*2.7. Bias Correction*

The CMA-GFS 4D-VAR system was used in this study. The basic theory of variational data assimilation is the Bayesian conditional probability theorem [35]. This theory assumes that the background error and observation error satisfy the Gaussian distribution, and that there is no systematic bias. However, in practical application, systematic biases generally exist in the background and are mainly caused by the continuous forward integration of the numerical model. Meanwhile, there are inevitably systematic errors in the radiation transfer model simulations. These also lead to a certain degree of systematic biases in the O-B, meaning effective bias correction is necessary.

The importance of bias correction for satellite radiances in data assimilation has been realized by many meteorologists, and a lot of studies have been conducted to develop effective bias correction methods. It is found that systematic bias mainly consists of the bias caused by the scanning position difference and the bias depending on the air-mass property. Harris and Kelly (2001) developed a static bias correction scheme [36]. After a lot of practical applications, it has proven to be an effective correction scheme and is widely used in operational NWP centers around the world [3,4]. In 2007, Liu et al. (2007) added this scheme to the CMA-MESO model and also achieved good results [37]. However, considering the limitation of the static bias correction scheme in estimating the bias caused by the change in the weather system, an air-mass bias correction method has been proposed to take into account the impact of weather systems on systematic biases [3]. In addition, a variational bias correction scheme has also been established, which considers the variation of biases in combination with the minimization process of the assimilation system [38]. At present, this scheme has been applied in many national operational forecast centers, such as the National Centers for Environmental Prediction (NCEP) and the ECMWF [3,39,40]. After selecting the appropriate forecast factors, the variational bias correction scheme statistically updates the correction coefficients in the minimization process of the cost function. This scheme has also been tested in the CMA-GFS, and it is expected to achieve operational application in 2023. However, only the scan bias correction and the air-mass bias correction are involved in this study.

#### 2.7.1. Scan Bias Correction

Since the scan angle bias obviously changes with the latitude, the statistics of scan bias also need to be conducted in different latitude bands. The whole hemisphere was divided into 18 latitudinal bands using 10◦ intervals. For each latitude band, the O-B difference between each scanning position and the nadir point in each scan line was calculated, and then the average value of all the O-B differences in the same latitude band was obtained as the systematic bias in this latitude band. A linear smoothing method was also applied to avoid discontinuous correction between the two adjacent latitudinal bands.

#### 2.7.2. Air-Mass Bias Correction

In this study, two predictors were selected for the air-mass bias correction, namely, the thicknesses between 300–1000 hPa and 50–200 hPa of the background. Using the two-week thickness data, a linear regression equation was established for each channel, and the coefficients, *ajo* and *aji*, in the regression equation were obtained for the channel *j* data with a scan angle of *θ*. The regression equation is as follows:

$$\text{Bias}\_{j}(\theta) = a\_{j0} + \sum\_{i=1}^{2} a\_{ji}(\theta) X\_{ji}(\theta)$$

Here Bias*<sup>j</sup>* is the O-B bias, and *Xji* is for the thickness. *ajo* and *aji* represent the linear relationship between the O-B bias and the two thickness data. Using these coefficients, the O-B bias was calculated and subtracted from each observation in the assimilation process.

After the bias correction, the QC module also removes the observation data with large O-B values, and the pixels with O-B values greater than two times that of the observation error are rejected. According to the analysis results in Figure 4, the observation errors were set to 0.55 K for MWTS-3 channels 9, 10, and 12–14, 0.4 K for channel 11, and 1.1 K for channel 15 in this study.

#### **3. Results**

#### *3.1. Experimental Design*

Four experiments were conducted to demonstrate the impact of MWTS-3 data on the CMA-GFS during the period from 24 September to 25 October 2021. Table 2 shows the specific experimental designs. Experiment 1 assimilated only the conventional observations, called CTRL1. The conventional observations contain a global set of surface and upper-air reports, including radiosondes, SYNOP, ship reports, Aireps, and AMVs from the Global Telecommunications System (GTS). Experiment 2 assimilated the conventional observations: NOAA-15/18/19 AMSU-A, NOAA-18/19 MHS, MetOp-A/B AMSU-A, MHS and IASI, NPP ATMS, FY-3C/D MWHS-2 and MWRI, FY-3D MWTS-2 and HIRAS radiance data, FY-3C/D GNOS, COSMIC RO data, etc., called CTRL2. The setup of the two sensitive experiments (TEST1 and TEST2) is identical to the control experiments (CTRL1 and CTRL2), except that the FY-3E MWTS-3 radiance data were added in TEST1 and TEST2.

**Table 2.** Experiment design for the four cycle experiments.


Notes: conventional data consists of radiosondes, SYNOP, ship, Airep, and AMVs.

#### *3.2. Analysis and Forecast of the Cycling Experiments*

#### 3.2.1. Characteristics of Data after Quality Control and Bias Correction

Figure 5 shows scatter plots of the observed and simulated brightness temperature of MWTS-3 channels 11 and 14 before and after QC during September 24–30, 2021. It can be seen that the differences between the O and B of channel 11 are larger before QC, which are scatter distributed, especially in the range of 210–220 K. Besides, the scatter plots obviously deviate from the diagonal. After QC, only the clear-sky observations over the ocean are retrained, which makes the distributions of O and B closer to each other, and the differences between them are from −3 K to −5 K. Figure 5b is for channel 14, where the scatter plots are already close to the diagonal before QC, only the plots with a brightness temperature higher than 230 K slightly deviate from the diagonal. The QC removes those abnormal observations effectively and makes the plots closer to the diagonal after QC.

Figure 6 shows the probability density functions of O-B for channels 11 and 14 before and after bias correction. Before bias correction, the biases of channels 11 and 14 are about −0.8 K and 0.8 K, and the STDs are 0.31 K and 0.55 K, respectively. The biases after correction are within ±0.1 K, and the STDs are slightly reduced to 0.29 K and 0.48 K, respectively. This indicates that the systematic biases of O-B have been corrected.

3.2.2. Comparisons of Observation Biases and Errors between MWTS-3 and Other Microwave Temperature Sounders

In order to further clarify the performance of MWTS-3, the bias and error characteristics of various microwave temperature-sounding data assimilated in TEST2 are given in this subsection, where the microwave temperature sounders include FY-3E MWTS-3, FY-3D MWTS-2, AMSU-A onboard NOAA-15/18/19, MetOp-A/B, and NPP ATMs. Figure 7 shows the biases and STDs of O-B from MWTS-3 and AMSU-A before and after bias correction in TEST2 during the period from 24 September to 25 October 2021. Among them, the frequencies of AMSU-A channels 5 and 6–14 are the same as those of MWTS-3 channels 7 and 9–17.

**Figure 5.** Scatterplots of observed (*y*-axis) and simulated (*x*-axis) brightness temperature for MWTS-3 channels 11 (**a**) and 14 (**b**) before (black dots) and after (green dots) quality control during 24–30 September 2021.

**Figure 6.** Frequency distributions of O-B differences for channels 11 (**top**) and 14 (**bottom**) before (hatched bars) and after (solid bars) bias correction for MWTS-3 channels 11 (upper panels) and 14 (down panels) during 24 September–3 October 2021.

As shown in Figure 7, the overall bias of AMSU-A mid- and low-level channels is generally small before bias correction, where most channels show negative biases. Among them, the negative bias of AMSU-A onboard NOAA-18 is the most obvious. The bias of MWTS-3 is slightly larger than that of the same frequency channel of other instruments, where channel 9 shows a positive bias, while channel 6 of AMSU-A with the same frequency shows a slightly smaller negative bias. The biases of MWTS-3 channels 10–11 are twice those of the AMSU-A channels with the same frequency. Channels 12–17 (of MWTS-3) show positive biases that are opposite to those of AMSU-A. The upper-level channels of MWTS-3 and AMSU-A both exhibit large biases, which may be related to the large temperature errors in the upper-level of the background. Figure 7c shows that the O-B STD of MWTS-3 is also larger than that of AMSU-A before the bias correction, which may be related to the fact that the MWTS-3 has more pixels per scan line and a shorter sampling residence time. After the bias correction, the biases of all instruments are close to 0 (Figure 7b), indicating that the bias correction method for the CMA-GFS data assimilation system has a good correction effect. Besides, the STDs of all instruments also obviously decrease after the correction (Figure 7d).

Figure 8 shows the biases and STDs of FY-3D MWTS-2 and NPP ATMS for the same period. It can be found that, before bias correction, the bias of ATMS is also smaller than that of MWTS-3, which is comparable to that of AMSU-A, but the STD is larger than that of AMSU-A and is only slightly smaller than that of MWTS-3. The magnitudes of the bias and STD of MWTS-2 are comparable to those of MWTS-3. After the bias correction, the biases of

all instruments are close to 0, and the STDs are also remarkably reduced. However, the STD of MWTS-3 is smaller than that of FY-3D MWTS-2 but is more similar to the STD features of the ATMS channels with the same frequency.

**Figure 8.** Bias (upper panels) and STD (lower panels) of the O-B for FY-3E MWTS-3, FY-3D MWTS-2 and NPP ATMS channels before (**a**,**c**) and after (**b**,**d**) bias correction calculated from the analysis results of the TEST2 experiment during 24 September–25 October 2021.

As indicated above, the comparisons among the observation errors of these microwavesounding data before and after bias correction reveal that the error of AMSU-A is the smallest, followed by that of MWTS-3 and ATMS, and the observation error of MWTS-2 is the largest.

#### 3.2.3. Analysis and Forecast

After investigating the characteristics of the MWTS-3 data, the assimilation effect of MWTS-3 data was further evaluated. The effect of adding the MWTS-3 data to the conventional data assimilation was explored first. Figure 9 shows that the RMSE of the geopotential height and the potential temperature differences between the analysis field and ERA-5 reanalysis data in the southern and Northern Hemispheres are reduced remarkably during the period from 24 September to 25 October 2021. Due to the lack of conventional observations in the Southern Hemisphere, the RMSE reduction in the Southern Hemisphere is most pronounced by adding the MWTS-3 data. Since only channels 9–15 of MWTS-3 are assimilated, and the peak heights of the weighting functions are located in the range of 10–400 hPa, the variables in the middle and high layers of the model are improved the most. Because there are a large number of conventional observations in the middle and lower layers of the Northern Hemisphere, the influence of MWTS-3 data assimilation over these regions is very small. However, as there are few conventional data above the height of

10 hPa, the improvement of adding MWTS-3 data on the geopotential height and potential temperature above 10 hPa is more obvious.

**Figure 9.** RMS of geopotential height from the analysis field difference between CTL1 and ERA (black) and TEST1 and ERA (red) in the (**a**) Southern Hemisphere and (**b**) Northern Hemisphere from 24 September–25 October 2021. (**c**,**d**) are similar to (**a**,**b**) but for the potential temperature.

Figure 10 shows the daily RMSE of the geopotential height differences between the analysis results and the ERA-5 reanalysis data for CTRL1 and TEST1 in the Southern Hemisphere at 10 hPa during the period from 24 September to 25 October 2021. It can be seen that, in the CTRL1, due to the lack of observation data above the altitude of 10 hPa, the model error increases rapidly with time. On the other hand, although only the MWTS-3 data is added in TEST1, the growth of the model error above 10 hPa is obviously suppressed, and the RMSE is greatly reduced in the first 15 days and then stably maintained within 60 gpm.

For operational assimilation applications, the impact of assimilating the FY-3E MWTS-3 data on the operational NWP system using all observation data needs to be paid more attention. CTRL2 assimilates all observation data used in the operations, including conventional and various satellite data, while TEST2 assimilates the MWTS-3 data additionally. The comparison shows that, after adding the MWTS-3 data, the errors of geopotential height, potential temperature, the U and V wind exhibit little change compared with the CTRL2 results at almost all altitudes. As shown in Figure 11, below an altitude of 2 hPa, the errors of the TEST2 results are slightly lower than those of the CTRL2 results. However, near the model top of above 2 hPa, the analysis results are slightly worse. This may be related to the imperfection of the bias correction scheme for the upper-level satellite data. Figure 12 shows that the error of wind below 5 hPa is slightly reduced. Overall, the effects of MWTS-3 data assimilation are neutral or slightly positive.

**Figure 10.** The daily RMS of geopotential height for the analysis field difference between CTL1 and ERA (black) and TEST1 and ERA (red) at 10 hPa in the Southern Hemisphere from 24 September– 25 October 2021.

**Figure 11.** RMS of geopotential height for the analysis field difference between CTL2 and ERA (black) and TEST2 and ERA (red) in the (**a**) Southern Hemisphere and (**b**) Northern Hemisphere from 24 September–25 October 2021. (**c**,**d**) are similar to (**a**,**b**) but for the potential temperature.

**Figure 12.** RMS of U wind for the analysis field difference between CTL2 and ERA (black), TEST2 and ERA (red) in the (**a**,**c**) Southern Hemisphere and (**b**,**d**) Northern Hemisphere.

Using the analysis results of CTRL2 and TEST2 (at 1200 UTC of each day) as the initial conditions, a 10-day prediction was achieved. The comprehensive scorecard for the evaluation of the forecast results shows the abnormal correlation coefficients (ACCs) and RMSEs of various variables at different levels and in different regions (Figure 13). It can be seen that the assimilation of MWTS-3 data has a positive contribution to the 10-day forecasts in the Northern and Southern Hemispheres, especially to the first two-day forecasts of the Southern Hemisphere. The overall impact in East Asia is neutral. In tropical areas, the impact on the ACCs is also generally neutral, but the RMSEs have increased, especially for the errors of geopotential height and potential temperature, which need to be further investigated in the future.

misphere during 24 September -25

**Figure 13.** The score card for TEST2 against CTL2.

### **4. Discussion**

This study demonstrates the impact of the FY-3E MWTS-3 radiances data assimilation for the first time. In the follow-up study, a further comparison of the impacts of data assimilation between MWTS-3 and MWTS-2 will be conducted to provide a reference for the improvement of the Fengyun satellite microwave temperature sounder. For the two newly added channels (6 (53.246 ± 0.08 GHz) and 8 (53.948 ± 0.081 GHz)) of MWTS-3, further assessment and application research for their assimilation is needed. In addition, as the new generation of early-morning orbiting satellites, the FY-3E, NOAA series, and the MetOp series polar-orbiting satellites have formed a complete three-orbit observation system. The supplementary effect of MWTS-3 is worth further exploration.

#### **5. Conclusions**

FY-3E is the fifth polar-orbiting satellite in the FY-3 series launched in July of 2021 in China, which carries the new-generation microwave temperature-sounding instruments. Compared with its predecessor satellites, two channels capable of retrieving the CLWP

have been designed for the first time, which is of great help for cloud detection in data assimilation. In addition, two detection channels have been added with their peak weighting functions near 700 hPa and 500 hPa, and the ability to detect atmospheric temperature has been improved compared with the previous generation MWTS-2.

After the effective QC, bias correction, and accurate error specification of the MWTS-3 data, the direct assimilation of MWTS-3 radiance data has been realized in the CMA-GFS. The near one-month cycling experiments have indicated that the errors of analysis results can be remarkably reduced by adding the MWTS-3 data to the conventional data, especially for the variables on the upper layer of the model, where there is a lack of sufficient conventional observations. When all the observations in operation are included, the MWTS-3 data assimilation has a neutral contribution to the forecasts in the Northern Hemisphere and a slightly positive contribution in the Southern Hemisphere. However, in the tropics, the forecast errors of geopotential height and potential temperature have increased after adding the MWTS-3 data, which needs further investigation.

**Author Contributions:** Conceptualization, J.L.; methodology, J.L.; software, J.L., X.Q. and G.L.; validation, J.L., X.Q. and G.L.; formal analysis, J.L. and X.Q.; investigation, J.L. and G.L.; data curation, G.L.; writing—original draft preparation, J.L. and G.L.; writing—review and editing, J.L. and Z.Q. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was jointly funded by the Fengyun Application Pioneering Project (FY-APP-2021.0201) and FY-3 Meteorological Satellite Ground Application System Project (FY-3 (03)-AS-11.08).

**Data Availability Statement:** All data used in this paper are available from the authors upon request (lj@cma.gov.cn).

**Acknowledgments:** The authors would like to acknowledge the National Satellite Meteorological Centre of CMA for providing the satellite data.

**Conflicts of Interest:** The authors declare no conflict of interest.

## **References**

