**1. Introduction**

In recent years, satellite observations have become a key component of the global operational numerical weather prediction (NWP) system due to their high spatial-temporal resolution and wide spatial coverage. Many studies have shown that direct assimilation of microwave-sounding data can remarkably improve the initial conditions of numerical models so as to improve the prediction levels of global and regional models [1–5]. Most NWP centers have reported a substantial reduction in the root mean square error (RMSE) in forecasts by effectively assimilating the data from the Advanced Television and Infrared Observation Satellite (TIROS) operational vertical sounder (ATOVS) onboard the National Oceanic and Atmospheric Administration satellites (NOAA-15, -16, -17, -18 -19, and -20), the Meteorological Operational satellite-A/B (MetOp-A/B) and the Aqua earth observing system. Adjoint sensitivity experiments [6] have proven that microwave temperature-sounding data has become the most influential observation in almost all operational forecasting systems [7–10].

**Citation:** 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

Academic Editor: Stephan Havemann

Received: 15 October 2022 Accepted: 21 November 2022 Published: 24 November 2022

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

Recently, China's polar-orbiting meteorological satellites have become an important part of the global polar-orbiting satellite observing system. Since the successful launch of China's new generation polar-orbiting satellite Fengyun-3A (FY-3A) on 26 May 2008 [11,12], Fengyun-3B/C/D (FY-3B/C/D) satellites have been launched successively. The performance of microwave sounders onboard these satellites is similar to those of the advanced microwave-sounding unit-A (AMSU-A) onboard the NOAA and MetOp satellites [11,12]. FY-3A/B are equipped with the first-generation microwave temperature sounder (MWTS-1), which has four channels with frequencies comparable to channels 3, 5, 7, and 9 of the AMSU-A [13]. FY-3C/D are equipped with the second-generation microwave temperature sounder (MWTS-2). MWTS-2 has 13 channels, and the channels located in the oxygen absorption band (50–60 GHz) are identical to those of the AMSU-A. Various studies on data evaluation [14,15] and assimilation have been carried out for the MWTS, and many of them have indicated that the assimilation of MWTS-1 and MWTS-2 data has positive impacts on NWP results [15–20].

FY-3E satellite was successfully launched on 5 July 2021, which is the world's first meteorological satellite sent into the early-morning orbit for civil use [21]. It has a local equatorial crossing time of about 5:40 am. This satellite carries a third-generation microwave temperature sounder (MWTS-3). A systematic evaluation study [22] has demonstrated that the performance of MWTS-3 is remarkably better than the previous two generations of instruments, with more observational information and well-suppressed observational noises.

The purpose of this study is to evaluate the impacts of the direct assimilation of the MWTS-3 radiance data on the China Meteorological Administration global forecast system (CMA-GFS) for the first time. By establishing the quality control (QC) and bias correction modules suitable for the MWTS-3 data, the effective assimilation of MWTS-3 data in the CMA-GFS is realized. The influence of MWTS-3 data assimilation on the CMA-GFS is evaluated based on the results of one-month assimilation and forecasting. It should be noted that the original name of the operational numerical prediction system in China was the Global and Regional Estimation and PrEdiction System (GRAPES) [23–25]. After September 2021, it was renamed CMA-GFS.

The remainder of this paper is organized as follows. Section 2 introduces the CMA-GFS four-dimensional variational assimilation (4D-Var) system. The general details of the FY-3E MWTS-3 radiance data is described here. Section 2 also provides the QC and bias correction scheme for the MWTS-3 radiance data, and the initial assessments of MWTS-3 data. Section 3 presents the analysis of the numerical results of the FY-3E MWTS-3 radiance data assimilation experiments. The discussion and conclusion are given in Sections 4 and 5.

### **2. Materials and Methods**

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

The main components of CMA-GFS include: four-dimensional variational (4D-Var) data assimilation; fully compressible non-hydrostatical model core with semi-implicit and semi-Lagrangian discretization scheme; modularized model physics package, and global and regional assimilation and prediction systems [23].

The CMA-GFS 4D-Var system is an analysis system designed for operational application [26]. This assimilation system adopts an incremental analysis method, and the assimilation process is divided into outer circulation and inner circulation. In order to reduce the amount of computation, the horizontal resolution of the nonlinear model in the outer circulation of the assimilation is 0.25 degrees, the horizontal resolution of the tangent linear model and the adjoint model in the inner circulation is 1.0 degrees, and only the simplified physical process is applied. The model has 87 vertical layers, with the top being approximately 0.1 hPa. The 4D-Var data assimilation system applies the incremental analysis scheme proposed by Courtier et al. (1998) [2]. By using the observations distributed within a time interval (t0, tn) in the assimilation, the cost function can be defined as follows:

$$J(\mathbf{x}(t\_0)) = \frac{1}{2} \left( \mathbf{x}(t\_0) - \mathbf{x}^b(t\_0) \right)^T \mathbf{B}^{-1} \left( \mathbf{x}(t\_0) - \mathbf{x}^b(t\_0) \right) + \frac{1}{2} \sum\_{i=0}^N \left( H(\mathbf{x}\_i) - y\_i^\rho \right)^T \mathbf{R}\_i^{-1} \left( H(\mathbf{x}\_i) - y\_i^\rho \right) + \mathbf{J}\_\sigma$$

where *x*(*t*0) is a state vector composed of atmospheric and surface variables; *xb*(*t*0) is a background estimate of the state vector provided by a 6 h forecast, and *y<sup>o</sup> <sup>i</sup>* is a vector of all the observations; *H* is the observation operator that transforms the state vector *x* into observation space; *Ri* is the estimated error covariance of the observations at time *i*; *Jc* is a constraint term added to control various noises and errors generated in variational analysis. For the CMA-GFS data assimilation system, *Jc* is the weak constraints of the digital filtering. **B** is the error covariance matrix of *xb*. In order to solve the problem that the inverse of the background error covariance matrix (**B***−***1**) is too large to be computed, the background term is preconditioned, which improves the convergence in the minimization process and avoids calculating **B***−***<sup>1</sup>** directly. In the CMA-GFS 4D-Var system, the limitedmemory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) algorithm [27] is used to perform the minimization.

Currently, the CMA-GFS can directly assimilate radiosonde data, surface synoptic observations (SYNOPs), ship reports, aircraft reports (Airep), atmospheric motion vectors (AMVs), the AMSU-A and the microwave humidity sounder (MHS) data of NOAA-15/18/19, the AMSU-A, MHS and infrared atmospheric sounding interferometer (IASI) data of MetOp-A/B, Suomi National Polar-orbiting Partnership (NPP) ATMS data, the MWHS-2, micro-wave radiation imager (MWRI) and Global Navigation Satellite System (GNSS) radio occultation sounder (GNOS) data of FY-3C/D, the MWTS-2 and hyperspectral infrared atmospheric sounder-2 (HIRAS) radiance data of FY-3D, the Constellation Observing System for Meteorology, Ionosphere and Climate radio occultation (COSMIC RO) data, etc.

The radiative transfer for TIROS operational vertical sounder-12 (RTTOV-12) [28] is used as the observation operator for the direct assimilation of satellite radiance data in the CMA-GFS 4D-Var system. The transmittance coefficients applicable to the RTTOV-12 for FY-3E MWTS-3 simulation are provided by the National Satellite Meteorological Center of CMA.
