# Direct Assimilation of Chinese FY-3E Microwave Temperature Sounder-3 Radiances in the CMA-GFS: An Initial Study

^{1}

^{2}

^{3}

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. CMA-GFS 4D-Var System

_{0}) is a state vector composed of atmospheric and surface variables; x

^{b}(t

_{0}) is a background estimate of the state vector provided by a 6 h forecast, and ${y}_{i}^{o}$ is a vector of all the observations; H is the observation operator that transforms the state vector

**x**into observation space;

**R**is the estimated error covariance of the observations at time i; J

_{i}_{c}is a constraint term added to control various noises and errors generated in variational analysis. For the CMA-GFS data assimilation system, J

_{c}is the weak constraints of the digital filtering.

**B**is the error covariance matrix of x

^{b}. In order to solve the problem that the inverse of the background error covariance matrix (

**B**) is too large to be computed, the background term is preconditioned, which improves the convergence in the minimization process and avoids calculating

^{−1}**B**directly. In the CMA-GFS 4D-Var system, the limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) algorithm [27] is used to perform the minimization.

^{−1}#### 2.2. FY-3E MWTS-3 Observations

#### 2.3. Cloud Detection

^{−1}.

#### 2.4. The Initial Evaluation of Observation Bias and Error

#### 2.5. Channel Selection

#### 2.6. Quality Control Based on Scan and Surface Characteristics

#### 2.7. Bias Correction

#### 2.7.1. Scan Bias Correction

#### 2.7.2. Air-Mass Bias Correction

_{jo}and a

_{ji}, in the regression equation were obtained for the channel j data with a scan angle of $\theta $. The regression equation is as follows:

_{ji}is for the thickness. a

_{jo}and a

_{ji}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.

## 3. Results

#### 3.1. Experimental Design

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

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

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

#### 3.2.3. Analysis and Forecast

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Weighting Functions of FY-3E MWTS-3 calculated by RTTOV based on US standard atmosphere profile.

**Figure 2.**Spatial distribution of observed brightness temperature of FY-3E MWTS-3 channel 1 (

**a**), channel 2 (

**b**) and retrieved cloud LWP (

**c**) for descending orbit data on 24 September 2021.

**Figure 3.**Spatial distribution of retrieved cloud LWP from FY-3E MWTS-3 channel 1 and 2, and brightness temperature of MERSI channel 7 during 0300–1500 UTC 24 September 2021.

**Figure 4.**Bias (

**a**) and standard deviation (STD) (

**b**) of the differences between the brightness temperature observations and ERA simulations for FY-3E MWTS-3 channels during 10–23 September 2021.

**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.

**Figure 7.**Bias (upper panels) and STD (lower panels) of the O-B for FY-3E MWTS-3, NOAA-15/18/19, and MetOp-A/B AMSU-A 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.

**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.

**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.**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.

Channel Number | Center Frequency (GHz) | Bandwidth (MHz) | Polarization | NEΔT (K) |
---|---|---|---|---|

1 | 23.8 | 270 | QH | 0.3 |

2 | 31.4 | 180 | QH | 0.35 |

3 | 50.3 | 180 | QV | 0.35 |

4 | 51.76 | 400 | QV | 0.3 |

5 | 52.8 | 400 | QV | 0.3 |

6 | 53.246 ± 0.08 | 2 × 140 | QV | 0.35 |

7 | 53.596 ± 0.115 | 2 × 170 | QV | 0.3 |

8 | 53.948 ± 0.081 | 2 × 142 | QV | 0.35 |

9 | 54.40 | 400 | QV | 0.3 |

10 | 54.94 | 400 | QV | 0.3 |

11 | 55.50 | 330 | QV | 0.3 |

12 | 57.290 | 330 | QV | 0.6 |

13 | 57.290 ± 0.217 | 2 × 78 | QV | 0.7 |

14 | 57.290 ± 0.3222 ± 0.048 | 4 × 36 | QV | 0.8 |

15 | 57.290 ± 0.3222 ± 0.022 | 4 × 16 | QV | 1.0 |

16 | 57.290 ± 0.3222 ± 0.010 | 4 × 8 | QV | 1.2 |

17 | 57.290 ± 0.3222 ± 0.0045 | 4 × 3 | QV | 2.1 |

EXP | Observation Data |
---|---|

CTL1 | Conventional data |

CTL2 | Conventional data+ NOAA-15/18/19 AMSU-A+ NOAA-18/19 MHS+ MetOp-A/B AMSU-A/MHS/IASI+ NPP ATMS + FY-3C/D MWHS-2/MWRI + FY-3D MWTS-2/HIRAS + FY-3C/D GNOS + COSMIC RO, etc |

TEST1 | CTL1+FY-3E MWTS-3 |

TEST2 | CTL2+FY-3E MWTS-3 |

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**MDPI and ACS Style**

Li, J.; Qian, X.; Qin, Z.; Liu, G.
Direct Assimilation of Chinese FY-3E Microwave Temperature Sounder-3 Radiances in the CMA-GFS: An Initial Study. *Remote Sens.* **2022**, *14*, 5943.
https://doi.org/10.3390/rs14235943

**AMA Style**

Li J, Qian X, Qin Z, Liu G.
Direct Assimilation of Chinese FY-3E Microwave Temperature Sounder-3 Radiances in the CMA-GFS: An Initial Study. *Remote Sensing*. 2022; 14(23):5943.
https://doi.org/10.3390/rs14235943

**Chicago/Turabian Style**

Li, Juan, Xiaoli Qian, Zhengkun Qin, and Guiqing Liu.
2022. "Direct Assimilation of Chinese FY-3E Microwave Temperature Sounder-3 Radiances in the CMA-GFS: An Initial Study" *Remote Sensing* 14, no. 23: 5943.
https://doi.org/10.3390/rs14235943