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Progress and Perspective of Convection and Cloud Parameterizations in Numerical Models

数值模式中对流与云参数化的回顾与展望

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Supported by the National Key Research and Development Program of China (2022YFF0802002) and National Natural Science Foundation of China (42475081).

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  • This article reviews the advances of convection and cloud parameterizations in numerical models, with a focus on the significant contributions of Chinese scientists in this field. It begins by outlining the evolution and development of convection parameterization, including the Kuo scheme, the moist convective adjustment scheme, the widely used mass flux schemes, and the machine learning-based schemes. It details the schemes developed and revised by Chinese scientists, as well as the resulting improvements to the numerical models by these schemes. Following this, this review delves into the progress of cloud parameterization schemes and elaborates on the achievements of Chinese scientists in constructing and improving both cloud macrophysics and microphysics schemes. At the end, the review discusses the possible future avenues in the development of convection and cloud parameterizations, highlighting the pivotal role anticipated for deep learning, and suggests pathways for the advancement of hybrid models and multiscale climate modeling methods.

    回顾了数值模式中对流与云参数化的发展历程。首先介绍了对流参数化的发展历程,包括早期的Kuo(郭晓岚)方案和对流调整方案,当前广泛使用的质量通量型方案和基于机器学习的方案,详细介绍了方案的研发和改进,以及这些方案对数值模式的改进效果。随后,探讨了云参数化方案的发展历程,介绍了云宏物理方案和云微物理方案取得的成果。最后,展望了未来对流与云参数化的发展方向,指出深度学习技术将在未来发挥重要作用,并提出了发展混合模型和多尺度气候建模方法的建议。限于篇幅,文中重点关注中国科学家及海外华裔科学家的相关成果。

  • Convection and clouds play crucial roles in weather and climate systems. Weather phenomena are associated with numerous natural disasters such as flash floods, hurricanes, and tornadoes. Climatically, the latent heat released by condensation serves as the primary thermal driver of the atmospheric circulation. The conversion from water vapor to hydrometeors and subsequently to precipitation plays a decisive role in the atmospheric water cycle. Meanwhile, convection and clouds modulate the Earth’s energy budget by influencing both shortwave and longwave radiation. Against the backdrop of global climate change, numerical models—as vital tools for weather and climate prediction—hold significant importance for human societal development through their accuracy and reliability. Since the scale of convection and clouds is smaller than the horizontal resolution of nume-ric models, their parameterizations become essential in numerical modeling. These parameterization schemes, being critical components of numerical models, have long remained both focal points and challenges in atmospheric science.

    Throughout history, China has frequently experienced meteorological disasters that severely impact people’s livelihoods and national economic development. To enhance disaster prevention/mitigation capabilities and improve weather/climate prediction accuracy, Chinese scientists have persistently pursued research on convection and cloud parameterizations in numerical models. Since the late 20th century, China’s research in this field has gradually gained international recognition, with a series of innovative achievements providing valuable theoretical foundations and practical experience for numerical model development.

    This paper briefly reviews historical progress in convection and cloud parameterizations. As a part of the special issue commemorating the 100th anniversary of Acta Meteorologica Sinica, the mother journal of Journal of Meteorological Research, we particularly focus on contributions from Chinese scientists both domestic and overseas. The review is organized as follows. Section 2 reviews convection parameterization, followed by cloud parameterization in Section 3. Section 4 examines machine learning-based schemes. The final section summarizes the paper and provides perspectives on future research directions in this field.

    Kuo (1965) first introduced the latent heat release of cumulus clouds into a two-layer hurricane model. He postulated that (1) convection occurs in conditionally unstable layers with low-level convergence; (2) convection lifts surface air to upper levels, with cloud temperature and humidity following a moist adiabatic process; (3) cloud base corresponds to the lifting condensation level of surface air, while cloud top approaches the neutral buoyancy level in upper layers; and (4) convection mixes cloud air with environmental air, thereby modifying environmental temperature and humidity. Kuo (1974) further refined this scheme by proposing that large-scale circulation-induced moisture convergence partially humidifies the atmosphere, with the residual portion generating precipitation. Though considered simplistic by modern standards, Kuo convective parameterization scheme established the foundational framework for subsequent developments in convection parameterization.

    To address the applicability limitations of the Kuo scheme over the Qinghai–Xizang Plateau, Chen and Qian (1992) modified the moistening coefficient b (representing the proportion of total moisture supply used for environmental humidification) and mesoscale moisture convergence parameter η based on plateau-specific atmospheric stratification and convective characteristics. These revisions improved precipitation and synoptic field predictions over both the Qinghai–Xizang Plateau and eastern China. Zhao et al. (1996) redefined the moistening parameter b as a piecewise linear function of relative humidity using high-resolution spatiotemporal observations, developing adjusted profile distributions better suited for East Asia. Deng et al. (2002) further investigated the modified Kuo-type profile distributions and the moistening coefficients optimized for low-latitude plateau regions.

    During the same period as the work of Kuo (1965), Manabe et al. (1965) developed an even simpler moist convective adjustment scheme in the first Geophysical Fluid Dynamics Laboratory (GFDL) general circulation model (GCM) incorporating the hydrological cycle. Their approach postulated that convection activates when the atmospheric lapse rate exceeds the moist adiabatic lapse rate, with supersaturated water vapor being removed through condensation. This scheme was later employed to investigate convection–radiation equilibrium and global climate change under doubled CO2 concentration (Manabe and Wetherald, 1967)—An investigation that ultimately earned Manabe the 2021 Nobel Prize in Physics.

    However, a critical limitation of the moist convective adjustment scheme emerged: its failure to perform convective adjustments in the stable upper troposphere resulted in excessive cold and dry biases at these levels. Building upon the convective adjustment principle, the Betts–Miller (BM) scheme (Betts and Miller, 1986) addressed this issue by relaxing atmospheric temperature and moisture profiles toward pre-defined reference states rather than strictly along the moist adiabats as in Manabe’s original formulation. This modification effectively mitigated upper-tropospheric cold/dry biases. Zhai et al. (2003) conducted systematic sensitivity experiments on several pivotal parameters controlling the reference state in the BM scheme: stability parameter α, saturation pressure difference Δp at cloud base and freezing level, and convective adjustment timescale τ. Through analyzing how different parameter configurations influenced regional climate simulation, they established optimal parameter values specifically tailored for flood season simulations over eastern China, significantly enhancing the model performance in this critical region.

    Arakawa and Schubert (1974) established a more systematic and rigorous mathematical framework for convection representation through their landmark Arakawa–Schubert (AS) scheme, which laid the foundation for numerous subsequent convective parameterization developments. A cornerstone of the AS scheme is the convective quasi-equilibrium hypothesis, positing a dynamic balance between convective instability consumption by storms and its generation through large-scale processes. Distinct from Kuo’s cloud–environment mixing concept, the AS scheme introduced compensatory subsidence processes that warm and dry the surrounding atmosphere through environmental air displacement. Most contemporary convective parameterizations in numerical weather prediction and global climate models trace their lineage to this framework, including the Zhang–McFarlane (ZM) scheme (Zhang and McFarlane, 1995), the Simplified Arakawa–Schubert (SAS) scheme (Grell, 1993), the Kain–Fritsch (KF) scheme (Kain and Fritsch, 1990, 1993; Kain, 2004), the Gregory scheme (Gregory and Miller, 1989; Gregory and Rowntree, 1990), and the Tiedtke scheme (Tiedtke, 1989).

    Yang et al. (2020) enhanced the physical consistency between deep and shallow convection in the ZM scheme by deducting shallow convective consumption of convective available potential energy (CAPE) from the closure assumption’s energy budget. Subsequent work by Yang et al. (2021) developed entrainment-profile-based closure equations incorporating cloud dynamics. Zhang (2002, 2003) fundamentally revised the ZM closure condition from total CAPE to free-tropospheric CAPE variations, addressing limitations of the classical AS quasi-equilibrium hypothesis in midlatitude continental and tropical oceanic convection. This free-tropospheric quasi-equilibrium implementation in NCAR Community Atmosphere Model version 3 (NCAR CAM3) significantly improved tropical climate simulations, particularly for Madden–Julian oscillation (MJO) and intertropical convergence zone (ITCZ) representation. Building on this foundation, Xie and Zhang (2000), Xie et al. (2019), and Cui et al. (2021) incorporated free-tropospheric CAPE dynamics into the triggering function of the ZM scheme, achieving substantial improvements in diurnal precipitation cycle simulations for both U.S. Department of Energy Energy Exascale Earth System Model (DOE E3SM) and NCAR CAM5 (Fig. 1). Wang (2012) modified the KF scheme and implemented it in the Global and Regional Assimilation and Prediction System (GRAPES) single-column model, improving upper-tropospheric potential temperature simulations. Tang et al. (2016) improved the KF scheme for East Asian torrential rainfall prediction through mesoscale convective system characterization. Chen and Bougeault (1993a, b) proposed prognostic mass-flux parameterization abandoning quasi-equilibrium assumptions (Chen, 1997). Xue et al. (1999) and Xue and Yan (1999) incorporated downdraft physics into mass-flux cumulus parameterization. Ping et al. (2003) and Ping and Gao (2004) improved the UK Met Office’s Gregory scheme and implemented it in China’s T63 global spectral model at the National Climate Centre of China Meteorological Administration.

    Fig  1.  Warm-season averaged (a–d) diurnal peak time and (e–h) amplitude of the diurnal cycle of precipitation (mm day−1) obtained from hourly data of (a, e) TRMM (Tropical Rainfall Measuring Mission), (b, f) CTRL (default CAM5), (c, g) DCAPE_ULL (experiment using convective trigger with dynamic CAPE and unrestricted air parcel launch level), and (d, h) DCAPEopt_ULL (experiment using convective trigger with dynamic CAPE and unrestricted air parcel launch level, and optimizing the entrainment rate and threshold value of the dynamic CAPE generation rate). The warm season is defined as June–August (JJA) for the Northern Hemisphere and December–February (DJF) for the Southern Hemisphere, respectively. The 24-h local solar time (LST) phase dial is given at the bottom right. In (a–d), pixels with amplitude under 0.1 mm day−1 are masked out, and colors of pixels with amplitude under 1 mm day−1 are desaturated (Cui et al., 2021).

    As model horizontal resolution increases, the reduced number of convective clouds within grid cells fails to meet the statistical ensemble requirements of traditional convective parameterization schemes that rely on grid-mean cloud population effects, leading to amplified convective precipitation variability. However, conventional schemes—lacking stochastic representations of convective randomness—cannot capture this inherent feature. To address this fundamental limitation, Wang et al. (2016) pioneered the integration of Plant and Craig (2008) stochastic convective model into the ZM scheme, developing a climate-model-adapted stochastic parameterization. This innovation enabled both NCAR Community Atmosphere Model version 5 (CAM5) and the U.S. Department of Energy Energy Exascale Earth System Model version 1 (E3SMv1) to substantially mitigate the pervasive CMIP5&6 (Coupled Model Intercomparison Project phase 5&6) bias of “excessive light precipitation and insufficient heavy precipitation” (Fig. 2) (Wang et al., 2021), while simultaneously enhancing underestimated precipitation variability across daily and subseasonal timescales.

    Fig  2.  (a) Frequency distributions of precipitation rate and (b) cumulative contribution from each binned precipitation rate based on daily mean precipitation data. The results are for the global belt of 20°S–20°N from TRMM observation (black line), CTL (blue line; default CAM5), and EXP (red line; experiment with stochastic convective parameterization) (Wang et al., 2016).

    Building upon this breakthrough, Wang et al. (2018) advanced the stochastic framework by dynamically coupling convective randomness with large-scale circulation variability. The refined scheme demonstrated particular success in improving the CAM5 model’s representation of South Asian monsoon precipitation evolution, achieving unprecedented fidelity in simulating both temporal progression and spatial organization of monsoon rainfall systems.

    In the formulation of convective parameterization sche-mes, cloud modeling constitutes an indispensable component alongside closure hypotheses and triggering mechanisms. Traditional convective updraft cloud models typically employ simple parameterization of microphysical processes through a single adjustable parameter. However, substantial evidence demonstrates aerosol’s significant influence on convective cloud development, necessitating explicit representation of cloud microphysics to properly capture aerosol–convection interactions. Furthermore, detrainment of cloud ice and hydrometeors from convective cores serves as a critical pathway for generating large-scale cloud systems and anvil clouds, which exerts profound radiative impacts on Earth’s energy balance. Given the climatic importance of aerosol–convection–cloud–radiation interplay, oversimplified treatments of convective microphysics become scientifically untenable. Recent advances have yielded sophisticated microphysical parameterizations—exemplified by Zhang and Mu (2005), Lohmann (2008), Song and Zhang (2011), and Song et al. (2012)—that successfully capture aerosol modulation of convective processes, thereby advancing more physically comprehensive frame-works for convective parameterization.

    Cloud macrophysical parameterization schemes primarily calculate stratiform cloud cover and condensation rates in models. Current coarse-resolution GCMs employ three major cloud macrophysical schemes: relative humidity (RH) schemes (Slingo, 1987; Rasch and Kristjánsson, 1998), statistical cloud schemes (Le Trent and Li, 1991; Golaz et al., 2002; Tompkins, 2002), and prognostic cloud schemes (Tiedtke, 1993; Tompkins, 2002; Wilson et al., 2008). The first two are diagnostic approaches, while the latter is prognostic.

    Early radiation-related cloud cover and hydrometeor specifications relied heavily on observational prescriptions (Manabe et al., 1965). A systematic treatment emerged with Sundqvist (1978), who linked cloud cover to moisture advection and RH. His formulation initiated cloud formation when grid-mean RH exceeded a critical threshold (below 100%), with cloud fraction monotonically increasing with RH. Precipitation was parameterized through autoconversion of cloud droplets to raindrops. Implemented in a mesoscale weather model (Sundqvist et al., 1989), this scheme generated realistic cloud properties and improved forecasts. While computationally efficient, its oversimplification ignored local dynamical influences. Subsequent refinements incorporated additional variables. For example, Slingo (1980, 1987) integrated vertical velocity with RH for stratiform cloud calculations. Slingo and Slingo (1991) applied lower tropospheric stability (LTS)–cloud relationships in NCAR Community Climate System Model (CCSM). Guo and Zhou (2014) enhanced LTS-based approaches using estimated inversion strength (EIS) correlations in China’s GAMIL2.0 [the Grid-point Atmospheric Model of IAP (Institute of Atmospheric Physics) LASG (State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics) version 2] atmospheric model. Xu and Randall (1996) derived regional empirical formulas combining RH and cloud water content. Modern RH-class schemes typically express the cloud fraction as functions of both RH and stability (Qu et al., 2014).

    Statistical cloud schemes are widely-used cloud macrophysics schemes as well. Originating from Mellor (1977) and Sommeria and Deardorff (1977), these schemes assume Gaussian-distributed joint PDFs (probability density functions) of grid-mean specific humidity and potential temperature to diagnose cloud cover and liquid water content (LWC). Smith (1990) employed symmetric triangular PDFs, whereas Bechtold et al. (1995) leveraged higher-order turbulence closure models to calculate subgrid variations. In general, the underlying principles of various statistical cloud schemes are consistent. They first assume that the subgrid water vapor PDF or the joint PDF of subgrid water vapor and temperature follows a specific distribution. Cloud cover and cloud water content are then obtained by integrating the portion of the PDF exceeding the saturation specific humidity. However, in practical applications, different studies propose statistical cloud schemes using distinct PDF distributions. The width of the PDF distribution is related to the relative humidity threshold, which operates similarly to relative humidity-based cloud schemes—condensation initiates when water vapor exceeds the critical relative humidity. Under certain conditions, PDF-based schemes can reduce to relative humidity-based cloud schemes (Le Trent and Li, 1991). Shiu et al. (2021) proposed a novel PDF-based scheme by replacing the critical relative humidity assumption with cloud condensate and saturation ratio. Experimental results demonstrate improved simulations of both water vapor and relative humidity fields.

    In contrast to PDF-based statistical methods, Tiedtke (1993) proposed a prognostic approach that utilizes a set of prognostic equations to calculate the temporal evolution of cloud cover and cloud condensate content. Subsequent studies (e.g., Wilson et al., 2008; Park et al., 2014) further developed this method. Compared to diagnostic schemes that cannot account for the temporal continuity of cloud cover between time steps, prognostic cloud schemes can predict cloud cover and cloud water content by directly incorporating the effects of turbulence, convection, and microphysics on cloud macrophysical properties, though the associated process calculations are relatively more complex. Tompkins (2002) introduced a hybrid framework termed the “prognostic statistical scheme,” which combines PDF-based and prognostic approaches. This scheme assumes that the subgrid total specific humidity follows a beta distribution and employs two prognostic equations to predict the shape parameters of the PDF. Other studies have proposed mixed methodologies, such as diagnostically computing cloud cover while prognostically calculating cloud condensate (Zhang et al., 2003). A current trend involves integrating boundary layer–shallow convection–cloud macrophysics schemes, such as the CLUBB (Cloud Layers Unified by Binormals) scheme (Bogenschutz et al., 2012, 2013). This integration helps mitigate the uncertainties arising from inconsistencies among different physical parameterization methods, albeit at the cost of significantly increased computational demands in models.

    Stratiform precipitation processes in numerical models are handled by cloud microphysics parameterization schemes (Rasch and Kristjánsson, 1998; Morrison and Gettelman, 2008; Gettelman and Morrison, 2015; Milbrandt et al., 2021). Based on their treatment of cloud and precipitation particle size distributions, cloud microphysics schemes are broadly categorized into bulk schemes and bin (spectral) schemes. Bulk schemes employ semi-empirical descriptions of particle size distributions to characterize microphysical properties. These schemes classify hydrometeors into distinct categories (e.g., cloud droplets, raindrops, cloud ice, snow, graupel, and hail) based on physical characteristics, assuming predefined particle size distribution forms for each class. They derive distribution parameters through prognostic variables like mass mixing ratios and number concentrations, ensuring high computational efficiency. In contrast, bin schemes explicitly resolve particle spectra by solving detailed microphysical equations, also termed explicit microphysics or spectral schemes. While offering greater precision in simulating cloud microphysics and precipitation evolution without prior size distribution assumptions, they incur substantial computational costs, making them impractical for long-term climate simulations and global models.

    Kessler (1969) pioneered the first warm-rain bulk microphysics scheme, enabling numerical models to replicate cloud microphysical properties—a prototype for modern bulk schemes. Subsequent advancements incorporated mixed-phase processes, beginning with Lin et al. (1983) and Rutledge and Hobbs (1984). Since the 1990s, bulk schemes have proliferated, with notable developments (Hu and Yan, 1986, 1987; Tao et al., 1989; Chen and Sun, 2002; Hong and Lim, 2006; Lin and Colle, 2011; Chen et al., 2013; Tan et al., 2013). These schemes emphasize diverse aspects such as precipitation efficiency, ice-phase processes, and aerosol effects. Most assume exponential or gamma distributions for particle sizes, with rare exceptions using log-normal distributions.

    From the 1960s to the 1980s, bulk microphysics schemes primarily existed in single-moment form, using a single parameter (typically mass mixing ratio) to describe hydrometeors in clouds. For instance, the Lin scheme (Lin et al., 1983) assumed that hydrometeor particle size followed an exponential distribution and predicted the temporal evolution of mass mixing ratios for water vapor, cloud water, cloud ice, raindrops, snowflakes, and hail. Kong et al. (1990) developed a fully elastic three-dimensional cold-cloud single-moment mo-del to calculate mass changes of water vapor, cloud water, rainwater, ice crystals, and graupel/hail. Beginning in the 1980s and 1990s, double-moment bulk microphysics schemes gained widespread application and development. These schemes employ two parameters—typically mass mixing ratio and number concentration—to characterize hydrometeor size distributions and microphysical processes. Compared to single-moment schemes, double-moment schemes better simulate cloud microphysics, particularly aerosol–cloud interactions. Representative double-moment schemes include those by Hu and Yan (1986, 1987), the Morrison–Gettelman (MG) scheme (Morrison et al., 2005; Morrison and Gettelman, 2008), the Thompson scheme (Thompson et al., 2004, 2008), and the WDM6 (Weather Research and Forecasting Double Moment 6-class) scheme (Lim and Hong, 2010). They predict mass mixing ratios of water vapor, cloud water, cloud ice, raindrops, snowflakes, and hail, along with number concentrations of raindrops, snowflakes, and hail, while assuming predefined particle shapes and size distributions. Three-moment schemes extend double-moment approaches by additionally predicting spectral shape parameters of particle size distributions. A notable example is the Milbrandt–Yau scheme (Milbrandt and Yau, 2005), which demonstrated significant impacts of spectral shape parameters on hydrometeor sedimentation and growth processes. Recently, He et al. (2023, 2024) expanded the double-moment MG scheme into a three-moment version, showing superior performance in simulating cloud radiative forcing, cloud cover, and precipitation compared to its double-moment counterpart. In terms of computational demands, bulk microphysics schemes exhibit progressively increasing costs from single- to double- to three-moment formulations, though they remain less computationally intensive than the spectral bin schemes.

    Another research trend in the development of bulk microphysics schemes involves increasingly refined representations of aerosol effects on cloud microphysics, particularly in the context of contemporary anthropogenic aerosols exerting significant climatic influence. Aerosols modulate cloud microphysics by altering cloud particle number concentrations and sizes (Twomey, 1977). Double-moment bulk microphysics schemes can capture the reduction in droplet size associated with elevated aerosol concentrations. For instance, Gao et al. (2012) incorporated aerosol activation processes into the Hu and Yan (1986, 1987) scheme and implemented the modified version in the Weather Research and Forecasting (WRF) model, demonstrating improved precipitation simulations. Liu and Penner (2005) accounted for aerosol effects in homogeneous freezing and heterogeneous ice nucleation processes for cirrus ice crystals, while Wang et al. (2014) considered dust and black carbon as ice nuclei in mixed-phase stratiform clouds.

    Over the past decade, deep learning methodologies centered on big data analytics have gained widespread application in climate science (Reichstein et al., 2019). While direct deep learning-based climate prediction remains challenging, integrating machine learning (ML) to enhance cloud and convection representation in GCMs has emerged as a pragmatic pathway. Within traditional convective parameterization frameworks, Zhang et al. (2021) developed a novel convective triggering function using the XGBoost classification model. This ML-driven trigger demonstrated superior performance over conventional CAPE-based methods in simulating convective activity across the North American Great Plains and the Manaus site in the Amazon, effectively mitigating GCMs’ overprediction of convection initiation and improving diurnal precipitation cycle simulations. Similarly, Chen M. X. et al. (2023) proposed a deep convective trigger based on a U-Net architecture, which reduced existing triggering biases and enhanced deep convection prediction accuracy in tropical regions while capturing diurnal cycle patterns over complex terrains. In a parallel advancement, Gao et al. (2024) optimized turbulent entrainment mixing between clouds and ambient air using light gradient boosting (LGB) machine models, yielding more accurate microphysical property predictions and demonstrating LGB’s potential to refine entrainment processes in weather/climate models.

    Mirroring progress in convection schemes, ML innovations are transforming cloud macrophysics and microphysics parameterizations. Chen G. X. et al. (2023) introduced a neural network-based cloud fraction diagnostic scheme that leverages grid-mean temperature, pressure, liquid/ice water mixing ratios, and relative humidity to predict subgrid cloud variability. This approach significantly improved cloud cover simulation accuracy (Fig. 3), enhanced spatial distributions of total cloudiness and vertical cloud structures, and exhibited robust performance across diverse climate regimes—highlighting its potential for broad climate modeling applications.

    Fig  3.  Joint probability density distributions between cloud fractions (CFs) from the scheme predictions and the CloudSat observations for clouds of different phases (ice-only, mixed, and liquid-only), estimated based on the test dataset: (a, c, e) results from the network-based scale-adaptive (NSA) scheme and (b, d, f) results from the tuned Xu–Randall scheme. The lower-right numbers indicate the correlation coefficient (r) and root-mean-square error (RMSE) of the predictions with respect to the observations for each type of clouds (Chen G. X. et al., 2023).

    To comprehensively address limitations in cloud–convection parameterization schemes, researchers are pioneering deep learning-based unified moist physics parameterizations that entirely replace traditional moist physical processes. These deep learning schemes preserve the host model’s dynamical framework while utilizing high-resolution simulations—such as global cloud-resolving models (GCRMs) or superparameterized Community Atmosphere Model (SPCAM) outputs—as training data for implementation in coarse-resolution GCMs. By leveraging rapid inference capabilities post-training, these hybrid systems combine cloud-resolving accuracy with computational efficiency. Current advancements include aquaplanet model replacements (Rasp et al., 2018; Yuval and O’Gorman, 2020) and real-world topography implementations (Han et al., 2020, 2023; Mooers et al., 2021; Bretherton et al., 2022; Wang et al., 2022a; Watt-Meyer et al., 2024).

    Han et al. (2020) pioneered the application of deep learning techniques to represent comprehensive moist physics schemes in global climate models. Using simulation outputs from the SPCAM with realistic land–sea distributions as training data, they employed a one-dimensional deep convolutional residual neural network (ResNet) that introduced convective historical memory as input variables for the first time internationally, while incorporating moist static energy conservation terms into the loss function. This approach successfully predicted moist physical heating/drying rates and cloud water/ice mass concentrations, achieving precise offline emulation.

    Wang et al. (2022a) utilized ensembles of deep residual fully connected neural networks to emulate SPCAM simulations, replacing conventional moist physics and radiation schemes in global climate models. Their work marked the first global implementation of deep learning-based schemes in a three-dimensional climate model with realistic topography and land–sea distributions, demonstrating stable 10-yr online coupled simulations that reproduced SPCAM’s annual mean precipitation patterns, extreme precipitation frequency, and MJO characteristics. However, residual biases persisted in simulating equatorial ITCZ precipitation and polar temperatures. Building upon Han et al. (2020), Han et al. (2023) enhanced their convolutional ResNet-based framework by reducing offline errors. The improved scheme achieved accurate offline testing under both baseline and warmed climate conditions (sea surface temperature +4 K) and successfully coupled with a three-dimensional global climate model featuring realistic land–sea distributions and topography, completing a 6-yr stable integration. The coupled results maintained reasonable climatological states, conserved model total energy and water content over time, and improved precipitation simulations over the western equatorial Pacific (Fig. 4), along with enhanced representations of extreme precipitation frequency and the diurnal cycle of convection. Nevertheless, significant simulation biases remained for equatorial land precipitation and polar temperature and humi-dity fields.

    Fig  4.  Global distributions of the mean precipitation rate (mm day−1) in June–July–August (left panels) and December–January–February (right panels) over the years of 1998–2002 for (a, b) TRMM 3B42, (c, d) SPCAM, (e, f) NCAM (the neural-network-enabled CAM5), and (g, h) CAM5. The spatial mean and root-mean-square error to the TRMM 3B42 observations are shown above each frame.

    Following Han et al. (2023), Hu et al. (2024) implemented next-generation deep learning architecture U-net in the DOE E3SM model to replace moist physics and radiation schemes. By using convective history memory and temperature/moisture large-scale forcings as input features, they successfully modeled tendency terms for cloud convection and radiation processes affecting temperature, moisture, and wind speed, achieving stable 5-yr online simulations with significantly reduced mean climate state errors. Lin et al. (2023) enhanced sampling of online-coupled deep learning parameterization schemes through software automation and evaluated hybrid deep learning climate model performance in aquaplanet mode. They found combining convective memory and relative humidity inputs improved online performance, though some discrepancies existed between offline and online error statistics. Additionally, Chen et al. (2024) employed four machine learning algorithms to extract local grid-point information from numerical forecast model variables. Their moist physics parameterization experiments for a South China Sea typhoon case successfully simulated thermal/moisture effects and captured spiral structures of heat sources and moisture sinks from convective activities. Zhong et al. (2024) improved multiscale Kain–Fritsch convective parameterization using machine learning, significantly enhancing convective triggering and precipitation rate forecasts. Wang et al. (2022) demonstrated that incorporating non-local inputs from adjacent 3 × 3 grid columns and vertical velocities in deep learning subgrid scheme training notably improved offline fitting test performance, suggesting that these variables enhance ML parameterization effectiveness.

    Numerical models, as critical tools for weather and climate prediction, hold immense significance for human societal development through their accuracy and reliability. Chinese scientists have made substantial contributions to core numerical model components—convection and cloud parameterizations—particularly in convective closure assumptions and triggering mechanisms based on the quasi-equilibrium theory of free atmospheric convection, stochastic convective schemes, cloud microphysics schemes, and machine learning-based cloud/convection parameterizations. The persistent systematic errors in coarse-resolution climate models have long driven efforts toward kilometer-scale global climate modeling to deliver more precise climate projections. However, century-scale simulations with such high-resolution models remain computationally prohibitive and limited in representing Earth system complexity. Reliable predictions of long-term forced climate responses and extreme events amidst internal climate variability still require coarse-resolution models capable of comprehensively simulating Earth system processes and feedbacks, implying that model performance—particularly the parameterization schemes—must achieve further breakthroughs (Eyring et al., 2024).

    While improvements are needed across most traditional convection/cloud parameterization domains to address remaining climate modeling challenges (e.g., persistent double ITCZ bias), a pressing issue is scale adaptability in convective schemes. Traditional schemes were developed for ~100-km grid-spacing global models. As computational power enables higher resolutions, achieving scale adaptability in these schemes has become an urgent research priority (Arakawa and Wu, 2013). Though progress exists (Grell and Freitas, 2014; Kwon and Hong, 2017; Wang et al., 2022b; Xia et al., 2022), more fundamental theoretical research remains necessary.

    Meanwhile, artificial intelligence (AI) empowerment will increasingly inform future parameterization development. Current AI advances in cloud–convection parameterization are encouraging—whether enhancing components like convective triggering functions (Zhang et al., 2021) and cloud entrainment–mixing (Chen M. X. et al., 2023), or fully replacing moist physics processes (Han et al., 2020, 2023; Wang et al., 2022a; Lin et al., 2023; Hu et al., 2024). However, deep learning moist physics schemes remain imperfect. First, they exhibit notable climate simulation biases—e.g., Wang et al. (2022a) and Han et al. (2023) identified errors in equatorial ocean/land precipitation, tropical humidity, and high-latitude temperature simulations. These may stem from incomplete representation of moist physics variables (e.g., cloud water/ice number concentrations and cloud fraction) still requiring traditional parameterizations. Though Hu et al. (2024) reduced errors by expanding input–output variables, incorporating radiation processes, and employing sophisticated U-nets, error patterns persisted, highlighting challenges in using superparameterization-style training targets and deep learning architectures. Moreover, most deep learning schemes fail to achieve radiation balance or maintain fundamental equilibrium relationships (e.g., precipitation–evaporation balance). Some basic neural network-based schemes show poor generalization from baseline to warmer climates (Beucler et al., 2024).

    These issues underscore the need for deep learning schemes to incorporate physical constraints and enhance interpretability. Regarding constraints, while Han et al. (2020, 2023) introduced moist static energy conservation in loss functions, the potential benefits of additional conservation constraints (e.g., total water mass, radiation balance) remain unexplored. Some studies prefer post-processing adjustments (Hu et al., 2024). Meanwhile, physical interpretability and domain knowledge can guide scheme development. For instance, studies show that including relative humidity inputs significantly impacts model stability and total water control (Lin et al., 2023; Hu et al., 2024), while convective memory variables enhance simulation accuracy (Han et al., 2023). Others demonstrate that retaining only causally significant inputs improves stability and realism (Iglesias-Suarez et al., 2024). Thus, future research requires comprehensive physical interpretation of deep learning cloud-convection schemes to enhance both interpretability/reliability and stability/accuracy.

    Deep learning cloud-convection schemes must transcend single-resolution, offline-trained implementations toward AI-powered multiscale climate modeling frameworks that integrate diverse Earth observations and reanalysis data through modernized infrastructure (Kochkov et al., 2024). We advocate climate modeling across complexity–resolution hierarchies.

    Collectively, these developments demonstrate that AI–physics hybrid models can enhance process representation and accuracy even at coarse resolutions, enabling century-long simulations, multiensemble runs, and observation-informed tuning. Building on this potential, we anticipate that deep learning methods will increasingly replace physical subprocesses in future climate modeling, evolving toward greater maturity, precision, and interpretability.

  • Fig.  1.   Warm-season averaged (a–d) diurnal peak time and (e–h) amplitude of the diurnal cycle of precipitation (mm day−1) obtained from hourly data of (a, e) TRMM (Tropical Rainfall Measuring Mission), (b, f) CTRL (default CAM5), (c, g) DCAPE_ULL (experiment using convective trigger with dynamic CAPE and unrestricted air parcel launch level), and (d, h) DCAPEopt_ULL (experiment using convective trigger with dynamic CAPE and unrestricted air parcel launch level, and optimizing the entrainment rate and threshold value of the dynamic CAPE generation rate). The warm season is defined as June–August (JJA) for the Northern Hemisphere and December–February (DJF) for the Southern Hemisphere, respectively. The 24-h local solar time (LST) phase dial is given at the bottom right. In (a–d), pixels with amplitude under 0.1 mm day−1 are masked out, and colors of pixels with amplitude under 1 mm day−1 are desaturated (Cui et al., 2021).

    Fig.  2.   (a) Frequency distributions of precipitation rate and (b) cumulative contribution from each binned precipitation rate based on daily mean precipitation data. The results are for the global belt of 20°S–20°N from TRMM observation (black line), CTL (blue line; default CAM5), and EXP (red line; experiment with stochastic convective parameterization) (Wang et al., 2016).

    Fig.  3.   Joint probability density distributions between cloud fractions (CFs) from the scheme predictions and the CloudSat observations for clouds of different phases (ice-only, mixed, and liquid-only), estimated based on the test dataset: (a, c, e) results from the network-based scale-adaptive (NSA) scheme and (b, d, f) results from the tuned Xu–Randall scheme. The lower-right numbers indicate the correlation coefficient (r) and root-mean-square error (RMSE) of the predictions with respect to the observations for each type of clouds (Chen G. X. et al., 2023).

    Fig.  4.   Global distributions of the mean precipitation rate (mm day−1) in June–July–August (left panels) and December–January–February (right panels) over the years of 1998–2002 for (a, b) TRMM 3B42, (c, d) SPCAM, (e, f) NCAM (the neural-network-enabled CAM5), and (g, h) CAM5. The spatial mean and root-mean-square error to the TRMM 3B42 observations are shown above each frame.

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