Particle-resolved direct numerical simulations (PR-DNS) play an increasing role in investigating aerosol-cloud-turbulence interactions at the most fundamental level of processes. However, the high computational cost associated with high resolution simulations poses considerable challenges for large domain or long duration simulation using PR-DNS. To address these issues, here we present a digital twin model of the complex physics-based PR-DNS developed by use of the data-driven Fourier Neural Operator (FNO) method. The results demonstrate high accuracy at various resolutions and the digital twin model is two orders of magnitude cheaper in terms of computational demand compared to the physics-based PR-DNS model. Furthermore, the FNO digital-twin model exhibits strong generalization capabilities for different initial conditions and ultra-high-resolution without the need to retrain models. These findings highlight the potential of the FNO method as a promising tool to simulate complex fluid dynamics problems with high accuracy, computational efficiency, and generalization capabilities, enhancing our understanding of the aerosol-cloud-precipitation system.

This introductory chapter discusses the atmospheric subgrid processes ─ collectively called "fast 11 physics" or "fast processes", and their parameterizations in large scale atmospheric models. It 12 presents a brief historical progression of the parameterization of fast processes in numerical 13 models. Despite great efforts and notable advances in understanding, progress in improving fast 14 physics parameterizations has been frustratingly slow, the underlying reasons for which are 15 explored. To guide readers, this chapter describes the main objectives and scope of this book and 16 summarizes each chapter. 

Preface Many physical processes that influence Earth's climate and weather occur on spatial (temporal) scales smaller (shorter) than typical grid sizes (time steps) of general circulation models, and thus must be parameterized. Computer models are essential tools for understanding atmospheric phenomena and for making accurate predictions of any changes in the Earth's climate, weather, and resources of renewable energy resulting from anthropogenic activities that generate greenhouse gases and particulates into the atmosphere. This book focuses on the atmospheric subgrid processes ─ collectively called fast physics ─by reviewing and synthesizing relevant physical understanding, parameterization developments, various measurement technologies, and model evaluation framework. The publication is divided into three parts, containing seventeen chapters (Chapters 2-17) to reflect and synthesize the multiple aspects involved. The first chapter briefly introduces the historical development of fast physics parameterizations and the involved complexities; the last chapter summarizes emerging challenges, new opportunities and future research directions. Part I deals with major subgrid processes, with eight chapters (Chapters 2-9) each covering different processes more or less in the conventional compartmentalized format with an emphasis on individual processes, including but, not limited to radiative transfer, aerosols, and aerosol direct & indirect effects, entrainment-mixing processes, their microphysical influences, convection & convective clouds, stratiform clouds such as stratus and stratocumulus clouds, planetary boundary layer processes, land surface and interactions with atmosphere, and gravity waves. On top of the conventional treatments, some promising ideas/approaches have recently emerged to unify the treatment of individual processes and thus allows for consideration of process interactions. Part II is devoted to such unifying efforts, with four chapters (Chapters 10-13) covering four different endeavors: the unifying parameterizations based on assumed probability density functions; the EDMF approach that combines the Eddy Diffusivity and Mass Flux approaches to unify turbulence and convection; application of machine learning techniques; and innovative top-down attempts that consider the involved totality by borrowing ideas from systems theory, statistical physics, and non-linear sciences. Part III (Chapters 14-17) is devoted to assessments, model evaluation, and model-measurement integration, with four chapters that focus on satellite and airborne remote sensing measurements, surface-based remote sensing measurements, in-situ and laboratory measurements, and model evaluation, and model-measurement integration, respectively.

Accurate forecast of solar irradiance remains a major challenge, especially under the influences of aerosols, clouds and aerosol-cloud interactions due to their inadequate parameterizations in numerical prediction models. This study focuses on the impacts of cloud microphysics and the indirect aerosol effect on solar irradiance. The state of art Weather Research and Forecasting model specifically designed for simulating and forecasting solar radiation (WRF-Solar) is employed to investigate the sensitivity of the total solar irradiance and its partitioning into direct and diffuse irradiances to aerosol and cloud properties. First, a number of microphysical schemes will be tested against the measurements of shallow cumulus and stratiform clouds at the DOE ARM SGP site. Efforts will be made to quantify the uncertainty spread. The effects of cloud microphysics on surface solar irradiance will be identified. Second, the indirect aerosol effect on cloud formation and thus surface solar irradiance will be investigated by using the Thompson aerosol aware microphysical scheme and different treatment of aerosols. In particular, we will examine the aerosol indirect effects in different cloud regimes. To address the aforementioned problems, we will introduce a new model evaluation framework based on different WRF-Solar setups (nested WRF, WRF-LES, and single column WRF). In addition, different evaluation metrics will be used, including the RMSE, MAPE, and relative Euclidean distance. The results will provide physical insight into the understanding of aerosol-cloud-radiation interactions and into improving solar radiation forecast in cloudy conditions.

Although it has been well recognized that clouds tremendously affect the surface solar irradiance and its direct and diffuse partitions, accurately forecasting solar radiation in cloudy conditions remains a major challenge. This study focuses on two aspects of the challenge: impacts of cloud microphysics and model domain size. First, we will examine the sensitivity of surface solar radiation and its partitions to cloud microphysics by using the state of art Weather Research and Forecasting model specifically designed for simulating and forecasting solar radiation (WRF-Solar). A number of microphysical schemes will be tested, and comparison against the measurements of shallow cumulus clouds and stratiform clouds selected at the DOE ARM SGP Site. Efforts will be made to quantify the resultant uncertainty spread. Second, identifying the physical causes of the underlying model differences is even more challenging. To address this, we will introduce a new model evaluation framework based on different setups of WRF-Solar (single column, LES, and nested WRF). In particular, we will examine the effect of the number of LES grid columns and its lower limit producing reasonable results. Commonly used evaluation metrics will be used in our model evaluation, including the used RMSE, MAE, MAPE, and relative Euclidean distance. The results will provide physical insight into the understanding of cloud-radiation interactions and forecasting of solar radiation in cloudy conditions.

Freezing rain has been normally considered to be composed of supercooled raindrops when the near surface air temperature is below freezing. However, according to a statistical survey of freezing rain events in China over the last two decades (from 2000 to 2019), we find that there were 656 cases occurring at near surface air temperature greater than 0℃ (hereafter warm freezing rain and denoted by WFR), which account for 7% of the total freezing rain events. To explain this phenomenon, a theoretical model is established by relaxing the equilibrium assumption to consider the transient heat exchange between raindrops and the surrounding atmosphere. Sensitivity analysis of the model shows that the temperature lag of raindrops to atmosphere is the main cause of WFR. The direction of raindrop temperature departure from the equilibrium depends on the sign of the temperature lapse rate Г, and the magnitude of the temperature lag is determined by the raindrop diameter D, Г, and relative humidity RH. An increase of D, an increase of Г, and a decrease of RH enhance the lag of raindrop temperature and thus the occurrence of the WFR events. Further simulations of 4 ideal and 25 real sounding profiles reveal that WFR events can form by the “melting of solid hydrometeors” or “supercooled warm rain process” when considering the temperature lag between raindrops and the atmosphere. With the assumption of initial raindrop diameter of 2mm, together the observed Г and RH, the model can diagnose more than 95% of WFR events.