to transform the high-resolution mesoscale model forecast into a probability forecast. In accordance with the rainfall forecast performance of WARMS 6 h before the starting time, the scale length of the neighborhood method is determined by applying the principle of the largest ROC area. As presented in

Table 4. Selection of scale length for WARMS_EPS for Typhoon Lekima (unit: km).

	Beginning Time	At 20:00 on the 8th	At 8:00 on the 9th	At 20:00 on the 9th	At 8:00 on the 10th	At 20:00 on the 10th	At 8:00 on the 11th	At 20:00 on the 11th
Threshold (unit: mm/6 h)
0.1		330	550	1000	495	330	600	600
5		330	660	1000	440	330	275	600
10		385	600	1200	550	330	330	600
25		385	600	1200	600	600	330	600

, the scale lengths for different starting times and different rainfall thresholds were determined, allowing WARMS_EPS to be obtained.

Figure 12 compares the ETS values of S1 and S2 with those of EC_EPS mean and WARMS. For all rainfall thresholds, the ETS values of S1 and S2 are greater than those of EC_EPS mean and WARMS, meaning that the new rainfall forecasts based on dual-resolution blending perform better than the original forecasts. A comparison of Figure 11a,b for light and moderate rainfall thresholds and Figure 11c,d for heavy and torrential rainfall thresholds reveals that the S1 and S2 rainfall forecasts have a more substantial correction effect on EC_EPS ensemble mean than on WARMS. Overall, S2 performs slightly better than S1 for Typhoon Lekima.

We selected three periods during Typhoon Lekima (from 08:00 CST on 9 August to 08:00 CST on 10 August, from 08:00 CST on 10 August to 08:00 CST on 11 August, and from 08:00 CST on 11 August to 08:00 CST on 12 August) and compared the 24 h cumulative rainfall distribution among the mean of EC_EPS forecasts, WARMS, S1, and S2. The starting time of the forecasts is 08:00 CST on 9 August, and three different forecast lead times are selected: 24, 48, and 72 h. Lekima made landfall on 9 August, and observations show that the main rainfall was concentrated mostly over Zhejiang Province, with a maximum rainfall of >400 mm (Figure 13a). In addition, there were two other rainfall centers with a maximum rainfall of >100 mm located at the junction of northern Jiangsu and northern Anhui provinces and at the junction of Henan, Shandong, and Hebei provinces. These two rainfall centers were caused by the peripheral spiral cloud bands of the typhoon. From 10 to 11 August, as the typhoon moved northward, the main rainfall moved from Zhejiang Province to Jiangsu and Shandong provinces, with the maximum rainfall in Shandong provinces reaching more than 400 mm during this time. In addition, more than 100 mm of rainfall occurred over southern Jiangsu Province. From 11 to 12 August, as the typhoon weakened, the main rainfall was concentrated over northern Shandong. The region of heavy rainfall continued to shrink in size, and the maximum rainfall amount reduced substantially compared with 9–11 August.

Figure 13d–f shows the 3-day rainfall pattern for Typhoon Lekima of the mean of the EC_EPS forecast. Figure 13d reveals that the position of the main rainfall center brought by the peripheral cloud belt is fairly consistent with the observed pattern, but the rainfall amount is obviously lower. The maximum forecast rainfall in Zhejiang is only around 50 mm, far lower than the observed maximum rainfall. Figure 13e shows that the main rainfall center of EC_EPS mean is located in Shandong and Jiangsu provinces, but the rainfall amount is still clearly lower than observations. Figure 13f shows that the main rainfall center travels northward to Bohai Bay, as observed, but the rainfall amount continues to be lower than observed. In summary, the forecast of the EC_EPS mean is fairly accurate in reproducing the position of typhoon rainfall, but the rainfall amount is lower than the observed amount.

Figure 13g–i shows the 3-day rainfall pattern for Typhoon Lekima from the WARMS forecast. In Figure 12g, the rainfall area in Zhejiang brought by the typhoon’s peripheral cloud belt is consistent with the observations, but the distribution is more scattered than the observed pattern. Figure 13h shows the northward movement of the main rainfall center as the typhoon migrates, but the location of the main rainfall center differs from the observed location. The rainfall center in Shandong Province is south of the observed center, whereas the rainfall center in Jiangsu Province is north of the observed center. In addition, the area and amount of rainfall forecast for the Shandong rainfall center are smaller and lower than the observations, respectively, and the location of heavy rainfall is more localized than observed. In Figure 13i, the forecast rainfall center in Bohai Bay is obviously south of the observed center, and the main center is located in eastern Shandong. On the whole, the higher resolution of WARMS generates a more accurate rainfall forecast compared with the EC_EPS mean and also reproduces the typhoon spiral structure. However, the locations and amounts of rainfall forecast by WARMS still show differences from the observed patterns.

Figure 14a–c shows the 3-day rainfall pattern for Typhoon Lekima based on the forecast from S1 after dual-resolution blending. Compared with observations, Figure 14a reveals that the amount of rainfall forecast from S1 is closer to the observed amount compared with the EC_EPS mean and WARMS. In Figure 14b, the rainfall center amount and area of S1 are both greater compared with the EC_EPS mean and WARMS, but the location of the center differs. In addition, S1 underestimates the size of the rainfall center in Shandong and overestimates the size of the rainfall center in Jiangsu. In Figure 14c, the rainfall center of S1 is accurately located compared with the observations, but the amount of rainfall is lower than observed.

Figure 14d–f shows the 3-day rainfall pattern for Typhoon Lekima, as forecasted from S2, after dual-resolution blending. Figure 14d shows that S2 forecasts the amount and location of high rainfall centers generated during and shortly after typhoon landfall in Zhejiang, which are close to observations but do not capture the rainfall belt generated by the peripheral spiral cloud belt. Figure 14e shows that the rainfall forecast of S2 performs better than the EC_EPS ensemble mean and WARMS with respect to the location and amount of rainfall, although it does not perfectly reproduce the observed pattern. Compared with the observations, the rainfall center in Shandong is further south and the amount is lower, whereas the rainfall amount over Jiangsu is higher. As seen in Figure 14f, although the rainfall amount forecast of S2 is closer to the observed amount than that forecast by the EC_EPS ensemble mean, the locations of the rainfall centers still differ from the observed centers. Overall, among the four forecasts, the rainfall forecast of S2 most closely reproduces the observed spatial pattern and amount of rainfall. Although the results for the 72 h lead time are less accurate than those of the shorter lead times, they still provide some indication of rainfall distribution for practical purposes.

5. Case Study Typhoon Rumbia (No. 1818)

Typhoon Rumbia (1818) formed over the southeastern sea of the East China Sea on 15 August 2018 and made landfall along the southern coast of Pudong New Area in Shanghai in the early morning of the 17th. Due to the influence of cold air in the north, Typhoon Rumbia stayed on land for three days and left Shandong Province on the morning of the 20th to enter Bohai Bay, further weakening at night. On the 21st, the Central Meteorological Administration stopped numbering it. Under its influence, Shanghai and the provinces of Zhejiang, Jiangsu, Anhui, Hubei, Henan, Shandong, Liaoning, and other provinces suffered heavy rainfall, most of which broke the extreme rainstorm. As shown in Figure 15b, between 19 and 21 August, the accumulated rainfall reached over 100 mm, and the maximum precipitation can reach over 250 mm in East China. Rumbia is the strongest typhoon that has affected Anhui Province in the past 6 years. During the impact of the typhoon, an area exceeding 100 mm of precipitation accounted for 51.2% of the province’s total area. Rumbia has been stranded in Henan Province for nearly 40 h, with several stations experiencing daily precipitation exceeding historical extremes, setting a record for the highest process rainfall since 1951.

Figure 16 shows the accumulated rainfall amount of ECMWF and WARMS forecasts during the main precipitation periods of Typhoon Rumbia. Compared to the observed rainfall (as shown in Figure 14a), the rainfall amount of the ECMWF forecast is obviously lower than the observed rainfall. Although the rainfall amount of the WARMS forecast can reach 100 mm in East China, the area is obviously bigger than the observed one.

Figure 17 compares the ETS values of S1 and S2 with those of the EC_EPS mean and WARMS. For all rainfall thresholds, the ETS values of S1 and S2 are greater than those of EC_EPS mean and WARMS, meaning that the new rainfall forecasts based on dual-resolution blending perform better than the original forecasts. Especially, the ETS advantages of S1 and S2 are more significant with the 48 h forecast times. As the forecast time increases, such advantages gradually disappear.

6. Conclusions and Discussion

This study proposes a new set of methods to improve typhoon track and rainfall forecasts. The forecasts analyzed in this paper include low-resolution ensemble forecasts (EC_EPS and NCEP_EPS) and high-resolution forecasts (WARMS). While the low-resolution ensemble forecast can provide a more accurate typhoon rainfall field pattern, the high-resolution forecast can provide enough typhoon rainfall amounts. So, in the typhoon track correction, three EMOMs are applied to low-resolution ensemble forecasts to derive a new low-resolution ensemble forecast. Then, by the neighborhood method, the high-resolution probability forecast WARMS_EPS is derived from deterministic forecast WARMS. For typhoon rainfall correction, two schemes of probability-matching technique are applied to blend low- and high-resolution forecasts for the new rainfall forecasts. Verification of the performance of the rainfall forecast and test cases, Typhoon Lekima (1909) and Rumbia (1818) led to the following conclusions:

(1) To correct track prediction of the low-resolution ensemble forecast, three EMOMs of EMOM_OP, EMOM_SF, and EMOM_OPSF are applied to correct EC_EPS, NCEP_EPS, and multi-model EPS, respectively. After comparison, the results show that correction of the track forecast of EC_EPS by EMOM_OPSF gives the smallest average track distance error. Historical statistical analysis reveals that the optimal number of selected ensemble members is 20. The rainfall forecast of the corrected ensemble forecast has a lower Brier score than the original forecasts, meaning that EMOM_OPSF improves forecasts of the typhoon track and rainfall distribution;

(2) The neighborhood method is adopted to select the best range for transforming WARMS to WARMS_EPS. We decided on the selected range based on the maximum ROC area of WAMRS performance during the 6 h before the forecast times;

(3) Through two schemes of probability-matching technique, the low-resolution ensemble forecast after track corrected and high-resolution probability forecast (WARMS_EPS) are blended. This corrected method of rainfall forecast includes two aspects: rainfall pattern adjustment and rainfall frequency adjustment. And the new rainfall forecasts of S1 and S2 are obtained: in S1, the rainfall pattern adjustment is provided by a low-resolution ensemble forecast, and the rainfall frequency adjustment is provided by a high-resolution probability forecast; in S2, the rainfall pattern adjustment is provided by the arithmetical average of low-resolution ensemble forecast and WARMS, and the rainfall frequency adjustment is provided by high-resolution probability forecast. In forecast verification, the results show that ETS values of S1 and S2 are higher than those of the original forecasts for all rainfall thresholds and forecast lead times, and S2 performs particularly well. In terms of bias score, S2 corrects the deviation of rainfall better for light rain and moderate rainfall, whereas S1 corrects the deviation of rainfall better for heavy and torrential rainfall;

(4) Finally, the application of the corrected method is tested using a case study. First, the EMOM_OPSF could improve the track and rainfall forecast. Second, after blending the dual-resolution by probability-matching technique, S1 and S2 perform much better than the EC_EPS mean and WARMS for all rainfall thresholds. In the analysis of the rainfall period in the case of Lekima, the rainfall forecasts of S1 and S2 could improve the reproduction of rainfall amount and location. And S2 is more accurate than S1 in forecasting the high amount of rainfall of the typhoon and the rainfall centers located in Shandong and Zhejiang for the 48 h lead time. However, as the accuracy of rainfall forecast decreases with increasing lead time, S1 and S2 show only limited ability to correct rainfall forecasts for the 72 h lead time.

In the existing post-processing research of the typhoon forecast, a lot of studies mainly focused on either the track forecast or the rainfall forecast. In this paper, both track and rainfall corrections are considered to construct a better forecast that performs more accurate rainfall patterns and amounts. In addition, the neighborhood method is first applied to the typhoon high-resolution deterministic forecast to derive the probability forecast. And the first attempt in research [38] has explored that through the neighborhood method and modified probability-matching technique of dual-resolution rainfall forecasts, the new rainfall forecasts could provide the rainfall amount accurately and reduce the bias to a certain extent in cases. Then, we explored this topic further in this paper, combining it with track forecast correction. Such rainfall correction could also improve the rainfall forecasts in typhoon cases from 2013 to 2019.

However, owing to the large extent of the study area, the use of the probability-matching method means that the typhoon rainfall pattern may not be fully corrected. In future research, target positioning and other methods could be used to better constrain the size and distribution of the main rainfall centers so that rainfall correction is more effective. In the research of Clark [39], an alternative method is developed to restrict the grid points within a determined radius of influence. Qiao [40] compared the forecast skill of different spatial distributions of the reference field in the probability-matching method. Because of the importance of the spatial placement of the probability matching method, alternative reference fields should be explored to improve the typhoon rainfall forecast. More comprehensive observed data should be used to analyze additional typhoon cases in eastern China, and correction methods for the typhoon rainfall location should be explored.