College of Meteorology and Oceanography, National University of Defense Technology, Changsha 410073
2.
National Meteorological Centre, China Meteorological Administration, Beijing 100081
3.
CMA Earth System Modeling and Prediction Centre, China Meteorological Administration (CMA), Beijing 100081
4.
State Key Laboratory of Severe Weather Meteorological Science and Technology, Chinese Academy of Meteorological Sciences, China Meteorological Administration, Beijing 100081
Numerical weather prediction (NWP) is the core technology for weather forecast and disaster prevention and mitigation. The research and operational applications of NWP have always been highly valued in China, and have achieved great progress with an appreciable international influence in the theories, algorithms, and operational system developments. This paper first summarizes the scientific and technological evolution of NWP in China, and then focuses on the current status and recent updates of the two homemade global NWP systems: GRAPES (Global/Regional Assimilation and PrEdiction System) and YHGSM (YinHe Global Spectral Model). (1) GRAPES possesses both deterministic and ensemble forecast systems, with global (regional) model versions running on 12–50-km (3–10-km) resolutions. Significant improvements have been made on its dynamic core, four-dimensional variational (4D-Var) assimilation, satellite and radar data assimilation, ensemble forecast, and cloud microphysics schemes, and so on. It is capable to perform subseasonal to seasonal forecast and has incorporated an atmospheric chemistry model, typhoon numerical forecast model, and ocean wave model. (2) YHGSM continues to follow the development route of spectral models, featured prominently with a dry-mass conserved spectral dynamical core, ensemble 4D-Var assimilation, coupled ocean–land–atmosphere ensemble forecast, and the medium-term and monthly-extended global high-resolution forecast as the baseline. These NWP systems autonomouly developed by the China Meteorological Administration and the national defense insitution benefit from long-term adherence to the national science and technology development strategies and close research to operation practices.
数值天气预报是天气预报业务和防灾减灾的核心科技。中国数值天气预报研究和业务应用一直受到高度重视,在基础理论研究、关键技术突破和业务系统研制方面取得了有广泛国际影响的研究成果。在回顾新中国数值天气预报技术及业务系统发展基础上,重点综述我国自主发展的GRAPES(Global Regional Assimilation and PrEdiction System)和YHGSM(YinHe Global Spectral Model)两大业务预报系统的重要科技进展。GRAPES在模式动力框架、四维变分资料同化、卫星资料同化技术、雷达资料同化应用、集合预报和云物理过程等方面实现了技术突破,建立了无缝隙的、包含确定性预报和集合预报系统的中国气象局数值天气预报业务体系。YHGSM持续走谱模式发展路线,突破了干空气质量守恒全球大气谱模式、集合四维变分资料同化、海陆气耦合集合预报等技术,建立了以高分辨率全球中期和月延伸数值预报系统为核心的数值预报体系。军地自主研发的数值天气预报系统是长期坚持既定科学技术方向、学术研究和业务研制紧密结合的结果。
Numerical weather prediction (NWP) has emerged as the cornerstone technology underpinning modern weather forecasting, climate prediction, and meteorological disaster prevention and mitigation (Shen et al., 2022). The conceptual foundation of NWP dates back to 1904, when Norwegian meteorologist Vilhelm Bjerknes proposed a scientific framework for weather prediction based on solving the governing equations of atmospheric dynamics (Bjerknes, 1904). This approach posited that future atmospheric states could be derived through numerical integration of hydrodynamic and thermodynamic equations initialized with observational data. A pivotal advancement occurred in 1922 when British meteorologist Lewis Fry Richardson implemented finite-difference methods to solve atmospheric motion equations numerically, producing the first 6-h surface pressure forecast—a groundbreaking demonstration of computational meteorology (Richardson, 1922). An important milestone in establishing the NWP system was the successful NWP research experiment conducted in 1950 by the Institute for Advanced Study at Princeton University on the first electronic computer, ENIAC (Electronic Numerical Integrator and Computer). By December 1954, the Swedish Air Force Meteorological Office, in collaboration with the International Meteorological Institute of Stockholm University, officially began operational 24-, 48-, and 72-h weather forecasts—the world’s first recognized operational application of numerical forecasting. Concurrently, in the United States, the Joint Numerical Weather Prediction Unit (JNWPU) was established in 1954 under the collaborative efforts of the U.S. Weather Bureau, Air Force Weather Service, and Naval Weather Service, driven by the foundational work of von Neumann and Charney (Lynch, 2006). The 1975 inception of the ECMWF and its subsequent deployment of a global medium-range forecasting system catalyzed a paradigm shift in multiscale numerical modeling, establishing ECMWF as a global leader in NWP innovation and forecast skill.
Technologically, NWP has evolved through successive generations: from barotropic and baroclinic models to primitive equation formulations and contemporary non-hydrostatic models. This progression has been accompanied by systematic enhancements in spatiotemporal resolution, physical parameterization schemes, and computational efficiency. Crucially, advances in high-performance computing (HPC) have been instrumental in model development. Empirical analyses from the 1980s suggested that each order-of-magnitude increase in computational capacity enabled approximately doubled horizontal resolution and a 15% improvement in forecast skill—a relationship substantiated by NWP advancements over the past two decades. In the last 20 years, three transformative breakthroughs have characterized recent NWP development. (1) The development of variational data assimilation schemes (e.g., 3D-Var and 4D-Var), which has enabled assimilation of large amounts of remote sensing data into NWP models, fundamentally addressing the issue of insufficient observational data. (2) The dynamic and physical processes included in NWP models are increasingly approaching the real atmosphere. Due to the improvement of resolution and computational methods, the dynamic simplifications of atmospheric models are greatly reduced, thus decreasing the errors in describing small and mesoscale dynamic processes. The physical and chemical processes included in the models are also more abundant, especially the cloud microphysical processes that are explicitly introduced into NWP models, and the coupling of the atmosphere with other earth system components improves the model’s ability to describe complex physical processes. (3) The full utilization of high-performance computing technology enables intensive development of the NWP systems, greatly shortening the system upgrade cycle.
Magnusson and Källén (2013) suggested that the continuous improvement and increased resolution of forecast models, advancements in data assimilation techniques, and the increasing availability of observational data (especially satellite data) are the three major contributing factors to the year-by-year improvement in ECMWF forecast skills. The “Seamless Prediction of the Earth System: From minutes to months” (WMO-No. 1156) pub-lished by the World Meteorological Organization in 2015 marks a consensus on the development direction of the next generation of operational NWP worldwide. Within the framework of earth system science, developing integrated weather–climate coupled NWP systems and corresponding operational forecasting service systems has become a research and application focus for major NWP operational centers worldwide. To further improve the forecast accuracy and extend the forecast lead time, very high resolution, multisphere coupling, multiscale nesting, multiscale ensemble, and numerical earth system modeling technologies are important development directions for the next generation of NWP.
Since its successful experimentation in the 1950s, NWP has become a complex and rigorous systematic project spanning multiple disciplines after 70 years of development. Weather forecasting has shifted from traditional synoptic methods based on statistics and experience to objective and quantitative science (Zeng, 2013; Benjamin et al., 2019). The history of NWP, from the conceptual proposal 100 years ago to its 70-yr operational application, demonstrates that the progress of NWP is built upon years of steady and continuous accumulation of scientific knowledge and technological advancements and is considered one of the most influential achievements in various fields of physics (Ji, 2011; Bauer et al., 2015). It is known that NWP is a comprehensive reflection of meteorological science and technology and an important component of the core technology that safeguards national welfare and national defense security. The remainder of this paper reviews the development of NWP technology and operational systems in China, focusing on summarizing the important scientific and technological progress of the two major operational forecasting systems independently developed in China: GRAPES (Global/Regional Assimilation and PrEdiction System) and YHGSM (YinHe Global Spectral Model).
2.
Development history of numerical weather prediction in China
China’s research in NWP technology began after the founding of the People’s Republic of China, with scholars such as Gu Zhenchao and Zeng Qingcun achieving a series of internationally influential results. The independent innovation and development path of China’s NWP operational system started in the 1970s and can be divided into four stages: initial exploration, establishment and improvement of the operational forecasting system, development of independent NWP systems, and the integrated development of artificial intelligence and NWP.
2.1
Initial exploration (1950s–1960s)
China’s engagement in the NWP research commenced in 1954, positioning the nation among the earliest adopters of this methodology globally. During this formative period, constrained by computational limitations and technological infrastructure, the research mainly focused on theoretical studies and exploration of numerical methods. The 1950s to the late 1960s marked a prolific phase in Chinese NWP research, yielding internationally recognized advancements (Gu, 1959; Blumen and Washington, 1973). Early efforts in the 1950s centered on quasi-geostrophic barotropic modeling. Gu (1959) provided a seminal synthesis of these foundational studies, emphasizing three critical NWP requirements: (1) comprehensive understanding of atmospheric process dynamics, (2) incorporation of essential physical forcing mechanisms, and (3) robust formulation of model dynamics, physical parameterizations, and numerical solvers. Chinese researchers pioneered innovative approaches during this era, employing manual graphical analysis to solve two-layer quasi-geostrophic equations. These techniques demonstrated operational utility in short-range cold air outbreak predictions and 500-hPa geopotential height forecasts across East Asia (Liao, 1956; Gu et al., 1957). Chen et al. (1957) conducted pioneering work on frontal system prediction using a two-layer isentropic coordinate model—an early international application of potential temperature as a vertical coordinate in NWP systems. In February 1960, the Numerical Prediction Group of the Central Meteorological Bureau, in cooperation with the Institute of Geophysics and the Institute of Computing Technology of the Chinese Academy of Sciences, used a quasi-geostrophic barotropic model to produce 24- and 48-h 500-hPa synoptic forecasts for the Asian–European region (Numerical Prediction Team of Central Meteorological Bureau, 1965). Shen and Mu (1965) systematically summarized the application of 48-h NWP charts of the 500 hPa from the barotropic model in the Central Meteorological Bureau from 1964 to 1965, pointing out that recognizing the errors and capabilities of NWP is important for its effective application.
While conducting research on quasi-geostrophic barotropic models and applying them in weather forecasting operations, Chinese scientists also carried out research on considering baroclinic processes and primitive equation models in quasi-geostrophic models. Zhu (1961, 1962) developed a three-layer nonlinear model (1000, 500, and 300 hPa) in spherical coordinates during his visit to the Institute of Applied Geophysics of the Soviet Academy of Sciences (1959–1960), studying the impact of topography on 24-h forecasts. In 1961, Zeng Qingcun made the first actual weather forecast using the primitive equations and achieved operational application at the Moscow World Meteorological Center (Zeng, 1961; Zeng, 2013). In particular, when solving the primitive equation model, Zeng Qingcun, based on the theory of adaptation processes in the atmosphere, proposed a “semi-implicit (or semi-explicit) difference scheme,” which uses an implicit scheme for fast waves that affect the time step and computational stability, increasing computational stability and significantly reducing computational cost (Zeng, 1961; Zeng, 1963a, c). Robert (1969) and Robert et al. (1985) further enriched and developed the semi-implicit scheme, and combined it with the semi-Lagrangian method to form the semi-implicit semi-Lagrangian method, which is still a widely used computational scheme in operational NWP models worldwide. To address the computational complexity caused by topography in numerical models, Zeng (1963b) proposed the static reduction (or standard stratification reduction) method, which eliminates the computational error of basic quantities in the calculation of the pressure gradient force, avoiding the problem of calculating small differences between two large terms. This static reduction method later played an important role in spectral models and in the semi-Lagrangian advection calculation to reduce the impact of topography (Simmons and Chen, 1991; Temperton et al., 2001). In 1965, Liu and Zhang (1965) developed a barotropic primitive equation for the Northern Hemisphere. The model used a central difference in time and space and a leapfrog grid proposed by Lilly (1961), with a spatial grid distance of 600 km. Simulation studies were conducted on four cases and compared with the results of the geostrophic barotropic model, obtaining relatively good results.
In the 1950s and early 1960s, the research achievements of the older generation of scientists represented by Zhao Jiuzhang, Gu Zhenchao, and Ye Duzheng in dynamic meteorology, atmospheric circulation, the dynamic and thermal effects of the Qinghai–Xizang Plateau, the theory of adaptation of atmospheric motion, the theory of atmospheric dispersion, and the balance relationship between wind and pressure fields (Xu, 1959; Zhao, 1959; Ye, 1963) directly or indirectly guided and promoted the development of NWP in China (Ji et al., 2005). The research achievements of scientists represented by Zhou Xiuji, Chao Jiping, and Zhou Xiaoping in cloud microphysics, cumulus dynamics, mesoscale dynamics, and boundary layer turbulence were not only theoretically at the international forefront at the time but also provided important theoretical support for considering non-adiabatic processes and understanding physical mechanisms in NWP (Su, 1958, 1959; Zhou, 1963; Chao and Zhou, 1964). Chinese scholars at this time proposed elevating the initial value problem of NWP to an innovative idea based on recent historical evolution (Gu, 1958a, b). Later, Chou (1974) further deepened the research on the use of historical data in NWP, transforming the differential equation solution problem of NWP into a functional extremum problem using multi-time historical observation data—a variational problem. Gu Zhenchao’s idea and the functional extremum processing method introduced by Chou Jifan are the main ideas of today’s four-dimensional variational data assimilation. During this period, although Chinese scientists did not have the conditions to carry out NWP system development work, they did a lot of exploratory work in the basic theory research of NWP (Tao et al., 2003). Zeng et al.’s achievements in computational fluid dynamics won the first prize of the Chinese Academy of Sciences Natural Science Award in 1989. This research clarified the mechanism of computational chaos and computational instability and demonstrated the close relationship between computational stability and the non-negativity and energy conservation of operators. It also constructed a format with complete square conservation for barotropic and baroclinic primitive equations and introduced the “standard layer structure” and “deduction method,” which reduced the computational truncation error and overcame the computational difficulties in areas with steep terrain.
2.2
Establishment and improvement of the operational system (1970s–1980s)
Internationally, NWP achieved operational application in the mid-1970s and became an indispensable scientific and technological support for daily weather forecasting. A pivotal milestone in this transition was the 1975 establishment of the ECMWF, whose global medium-range forecasting system set new benchmarks in operational NWP capabilities. During this period of rapid international advancement, the NWP Research Group at the Institute of Atmospheric Physics (IAP), Chinese Academy of Sciences, actively engaged with global developments by introducing cutting-edge NWP methodologies to China (Numerical Prediction Research Team, 1975). A seminal contribution emerged through Zeng Qingcun’s treatise Mathematical and Physical Foundations of Numerical Weather Prediction (Volume 1) (Zeng, 1979), which systematically elucidated the theoretical underpinnings of NWP model development. This work transcended atmospheric fluid dynamics computations by formalizing a rigorous mathematical–physical framework for NWP, significantly advancing its theoretical foundations. Chinese scientists concurrently conducted foundational studies to support the establishment of modern NWP operations, focusing on critical numerical formulation challenges (Tao et al., 2003). Research priorities included computational stability theory and the design of finite-difference schemes—key determinants of model fidelity (Zeng, 1978; Zeng and Ji, 1981; Ji and Zeng, 1982). A central objective in NWP model development involves constructing discretized equations that preserve essential physical invariants, such as total energy, mass, and enstrophy conservation. These conservation properties not only ensure numerical stability during extended integration but also enhance dynamical consistency with atmospheric physics. The pioneering work of Arakawa (1972, 1997) demonstrated this principle through vorticity–kinetic energy-conserving advection Jacobian formulations, achieved via carefully designed grid-point interactions. Chinese researchers subsequently identified limitations in Arakawa’s instantaneous conservation framework (Ji, 1981; Zeng and Ji, 1981), leading to innovative advancements. Zeng and Ji (1981) developed an implicit advection term discretization scheme that rigorously maintains total energy conservation while exhibiting computational stability across arbitrary initial conditions and temporal discretizations. This formulation additionally preserves generalized energy and mean-scale invariants, representing significant theoretical refinement in numerical scheme design.
The post-reform era marked a transformative phase in China’s NWP development, catalyzing both research advancements and operational implementation. China established a modern NWP operational system and played a core role in weather forecasting operations. By the 1980s, China had established a modern NWP operational framework that became central to national weather forecasting services. This system initially comprised two cornerstone models: the hemispheric-scale Model A and regional-scale Model B, forming the backbone of short-term operational NWP capabilities. Pioneering efforts included Zhu et al. (1980)’s development of a three-layer adiabatic primitive equation model for the Northern Hemisphere. The National Meteorological Bureau and the Institute of Atmospheric Physics jointly developed a three-layer adiabatic primitive equation model for the Asian–European region (then called the A model, which began to release 48-h synoptic forecasts in 1980). Concurrently, a tripartite collaboration involving the Institute of Atmospheric Physics, Peking University, and the National Meteorological Centre produced Model B: a five-layer gridpoint model for hemispheric applications (operationalized in 1982) and its limited-area counterpart (Model B-Small) for mesoscale prediction (Tao et al., 2003). Notable among China’s autonomous innovations have been the Limited Area Forecast System (LAFS), later upgraded to the High-Resolution LAFS (HLAFS). Developed by the National Meteorological Centre based on foundational work by Peking University’s Prof. Zhang Yuling (Guo et al., 1995), this system underpinned national forecasting and disaster mitigation from the mid-1980s until its phased replacement by the GRAPES_Meso model in 2006 (Chen and Xue, 2004). Regional meteorological centers further diversified modeling capabilities: Shanghai implemented typhoon-specific NWP systems (Zhu and Yin, 1987), Guangzhou developed tropical meteorological models (Xue et al., 1988), and Lanzhou pioneered complex terrain-optimized formulations (Yan, 1987). To address the complex terrain and heavy rain forecasting problems in China, Yu Rucong started to develop a forecasting model that considers steep terrain by introducing η coordinates in 1986, referring to the work of Mesinger (1984) (later called REM, Regional Eta-coordinate Model; Yu et al., 1994). After years of updating and improving the physical processes of the model, REM was further developed into AREM (Advanced Regional Eta-coordinate Model), which has been used in scientific research and operations in the Wuhan Institute of Heavy Rain and the military (Yu et al., 2004).
China’s pursuit of a global medium-range NWP operational system commenced in the mid-1980s, receiving formal designation as a national key scientific–technological project under the “Seventh Five-Year Plan” (1986–1990) by the State Science and Technology Commission (SSTC) (Li, 2010). Facing substantial technological and infrastructural disparities compared to leading NWP nations, Chinese authorities adopted a strategic technology transfer approach: initial acquisition of advanced NWP systems followed by phased localization through digestive absorption. This initiative leveraged domestic high-performance computing (HPC) resources, notably the indigenous Yinhe (Galaxy) series supercomputers. Under the “Seventh Five-Year Plan,” Prof. Li Zechun spearheaded a multidisciplinary consortium comprising 300 researchers from 17 institutions to develop the T63L16 global forecasting system. This system integrated ECMWF’s global spectral model (GSM) as its dynamical core, marking China’s first operational medium-range NWP capability. A pivotal milestone emerged in 1991 through collaboration between the National Meteorological Centre (NMC) and the National University of Defense Technology (NUDT), achieving successful parallelization of NWP operations on Yinhe HPC infrastructure. Subsequent iterative upgrades throughout the 1990s and early 2000s—progressing through T106L19, T213-L31, and T639L60 configurations (collectively termed the T-series)—substantially enhanced forecast resolution and vertical layering (60 levels in final iterations). These advancements not only fortified operational meteorological services but also established critical foundations for subsequent autonomous NWP development. The T-series’ evolution, anchored in GSM architecture with con-tinuous algorithmic optimization, demonstrated China’s growing proficiency in maintaining modern NWP operations. Its operational deployment validated three key national capabilities: (1) assimilation of international NWP advancements into localized frameworks, (2) integration of domestic HPC resources with numerical modeling, and (3) cultivation of institutional expertise for independent system upgrades. This trajectory ultimately enabled the transition from technology adoption to genuine innovation in later decades.
After the 1990s, China has seen internationally influential achievements in the fields of predictability, new algorithms for atmospheric numerical models, and new methods for data assimilation. Wang and Ji (1990) and Ji and Wang (1991) proposed an explicit complete square conservation format, and Zhong (1992, 1993) further developed a complete square sum and third-order conservation format on the explicit complete square conservation format. Some scholars have also explored the possible applications of fully implicit difference schemes (Chen et al., 2007). These studies related to the calculation format show the consistent emphasis of Chinese scientists on the research of basic methods of numerical calculation.
2.3
Innovative development of fully independent operational numerical prediction system (2000s–2024)
The turn of the 21st century witnessed a paradigm shift in China’s NWP development strategy under the China Meteorological Administration (CMA). Recognizing the imperative for technological sovereignty, CMA initiated a strategic transition from technology importation to autonomous innovation in operational NWP systems. This pivotal decision marked the genesis of China’s next-generation indigenous NWP framework. In 2001, catalyzed by the national key science and technology project Innovative Research on China Meteorological Numerical Prediction Systems under the Tenth Five-Year Plan (2001–2005), CMA launched a multi-institutional collaboration to develop GRAPES—a unified numerical framework integrating multiscale data assimilation and prediction capabilities (Xue and Chen, 2008). Sustained through successive national initiatives, including the Eleventh (2006–2010) and Twelfth (2011–2015) Five-Year Plan science programs and dedicated CMA-GRAPES funding, this 15-yr research and development endeavor achieved three transformative milestones: (1) establishment of a fully autonomous NWP operational architecture spanning mesoscale regional configurations (1–10-km resolution) to global deterministic (12.5–50 km) and ensemble prediction systems; (2) cultivation of a vertically integrated research and development cohort encompassing theoretical innovation, system development, and operational implementation; and (3) breakthrough innovations in core NWP technologies including non-hydrostatic dynamics, hybrid data assimilation, and physics–dynamics coupling. The GRAPES initiative established critical scientific infrastructure and human capital reserves for China’s numerical prediction ecosystem, particularly through pioneering work in (1) generalized coordinate system formulations for multiscale applications, (2) scalable parallel computing architectures optimized for domestic supercomputers, and (3) multivariate ensemble-based predictability analysis. Concurrently, scholarly syntheses have systematically documented China’s NWP evolution across development phases (Li, 2010; Shen et al., 2010; Shen et al., 2022), providing critical historiographical perspectives on technological transition strategies.
Current global NWP models, employing spectral or grid-point frameworks with spherical Gaussian/latitude–longitude grids and semi-implicit semi-Lagrangian (SISL) time integration schemes, face computational bottlenecks in accuracy and scalability when targeting kilometer-scale resolutions. To address these limitations, major operational centers are developing next-generation models prioritizing two advancements: (1) high-precision, conservative, and scalable dynamical cores applicable across 100-m–10-km resolutions, and (2) scale-adaptive physical parameterizations for convection, turbulence, and cloud processes (Mengaldo et al., 2019). Notably, Shen’s team pioneered a multimoment constrained finite volume (MCV) method that rigorously enforces numerical conservation while exhibiting superior scalability, grid flexibility, and algorithmic locality compared to traditional finite volume approaches—a methodology validated in international next-generation model development (Li et al., 2013; Chen et al., 2014, Smolarkiewicz et al., 2016). Concurrently, scale-adaptive physics research has yielded Huang et al. (2018)’s resolution-dependent cumulus parameterization, dynamically coupling subgrid and resolved motions based on Arakawa’s scale adaptation concept, and Zhang et al. (2018)’s three-dimensional (3D) turbulence scheme achieving physically consistent simulations at 100-m–1-km resolutions through energy spectrum-aware eddy viscosity. These advances collectively address critical challenges in spatiotemporal discretization and scale-aware modeling for future NWP systems.
Advanced data assimilation techniques are recognized as a pivotal factor contributing to the notable enhancements in the operational implementation of NWP systems (Bannister, 2017). Research on data assimilation conducted by Chinese scientists commenced relatively later than investigations into computational methodologies; however, it has progressed rapidly. In response to the operational requirements of NWP, a hybrid initialization scheme that integrates optimal interpolation objective analysis with nonlinear normal mode initialization was developed during the period from the 1980s to the early 1990s (Xue et al., 1992; Zhu et al., 1992; Tu and Zhang, 1995). Notably, since the onset of the 21st century, the data assimilation systems designed and developed by Chinese researchers have attained functionalities and assimilation capabilities comparable to those of leading data assimilation systems (Zhang L. et al., 2019). The GRAPES three/four-dimensional variational data assimilation system exemplifies a significant achievement in the realm of variational data assimilation methods resulting from Chinese research efforts in the 21st century (Xue and Chen, 2008). Furthermore, the NUDT established the global meteorological data four-dimensional variational data assimilation system, YH4DVAR, which was implemented in China and integrated into the military NWP operational system in 2008, thereby playing a crucial role in its functionality (Zhang et al., 2010).
Chinese scientists have also carried out research on new data assimilation methods. The dimension-reduced projection four-dimensional variational data assimilation (DRP4D-Var, 4D-Var based on a Dimension-Reduced Projection) proposed by Wang et al. (2010) and the ensemble four-dimensional variational data assimilation method (NLS-En4D-Var, Nonlinear Least Squares enhanced proper orthogonal decomposition-based Ensemble 4D-Var algorithm) proposed by Tian et al. (2018) are representative research works. The DRP4D-Var method employs ensemble-based gradient estimation to circumvent the computational demands of traditional adjoint models. Its algorithmic workflow comprises three stages: (1) dimensionality reduction of model and observation spaces through principal component analysis, projecting variables onto a reduced-order ensemble subspace; (2) expansion of the subspace via localized correlation eigenmodes to enhance error covariance representation; and (3) execution of four-dimensional variational analysis within the augmented subspace. This approach eliminates dependency on tangent linear and adjoint models, reducing computational complexity by O(n²) compared to conventional 4D-Var implementations. Complementarily, the NLS-En4D-Var method achieves theoretical unification of ensemble Kalman filtering and 4D-Var through rigorous reformulation of the assimilation problem as a nonlinear least squares optimization. The framework systematically integrates the ensemble-derived flow-dependent error covariances, the four-dimensional observational trajectory matching, and the regularized background term constraints. These hybrid methodologies demonstrate operational potential through improved balance between computational efficiency and analysis accuracy. Recent advancements by Zhang W. M. et al. (2022) further enhance hybrid data assimilation through localized weight-optimized ensemble Kalman filtering and implicit equal-weight variational particle smoothing, establishing a unified theoretical foundation for nonlinear ensemble-variational integration.
China has made significant contributions to the field of predictability research that have garnered international recognition. Mu et al. (2003) expanded the concept of linear singular vectors (LSV) into the nonlinear domain, introducing the notion of conditional nonlinear optimal perturbation (CNOP). The linear singular vector identifies a specific set of initial perturbations that exhibit the highest growth rate within a tangent linear model, whereas the conditional nonlinear optimal perturbation characterizes a set of initial perturbations that achieve the maximum nonlinear development at a specified forecast time, subject to certain physical constraints. In a subsequent study in 2010, Mu et al. (2010) further developed the concept of conditional nonlinear optimal perturbation to account for scenarios involving both initial errors and model parameter errors. They designated the conditional nonlinear optimal perturbation associated solely with initial perturbations as CNOP-I, while the perturbation related to model parameter variations was termed CNOP-P. The conditional nonlinear optimal perturbation framework holds considerable promise for applications in predictability research, targeted observational strategies, and ensemble forecasting across various temporal scales.
2.4
Integrated development of artificial intelligence and numerical prediction (post-2022)
While the NWP now constitutes the cornerstone of modern meteorological forecasting, its ascendancy represents the culmination of seven decades of sustained technological advancement rather than an abrupt paradigm shift. Bauer et al. (2015) from the ECMWF aptly characterized this gradual transformation as “the Quiet Revolution of Numerical Weather Prediction” in their seminal Nature publication. Contemporary NWP development faces a critical computational challenge: the pursuit of enhanced predictive skill through increased horizontal resolution (currently approaching sub-kilometer scales) drives exponentially growing computational requirements. This resolution–computation nexus has elevated the HPC capacity as the critical limiting factor in NWP system advancement—a barrier constraining both temporal forecasting horizons and spatial fidelity improvements.
The NWP and artificial intelligence (AI) represent complementary methodologies for atmospheric modeling: the former relies on first-principles physics encoded in deterministic mathematical equations, while the latter employs data-driven approaches to discern complex nonlinear relationships within observational and model datasets. AI techniques, particularly machine learning (ML), demonstrate exceptional proficiency in processing high-dimensional meteorological data, enabling advancements across the NWP workflow. ML algorithms enhance NWP through three primary pathways. (1) Initialization optimization: neural networks improve data assimilation by extracting spatiotemporal patterns from multisource observations (satellite, radar, in situ), refining initial condition accuracy. (2) Model parameterization: deep learning architectures, such as convolutional neural networks (CNNs), can replace or augment traditional physical parameterizations of subgrid-scale processes (e.g., cloud microphysics, boundary layer turbulence) through training on high-resolution model outputs. (3) Post-processing refinement: ensemble-based ML techniques statistically correct systematic model biases and quantify forecast uncertainty through historical error pattern recognition. The synergy between AI and NWP has catalyzed transformative innovations in forecast systems. A landmark achievement in 2022 saw Huawei’s Pangu-Weather model—a 3D vision transformer trained on ECMWF’s ERA5 reanalysis data—demonstrate comparable skill to the ECMWF Integrated Forecasting System (IFS) in midlatitude 500-hPa geopotential height predictions, achieving a root-mean-square error (RMSE) reduction of 15% over traditional methods at 6-day lead times (Bi et al., 2023). This breakthrough highlights ML’s capacity to emulate complex atmospheric dynamics while bypassing computationally intensive numerical integrations. Current research prioritizes hybrid modeling frameworks that embed ML components within NWP architectures, combining physics-based constraints with data-driven corrections. Such integrations address longstanding challenges in convective-scale prediction and extreme weather forecasting, positioning AI–NWP convergence as a paradigm-shifting frontier in computational meteorology. In May 2023, the Shanghai Artificial Intelligence Research Institute released the Fengwu large model (Chen K. et al., 2023), and in June 2023, Fudan University released the Fuxi large model (Chen L. et al., 2023). In January 2024, the NUDT released the eddy-resolving ocean environment forecast Xihe large model (Wang et al., 2024). In 2024, the China Meteorological Administration simultaneously released the AI global medium–short term forecast system “Fengqing,” the AI nowcasting system “Fenglei,” and the AI global sub-seasonal–seasonal prediction system “Fengshun.”
For “Fengqing,” this CMA–Tsinghua University collaborative system generates global meteorological forecasts at 25-km horizontal resolution with 6-h temporal resolution, delivering 15-day deterministic predictions of key variables including geopotential height, temperature, and precipitation intensity. “Fenglei,” jointly developed by CMA and Tsinghua University, this nowcasting platform produces high-frequency radar echo extrapolation products at 6-min intervals, enabling 0–3-h convective-scale forecasts with 1-km spatial resolution through deep learning-based motion vector analysis. “Fengshun,” a tripartite initiative between CMA, Fudan University, and the Shanghai Institute of Scientific Intelligence, this ensemble prediction system employs generative adversarial networks (GANs) to produce 100-member global ensemble forecasts daily. The system provides probabilistic guidance for subseasonal timescales (up to 60 days), particularly targeting extreme event prediction through anomaly detection in key variables like 500-hPa vorticity and precipitable water. These systems exemplify the paradigm-shifting potential of AI–NWP synergy, leveraging transformer architectures and graph neural networks to overcome traditional computational barriers. As AI processor capabilities approach exascale performance metrics, ongoing integration efforts aim to achieve three strategic objectives: (1) kilometer-scale global ensemble forecasting through adaptive mesh refinement, (2) unified modeling of weather and climate timescales via attention mechanism-enhanced temporal embeddings, and (3) operational deployment of hybrid physics–ML frameworks combining numerical stability constraints with data-driven pattern recognition.
3.
Establishment and development of GRAPES
GRAPES is a self-developed regional and global integrated assimilation and forecasting system in China. By the end of the tenth Five-Year Plan (2001–2005), GRAPES achieved breakthroughs in its semi-implicit semi-Lagrangian non-hydrostatic dynamic framework, physical processes for mesoscale NWP, regional isobaric 3D-Var data assimilation, and parallel computing. In July 2006, GRAPES_Meso 2.0 with a horizontal resolution of 30 km replaced the HLAFS system, becoming the operational mesoscale forecasting system at the CMA. By 2023, CMA-MESO (the unified operational name for GRAPES_Meso), with 1-km resolution over nationwide coverage and hourly updates, significantly enhanced forecasts for convective and small-scale weather systems.
The development of the global medium-range NWP system (GRAPES_GFS) began in July 2007, with a quasi-operational version (GRAPES_GFS 1.0) completed in 2009 (Shen et al., 2009). In 2018, CMA successfully operationalized the GRAPES-4DVar system, becoming one of the few global centers capable of independently developing and applying 4D-Var assimilation. By 2023, the 12.5-km-resolution CMA-GFS (operational GRAPES_GFS) forecast skill [defined as the leading time with the anomaly correlation coefficient (ACC) of 500-hPa geopotential height forecast higher than 60%] is 8.1 days in the Northern Hemisphere, with precipitation forecasts approaching the performance of leading international centers like ECMWF and NCEP.
Through independent innovation, CMA has established a comprehensive NWP framework including deterministic and ensemble forecasts at regional (1–10 km) to global (12.5–50 km) resolutions. This system also integrates full-chain supporting components, including observational data preprocessing, quality control, post-processing, forecast verification, product interpretation, database management, experimental platforms, and real-time monitoring.
3.1
Major scientific and technological breakthroughs
The development of GRAPES involved continuous breakthroughs in core technologies, focusing on six key areas: dynamic framework, global 4D-Var assimilation, satellite data assimilation, ensemble forecasting, cloud and microphysics parameterization, and kilometer-scale data assimilation.
The dynamic framework of the GRAPES model employs a two-time-layer semi-implicit semi-Lagrangian algorithm, which offers significant advantages in reducing computational memory usage and improving efficiency. However, challenges arise in addressing computational accuracy and stability, including the use of an isothermal reference atmosphere during linearization, weight coefficient selection in semi-implicit schemes, and errors introduced by nonlinear term extrapolation and intermediate wind speed interpolation at upstream points (Ritchie and Tanguay, 1996; Simmons and Temperton, 1997; Temperton et al., 2001). To resolve these issues, a predictor–corrector semi-implicit semi-Lagrangian algorithm was developed, incorporating a three-dimensional reference atmosphere (Côté et al., 1998). This algorithm reduces nonlinear term magnitudes and allows smaller semi-implicit coefficients, improving model stability, efficiency, and accuracy (Su et al., 2018).
Additionally, to ensure positivity and conservation in scalar advection, a piecewise rational method (PRM) was developed. The PRM reformulates the scalar prediction equation into a flux form for easier conservation, combined with a semi-Lagrangian algorithm for efficient, high-precision water vapor advection (Su et al., 2013).
3.1.2
Global non-hydrostatic 4D-Var assimilation
4D-Var has long been regarded as an advanced data assimilation technique (Rabier et al., 2000; Bannister, 2017; Bonavita et al., 2017; Kwon et al., 2018). The tangent-linear and adjoint models of the global non-hydrostatic GRAPES model were developed, along with a tangent-linear formulation of simplified physical processes, including cumulus convection, cloud physics, boundary layer vertical diffusion, and subgrid-scale orographic drag. The global GRAPES 4D-Var employs an incremental analysis scheme, incorporating digital filtering as a weak constraint in the cost function to suppress high-frequency gravity waves. The system is designed with multiple outer loops (currently, a single outer loop is used operationally). The minimization algorithm utilizes the Lanczos-CG method (Liu et al., 2018). The 4D-Var analysis framework adopts a background error covariance model that is inseparable in both horizontal and vertical directions. The horizontal correlation uses a second-order autoregressive model, with the correlation scale varying with height, while the vertical correlation is directly derived from ensemble sample statistics. Balance constraints, including the relationship between the rotational wind and divergence wind, rotational wind and mass field, and the non-equilibrium divergence wind and mass field, are achieved through a combined dynamical and statistical approach. In terms of analysis quality, the global 4D-Var significantly outperforms 3D-Var, especially for mass and wind fields. For precipitation forecasts, the global 4D-Var substantially improves forecast skill for moderate and heavy precipitation events. In typhoon prediction, both track and intensity forecasts show significant improvements, with track forecast errors reduced by approximately 15%.
3.1.3
Satellite data assimilation
Satellite data have been acknowledged as an essential component in global NWP, significantly contributing to the enhancement of forecasting accuracy (Eyre, 1964). The initial implementation of the three-dimensional variational data assimilation system, known as GRAPES, included the direct assimilation of emissivity data from the NOAA-16 Advanced Microwave Sounding Unit-A (AMSU-A) microwave radiometer (Zhang et al., 2004). The advancement of batch satellite data assimilation methodologies, which encompassed data from the NOAA series (NOAA 15, 16, 17, 18) Advanced TOVS (ATOVS), GPS occultation data, and cloud motion winds from both geostationary and polar satellites, coincided with the establishment of the global medium-range forecasting system GRAPES_GFS (Shen et al., 2009). Throughout the semi-operational and operational stages of GRAPES_GFS, a variety of satellite radiometric data—including those from the Chinese Fengyun series, European MetOp AMSU-A, Microwave Humidity Sounder (MHS), Infrared Atmospheric Sounding Interferometer (IASI), and Atmospheric Infrared Sounder (AIRS) hyperspectral atmospheric infrared measurements—were successfully integrated. The assimilation of multiplatform satellite data has been instrumental in the ongoing enhancement of GRAPES_GFS’s forecasting capabilities (Shen and Wang, 2015).
As depicted in Fig. 1, which illustrates the annual fluctuations in the types and sources of satellite data assimilated within the GRAPES system, the advancement in satellite data assimilation has been notably swift over the past decade, particularly following the operational launch of GRAPES_GFS 2.0 in 2016 (Shen et al., 2017). Presently, satellite remote sensing data constitute approximately 80% of the total observational data and have proven to be pivotal in augmenting the forecasting performance of GRAPES_GFS. Building upon the concept of “regularized solutions” in the context of inverse problems in mathematical physics, a constrained bias correction (CBC) technique was developed (Han, 2014; Han and Bormann, 2016), which effectively mitigates systematic biases in the data and optimizes the utilization of observational information. This technique was operationalized in the ECMWF 2018 operational version (IFS CY46R1) (ECMWF, 2018a) and was also employed in ECMWF’s sixth generation atmospheric reanalysis (ECMWF, 2018b).
Fig
1.
Satellite instruments and number of platforms that provide observations to be assimilated by GRAPES_GFS (CMA-GFS).
The inaugural generation of Chinese geostationary meteorological satellites, known as Fengyun-2 (FY-2), significantly contributed to both global and regional assimilation forecasting within the GRAPES framework, particularly through its satellite cloud motion wind product (Han et al., 2006; Wan et al., 2017, 2018). The radiative data from the visible and infrared spin scan radiometer (VISSR) clear-sky water vapor channel were integrated into the GRAPES global 4D-Var system. The subsequent generation, the Fengyun-3 polar-orbiting meteorological satellites, introduced advanced algorithms for integrated cloud and precipitation detection, facilitating the assimilation of microwave temperature (MWTS), humidity (MWHS), imaging (MWRI), and occultation observations (GNOS) into the operational framework of GRAPES (Li and Liu, 2016; Wang R. C. et al., 2018). The successful launch of the FY-4A geostationary meteorological satellite in 2016 represented a significant milestone, as it was the first instance of hyperspectral detection in geostationary orbit on an international scale (Yang J. et al., 2017). Within the GRAPES assimilation system, several key technologies were developed, including the Geostationary Interferometric Infrared Sounder (GIIRS) observation operator (Di et al., 2018), channel selection methodologies (Yin R. Y. et al., 2019), and algorithms for online bias estimation and correction (Yin F. K. et al., 2019). By December 2018, the assimilation of GIIRS radiance data into the operational GRAPES global 4D-Var system was successfully achieved. Additionally, by capitalizing on the versatile observational capabilities of the FY-4A and the cloud forecasting and sensitive area identification technologies inherent to the NWP system, a geostationary satellite detection mode aimed at forecasted objects was implemented in real-time operational settings. This mode was integrated into the GRAPES global 4D-Var system, resulting in enhanced accuracy in typhoon track predictions.
3.1.4
Kilometer-scale 3D-Var
The GRAPES kilometer-scale 3D-Var data assimilation system (hereafter referred to as km-scale 3D-Var) is developed based on the GRAPES global–regional integrated variational data assimilation framework (Xue and Chen, 2008). The km-scale 3D-Var analysis framework is specifically designed to meet the needs of kilometer-scale NWP (Wang R. C. et al., 2018). In this system, the control variables are transformed from stream function (ψ), velocity potential (χ), and π to u wind, v wind, temperature (T), and surface pressure (ps), with the geostrophic balance between control variables no longer considered. The analysis increments in km-scale 3D-Var are more localized, making them more suitable for prediction of mesoscale systems. Additionally, multiscale analysis schemes have been developed (Wu et al., 2018; Yang et al., 2019). To adapt to the rapid development and short lifecycle of mesoscale information, km-scale 3D-Var operates with a fast assimilation–forecast cycling update system, with an assimilation analysis interval of 1–3 h. Digital filtering is applied to suppress noise in the rapid cycling process.
In terms of advanced observation data applications, km-scale 3D-Var can assimilate radar radial winds and wind profiler radar data. Reflectivity data are used within the cloud analysis system to diagnose hydrometeor and latent heat tendency information. Km-scale 3D-Var is also capable of assimilating data from China’s new generation geostationary satellite FY-4A. Furthermore, in response to the growing abundance of data from ground-based automatic meteorological stations, km-scale 3D-Var is enhancing its research on assimilating such data, particularly in complex terrain.
Km-scale 3D-Var can effectively improve the short-term forecasting performance of the model (within the first 12 h), including short-term precipitation and near-surface meteorological element forecasts. The GRAPES kilometer-scale rapid cycle NWP system (CMA-MESO V5.1) was operationally implemented in 2020.
3.1.5
Regional mesoscale and global medium-range ensemble forecasting
The GRAPES_GEPS global ensemble forecasting system was developed using the singular vector (SV) initial perturbation method. Research shows that the GRAPES global singular vectors can represent the baroclinic instability growth characteristics of disturbances in the mid-to-high latitudes of the troposphere (Liu et al., 2013). A Gaussian sampling method was employed to construct the initial perturbation field for global ensemble forecasting (Li et al., 2019; Li and Liu, 2019). In 2018, the GRAPES global ensemble forecast was operationalized (Li and Liu, 2019). GRAPES_GEPS forecast skill, from January to May 2019, was 8.6 days, compared to 7.6 days for the control forecast, showing an improvement of 1.06 days. In the Southern Hemisphere, the forecast skill was 7.46 days, with the control forecast at 6.94 days, improving by 0.52 days.
The GRAPES_REPS regional ensemble forecasting system was developed using the ensemble transform Kalman filter (ETKF) initial perturbation method (Zhang et al., 2014). A multiscale hybrid initial perturbation method (MSB) was further developed (Zhang et al., 2015), along with a three-dimensional bias correction method (Wang J. Z. et al., 2018). The 10-km regional ensemble forecast driven by GRAPES_REPS was operationalized in August 2019.
To address model uncertainty in ensemble forecasting, various stochastic physical perturbation methods were developed, including the stochastic physics tendencies perturbation (SPPT) method (Buizza et al., 1999), stochastic kinetic energy backscatter (SKEB) method (Berner et al., 2009), and the stochastic perturbed parameterization (SPP) method, which describe physical process uncertainties in both GRAPES global and regional models. A key focus of the stochastic physical perturbation methods is how to construct the random fields. The random perturbation schemes for both GRAPES global and regional ensemble forecasts are based on a first-order Markov process with time correlation characteristics and a Gaussian distribution (Yuan et al., 2016). Additionally, experiments with SKEB showed improvements in the prediction of atmospheric kinetic energy spectra and error diffusion relationships in GRAPES_GFS, especially in tropical regions (Peng F. et al., 2019). The random parameter perturbation scheme (SPP) was also studied (Xu et al., 2019).
3.1.6
Cloud scheme
Ma et al. (2018) developed a new cloud physics and cloud amount forecasting scheme in GRAPES_GFS, based on the Tiedtke cloud scheme (Tiedtke, 1993). This scheme considers the influence of boundary layer turbulence, cumulus convection entrainment, large-scale stratiform cloud condensation processes, and evaporation processes due to horizontal turbulent mixing between clouds and unsaturated air on cloud amount formation and dissipation. When compared with the original cloud amount parameterization scheme in GRAPES_GFS, which diagnosed cloud amount based on relative humidity and cloud water content (Xu and Randall, 1996), the new cloud amount forecast scheme was found to better simulate the diurnal variation of stratocumulus–cumulus clouds over the ocean and correct significant underestimations of low and high cloud amounts. The improvement in cloud amount also indirectly enhanced the radiation calculation accuracy of the GRAPES_GFS model. This new cloud amount forecasting scheme has been applied in the operational GRAPES_GFS forecasting system (Ma et al., 2018).
3.2
Establishment of GRAPES and related applications
By 2018, a complete numerical weather prediction system was established based on the GRAPES framework, featuring an appropriate combination of high and low resolution, as well as the integration of deterministic and ensemble forecasts. Compared to systems based on imported technologies, the establishment of an independent operational system not only required extensive work to translate model and assimilation research outcomes into operational applications but also involved the reconstruction or development of various processes, from observation data retrieval, preprocessing, and monitoring, to forecast data post-processing, verification, and visualization. In the process of building the GRAPES operational system, significant progress was made not only in the model, assimilation, and observational data application areas but also in the development and application of supporting systems such as large databases, experimental platforms, analysis and diagnostic tools, and verification platforms.
The GRAPES operational system consists of the following components: global deterministic and ensemble forecasting systems with a horizontal resolution of 0.125 degrees and 87 vertical layers, and 0.5° × 0.5° horizontal resolution with 60 vertical layers respectively; a mesoscale deterministic forecasting system for the Asia–Pacific region with a horizontal resolution of 0.09° × 0.09° and 68 vertical layers; a high-resolution numerical weather prediction system covering China with a horizontal resolution of 0.01 degrees and 70 vertical layers; and a mesoscale ensemble forecasting system covering China with a horizontal resolution of 0.1° × 0.1° and 50 vertical layers. Additionally, the GRAPES system also includes specialized models such as the global/regional wave forecasting system, East Asia dust storm forecasting system, and nuclear contamination emergency forecasting system, all of which are important components of the GRAPES framework.
It should be noted that there have been rapid developments in NWP technology in the past 20 years, with many countries significantly increasing their investment in NWP. Along with these great achievements, the GRAPES operational system still faces certain gaps compared to internationally advanced systems. These gaps include the capability of ensemble data assimilation in the GRAPES global forecasting system, the absence of advanced techniques like satellite data assimilation for cloud and precipitation regions and satellite data variational bias correction, insufficient coordination in physical processes, and a limited number of ensemble members with relatively low resolution. These issues are inevitable at the early stage of developing a new numerical weather prediction operational system, but must be seriously addressed, and will be the focus of future efforts to accelerate improvements.
Figure 2 shows the year-by-year improvement of precipitation forecast scores for the operational GRAPES_Meso system. It is evident that GRAPES_Meso has made significant progress in precipitation forecasting across all levels, becoming an indispensable support for daily weather forecasts at the National Meteorological Centre. The improvements in GRAPES_Meso include higher resolution, enhancements in model dynamics and physical processes, and the introduction of a cloud analysis system that effectively utilizes radar data. In June 2019, the GRAPES_Meso system with a horizontal resolution of 3 km was officially launched, and in July 2024, the GRAPES_Meso system with a 1-km horizontal resolution and covering all of China, will be officially launched. This system will elevate GRAPES’ forecasting capabilities for heavy precipitation, advancing the operational application level of GRAPES to a new stage.
Fig
2.
Monthly-averaged threat score (TS) and its linear trend of GRAPES_Meso 24-h forecasts since its operational application in July 2006.
Figure 3 presents the equitable threat scores (ETS) for 3-h heavy rainfall forecasts from the GRAPES_Meso 1-km model, averaged for July 2024, with a comparison to the ECMWF forecast (with a horizontal resolution of 9 km × 9 km). As shown in Fig. 3, the GRAPES_Meso 1-km model consistently outperforms the ECMWF forecast in terms of ETS scores for precipitation across almost all forecast periods.
Fig
3.
Equitable threat scores (ETS) of 3-h heavy rainfall forecast by the GRAPES_Meso 1-km model (red bars) and the ECMWF model (black bars).
Figure 4 displays the time series of the ACC for the 500-hPa geopotential height forecast on the 5th day from the GRAPES_GFS model since 2010. The figure also includes the forecast results from ECMWF and NCEP as references. It is evident that the forecasting skill of the GRAPES_GFS model for the synoptic scale variables has steadily improved over the past decade. While there is still a gap compared to ECMWF and NCEP, the year-on-year improvement in forecasting skill reflects significant progress in the GRAPES_GFS model, assimilation, and the application of observational data.
Fig
4.
Anomaly correlation coefficient (ACC) of 500-hPa geopotentail height forecast on the 5th day from the GRAPES_GFS (CMA-GFS) from 2010 to 2024.
Since the 2019 flood season, the GRAPES_GFS model has been consistently comparable with the ECMWF in forecasting heavy rainfall events across China. For example, during the large-scale warm front precipitation event in the Jiangnan, Jianghuai, and Jianghan regions (26 May 2019), GRAPES_GFS showed better performance, with a TS score of 0.29 compared to ECMWF’s TS score of 0.16. Similarly, for strong cold front-induced heavy rainfall in the Jianghuai, Jiangnan, Jianghan, and South China regions (6–7 and 12 June 2019), GRAPES_GFS also outperformed ECMWF, providing forecasters with important reference data.
Currently, for deterministic forecasts, the GRAPES_GFS and GRAPES_Meso models complement each other well. GRAPES_GFS is adept at capturing medium-term changes in the synoptic fields and rainfall bands, while GRAPES_Meso focuses on providing detailed forecasts of heavy rainfall amounts and locations for forecasters. These two systems have become key components of daily weather forecasting at the national and provincial meteorology centers. Similarly, the operational use of both global and regional ensemble forecasts within the GRAPES system has enriched the “GRAPES family” with valuable probabilistic forecasting products. These products have played a critical role in predicting the probability of large-scale heavy rainfall and providing localized, quantitative, and point-based forecasts for severe weather events up to one week in advance.
4.
Establishment and development of YHGSM
After more than 30 years of development, the NUDT has established and advanced the YHGSM global numerical prediction operational system. The innovative progress of YHGSM is summarized below in three aspects: numerical prediction models, data assimilation, and operational application effectiveness.
4.1
Breakthrough NWP modeling technologies
4.1.1
Dry-mass conserving global hydrostatic spectral dynamical framework
The YHGSM’s dynamical framework before 2016, like the mainstream operational models internationally (e.g., the IFS model of ECMWF), adopted the assumption of total air mass conservation. However, since phase changes of moist substances directly alter the mass of water vapor in the air, leading to an increase or decrease in moist air mass (Smolarkiewicz et al., 2017), this assumption introduces artificial sinks/sources of dry air mass for any sources/sinks of total moist substance mass in the numerical model. Taking heavy precipitation as an example, it not only causes artificial growth in dry air mass, but also results in erroneous descriptions of mass forcing effects, thereby affecting the model’s forecasting performance for severe convective processes. For this reason, major international numerical weather prediction development centers have increasingly emphasized the issue of dry air mass conservation. By introducing vertical coordinates based on dry air mass and reconstructing the mass continuity equation accordingly, Lauritzen et al. (2018) developed a dry-mass conservation version of the NCAR spectral element dynamical kernel (CAM-SE), but there are still shortcomings such as the inaccuracy of the diagnostic equation for full pressure vertical velocity and the continuity equation without sources/sinks term for the dry air and water species mass. Malardel et al. (2019) addressed the IFS model of ECMWF by retaining the total mass continuity equation in the governing equation. To ensure dry air mass conservation, additional source/sink terms were incorporated into the total surface pressure tendency equation and the full pressure vertical velocity diagnostic equation. This can be regarded as a corrected dry-mass conserving version of IFS, though it has not yet fully resolved the so-called “dry air mass conservation problem.”
Peng et al. (2020) developed a dry-mass conserving global hydrostatic spectral dynamical framework in YHGSM. This framework employs dry-air mass as the vertical coordinate and rigorously derives the calculation formula for the full pressure vertical velocity. As is shown in Fig. 5, idealized tropical cyclone tests demonstrate that the newly developed hydrostatic spectral dynamical framework simulates tropical cyclones with greater intensity, more compact structure, and more concentric circular morphology, thus aligning more closely with actual tropical cyclone observations and simulations from other global grid-point models (Peng et al., 2020). Practical operational applications also indicate that the dry-mass conserving global hydrostatic spectral dynamical framework significantly improves the forecasting of severe convective weather processes, such as heavy rainfall (Yang X. R. et al., 2023) and tropical cyclones (Li S. Y. et al., 2023), enhancing the accuracy of global medium-range numerical weather prediction.
Fig
5.
Comparison of simulation results from idealized experiments (a–d) with and (e–h) without dry-air mass conservation. (a, e) Zonal-mean precipitation rate and (b, f) vertical velocity from the moist Held–Suarez simulations; (c, g) horizontal wind speed at a height of 1500 m and (d, h) zonal velocity at a height of 100 m from an idealized simulation of a tropical cyclone on the 10th day. Adapted with permission from Peng et al. (2020) and Peng et al. (2023).
4.1.2
Dry-mass conserving global non-hydrostatic spectral dynamical framework
When the horizontal resolution of a model falls below 10 km, particularly in scenarios involving steep topography or significant meteorological phenomena characterized by intense vertical motion, the conventional hydrostatic balance becomes inadequate. This limitation necessitates the incorporation of non-hydrostatic effects. In response, numerous research and operational centers focused on numerical weather prediction have undertaken relevant advancements. The UK Met Office (UKMO) has implemented a non-hydrostatic variant of the Unified Model (UM), which is based on a semi-implicit semi-Lagrangian framework (Davies et al., 2005). The German Weather Service (DWD) has developed a non-hydrostatic model that utilizes terrain-following vertical coordinates and adopts a horizontally explicit, vertically implicit approach for the treatment of sound and gravity waves (Steppeler et al., 2006). The Japan Meteorological Agency (JMA) has created a non-hydrostatic model that encompasses Japan and its adjacent regions (Saito et al., 2006). The U.S. NCEP has also developed a non-hydrostatic model, which is based on a conservative split-explicit time integration scheme (Klemp et al., 2007). Additionally, the French meteorological service has produced a non-hydrostatic version of the ALADIN model, which employs hydrostatic pressure as the vertical coordinate and introduces pseudo-vertical velocity and pressure deviation as non-hydrostatic forecast variables (Bénard and Mašek, 2013).
Wu et al. (2011) preliminarily designed and implemented a global non-hydrostatic spectral dynamical framework under the shallow atmosphere approximation based on the operational spectral model YHGSM and validated its correctness through idealized Rossby wave experiments. Building upon this foundation, and after a thorough analysis of the shortcomings in the deep-atmosphere dynamical frameworks of the ECMWF IFS and the UK Unified Model, which use Π as the vertical coordinate (Wood and Staniforth, 2003), the team developed a deep-atmosphere dynamical core based on hydrostatic pressure π. Idealized experiments demonstrated that the developed deep-atmosphere dynamical framework enables more accurate simulation of baroclinic waves (Yang J. H. et al., 2017). Simultaneously, by integrating non-hydrostatic modeling techniques with dry air mass conservation methods, a non-hydrostatic moist atmospheric spectral model dynamical framework was developed. Idealized supercell experiments showed that this non-hydrostatic framework better simulates the structure and evolution characteristics of idealized supercells (Peng J. et al., 2019). Further systematic experiments (Fig. 6) revealed that the non-hydrostatic framework simulates tropical cyclones with lower central pressure, stronger wind speeds, and faster northward movement, yielding results closer to those of the global non-hydrostatic model MPAS. Additionally, it enhances upward motion and precipitation rates in tropical regions, which to some extent compensates for insufficient vertical transport of moist air due to the absence of deep convection parameterization (Peng et al., 2023).
The global non-hydrostatic spectral model based on mass coordinates cannot ensure operator conservation in the spectral space when employing high-precision finite element discretization in the vertical direction; only meticulously designed finite difference schemes can satisfy this requirement (Bubnová et al., 1995). To achieve overall high precision in numerical discretization in the vertical direction and relative consistency in discretization accuracy between grid space and spectral space, the team developed a hybrid finite-difference finite-element vertical discretization scheme (Yang et al., 2015). The linear part adopts a finite difference scheme to meet conservation requirements while increasing the number of vertical layers to enhance computational accuracy, which only needs to be addressed in the spectral space. The nonlinear part employs a finite element scheme, effectively improving integration accuracy without altering the number of vertical layers. Experiments show that the hybrid scheme can significantly enhance the vertical discretization accuracy of non-hydrostatic models with minimal impact on overall computational efficiency. Additionally, a hybrid finite-difference finite-element vertical discretization scheme based on Gaussian integration can be adopted, constructing Gaussian integration formulas to replace the original uniform integration scheme, further improving vertical discretization accuracy and integration stability (Yang J. H. et al., 2017).
Fig
6.
Distributions of (a) horizontal wind speed at a height of 1500 m, (b) zonal velocity at a height of 100 m, and (c) temperature anomaly at a height of 5000 m from the idealizded simulation of a tropical cycle on the 10th day by the global non-hydrostatic spectral dynamical core based on the dry-air mass conservation. (d) Accumulated precipitation through the 10 days. Reproduced from Peng et al. (2023).
4.1.3
Efficient algorithms and scalable parallel algorithms
The operational implementation of NWP requires certain real-time performance criteria. For global medium-range NWP, it is typically required to complete within one hour (Wedi et al., 2015). Therefore, when executing the operational forecast system, it is essential to fully consider the characteristics of the forecasting model and the underlying high-performance computing system. On one hand, efficient serial computation methods must be thoroughly explored, and on the other hand, scalable parallel computing must be implemented, to minimize execution time to the greatest extent. Since 1995, when ECMWF introduced a parallel computing framework based on data redistribution, this framework has become the mainstream for spectral models in global NWP (Barros et al., 1995). YHGSM has also adopted this framework, dividing the computation within a single time step into three parts: grid space, Fourier space, and spectral space. The main computational process, excluding the setup phase, is divided into six stages: grid space computation, Fourier transform, Legendre transform, spectral space computation, inverse Legendre transform, and inverse Fourier transform. Each stage undergoes domain decomposition in two directions, with data redistribution between stages to meet the data dependencies required for computation at each stage. In recent years, to enhance the real-time performance of the YHGSM model, the team has focused on targeted innovations in the Legendre transform, three-dimensional array redistribution, and semi-Lagrangian interpolation in grid space computation.
The Legendre transform has long lacked fast algorithms, leading to a rapid increase in computational load as model resolution improves, making it one of the main bottlenecks in enhancing the resolution of spectral models. To address this issue, Yin et al. (2018) conducted extensive research. By leveraging the sparse properties of interpolation decomposition matrices and column skeleton matrices, they designed and implemented a fast spherical harmonic transform algorithm based on sparse data structures and butterfly matrix multiplication, effectively reducing storage requirements and computational complexity. Subsequently, they investigated the error characteristics of the interpolation decomposition process in the Legendre transform, derived the error bounds and sources, and proposed a butterfly fast Legendre transform algorithm based on block partitioning of the Legendre–Vandermonde matrix, resolving the instability issue in ultra-high-resolution spherical harmonic transforms (Yin F. K. et al., 2019). Additionally, they developed a mixed-precision fast spherical harmonic transform algorithm, further reducing computational load and communication overhead, thereby improving the scalability of spectral transforms (Yin et al., 2021). Yang et al. (2023a) introduced a finite-volume method into global spectral models to compute horizontal local derivatives, maintaining wind-related quantities in spectral space while computing horizontal derivatives of temperature, humidity, and other variables using finite volumes in grid space. This approach significantly reduced the number of spectral transforms, minimized communication overhead during spectral-grid transformations without compromising model accuracy, and greatly enhanced the computational efficiency and scalability of spectral models. Later, this technique was further applied to the non-hydrostatic version of YHGSM, where the reduction in spectral transforms was even more substantial, significantly improved its computational efficiency (Yang et al., 2024).
In the development of parallel algorithms for global spectral models, the research team focused on semi-Lagrangian interpolation by employing a computation–communication overlap strategy that involved the categorization of physical quantities. These quantities were organized into three distinct groups, allowing for the overlap of communication necessary for the subsequent group’s computation with the ongoing computation of the current group. This method effectively concealed communication delays and diminished execution time during the interpolation phase (Jiang et al., 2021). Following this, improvements were made by further grouping vertical layers, taking into account the limited number of physical quantity groups. A meticulous analysis of data dependencies, coupled with the design of a pipelined algorithm, significantly reduced the parallel execution time (Liu et al., 2024). In the realm of adaptive communication for parallel computation within semi-Lagrangian frameworks, a statistical analysis of monthly maximum wind speeds was performed utilizing reanalysis data. This analysis led to the substitution of the original global maximum wind parameter with monthly adaptive maximum winds, facilitating the design and implementation of an optimized semi-Lagrangian parallel computing scheme. This innovative approach resulted in a notable reduction in the parallel execution time of the global spectral model YHGSM, achieved with minimal modifications to the code (Liu et al., 2021). Furthermore, Jiang et al. (2020) investigated the replacement of bilateral communication mechanisms with unilateral communication mechanisms based on the Message Passing Interface (MPI), which contributed to a reduction in both communication frequency and data volume, thereby enhancing communication efficiency.
4.1.4
Parameterization of near-surface physical processes and model terrain treatment
Radiative transfer, turbulent diffusion, subgrid-scale topographic drag, non-topographic gravity wave drag, water vapor exchange, and cloud and surface processes, among others, have a strong influence on large-scale atmospheric motion. However, these mechanisms typically operate at scales smaller than the horizontal grid size, necessitating the parameterization of these physical processes to accurately describe their impacts on large-scale atmospheric flow. In recent years, YHGSM has conducted innovative research primarily in describing topographic effects and air–sea interactions.
In order to enhance the representation of model terrain, the YHGSM research team has developed a global spectral terrain construction utilizing the most recent version of ASTER elevation data. This methodology thoroughly addresses the alignment between the filtering scale, which varies by geographic location, and the scales of model resolution and parameterizations of terrain-related physical processes. This is achieved through the integration of grid-point spatial filtering with spectral-spatial filtering (Wang et al., 2022). Numerical simulations of typical heavy rainfall events demonstrated that the newly developed model terrain surpasses the original model terrain, particularly exhibiting notable enhancements in the simulation of rainstorms and high-intensity precipitation events. Furthermore, for the terrain parameters needed by the terrain-related physical parameterizations, an accurate calculation method that aligns with the model terrain has been directly derived from high-resolution terrain data (Wang et al., 2024). Analyses indicate that the newly derived terrain parameters present finer distributions compared to the original ones, thereby effectively capturing small-scale topographic features. Numerical simulations of typical heavy rainfall events showed that the application of these newly constructed terrain parameters enhances rainfall simulation in regions with complex terrain. Additionally, built upon the classical Lott and Miller (1997) scheme, a topographic gravity wave drag parameterization scheme was formulated, which fully incorporates the effects of moist air and demonstrates improvements in the simulation of heavy precipitation.
The interactions between the atmosphere and ocean waves are characterized by a complex interplay that encompasses not only traditional turbulence arising from shear and buoyancy but also smaller-scale phenomena such as wave-induced disturbances and sea spray. These interactions between waves and air play a crucial role in modifying the transfer of matter and energy between the ocean and the atmosphere. The research team successfully established a two-way coupling between the global wave model WAM and the YHGSM by parameterizing relevant physical processes. The atmospheric model supplies the wave model with 10-m wind fields and sea surface atmospheric density, while the wave model reciprocates by providing sea surface roughness data to the atmospheric model (Yang et al., 2023b). This tightly coupled methodology significantly enhanced the operational efficiency of the integrated system while ensuring the stability of the overall integration process. In the absence of assimilation support for the wave model, the team adeptly resolved the challenge of missing initial conditions by utilizing output from a preceding 48-h integration as the initial field. Experimental findings indicate that the incorporation of the wave model leads to improvements in various evaluation metrics for 10-day atmospheric forecasts, including root-mean-square error and correlation coefficients, with particular enhancements noted in the accuracy of typhoon track predictions and landfall point forecasts. Furthermore, the team developed a novel parameterization scheme for sea surface dynamic roughness, based on wave steepness and wave age, which is particularly suited for high wind speed conditions. This innovative approach optimized the spray-mediated heat flux parameterization scheme and strengthened ocean–atmosphere feedback mechanisms, resulting in a significant increase in the accuracy of typhoon intensity forecasts (Sun et al., 2021). Notably, in numerical simulations of super typhoons in the Northwest Pacific, the new parameterization scheme exhibited superior performance compared to commonly employed roughness schemes (Lan et al., 2022).
4.1.5
New methods for dynamic diagnostic evaluation of global atmospheric models
The energy spectrum is one of the fundamental physical properties of earth’s atmosphere, characterized by a distinct slope transition. To date, there is no unified understanding of the dynamical mechanisms underlying the observed atmospheric energy spectrum. Nevertheless, the atmospheric energy spectrum has become a crucial theoretical foundation for constructing atmospheric model dynamical frameworks, designing physical processes parameterizations, evaluating simulation performance, and studying mesoscale atmospheric predictability. For example, calculating the atmospheric kinetic energy spectrum simulated by models has emerged as the most direct and effective method for assessing the effective resolution of numerical models. However, the long-standing lack of an energy spectrum budget theory applicable to global mesoscale atmosphere has somewhat limited the depth of its application in diagnosing the dynamics of global atmospheric models. To address this, based on the YHGSM spectral model dynamical framework and Helmholtz decomposition, a budget equation for the rotational kinetic energy (RKE)/divergent kinetic energy (DKE) spectrum suitable for global hydrostatic primitive atmosphere was derived. It precisely constructs the rotational/divergent kinetic energy cascade terms and the spectral conversion terms between them, quantitatively revealing the multiscale interaction mechanisms between atmospheric rotational/divergent motions (i.e., balanced/unbalanced motions, Fig. 7) (Li et al., 2023a). Based on this spectral budget theory, the dynamic evaluation of the reanalysis data of different global atmospheric models was carried out. The results show that the horizontal kinetic energy spectrum of NCEP-FNL is stronger and shallower than ERA5 at the sub-synoptic and mesoscale scales, which is related to the stronger dissipation at the corresponding scales in ERA5. Moreover, the amplitude difference of the pressure vertical velocity spectrum between the two types of reanalysis data is consistent with the amplitude difference of the large-scale precipitation spectrum related to the cloud microphysical process, illustrating that vertical motion is the key dynamic factor to explain the difference in the mesoscale energy spectrum (Li et al., 2024). Furthermore, based on the global unstructured grid model (MPAS), the response of atmospheric kinetic energy spectra to different cumulus convective parameterization in global high-resolution simulations was investigated, and the dynamic mechanism of different cumulus convective parameterization affecting the global atmospheric mesoscale energy spectra was revealed, that is, the more latent heat released by cumulus convective parameterization, the less latent heat released by cloud microphysical parameterization, the weaker the rotational kinetic energy downscale cascade, and the steeper the mesoscale energy spectra (Li et al., 2023b).
Fig
7.
Schematic diagrams showing the spectral kinetic energy budgets of global atmospheric rotational/divergence motion components in the (upper panel) stratosphere and (lower panel) upper troposphere, as diagnosed from the ERA5 reanalysis data. Reproduced from Li et al. (2023a).
4.2
Breakthrough data assimilation technologies
4.2.1
Global atmospheric 3D-Var
NWP represents a quintessential initial value problem, wherein the precision of the initial conditions plays a crucial role in determining the efficacy of the forecast. The data assimilation methodologies employed to construct the initial field have consistently been of paramount importance in NWP. In light of the current prevalence of remote sensing observations, including satellite and radar data, in atmospheric monitoring, such data have substantially improved the spatial and temporal coverage of meteorological observations, effectively addressing data deficiencies over oceanic regions and areas lacking monitoring. Nevertheless, the intricate nonlinear relationships between the observed variables derived from remote sensing data and the forecast variables utilized in the model render traditional optimal interpolation (OI) methods inadequate for the direct assimilation of remote sensing observations. Conversely, indirect assimilation through the use of retrieved data is considerably influenced by the inherent limitations associated with the accuracy of retrieval techniques, which in turn significantly impacts the outcomes of the assimilation process.
Zhang Weimin and his colleagues were pioneers in China in the exploration of variational data assimilation theory and its implementation techniques, addressing several critical challenges. These challenges include the non-global optimality associated with optimal interpolation objective analysis, the limitations in integrating complex observation operators such as radiative transfer models, and the propensity for physically inconsistent initial fields to generate spurious inertial gravity waves. Their initial contribution involved the development of a global 3D-Var framework, which was based on control variable transformation operators (Zhang et al., 2005). This framework incorporated three distinct sub-transformations: physical transformation, vertical transformation, and horizontal transformation, which collectively convert atmospheric state variables—namely temperature, pressure, humidity, and wind—into control variables. The NMC method was employed to statistically derive background error statistics at each stage of these transformations. The implementation of control variable transformations and their adjoint not only mitigated correlations among variables and enhanced the efficiency of minimization algorithms but also implicitly modeled the large-scale background error covariance matrix within the 3D-Var framework.
Subsequently, the researchers developed tangent linear and adjoint models for various conventional observation operators, including radiosondes, wind measurements, and surface and ship reports, thereby facilitating the application of 3D-Var to global conventional atmospheric observations. Numerical comparison experiments indicated that global 3D-Var significantly outperformed optimal interpolation objective analysis in terms of improving the skill of NWP for global circulation fields. Furthermore, to enhance the parallel computing capabilities of global 3D-Var, they proposed and implemented a multistage region decomposition strategy, an adaptive partition algorithm for observational data, matrix transposition, and peripheral region communication with overlapping calculations and communications. This led to the realization of an MPI parallel 3D variational system, achieving a parallel acceleration ratio of 11.9 on a high-performance computing cluster comprising eight dual-CPU nodes (Zhang, 2005). Ultimately, through systematic optimization and enhancements, the development of the 3D-Var system YH3DVAR for global meteorological data was completed in 2005. This system was subsequently adopted by the military meteorological support unit, which replaced the optimal interpolation objective analysis with this data assimilation service software. The system operates bi-daily, in accordance with the schedule established by the numerical prediction business process, and provides the initial field for a 10-day forecast of the global spectral model following the assimilation of real-time global atmospheric observation data (Zhang et al., 2005).
4.2.2
Global atmospheric 4D-Var
The 4D-Var transforms observational data processing into a functional minimization problem constrained by dynamic models. Adjusting control variables minimizes the discrepancy between model forecasts derived from these variables and actual observational data within a specified time window. As an extension of 3D-Var along the time dimension, 4D-Var integrates meteorological observations from different times, regions, and characteristics as a unified whole, ultimately yielding an initial field consistent with the forecast model. Key advantages of 4D-Var include: directly utilizing observational data at the time of measurement without temporal approximation, making it more effective for assimilating continuous data from satellites, radars, and automatic surface stations; implicitly defining flow-dependent background covariance within the assimilation window, enabling effective adaptation to rapidly evolving weather systems; and incorporating the forecast model as a direct constraint, ensuring dynamical balance in the resulting analysis field. Consequently, 4D-Var is widely regarded as the data assimilation method with the greatest developmental potential, playing a crucial role in enhancing the performance of high-resolution NWP models. It is the long-adopted and prioritized assimilation scheme by leading international meteorological institutions such as ECMWF.
Zhang et al. (2010) and Cao et al. (2008) researched, designed, and implemented a global meteorological data 4D-Var data assimilation method compatible with global spectral models, focusing on the background field consistent with the spectral model’s dynamic framework, variational quality control of observational data, gravity wave control, deviation revised integration objective function definition, incorporating spectral model surface balance relations, spherical wavelet background error covariance processing, the construction of tangent-linear/adjoint models for the spectral model’s dynamical framework and physical process parameterization schemes, and key technologies such as the direct assimilation of satellite remote sensing radiance data. Finally, the structural functions of a global meteorological data 4D-Var system (hereinafter referred to as YH4DVAR), designed and implemented based on these methods, along with the assimilation and forecast statistical test results of the analysis–forecast system composed with the global spectral model, are presented (Zhang et al., 2012). The calculation process of the YH4DVAR is shown in Fig. 8. The main features of YH4DVAR include: the introduction of a wavelet background error covariance model; the adoption of a multi-resolution incremental approach; the integrated consideration of variational bias correction for satellite data, weak-constraint digital filtering, and variational quality control within the 4D-Var framework design (Wang et al., 2011; Zhang et al., 2012); and the support for scalable parallel computing. The computational workflow of YH4DVAR is illustrated below. By employing a multi-resolution, multi-incremental 4D-Var method that combines inner and outer loops, it accelerates the convergence speed of inner-loop optimization iterations and reduces computational load. Calculating observation update vectors at high resolution and performing data screening, while conducting optimization computations at low resolution, preserves atmospheric information across different scales, thereby yielding higher-resolution analysis increments and more accurate analysis fields (Zhang et al., 2012; Cao et al., 2014). In 2008, the operational software for the 4D assimilation of global conventional observation data was completed, followed by the completion of the global ATOVS satellite data 4D-Var software in 2010 (Zhang et al., 2012).
Fig
8.
Schematic diagram showing the calculation processes in the multi-resolution and multi-incremental global 4D-Var data assimilation system, i.e., the YH4DVAR.
4.2.3
Flow-dependent spherical wavelet background error model and global ensemble 4D-Var
Due to the rapid development of high-performance computing technology and atmospheric remote sensing, the introduction of vast satellite data, and improvements in assimilation methods and numerical models, the effective forecast lead time of NWP and Earth system models has steadily increased at a rate of one day per decade over the past 30 years. Data assimilation, as a critical factor in enhancing forecast skill, has seen its role and importance that are fully demonstrated through forecast experiments. The background error covariance matrix describes the error distribution of the numerical model’s background field. It not only determines the weight of the background field during assimilation but also significantly influences information propagation, smoothing, balance relationships among analysis variables, and flow-dependent characteristics within the assimilation system. Ensemble data assimilation has emerged as a cornerstone technique for operational NWP centers to estimate flow-dependent background error covariance. However, due to computational cost constraints, the number of ensemble members is far smaller than the dimensionality of the model state. Consequently, flow-dependent background error covariance estimated by ensemble methods is always plagued by issues such as estimation noise, rank deficiency, and spurious correlations caused by insufficient sampling. Since 2010, operational centers worldwide began researching and developing hybrid data assimilation techniques, aiming to combine the strengths of multiple assimilation methods or systems to address problems encountered in single-method assimilation, such as filter dissipation and the inability to propagate and update background error information.
In 2020, based on the advanced theories and success experiences of ECMWF, the NUDT designed a flow-dependent spherical wavelet background error covariance model, leveraging the YH4DVAR data assimilation system. This breakthrough addressed key technologies such as the characterization of observational data and SST perturbations, numerical model uncertainty representation, and flow-dependent error information extraction. The team successfully developed the operational global ensemble 4D-Var software YHEDA (Zhang et al., 2016). YHEDA employs the Monte Carlo method by superimposing perturbations that conform to their error distribution onto the observational data, boundary fields (e.g., SST), and background fields into the system. This process generates multiple perturbed members capable of representing the uncertainties in the YH4DVAR assimilation analysis cycle. Based on these perturbed members, it is possible to statistically derive the grid-space background error variance required by YH4DVAR, which evolves with flow patterns, as well as vertical and horizontal correlation coefficients defined in spherical wavelet space and equilibrium coefficients in spectral space. These coefficients are the fundamental components that constitute the full-flow-dependent spherical wavelet background error covariance, enabling YH4DVAR to effectively characterize uncertainty information in the vicinity of typhoons and assimilate more “extreme” observational data, significantly enhancing the accuracy of assimilation analysis and forecasting for both intensity and track of the TC (Zhang W. et al., 2022).
In the domain of satellite data assimilation, significant advancements have been made in the technological research pertaining to infrared hyperspectral clear-sky channel cloud detection, specifically utilizing data from the U.S. Aqua satellite’s Atmospheric Infrared Sounder (AIRS) and Europe’s Meteorological Operational satellite’s Infrared Atmospheric Sounding Interferometer (IASI) (Liu and Xue, 2014; Yu et al., 2017a). These developments have notably enhanced the application of infrared hyperspectral data in cloud-affected regions and have improved the forecasting capabilities for typhoons Noul and Meranti. To address the challenges posed by the substantial volume of data, channel redundancy, and data correlation inherent in infrared hyperspectral datasets, Yu et al. proposed a method based on principal component analysis (PCA) to compress and denoise IASI channel radiance. This approach facilitated the assimilation of reconstructed infrared hyperspectral radiance data, thereby enhancing the accuracy of relative humidity assimilation analyses (Yu, 2017). Duan et al. (2021) examined the conversion of wind speed and direction into (u, v) wind components from a foundational perspective, introducing the law of error propagation to develop a diagnostic method for observing errors and correlations in (u, v) wind components. Their theoretical framework elucidated how these errors and correlations are influenced by the observations of wind speed and direction, providing a novel insight into satellite wind field data assimilation (Duan et al., 2021). Furthermore, Yu et al. conducted assimilation experiments utilizing high-spatial-resolution sea surface wind fields derived from synthetic aperture radar (SAR), thereby confirming the substantial value of integrating high-resolution SAR observations into numerical simulations. They also proposed a joint quality control methodology aimed at filtering out a significant number of substandard observations while effectively preserving high-quality sea surface wind field data. This approach resulted in more accurate analysis fields and improved forecasts regarding typhoon tracks and intensities (Yu et al., 2017b).
In the context of assimilating domestically developed satellite data, Zhang Q. et al. (2019) investigated advanced algorithms, including machine learning-based cloud detection techniques for GIIRS data. Comparative analyses indicated that twelve machine learning algorithms achieved varying degrees of accuracy in cloud detection, with the extremely randomized trees (ET) and random forest (RF) models attaining over 93% correct detection rates across both channel sets (689 channels and 38 channels). These algorithms, operating within reasonable time and computational constraints, significantly improved the accuracy of infrared hyperspectral GIIRS cloud detection, thereby facilitating its application in the NWP assimilation.
A domestic infrared hyperspectral data assimilation framework has been established for the FY-3 infrared hyperspectral HIRAS instrument, which is designed to perform quality control and bias correction on autonomous satellite infrared hyperspectral data. This framework incorporates the foundational principles of the McNally cloud detection scheme (McNally and Watts, 2003) to develop and implement a cloud detection algorithm specifically for HIRAS infrared hyperspectral data. The algorithm employs various techniques, including channel sorting, band separation, numerical filtering, and cloud identification, thereby enhancing the utilization of HIRAS observations in cloud-affected regions. This advancement has significantly increased the representation of domestically developed satellite data in assimilation applications. Furthermore, a selection of 60 channels from the HIRAS instrument was utilized for seasonal data assimilation and statistical validation of forecasts during winter and summer, resulting in marked improvements in the anomaly correlation coefficients for the 850-hPa temperature and 500-hPa geopotential height fields.
The challenges associated with accurately characterizing surface emissivity in complex terrains, coupled with the absence of precise rapid radiative transfer models, have resulted in the inability to assimilate a substantial volume of satellite observational data that is influenced by cloud cover, precipitation, and surface emissivity variations. Ma et al. (2022) investigated all-sky data assimilation techniques, utilizing the FY series second-generation microwave humidity sounder, MWHS-2, as a focal point. They devised a dynamic surface emissivity calculation framework and formulated an observation error model tailored for all-sky conditions, which is predicated on the correlation between biases in microwave observation simulations and scattering factors. This advancement facilitated the integration of all-sky microwave data assimilation capabilities within the YH4DVAR framework. Long-term observational system experiments indicated that the assimilation of FY series satellite microwave data under all-sky conditions significantly enhances the quality of the analysis field and yields substantial positive impacts on forecasting outcomes (Ma et al., 2022).
4.2.4
Hybrid data assimilation
Data assimilation techniques play a crucial role in enhancing the quality of initial conditions in Earth system models. However, prevalent operational data assimilation methods, such as variational techniques and ensemble Kalman filter approaches, are predicated on linear (or weakly nonlinear) and Gaussian assumptions. Consequently, these methods are limited to providing only first-order and second-order moment information regarding the probability density function, which fails to adequately address the complexities of real geophysical systems. In contrast, particle filtering represents a sophisticated filtering technique rooted in the principles of sequential importance sampling as articulated in Bayesian theory. The fundamental premise of the particle filtering algorithm is to approximate the probability density distribution of the state by utilizing a collection of weighted random sample particles within the state space. As the number of particles increases, the probability density function represented by these particles converges towards the true probability density function of the state. Notably, the particle filtering algorithm is not constrained by assumptions regarding the model state quantities or Gaussian error distributions, rendering it applicable to any nonlinear and non-Gaussian dynamic system.
Traditional particle filtering methods primarily adjust the weights of the particles without altering their numerical values. The weights assigned to the particles are proportional to the likelihood function values, which are determined by the proximity of the particles to the observed data. However, when the dimensionality of independent observations is high, the disparities between the particles and the observations can become excessively pronounced, resulting in the generation of uninformative weights. In such scenarios, only a limited number of particles effectively contribute to the characterization of the posterior probability density, while the majority become ineffective. This phenomenon is referred to as the filter degeneracy problem, which directly leads to a decrease in the effective sample size.
In response to the limitations observed in standard ensemble Kalman filters and particle filters when tasked with accurately characterizing the posterior probability density function (PDF) using a limited number of particles, an enhanced particle filter methodology has been proposed. This method incorporates the concept of pseudo-observations during periods without observations and a pre-resampling strategy during observation intervals. Simulation results indicate that this improved particle filter effectively estimates the states of nonlinear non-Gaussian stochastic systems (Leng et al., 2012).
For the first time, a hybrid assimilation technique that integrates 3D-Var and particle filter methodologies has been introduced, capitalizing on the advantages inherent in both approaches. By minimizing the associated cost function, this method yields a superior posterior state distribution. Empirical results demonstrate that this novel approach surpasses traditional ensemble Kalman filters and particle filters, particularly in the context of highly nonlinear systems (Leng and Song, 2013).
To leverage the benefits of particle filters while addressing the issue of filter degeneracy, innovative research has led to the development of two hybrid assimilation methods: one that combines particle filters with ensemble Kalman filters and another that integrates particle filters with 4D-Var. The locally weighted ensemble Kalman filter method has been proposed, merging the strengths of both particle filters and ensemble Kalman filters. Within the framework of the particle filter, the ensemble Kalman filter has been utilized as a proposal density (Chen et al., 2020a), accompanied by the design of a localized proposal weighting scheme (Chen et al., 2020b; Chen, 2021). Furthermore, a K-Dimensional Tree observation sparsification technique for unstructured grids has been established (Chen Y. et al., 2023). With these advancements, the global ocean locally weighted ensemble Kalman filter hybrid data assimilation system became operational in August 2024. The implicit equal-weight particle smoother method employs 4D-Var as the proposal density and achieves equal-weight particles through implicit sampling (Zhu et al., 2016; Zhu, 2019; Wang et al., 2020). Within the weak-constraint 4D-Var framework (Wang et al., 2020, 2021), dimensionality reducing techniques have been introduced, significantly decreasing computational costs. This has culminated in the successful establishment of an implicit equal-weight particle smoother hybrid data assimilation system.
Coupled data assimilation can be categorized into two primary types: weakly coupled assimilation and strongly coupled assimilation. In the case of weakly coupled assimilation, observational data from various components are permitted to propagate dynamically to other components solely during the model forecasting phase. Conversely, strongly coupled assimilation employs coupled cross-error covariances, allowing observational data from one component to affect other components both dynamically during the forecasting phase and statistically during the analysis phase. This study focuses on the ensemble filtering algorithm for sea–air coupling data assimilation, examining the application of weakly coupled assimilation in climate dynamics research, as well as the influence of model bias on the mechanisms underlying strongly coupled assimilation. Furthermore, it discusses the development of a parallel high-efficiency coupling assimilation system for high-resolution Earth system simulations (Sun, 2020). By utilizing an ensemble-based weakly coupled air–sea assimilation system within a low-resolution coupled model, a systematic comparison was conducted between uncoupled assimilation and weakly coupled assimilation. The findings reveal that weakly coupled assimilation enhances the efficiency of observational data utilization and significantly improves the quality of both atmospheric and oceanic analysis fields when compared to uncoupled assimilation (Sun, 2020).
4.3
Establishment of YHGSM and associated applications
The operational process of the YHGSM assimilation and forecasting system is configured as illustrated below. It incorporates a 12-h assimilation cycle process, a background field forecast process, and a 10-day forecast process (Fig. 9). The analysis field output from the 6-h assimilation is combined with the underlying surface data to form the model initial field, after which the model initiates the 10-day forecast.
Fig
9.
Workflow of the YHGSM operational data assimilation and weather forecast system.
According to the World Meteorological Organization standard statistical verification (WMO-CBS) method, using the 2020 YHGSM version, statistical verification was conducted on the forecast products of the circulation pattern field during January 2020 to August 2022, with focus on the monthly average statistical results of ACC and RMSE for the 500-hPa geopotential height forecasts against analyses in the Northern and Southern Hemispheres. The YHGSM Northern Hemisphere circulation pattern forecasts consistently showed ACC greater than 0.6 within 7 days, with significantly better forecast performance in winter than in summer. For 8-day forecasts, summer months fell below 0.6, while winter months remained above 0.6, with the annual average above 0.6. The Southern Hemisphere circulation forecasts performed notably better than those in the Northern Hemisphere, with relatively stable forecast performance across different seasons. For 8-day forecasts, only a few months in the Southern Hemisphere fell below 0.6. Regarding RMSE, both hemispheres exhibited smaller values in summer and larger values in winter.
5.
Prospects
Over the past 70 years, China has made significant strides in the field of NWP, achieving notable advancements. In the formative years of China, scholars such as Gu Zhenchao and Zeng Qingcun produced a series of results that garnered international recognition. During the 1970s, these scholars initiated the development of operational numerical prediction systems, culminating in the establishment of a modern operational framework in the 1980s, which became integral to weather forecasting operations. Currently, the China Meteorological Administration has implemented a numerical prediction operational system centered around the GRAPES_GFS model. Concurrently, the National University of Defense Technology and military operational units have developed their own numerical prediction system based on the dry air mass conservation global atmospheric spectral model (YHGSM) and the associated four-dimensional variational data assimilation (YH4DVAR), thereby achieving comprehensive independent research and development of core weather forecasting technologies.
The continuous enhancement of NWP capabilities over the past seven decades can be attributed to three primary factors: advancements in numerical models and resolution, improvements in data assimilation techniques, and the increasing availability of observational data, particularly satellite data. Nevertheless, it is essential to acknowledge that, in comparison to the leading NWP operational centers globally, China still exhibits deficiencies in global forecasting capabilities and the integration of satellite data assimilation. There remains a notable absence of data assimilation systems for land surface, snow cover, and sea ice, and the complete operational integration of multisphere component model assimilation forecasting has yet to be realized. Furthermore, there is a pressing need for foundational research and capabilities in the development of forecasting technologies and systems grounded in Earth system science. Consequently, enhancing the forecasting capabilities of independent NWP operational systems to address China’s specific weather forecasting requirements is a paramount objective for the next two to three years. Additionally, it is imperative to expedite the development of high-precision, scalable numerical prediction technologies and innovative support systems that align with future operational needs and advancements in numerical prediction technology. To effectively respond to the evolving demands for refined and seamless weather forecasting and climate prediction operations, as well as the challenges posed by the development of heterogeneous many-core high-performance computing, it is crucial to strengthen research and organizational efforts in several key areas to facilitate the accelerated advancement of the independent numerical prediction technology system.
In the realm of data assimilation technology, the following advancements are proposed. (1) The development of sophisticated assimilation techniques for novel satellite data, which encompass all-sky and all-surface assimilation technologies for radiance data, scene-dependent observational data quality control, and hybrid data assimilation methods. These innovations aim to enhance the operational efficacy of data assimilation. (2) The advancement of data assimilation and fusion technologies pertaining to land surfaces, snow cover, and oceanic systems, alongside the further development of multisphere coupled data assimilation methodologies.
With respect to numerical model technology, the following initiatives are recommended. (1) The creation of a next-generation high-precision and scalable atmospheric modeling framework, which incorporates scale-adaptive physical processes. This framework should continuously enhance computational accuracy, efficiency, and scalability, while optimizing the parameterization of critical physical processes and improving the representation of mesoscale energy spectrum characteristics within the numerical model. A significant future direction for the YHGSM is the establishment of a robust model dynamic framework capable of addressing non-hydrostatic effects and mitigating the introduction of vertically-propagating sound waves to facilitate efficient computations. A pivotal focus for GRAPES will be the implementation of the multimoment finite volume method (MCV) to achieve a high-precision and highly scalable atmospheric model. (2) The development of high-resolution Earth system model forecasting technology should prioritize the creation of seamless weather–climate integrated models, leveraging domestic coupler technology to enable high-resolution coupling across multisphere layers of ocean, land, and atmosphere.
Lastly, in the integration of numerical computation and artificial intelligence, the following advancements are suggested. (1) The development of intelligent data assimilation technologies, with an emphasis on applying artificial intelligence in observational data quality control, bias correction, observation operators, and model tangent linear and adjoint operators. (2) The advancement of intelligent numerical model technologies, focusing on the application of AI in the formulation of physical process parameterization schemes, AI bias correction, and post-processing of forecast products, thereby addressing uncertainties associated with model physical processes and forecast outputs.
To ensure the autonomous advancement and sustainable development of core NWP technologies, it is imperative to strengthen cross-institutional collaboration for overcoming persistent computational bottlenecks and fostering next-generation innovations. Concurrently, maintaining a vertically integrated research and development workforce with comprehensive technical expertise remains critical for achieving technological sovereignty in high-resolution ensemble forecasting systems. Strategic institutional frameworks must prioritize: (1) centralized resource allocation to stabilize multidisciplinary talent pools, (2) hierarchical optimization of research-to-operations (R2O) pipelines, and (3) unwavering adherence to indigenous innovation roadmaps. These measures constitute foundational imperatives for elevating national meteorological capabilities and fortifying strategic scientific infrastructure.
Acknowledgments
Thanks go to Liu Bainian, Yu Yi, Ma Shuo, Yin Fukang, Yang Jinhui, Yang Xiangrong, Duan Boheng, Leng Hongze, Chen Yan, Wang Pinqiang, Han Wei, Su Yong, Zhang Lin, Li Xingliang, Zhang Hua, Sun Jian, Chen Jing, Liu Yongzhu, Zhu Lijuan, Wang Ruichun, Wang Jincheng, Huang Liping, Chen Qiying, Ma Zhanshan, Ma Suhong, Dai Kan, Wang Yu, and others for providing textual materials and charts.
Fig.
8.
Schematic diagram showing the calculation processes in the multi-resolution and multi-incremental global 4D-Var data assimilation system, i.e., the YH4DVAR.
Fig.
5.
Comparison of simulation results from idealized experiments (a–d) with and (e–h) without dry-air mass conservation. (a, e) Zonal-mean precipitation rate and (b, f) vertical velocity from the moist Held–Suarez simulations; (c, g) horizontal wind speed at a height of 1500 m and (d, h) zonal velocity at a height of 100 m from an idealized simulation of a tropical cyclone on the 10th day. Adapted with permission from Peng et al. (2020) and Peng et al. (2023).
Fig.
6.
Distributions of (a) horizontal wind speed at a height of 1500 m, (b) zonal velocity at a height of 100 m, and (c) temperature anomaly at a height of 5000 m from the idealizded simulation of a tropical cycle on the 10th day by the global non-hydrostatic spectral dynamical core based on the dry-air mass conservation. (d) Accumulated precipitation through the 10 days. Reproduced from Peng et al. (2023).
Fig.
7.
Schematic diagrams showing the spectral kinetic energy budgets of global atmospheric rotational/divergence motion components in the (upper panel) stratosphere and (lower panel) upper troposphere, as diagnosed from the ERA5 reanalysis data. Reproduced from Li et al. (2023a).
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Zhang, W. M., X. S. Shen, X. Q. Cao, et al., 2025: 70 years of development in China’s operational numerical weather prediction. J. Meteor. Res., 39(3), 485–516, https://doi.org/10.1007/s13351-025-4917-4.
Zhang, W. M., X. S. Shen, X. Q. Cao, et al., 2025: 70 years of development in China’s operational numerical weather prediction. J. Meteor. Res., 39(3), 485–516, https://doi.org/10.1007/s13351-025-4917-4.
Zhang, W. M., X. S. Shen, X. Q. Cao, et al., 2025: 70 years of development in China’s operational numerical weather prediction. J. Meteor. Res., 39(3), 485–516, https://doi.org/10.1007/s13351-025-4917-4.
Citation:
Zhang, W. M., X. S. Shen, X. Q. Cao, et al., 2025: 70 years of development in China’s operational numerical weather prediction. J. Meteor. Res., 39(3), 485–516, https://doi.org/10.1007/s13351-025-4917-4.
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Manuscript History
Received: 11 January 2025
Available online: 14 May 2025
Final form: 28 April 2025
Issue in Progress: 15 May 2025
Published online: 26 June 2025
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Abstract
摘要
1.
Introduction
2.
Development history of numerical weather prediction in China
2.1
Initial exploration (1950s–1960s)
2.2
Establishment and improvement of the operational system (1970s–1980s)
2.3
Innovative development of fully independent operational numerical prediction system (2000s–2024)
2.4
Integrated development of artificial intelligence and numerical prediction (post-2022)
3.
Establishment and development of GRAPES
3.1
Major scientific and technological breakthroughs
3.2
Establishment of GRAPES and related applications
4.
Establishment and development of YHGSM
4.1
Breakthrough NWP modeling technologies
4.2
Breakthrough data assimilation technologies
4.3
Establishment of YHGSM and associated applications