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This book aims to promote the understanding of some of the basic mathematical and scientific issues in the subjects relating to climate dynamics, chaos and quantum mechanics. It is based on substantial research work in atmospheric science carried out over twenty years. Atmospheric flows exhibit self similar fractal fluctuations, a signature of long-range correlations on all space-time scales. Realistic simulation and prediction of atmospheric flows requires the incorporation of the physics of observed fractal fluctuation characteristics in traditional meteorological theory. A general systems theory model for fractal space-time fluctuations in turbulent atmospheric flows is presented and applied to the formation of rain in warm clouds. This model gives scale-free universal governing equations for cloud growth processes. The model predicted cloud parameters are in agreement with reported observations, in particular, the cloud drop-size distribution. Rain formation can occur in warm clouds within 30 minutes as observed in practice under favourable conditions of moisture supply in the environment. Traditional cloud physical concepts for rain development requires over an hour for a full-sized raindrop to form. The book provides background reading for postgraduate students of Meteorology, Atmospheric Sciences/Physics, Environmental Sciences, and scientists working in the field of the topic of the book as well as the multidisciplinary field of Nonlinear Dynamics and Chaos.

In the atmosphere, microphysics refers to the microscale processes that affect cloud and precipitation particles and is a key linkage among the various components of Earth's atmospheric water and energy cycles. The representation of microphysical processes in models continues to pose a major challenge leading to uncertainty in numerical weather forecasts and climate simulations. In this paper, the problem of treating microphysics in models is divided into two parts: (i) how to represent the population of cloud and precipitation particles, given the impossibility of simulating all particles individually within a cloud, and (ii) uncertainties in the microphysical process rates owing to fundamental gaps in knowledge of cloud physics. The recently developed Lagrangian particle‐based method is advocated as a way to address several conceptual and practical challenges of representing particle populations using traditional bulk and bin microphysics parameterization schemes. For addressing critical gaps in cloud physics knowledge, sustained investment for observational advances from laboratory experiments, new probe development, and next‐generation instruments in space is needed. Greater emphasis on laboratory work, which has apparently declined over the past several decades relative to other areas of cloud physics research, is argued to be an essential ingredient for improving process‐level understanding. More systematic use of natural cloud and precipitation observations to constrain microphysics schemes is also advocated. Because it is generally difficult to quantify individual microphysical process rates from these observations directly, this presents an inverse problem that can be viewed from the standpoint of Bayesian statistics. Following this idea, a probabilistic framework is proposed that combines elements from statistical and physical modeling. Besides providing rigorous constraint of schemes, there is an added benefit of quantifying uncertainty systematically. Finally, a broader hierarchical approach is proposed to accelerate improvements in microphysics schemes, leveraging the advances described in this paper related to process modeling (using Lagrangian particle‐based schemes), laboratory experimentation, cloud and precipitation observations, and statistical methods. Plain Language Summary In the atmosphere, microphysics—the small‐scale processes affecting cloud and precipitation particles such as their growth by condensation, evaporation, and melting—is a critical part of Earth's weather and climate. Because it is impossible to simulate every cloud particle individually owing to their sheer number within even a small cloud, atmospheric models have to represent the evolution of particle populations statistically. There are critical gaps in knowledge of the microphysical processes that act on particles, especially for atmospheric ice particles because of their wide variety and intricacy of their shapes. The difficulty of representing cloud and precipitation particle populations and knowledge gaps in cloud processes both introduce important uncertainties into models that translate into uncertainty in weather forecasts and climate simulations, including climate change assessments. We discuss several specific challenges related to these problems. To improve how cloud and precipitation particle populations are represented, we advocate a “particle‐based” approach that addresses several limitations of traditional approaches and has recently gained traction as a tool for cloud modeling. Advances in observations, including laboratory studies, are argued to be essential for addressing gaps in knowledge of microphysical processes. We also advocate using statistical modeling tools to improve how these observations are used to constrain model microphysics. Finally, we discuss a hierarchical approach that combines the various pieces discussed in this article, providing a possible blueprint for accelerating progress in how microphysics is represented in cloud, weather, and climate models. Key Points Microphysics is an important component of weather and climate models, but its representation in current models is highly uncertain Two critical challenges are identified: representing cloud and precipitation particle populations and knowledge gaps in cloud physics A possible blueprint for addressing these challenges is proposed to accelerate progress in improving microphysics schemes

\"This key new textbook provides a state-of-the-art view of the physics of cloud and precipitation formation, covering the most important topics in the field: the microphysics, thermodynamics, and cloud-scale dynamics. Highlights include: the condensation process explained with new insights from chemical physics studies; the impact of the particle curvature (the Kelvin equation) and solute effect \"-- Provided by publisher.

This paper provides a description of the integrated representation for the cloud processes in the Community Atmosphere Model, version 5 (CAM5). CAM5 cloud parameterizations add the following unique characteristics to previous versions: 1) a cloud macrophysical structure with horizontally nonoverlapped deep cumulus, shallow cumulus, and stratus in each grid layer, where each of which has its own cloud fraction, and mass and number concentrations for cloud liquid droplets and ice crystals; 2) stratus–radiation–turbulence interactions that allow CAM5 to simulate marine stratocumulus solely from grid-mean relative humidity without relying on a stability-based empirical formula; 3) prognostic treatment of the number concentrations of stratus liquid droplets and ice crystals, with activated aerosols and detrained in-cumulus condensates as the main sources and with evaporation, sedimentation, and precipitation of stratus condensate as the main sinks; and 4) radiatively active cumulus and snow. By imposing consistency between diagnosed stratus fraction and prognosed stratus condensate, unrealistically empty or highly dense stratus is avoided in CAM5. Because of the activation of the prognostic aerosols and the parameterizations of the radiation and stratiform precipitation production as a function of the cloud droplet size, CAM5 simulates various aerosol indirect effects as well as the direct effects: that is, aerosols affect both the radiation budget and the hydrological cycle. Detailed analysis of various simulations indicates that CAM5 improves upon CAM3/CAM4 in global performance as well as in physical formulation. However, several problems are also identified in CAM5, which can be attributed to deficient regional tuning, inconsistency between various physics parameterizations, and incomplete treatment of physics. Efforts are continuing to further improve CAM5.

The formation of secondary ice in clouds, that is, ice particles that are created at temperatures above the limit for homogeneous freezing without the direct involvement of a heterogeneous ice nucleus, is one of the longest-standing puzzles in cloud physics. Here, we present comprehensive laboratory investigations on the formation of small ice particles upon the freezing of drizzle-sized cloud droplets levitated in an electrodynamic balance. Four different categories of secondary ice formation (bubble bursting, jetting, cracking, and breakup) could be detected, and their respective frequencies of occurrence as a function of temperature and droplet size are given. We find that bubble bursting occurs more often than droplet splitting. While we do not observe the shattering of droplets into many large fragments, we find that the average number of small secondary ice particles released during freezing is strongly dependent on droplet size and may well exceed unity for droplets larger than 300 μm in diameter. This leaves droplet fragmentation as an important secondary ice process effective at temperatures around −10°C in clouds where large drizzle droplets are present.

The NASA Cloud, Aerosol, and Monsoon Processes Philippines Experiment (CAMP 2 Ex) employed the NASA P-3, Stratton Park Engineering Company (SPEC) Learjet 35, and a host of satellites and surface sensors to characterize the coupling of aerosol processes, cloud physics, and atmospheric radiation within the Maritime Continent’s complex southwest monsoonal environment. Conducted in the late summer of 2019 from Luzon, Philippines, in conjunction with the Office of Naval Research Propagation of Intraseasonal Tropical Oscillations (PISTON) experiment with its R/V Sally Ride stationed in the northwestern tropical Pacific, CAMP 2 Ex documented diverse biomass burning, industrial and natural aerosol populations, and their interactions with small to congestus convection. The 2019 season exhibited El Niño conditions and associated drought, high biomass burning emissions, and an early monsoon transition allowing for observation of pristine to massively polluted environments as they advected through intricate diurnal mesoscale and radiative environments into the monsoonal trough. CAMP 2 Ex’s preliminary results indicate 1) increasing aerosol loadings tend to invigorate congestus convection in height and increase liquid water paths; 2) lidar, polarimetry, and geostationary Advanced Himawari Imager remote sensing sensors have skill in quantifying diverse aerosol and cloud properties and their interaction; and 3) high-resolution remote sensing technologies are able to greatly improve our ability to evaluate the radiation budget in complex cloud systems. Through the development of innovative informatics technologies, CAMP 2 Ex provides a benchmark dataset of an environment of extremes for the study of aerosol, cloud, and radiation processes as well as a crucible for the design of future observing systems.

In Part 1 of this study (Ireland et al., J. Fluid Mech., vol. 796, 2016, pp. 617–658), we analysed the motion of inertial particles in isotropic turbulence in the absence of gravity using direct numerical simulation (DNS). Here, in Part 2, we introduce gravity and study its effect on single-particle and particle-pair dynamics over a wide range of flow Reynolds numbers, Froude numbers and particle Stokes numbers. The overall goal of this study is to explore the mechanisms affecting particle collisions, and to thereby improve our understanding of droplet interactions in atmospheric clouds. We find that the dynamics of heavy particles falling under gravity can be artificially influenced by the finite domain size and the periodic boundary conditions, and we therefore perform our simulations on larger domains to reduce these effects. We first study single-particle statistics that influence the relative positions and velocities of inertial particles. We see that gravity causes particles to sample the flow more uniformly and reduces the time particles can spend interacting with the underlying turbulence. We also find that gravity tends to increase inertial particle accelerations, and we introduce a model to explain that effect. We then analyse the particle relative velocities and radial distribution functions (RDFs), which are generally seen to be independent of Reynolds number for low and moderate Kolmogorov-scale Stokes numbers $St$ . We see that gravity causes particle relative velocities to decrease by reducing the degree of preferential sampling and the importance of path-history interactions, and that the relative velocities have higher scaling exponents with gravity. We observe that gravity has a non-trivial effect on clustering, acting to decrease clustering at low $St$ and to increase clustering at high $St$ . By considering the effect of gravity on the clustering mechanisms described in the theory of Zaichik & Alipchenkov (New J. Phys., vol. 11, 2009, 103018), we provide an explanation for this non-trivial effect of gravity. We also show that when the effects of gravity are accounted for in the theory of Zaichik & Alipchenkov (2009), the results compare favourably with DNS. The relative velocities and RDFs exhibit considerable anisotropy at small separations, and this anisotropy is quantified using spherical harmonic functions. We use the relative velocities and the RDFs to compute the particle collision kernels, and find that the collision kernel remains as it was for the case without gravity, namely nearly independent of Reynolds number for low and moderate $St$ . We conclude by discussing practical implications of the results for the cloud physics and turbulence communities and by suggesting possible avenues for future research.

In this study, we examined the key parameters within deep convection scheme and cloud physics scheme of the CAM6 model to ascertain their significance and influence on simulating mean precipitation in the tropical Pacific. Through simultaneously perturbing 12 selected parameters from deep convection and cloud physics schemes, we conducted perturbed parameter ensemble (PPE) experiments with 128 members. Our analysis uncovered that the parameters showing the most influential effects on tropical Pacific precipitation simulations can be separated into two distinct categories: those primarily governed by the convection scheme, which reflects the competition between convective and large‐scale precipitation, and those predominantly influenced by cloud ice processes. Furthermore, we revealed the importance of nonlinear effects of these perturbed parameters on the simulation of mean precipitation and interpreted the underlying mechanisms. Some biases in simulating precipitation revealed by our PPE experiments align with those in AMIP simulations, offering valuable insights for the AGCM's advancement.

We present for the first time within the cloud physics context, the application of wavelet phase coherence analysis to disentangle counteracting physical processes associated with the lead‐lag phase difference between cloud‐proxy liquid water path (LWP) and aerosol‐proxy cloud droplet number concentration (Nd) in an Eulerian framework using satellite‐based observations and climate model outputs. This approach allows us to identify the causality and dominant adjustment timescales governing the correlation between LWP and Nd. Satellite observations indicate a more prevalent positive correlation between daytime LWP and Nd regardless of whether LWP leads or lags Nd. The positive cloud water response, associated with precipitation processes, typically occurs within 1 hr, while the negative response resulting from entrainment drying, usually takes 2–4 hr. CAM6 displays excessively rapid negative responses along with overly strong negative cloud water response and insufficient positive response, leading to a more negative correlation between LWP and Nd compared to observations.

Satellite observations and their corresponding instrument simulators are used to document global cloud biases in the Community Atmosphere Model (CAM) versions 4 and 5. The model–observation comparisons show that, despite having nearly identical cloud radiative forcing, CAM5 has a much more realistic representation of cloud properties than CAM4. In particular, CAM5 exhibits substantial improvement in three long-standing climate model cloud biases: 1) the underestimation of total cloud, 2) the overestimation of optically thick cloud, and 3) the underestimation of midlevel cloud. While the increased total cloud and decreased optically thick cloud in CAM5 result from improved physical process representation, the increased midlevel cloud in CAM5 results from the addition of radiatively active snow. Despite these improvements, both CAM versions have cloud deficiencies. Of particular concern, both models exhibit large but differing biases in the subtropical marine boundary layer cloud regimes that are known to explain intermodel differences in cloud feedbacks and climate sensitivity. More generally, this study demonstrates that simulator-facilitated evaluation of cloud properties, such as amount by vertical level and optical depth, can robustly expose large and at times radiatively compensating climate model cloud biases.