1 Introduction

Improving the accuracy of initial conditions is a crucial prerequisite for the improvement of typhoon numerical prediction. However, typhoons commonly occur in the open ocean, where conventional observation data are scarce. Therefore, the high spatio-temporal resolution data obtained by meteorological satellites have become an essential source of observation information in marine areas.

The application of satellite data assimilation is of great importance for the continuous improvement of typhoon numerical forecasts (Shen et al. 2020). In the 1990s, Eyre et al. (1993) directly assimilated the satellite radiance data in the framework of variational data assimilation, and since then, the application of satellite data in numerical predictions has entered a new era. Using advanced data assimilation methods, many meteorologists have proved that the assimilation of various satellite radiance data can dramatically improve typhoon forecasts (Zhu et al. 2002; Marshall et al. 2002; Zhang et al. 2007, 2013, 2016; Chou and Huang 2011; Liu et al. 2012; Xu et al. 2013; Zou et al. 2016; Zheng et al. 2015; Yang et al. 2016; Wu et al. 2019; Pu et al. 2019; **ao et al. 2020).

Among numerous satellite data, microwave temperature-sounding observations from polar-orbiting meteorological satellites have contributed most noticeably to the improvement of numerical forecasts (Gelaro et al. 2010). Currently, the microwave temperature sounders used for operational assimilation are mainly on board polar-orbiting satellites of the National Oceanic and Atmospheric Administration (NOAA) series in the United States, Meteorological Operational (MetOp) series in Europe and Fengyun series in China. On July 5, 2021, China launched the new-generation polar-orbiting satellite Fengyun-3E (FY-3E), which is the first early-morning-orbit meteorological satellite of China. This satellite, together with the NOAA afternoon-orbit satellites and the MetOp mid-morning-orbit satellites, constitutes a complete 3-orbit observation system (Zhang et al. 2022). Currently, the FY-3E polar-orbiting satellite fills the data gap left by the NOAA and MetOp satellites.

Improving the numerical forecasts through assimilating data from different instruments onboard Fengyun series satellites has received much attention (Lu et al. 2015; Lawrence et al. 2018; Carminati et al. 2018; Wang et al. 2018). The study of the assimilation of Fengyun satellite data on the numerical forecasts of high-impact weather such as typhoons deserves special attention. Yang et al. (2012), Sun and Xu (2021) and Niu et al. (2021), respectively, evaluated the impact of direct assimilation of the microwave-sounding data from the polar-orbiting satellites of the Fengyun series satellites on typhoon forecasts. They proved that satellite data assimilation could positively improve typhoon track and intensity predictions. For the key techniques of Fengyun satellite data assimilation, many scientists have also conducted further detailed research. For example, Du et al. (2012) discussed the influence of bias correction based on the FY-3A microwave temperature sounding data on typhoon track forecasts. Li and Zou (2014) further improved typhoon forecasts based on the FY-3A microwave temperature-sounding data assimilation by improving the quality control method. Dong et al. (2014) analyzed the improvement of FY-3A microwave-sounding data assimilation for typhoon forecasts under clear and cloudy sky conditions. Xu et al. (2016) and **an et al. (2019) investigated the effectiveness of the FY-3B MWHS and FY-3C MWHS-2 data assimilation on the double-typhoon forecasts, respectively.

The third generation of the Microwave Temperature sounder (MWTS-3), onboard the FY-3E, belongs to the newest generation of meteorological satellite instruments. The previous analyses have demonstrated the characteristics of observation errors, biases and various noises of the MWTS-3 data (Qian et al. 2022). The application of the MWTS-3 data assimilation has become an urgent task. This study focuses on the evaluation of the improvement of the MWTS-3 data assimilation on typhoon forecasts. The Weather Research and Forecast data assimilation system (WRFDA; Barker et al. 2012) is selected, and the assimilation-related quality control, bias correction and observation error specification are completed by adding an assimilation module of the MWTS-3 to the WRFDA. In this way, the effective assimilation of the MWTS-3 data by the WRFDA system is achieved. Super Typhoon Chanthu (2021), which affected China, is selected to verify the improvement of the MWTS-3 data assimilation for typhoon forecasts through several sensitivity experiments.

The remainder of the paper is organized as follows. The data characteristics of the MWTS-3 instrument are briefly described in Sect. 2. Section 3 introduces the model and assimilation system used in this study. Section 4 shows the main features of Typhoon Chanthu and the relevant experimental design. Section 5 presents the MWTS-3 data assimilation module, including the cloud detection, bias correction and module inspection. Section 6 analyzes the increment of MWTS-3 assimilation and the differences in the typhoon forecast caused by the data assimilation. Section 7 provides the improvement of assimilation on the spatial distribution and score of precipitation forecasts. The conclusions and discussion are presented in Sect. 8.

2 Data

On July 5, 2021, China’s first civilian early-morning-orbit satellite, FY-3E, was successfully launched, and the MWTS-3 it carries was also successfully put into operation. Compared with the MWTS-2, the sensitivity and calibration accuracy of the MWTS-3 were greatly improved (Zhang et al. 2022). The spatial resolution at the nadir point increased to 33 km. The orbit width increased from 2250 to 2700 km, greatly improving the observation coverage. Four channels with frequencies of 23.8 GHz, 31.4 GHz, 53.246 ± 0.08 GHz and 53.948 ± 0.081 GHz were added. Among them, the 23.8 GHz and 31.4 GHz channels are used to enhance the measurement of total water content, and the 53.246 ± 0.08 GHz and 53.948 ± 0.081 GHz channels are used to supplement the temperature detection in the troposphere at 4 km and 6 km from the surface, respectively. More detailed information can be found in Zhang et al. (2022).

The typhoon track used for verification is from the best track dataset provided by the Shanghai Typhoon Institute of the China Meteorological Administration (Ying et al. 2014; Lu et al. 2021).

The Climate Precipitation Center Morphing (CMORPH) precipitation product is selected for verification. It is obtained by fusing the hourly precipitation data from more than 30,000 automatic weather stations in China with the data obtained by optimal interpolation based on the probability density function and climatic precipitation data (Shen et al. 2014).

3 Numerical model and data assimilation system

The Advanced Research Weather Research and Forecast (WRF-ARW) model is a new generation mesoscale regional weather and climate model jointly developed by the National Center for Atmospheric Research (NCAR), National Center for Environmental Prediction (NCEP) and other scientific research institutions. The WRF-ARW version 4 is selected for this study (Skamarock et al. 2008). Figure 1 shows the model domains, the 500 hPa geopotential height and relative humidity fields from the NCEP Final analysis (FNL) data at 0000 UTC on September 12, 2021. The horizontal resolution of the model is 9 km, and the vertical layers are 61 from the surface to the model top (about 50 hPa). The total grid points in the model domains are 600 × 500 × 61. To obtain stable assimilation impacts, this study only selected a fixed domain and did not use moving domains that are more suitable for typhoon simulation.

Fig. 1
figure 1

Spatial distributions of the 500 hPa geopotential height (contours, 20 m interval) and relative humidity (shaded area, unit: %) from the NCEP Final analysis (FNL) dataset at 0000 UTC on September 12, 2021. The thick black circle presents the model coverage. The typhoon symbols represent the best track of the typhoon from 1800 UTC on September 10 to 0000 UTC on September 14 with an interval of 6 h, and the white one is the typhoon position at that time

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The parameterization schemes include the WRF single-moment 6 microphysical scheme (Hong and Lim 2006), Kain-Fritsch cumulus parameterization scheme (Kain 2004) and Yonsei University planetary boundary layer scheme (Hong et al. 2006).

The WRFDA system was developed by the NCAR, which includes the three-dimensional variational and four-dimensional variational systems and the hybrid assimilation system (Barker et al. 2012). In this study, the three-dimensional variational assimilation method is selected. The WRFDA system can assimilate a variety of conventional and non-conventional observations, and as the observation operators of satellite data, it is compatible with the Radiative Transfer for TOVS model developed by the European Organization for the Exploitation of Meteorological Satellites (Saunders et al. 2018) and the community radiative transfer model (Weng 2007) developed by the Joint Center for Satellite Data Assimilation. By using these two radiative transfer models, the WRFDA achieves the assimilation of microwave and infrared data from various polar-orbiting and geostationary satellites. In this study, the Radiative Transfer for the TOVS model is used to simulate the MWTS-3 radiance data.

At present, the public version of the WRFDA is not able to assimilate the MWTS-3 data. By adding the assimilation module applicable to the MWTS-3 data in the WRFDA, the steps of quality control, bias correction and observation error specification related to assimilation can be completed, and the effective assimilation of the MWTS-3 data by using the WRFDA system can be achieved. The assimilation window is set to 1.5 h according to the past experience, so as to minimize the impact of the difference between observation time and assimilation time.

The background error covariance of the CV5 type is generated by using the auxiliary program included in the WRFDA system. The 12 h and 24 h forecasts are made every 6 h from August 1 to 31, 2021 by the WRF-ARW model with the same parameter setting as the control and sensitivity experiments. Then, the NMC (National Meteorological Center) method is applied to generate domain-specific background error covariance (Parrish and Derber 1992). Control variables of the CV5 error covariance are composed of the following variables: streamfunction (ψ), unbalanced velocity potential (χu), unbalanced temperature (Tu), pseudo relative humidity (RHs), and unbalanced surface pressure (Ps,u).

As a preliminary study, this study only focuses on data assimilation in the clear sky area. To further reduce the influences of inaccurate surface and cloud emissivity on data assimilation, the observation data at channels 1–8 are not considered, and the data at channels 13–17 are not assimilated to avoid the influence of insufficient model top height (Zou et al. 2015a, b). Thus, only the observation data at channels 9–12 are assimilated in this study. To eliminate the limb effect, only the data in the 10–90 fields of view are assimilated. In addition, observations with the fields of view covering the coastline and mixed underlying surface types are also excluded. To reduce the correlation of observation errors, we thinned the spatial resolution of the observation data to 60 km, which is mainly determined by the distance between the position of observations and the center of the nearest model grid points. According to Qian et al. (2022), the observation errors at channels 9–12 of the MWTS-3 are set as 0.48 K, 0.43 K, 0.38 K and 0.57 K, respectively.

4 Case overview and experiment design

4.1 Typhoon Chanthu (2021)

At 1600 UTC on September 7, 2021, Typhoon Chanthu was generated in the Northwest Pacific Ocean. On September 8, it strengthened to a super typhoon and continued to intensify. The minimum sea level pressure (SLP) in the typhoon center was 930 hPa, and the maximum wind speed near the center was over 68 m s−1. On September 11, this typhoon gradually weakened to the typhoon grade. After typhoon genesis, Typhoon Chanthu gradually moved northwestward from the east of Taiwan and reached the southeast of Hangzhou at 1300 UTC on September 12. On September 14, it slowly moved to the ocean area about 225 km east of Shanghai, then gradually moved eastward, made landfall in Japan on September 17, weakened to a tropical depression on September 18, and gradually dissipated.

4.2 Experiment design

From September 11 to 14, 2021, Typhoon Chanthu moved along the coast of China and affected Zhejiang, Shanghai and Jiangsu provinces. This research focuses on the typhoon forecasts during this period. To better highlight the influence of the assimilation of the FY-3E microwave temperature sounding data on typhoon forecasts, we designed a total of five experiments in the study. The first and second experiments are non-assimilation experiments. In experiment 1, we directly use the FNL data at 1800 UTC on September 10, 2021 as the initial field for the 78 h forecast (called FNL78). In experiment 2, we adopt the FNL data at 0000 UTC on September 12, 2021 as the initial field for the 48 h forecast (called FNL48). Experiments 3–5 are assimilation experiments. In experiment 3, only conventional observations are assimilated, i.e., the CONV experiment. In experiment 4, we only assimilate the MWTS-3 data from the FY-3E (MWTS experiment). Both conventional data and MWTS-3 data are assimilated in experiment 5, which is called the SAT experiment.

The conventional observations consist of a global dataset of surface and upper-air reports operationally collected by the NCEP, including the observations from the land surface, sea surface, the radiosonde and aircraft reports from the Global Telecommunications System, the profiler-derived and U.S. radar-derived wind, the Special Sensor Microwave Imager oceanic wind and atmospheric total column water retrievals, and the satellite wind data.

In all the assimilation experiments, the initial condition of assimilation is the 6 h forecast initialized at 1800 UTC on September 10, 2021. After 5 assimilation cycles, the total period of the forecast is 48 h from 0000 UTC on September 12 to 0000 UTC on September 14.

5 Analysis of assimilation results

5.1 Cloud detection

Four new channels have been added to the MWTS-3, two of which are located at 23.8 GHz and 31.4 GHz. The two new channels of 23.8 GHz and 31.4 GHz also enable the MWTS-3 to have the capability to retrieve the cloud liquid water path (CLW) over the ocean (Dong et al. 2022). In consideration of the strong angle dependence of O-B for MWTS-3, the empirical correction scheme has been developed based on one-month MWTS-3 data over the ocean, to adjust the asymmetry of each relevant channel according to Weng et al. (2000). By using the retrieved CLW, the cloud radiance over the ocean can be accurately identified.

For the data over the ocean, when the retrieved CLW is greater than 0.02 g kg−1, it is recognized as cloudy data (Zou et al. 2016). Of course, the retrieved CLW can only be used for the observations in ocean areas, and the cloud detection in the land area is based on the cloud detection index calculated according to the interchannel variability of low-level channel brightness temperatures (Wu et al. 2021).

5.2 Bias correction

The bias correction method follows the variational bias correction scheme included in the WRFDA system (Auligné et al. 2007; Dee 2004), and before the assimilation experiment, we conduct 50 assimilation cycles to ensure the stability of variational bias correction coefficients. Figure 2 shows the spatial distribution of the observation-minus-background (O-B) biases of the MWTS-3 brightness temperature at channel 9 before and after the variational bias correction. The results show that there are obvious positive O-B biases of the MWTS-3 brightness temperature before the bias correction (Fig. 2a), with an average bias of 1.7 K. However, after the bias correction, the O-B MWTS-3 temperature bias shows apparent “positive–negative” distribution characteristics, with an average value of 0.07 K. Among them, the biases in the eastern area of the Qinghai Tibet Plateau are mostly positive, while in the surrounding areas, they are mainly negative. The weighting function of channel 9 is about 400 hPa, and the O-B temperature biases do not exhibit characteristics of varying with topographic height.

Fig. 2
figure 2

Spatial distribution of the observation-minus-background (O-B) biases of the MWTS-3 brightness temperature (color point, unit: K) at channel 9 at 0000 UTC on September 10, 2021 before (a) and after (b) the bias correction. The small black dots represent the observation data rejected by quality control, and the thick black lines represent the areas with a terrain height greater than 3000 m

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5.3 Comparison of observation-minus-background and observation-minus-analysis brightness temperature biases

To clarify the assimilation effectiveness of the data assimilation system on the MWTS-3 observation information, Fig. 3 shows the spatial distribution of the O-B and observation-minus-analysis (O-A) MWTS-3 brightness temperature biases for channels 9 and 10. The results suggest that the O-B biases at the two channels are positive in the east of the Qinghai Tibet Plateau, while they are dominated by negative values in the north and south parts, and the negative values for channel 10 are more noticeable. The O-A biases for the two channels are basically characterized by spatially random variation. The positive values of the O-B in the central part are markedly reduced, and the negative biases for channel 10 on the north and south sides are also obviously reduced. In general, the simulated brightness temperature after assimilation is noticeably closer to the observations, which also indicates that the data assimilation system can integrate the observation information well.

Fig. 3
figure 3

Spatial distributions of the O-B (a, c) and O-A (b, d) for channels 9 (a, b) and 10 (c, d) at 0000 UTC on September 12, 2021. The thick black line represents the area where the terrain height is more than 3000 m

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6 Numerical results

6.1 Increment of air temperature and geopotential height at 500 hPa

After clarifying the performance of the assimilation system, we further analyze the influence characteristics of data assimilation. Figure 4 displays the spatial distribution of the analysis results of the atmospheric temperature and the geopotential height at 500 hPa in the SAT experiment at 0000 UTC on September 12, 2021 (time of the last assimilation). There are two centers of temperature, a cold center located in the north of the region and a large-scale warm center located in the south. The increment between the SAT and FNL experiments (SAT minus FNL) indicates that the temperature around the typhoon is reduced after data assimilation, but there is a weak warming in the north and south sides of the typhoon. In addition, there is also a cooling phenomenon in the southwest of the typhoon. The cold center in the north further intensifies, and the maximum temperature drop can exceed 2 K. The left positive and right negative phenomenon of temperature increment near the low-temperature center also indicates that data assimilation causes the cold center to move eastward.

Fig. 4
figure 4

Spatial distributions of the air temperature (a contours with an interval of 1 K) and geopotential height (b contours with an interval of 20 m) at 500 hPa and the corresponding increment differences (shaded areas) in the temperature and geopotential height between the SAT and FNL experiments (SAT results minus FNL48 results) at 0000 UTC on September 12, 2021

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The 500 hPa geopotential height (Fig. 4b) clearly shows the typhoon structure. Corresponding to the temperature decrease, the low-pressure center in the north strengthens further and extends southward. Meanwhile, the high-pressure ridge west of the low-pressure center also strengthens. In the typhoon area, there is an apparent low-pressure center in the 500 hPa geopotential height. After assimilation, the geopotential height around the typhoon increases, while the typhoon center has a decrease in the geopotential height, which indicates that the typhoon intensity in the background is enhanced further after data assimilation. In the ocean area east of the typhoon, the geopotential height mainly decreases. The geopotential height southwest of the typhoon is also reduced slightly. This reduction of the geopotential height is more conducive to the westward extension of the western Pacific subtropical high (WPSH). The follow-up forecast results suggest that the decrease of the geopotential height is also favorable to the slight eastward turn of the typhoon.

Of course, more noteworthy is the influence of the MWTS-3 data assimilation. The increment difference between the SAT and CONV experiments, i.e., the SAT minus the CONV (Fig. 5) shows that the extra influence of MWTS-3 data assimilation on the temperature is similar to that of the SAT experiment in terms of the spatial structure. However, adding the MWTS-3 data to the CONV experiment can further increase the atmospheric temperature in the surrounding areas of the typhoon and also contribute to the temperature decrease in the low-temperature center in the north. For the geopotential height, the most important effect is that the assimilation of the MWTS-3 data makes the decrease in the geopotential height in the typhoon center more obvious, indicating that the typhoon in the model further strengthens by the MWTS-3 data assimilation. Similarly, an increase in geopotential height to the south of the typhoon further facilitates the northeasterly turning of the typhoon.

Fig. 5
figure 5

Spatial distributions of the atmospheric temperature (a contours with an interval of 1 K) and geopotential height (b contours with an interval of 20 m) at 500 hPa and the corresponding increment differences (shaded areas) between the SAT and CONV experiments (SAT results minus CONV results) at 0000 UTC on September 12, 2021. The dashed line in (b) represents the position of the cross section in Fig. 6

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Figure 6 shows the cross-section of the increment difference in temperature and geopotential height at 0000 UTC on September 12, 2021 to further investigate the vertical range of the influence of MWTS-3 data assimilation on the typhoon. Typhoon Chanthu is located in the east of Taiwan Island. From Fig. 6a, it can be found that the temperature of the typhoon center obviously increases by the assimilation of the conventional and MWTS-3 data, and the temperature increment can exceed 2.5 K. The most apparent temperature increase is near 500 hPa. Meanwhile, the air temperature at 850 hPa on the east and west sides of the typhoon shows a certain decrease, while the atmospheric temperature far from the typhoon generally increases, with an increment of more than 0.5 K.

Fig. 6
figure 6

Cross-section of increment differences in air temperature (shaded areas) and geopotential height (contours with an interval of 5 m) at 0000 UTC on September 12, 2021 a between the SAT and FNL78 experiments (SAT results minus FNL78 results) and b between the SAT and CONV experiments (SAT results minus CONV results). The white typhoon symbols represent the position of Typhoon Chanthu in the best track data at the corresponding time

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Corresponding to the temperature increase, the geopotential height in the typhoon center decreases to 100 m, but the geopotential height on the right side of the typhoon increases, with a maximum increment of 10 m. This result indicates that the typhoon strengthens remarkably, while the typhoon range is reduced to a certain extent.

The increment differences between the SAT and CONV experiments can better reflect the influence of the MWTS-3 data assimilation. The temperature increase caused by the MWTS-3 data assimilation appears mainly in the typhoon center area, with an increment of about 2 K. Note that the center of the temperature increase is mainly located at 700 hPa. However, the reduction of geopotential height can reach about 70 m, which is similar to the results in the SAT experiment, demonstrating that the intensification of the forecasted typhoon is mainly caused by the MWTS-3 data assimilation.

Figure 7 shows the impact of data assimilation on the 500 hPa water vapor. There is a belt area with high specific humidity around the typhoon, covering the southwestern region of China and the ocean area south of the Korean Peninsula. From the shadow in Fig. 2a, it can be seen that compared to the FNL78, the specific humidity in the SAT experiment is increased over the ocean in the east and south of the typhoon, especially in the south of the typhoon where the increase of water vapor is most significant (over 2.0 g/kg). At the same time, the specific humidity is reduced over the ocean to the north of the typhoon. Under the influence of counterclockwise wind caused by the typhoon, the decrease in the specific humidity will help reduce the error of overpredicted precipitation in the land area. Adding MWTS-3 data to the CONV experiment will further reduce the specific humidity over the ocean north of the typhoon, and the specific humidity over the ocean east of the typhoon is also slightly increased. The shadow structure in Fig. 7b is very similar to that of Fig. 7a, which also proves that MWTS-3 can further improve the spatial distribution characteristics of specific humidity. The addition of MWTS data further increases the water vapor in the southern area of the Korean Peninsula. Subsequent analysis also proves that this has a certain effect on improving the insufficient precipitation forecast over ocean.

Fig. 7
figure 7

Spatial distributions of the 500 hPa specific humidity (countours, unit: g/kg) and wind vector (vectors, unit: m/s) of the SAT experiment and the corresponding differences (shaded, unit: g/kg) between SAT and FNL78 (CONV) at 0000 UTC on September 12, 2021. The hurricane symbol shows the position of Typhoon CHANTHU from the best track data at the current time. a SAT − FNL78; b SAT − CONV

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6.2 Forecast validation

Figure 8 presents the spatial distribution of the SLP forecasted in the SAT experiment with an interval of 12 h from 0000 UTC on September 12 to 0000 UTC on September 14, 2021. The forecast results in the SAT experiment will reproduce the movement of the typhoon to the northeast and its stay on the ocean east of Shanghai. The forecast results show that Typhoon CHANTHU does not directly make landfall on the eastern coast of China. However, the forecasted typhoon intensity is slightly weaker than the observations. Additionally, the minimum SLP of the best track data is around 950 hPa during this period, while the minimum SLP forecasted in the SAT experiment is around 970 hPa.

Fig. 8
figure 8

Spatial distributions of the sea level pressure forecasted in the SAT (solid lines, unit: hPa, interval: 2 hPa) and FNL48 experiments (dotted lines, unit: hPa, interval: 2 hPa) at an interval of 12 h from 0000 UTC on September 12 to 0000 UTC on September 14, 2021. The shaded areas indicate the sea level pressure differences between the SAT and FNL48 experiments (SAT results minus FNL48 results). The white typhoon symbol represents the best track data with an interval of 12 h

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The forecasts in the FNL48 experiment (dashed contours in Fig. 8) show that the typhoon makes landfall in Fujian Province at 0000 UTC on September 13 and has been located on the land of eastern China since then, which is markedly different from the best track data. Compared with the FNL48 experiment, after 12 h of the forecast, the SLP differences between the SAT and FNL48 experiments (SAT minus FNL48) are positive on the west side of the typhoon and negative on the east side, suggesting that the typhoon center forecasted by the SAT experiment is obviously more eastward than the FNL48 forecast, and this eastward phenomenon is more obvious with the increase of the forecast time. Compared with the best track data, it can be seen that the improvement effect of SAT experiments on track forecast becomes more significant as the forecast time-length increases.

6.3 Impact of the MWTS-3 data assimilation

Impact of the MWTS-3 data assimilation on the forecast of 500 hPa geopotential height is shown in Fig. 9. From the forecast results, it can be seen that the reduction of the geopotential height in the southwest is conducive to the westward extension of the WPSH, and the 5880 isoline extends westward to the south of the typhoon after 12 h of the forecast and then further westward. It is reasonable to believe that the westward extension of the WPSH favors the typhoon track more northeastward. Failure to forecast the location of the WPSH well may also be responsible for the westward deviation of the track in the FNL48 forecast results.

Fig. 9
figure 9

Spatial distribution of the 500 hPa geopotential height (contours with an interval of 20 m) forecasted by the SAT experiment from 0000 UTC on September 12 to 0000 UTC on September 14, 2021. The shaded areas indicate the difference in the geopotential height between the SAT and CONV experiments. The white typhoon symbols represent the best track of the typhoon with an interval of 12 h

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From the 12 h forecast on, the SAT experiment shows higher geopotential height on the south of the typhoon than the CONV experiment, but lower geopotential height on the north of the typhoon. This indicates that the typhoon predicted by the SAT experiment moves faster than that of the CONV experiment, and the position difference between the two does not disappear until September 14th.

To clarify the accuracy of typhoon track forecasts by different experiments, we compare the forecasted tracks and the best track data from 0000 UTC September 12 to 0000 UTC September 14, 2021 (Fig. 10). It can be clearly seen that in the best track results, CHANTHU moved along the eastern coast of China, and gradually turned northeast. Then, it made a brief stop in the eastern ocean of Shanghai. Two unassimilated experiments, FNL48 and FNL78, both incorrectly predict that this typhoon would make landfall in Zhejiang Province of China at 0000 UTC on September 13. All assimilation experiments have successfully predicted the non-landing characteristics of this typhoon. Even the MWTS experiment, which only assimilates MWTS-3 data, can significantly improve the track prediction. By simultaneously assimilating conventional data and MWTS-3 data, the improvement of track prediction by the SAT experiment is more remarkable. Especially after 12 h forecast, the track accuracy predicted by the SAT experiment is stably better than that of the CONV experiment.

Fig. 10
figure 10

Tracks for the typhoon CHANTHU from 0000 UTC September 12 to 0000 UTC September 14, 2021. Black line is the best track. Blue, green and cyan lines are for SAT, CONV and MWTS experiments, respectively. Red and orange lines are for FNL48 and FNL78, respectively

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To further clarify the stability of MWTS-3 data assimilation in improving typhoon track forecasting, the study also conducted rolling forecast experiments on Typhoon CHANTHU. During September 11–12, 2021, the typhoon CHANTHU passing through the east coast of China, seven forecasts with 6 h interval were conducted, and all experiment settings were consistent with the previous description. Track errors of different experiments are shown in Fig. 11, bars in the figure represent average track errors at different forecast lengths. The vertical black lines represent the standard deviation of track errors. From the figure, it can be seen that the SAT experiment outperforms the CONV experiments at all forecast lengths, which also indicates that MWTS-3 data assimilation has a stable positive effect on typhoon track forecasts, and the standard deviation can also be reduced to a certain extent, indicating that the differences between different forecasts are also reduced by MWTS-3 data assimilation. However, the improvement effect also decreases with the increase of the forecast time.

Fig. 11
figure 11

The variation of the average and standard deviation of track forecast errors for rolling tests with the forecast time. Red and blue bars are for the CONV and MWTS experiments, respectively. Black vertical lines represent the standard deviation of track forecast errors at different forecast time

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7 Validation of precipitation forecast

Heavy rainfall is one of the direct impacts of typhoons on human beings. The previous analysis demonstrated that data assimilation can improve the forecasts of typhoon track and intensity. To further explore the role of data assimilation in the improvement of typhoon forecasts, we take precipitation as an example to analyze the impact of the improvement of typhoon forecasts on precipitation forecasts.

The equitable threat score (ETS) is used to quantitatively evaluate the rainfall forecast skill of those experiments. The ETS is calculated as follows (Junker et al. 1992; Wilks 1995):

$$\mathrm{ETS}=\frac{h-{h}_{R}}{h+m+f-{h}_{R}},$$
$${h}_{R}=\frac{(h+m)(h+f)}{a}.$$

Here, a is the total number of grids of the verification domain, h is the number of correct forecasts at a specified threshold of the observed rainfall events, and m is the number of incorrect forecasts. f is the ratio of the number of grids where there is rainfall in the forecasts but no rainfall in the observations to the total number of grids. \({h}_{R}\) is a measure of the hits (h) by random forecast (Junker et al. 1992). The ETS indicates how well the observed rainfall events are correctly forecasted when the hits from random chance are eliminated. The ETS varies from − 1/3 to 1. The highest value of ETS is 1, indicating a perfect rainfall forecast.

Figure 12 displays the ETS of the 3 h accumulated precipitation forecasts. The FNL78 and FNL48 experiments (no assimilation) have better ETS values with a threshold of 1 mm in the first 15 h of the forecast. But for the scores with larger thresholds, the ETSs for the two experiments without assimilation are considerably lower than those of the SAT and CONV experiments. From the comparison of the histograms, it can be found that the ETSs for the SAT experiment are higher than the other two assimilation experiments at most of the forecast time.

Fig. 12
figure 12

The equitable threat scores (ETSs) of the 3 h accumulated precipitation forecasts at the thresholds of a 1 mm, b 5 mm, c 10 mm and d 15 mm for the MWTS (red), CONV (gray), SAT (blue), FNL78 (black dotted line) and FNL48 (green dotted line) experiments in the period from 0000 UTC on September 12 to 0000 UTC on September 14, 2021

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To more intuitively see the reasons for the improvement of ETSs, we analyze the spatial distribution of the observed and forecasted 3 h accumulated precipitation during 0600–0900 UTC on September 13, 2021 (Fig. 13). At this moment, the typhoon center is located on the eastern ocean of Shanghai, and the observed precipitation is mainly located in the northeast of the typhoon. The highest 3 h precipitation reaches over 60 mm. There is a strong spiral rain belt on the east of the typhoon center. But, in the coastal areas of Southeast China, there is mainly light rain (below 5 mm). The SAT experiment has well predicted the main characteristics of precipitation, especially the characteristics of light rain on land, but the precipitation forecast in the east of the typhoon is poor. The shortage of underestimated rainfall in the ocean area of the CONV experiment is more obvious, and there is basically no prediction of the spiral rain belt in the east of the typhoon. Moreover, there is an obvious overpredict error of precipitation over land, which is possibly caused by its deviation in predicting the track of the typhoon. For the other three experiments, there is also an error of excessive land precipitation and less precipitation in the eastern ocean area.

Fig. 13
figure 13

Spatial distributions of the a observed and predicted 3 h accumulated precipitation (unit: mm) by the b SAT, c CONV, d MWTS, e FNL48 and f FNL78 experiments during 0600–0900 UTC on September 13, 2021

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To further verify the stability of MWTS-3 data assimilation impact, a 10 day 6 h rolling assimilation experiment is conducted. The model parameter specification of the rolling test is similar to the above cases, except that five-cycle assimilation and 24 h forecast tests will be conducted every 6 h starting from 0000 UTC September 11, 2021 to 1800 UTC September 19, 2021. A total of 37 experiments were conducted. Finally, the average results of ETS scores with different forecast time lengths are calculated. The results are shown in Fig. 14. The precipitation observation data CMORPH mentioned above is also selected for the precipitation verification of the rolling test.

Fig. 14
figure 14

The averaged equitable threat scores (ETSs) varying with forecast time for the 3 h accumulated precipitation forecasts at the thresholds of 1, 5, 10 and 15 mm forecasted by the SAT (blue) and CONV (red) experiments

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It can be seen from the average results of ETS that MWTS-3 data assimilation has a small improvement on the ETS at 1-mm threshold, but for thresholds above 5 mm, MWTS-3 assimilation has a significant improvement effect on precipitation prediction skills, and with the increase of threshold, the improvement effect is more stable, especially after the first 12 h of the forecast. With the increase of forecast time, the improvement effect of MWTS-3 assimilation is gradually weakened. In general, the results of the rolling test can prove that MWTS-3 data assimilation has a stable improvement effect on the skill of precipitation forecast when the rainfall is heavier than 5 mm.

8 Conclusions and discussion

The polar-orbiting satellite microwave temperature sounder data are the most influential data in the operational assimilation system. The assimilation of the FY-3E data deserves serious study and is also essential for the application of satellite data.

Based on the previous analysis of observation errors (Qian et al. 2022) and the CLW retrieval research (Dong et al. 2022), the corresponding MWTS-3 data assimilation module is added to the WRFDA data system to evaluate the impact of the MWTS-3 data assimilation on the forecast of Typhoon CHANTHU affecting China. The results indicate that the MWTS-3 data assimilation can improve the forecast accuracy of the atmospheric temperature and geopotential height around the typhoon. Meanwhile, the intensity and range of the WPSH can also be improved, which eventually improves the error of the track forecast in the experiments without assimilation. Comparing those forecast results from the three assimilation experiments. The simultaneous assimilation of the conventional data and MWTS-3 data can make the best forecasts of the typhoon track, intensity and related precipitation. The results of the rolling test also proved that MWTS-3 data assimilation has a stable improvement effect on the typhoon track forecasts and the forecast skill of precipitation heavier than 5 mm.

In the follow-up study, we will try to further improve the MWTS-3 data assimilation, mainly including the detailed analysis of observation errors, especially the error analysis and assimilation in the land area. Moreover, we will also pay attention to the collaborative assimilation of microwave temperature sounder and humidity sounder data to further realize the coordinated variations of temperature and water vapor in the background field and ultimately improve numerical prediction.