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At least 19 records

A Theory for the Balance between Warm Rain and Ice Crystal Processes of Precipitation in Mixed-Phase Clouds

Abstract Mixed-phase clouds contain both supercooled cloud liquid and ice crystals. In principle, precipitation may be initiated either by the liquid phase or by the ice phase. Ice crystals may grow by vapor diffusion to become snow (“ice crystal process”), forming “cold” precipitation. Equally, cloud droplets, when large enough, coalesce to form “warm” precipitation by the “warm rain process.” Warm rain could be supercooled and freeze as “warm” graupel. In the present paper, a new simplified theoretical analysis is provided to examine the microphysical system consisting of three species of hydrometeor, namely, cloud liquid, “cold ice” (crystals, snow), and “warm rain” (frozen or supercooled). This is obtained by nondimensionalizing and simplifying the evolution equations for the mass of each species. Analytical formulas are given for equilibria. Feedback analysis shows that the sign of the feedback is linked to the abundance of precipitation, with a neutral surface in the 3D phase space. The system’s precipitation amount explodes while in the initial unstable regime, crossing the neutral surface and approaching the equilibrium point that is a stable attractor. Positive and negative feedbacks are elucidated. In a standard case, the cold ice mass is about 1000 times larger than the warm rain mass. To illustrate the physical behavior of the theory, sensitivity tests are performed with respect to environmental conditions (e.g., aerosol, updraft speed) and microphysical parameters (e.g., riming and sedimentation rates for cold ice). Cold ice prevails, especially in fast ascent, due to its low bulk density, favoring slow sedimentation and a wide cross-sectional area for riming. Significance Statement The theory elucidates how the ice phase can prevail in the precipitation from any mixed-phase clouds with supercooled cloud liquid and crystals. The ice phase radically suppresses cloud liquid by riming when active and “wins” the competition against coalescence. This prevalence of ice is shown to arise from the low bulk density of snow. The cloud is viewed as a system of negative and positive feedbacks that prevail in realms of stability and instability in a 3D phase space.

Meteorology & Atmospheric Sciences↗

Multi–year analysis of rain–snow levels at Marquette, Michigan

This study uses observations from a ground-based instrument suite to investigate the rain-snow level in stratiform rainfall from January 2014 to April 2020 in the Upper Great Lakes Region. The height above the surface where ice melts to rain, the rain-snow level (RSL), influences microphysical assumptions in remote sensing precipitation retrievals and the ability of space-based radar to discriminate surface precipitation phase because of ground clutter. The instrument suite is installed at the Marquette, MI (MQT) National Weather Service station adjacent to Lake Superior. Rain events and the RSL are studied through a ground-based vertically profiling radar (Micro Rain Radar), a custom NASA-developed video disdrometer (Precipitation Imaging Package), and reanalyses products from ECMWF ERA5 and NASA MERRA-2. Further, distinct macro and micro physical characteristics are observed in precipitation events with shallow RSL ( < 1.8 km above ground level [AGL]) and intermediate RSL ( > 1.8 km AGL). Intermediate RSL correspond to rain events with relatively higher rain rates and a higher concentration of small drops in the drop size distributions (DSDs). Shallow RSL DSDs contain relatively higher concentrations of large drops with lower fall speeds suggesting that partially melted snowflakes may be reaching the surface. Reflectivity-rain-rate relationships are also impacted by microphysical differences associated with RSL regimes. Radar-detected RSL agree with reanalysis-derived melt levels- especially at wet-bulb isotherms of 0.5°C and 1°C. Seasonal differences such as shallow rain-snow levels in winter, fall, and spring have subsequent implications for satellite detectability.

54 ENVIRONMENTAL SCIENCES↗

Light rain exacerbates extreme humid heat

Abstract Humid heat waves pose significant risks to human health and the ecosystem. Intuitively, rainfall often alleviates extreme humid heat. However, here we show that light rain often accompanies extreme humid heat, exacerbating its frequency and intensity, especially over arid and semi-arid regions compared to no rain and moderate-to-heavy rain cases. This is because light rain does not dramatically reduce solar radiation but increases near-surface humidity through enhanced surface evaporation. The water replenishment from light rain as well as a shallower planetary boundary layer is crucial for consecutive extremes where there are commonly sporadic drizzle days amidst several rain-free days. These extremes last longer than rain-free extremes. Current global climate models (GCMs) overestimate light rain. After reducing this bias in a GCM, underestimations of humid heat waves in energy-limited regions and overestimations in water-limited regions are largely alleviated. These findings underscore the underappreciated impact of light rain on extreme humid heat.

Science & Technology - Other Topics↗

Widespread underestimation of rain-induced soil carbon emissions from global drylands

Dryland carbon fluxes, particularly those driven by ecosystem respiration, are highly sensitive to water availability and rain pulses. However, the magnitude of rain-induced carbon emissions remains unclear globally. Here we quantify the impact of rain-pulse events on the carbon balance of global drylands and characterize their spatiotemporal controls. Using eddy-covariance observations of carbon, water and energy fluxes from 34 dryland sites worldwide, we produce an inventory of over 1,800 manually identified rain-induced CO2 pulse events. Based on this inventory, a machine learning algorithm is developed to automatically detect rain-induced CO2 pulse events. Our findings show that existing partitioning methods underestimate ecosystem respiration and photosynthesis by up to 30% during rain-pulse events, which annually contribute 16.9 ± 2.8% of ecosystem respiration and 9.6 ± 2.2% of net ecosystem productivity. We show that the carbon loss intensity correlates most strongly with annual productivity, aridity and soil pH. Finally, we identify a universal decay rate of rain-induced CO2 pulses and use it to bias-correct respiration estimates. Our research highlights the importance of rain-induced carbon emissions for the carbon balance of global drylands and suggests that ecosystem models may largely underrepresent the influence of rain pulses on the carbon cycle of drylands.

Nguyen, Ngoc B↗

Impacts of stochastic coalescence variability on warm rain initiation using Lagrangian microphysics in box and large-eddy simulations

Various coalescence methods for Lagrangian microphysics schemes are tested in box and large-eddy simulation (LES) models, including the stochastic all-or-nothing super-droplet method (SDM) and a version of SDM (dSDM) that applies a fractional approach similar to the average impact method. In LES, variabilities driven by microphysics and by flow realizations are separated using the “piggybacking” technique. Rain initiation averaged over many realizations of the box model is delayed and rain variability increases as the number of super-drops per collision volume ( N SD ) is decreased using SDM. In contrast, rain initiation time using SDM in LES is insensitive to N SD for 32 ≤ N SD ≤ 512. This is explained through the interaction between LES grid boxes, each acting as a separate collision volume. Variability across the ensemble of LES collision volumes using SDM results in rain quickly initiating in some of the LES grid cells at low N SD and leading to a similar overall timing of rain initiation from the cloud compared to simulations with high N SD . There is a ~20% decrease in the total rain mass and mean rain flux as N SD is increased from 32 to 256, with little additional change as N SD is increased from 256 to 512. The fractional coalescence approach in dSDM leads to reduced microphysical variability and a 15-18 min delay in rain initiation compared to SDM. Finally, an additional LES ensemble with microphysical variability feeding back to the dynamics shows that flow variability dominates the impact of microphysical variability on rain properties. Thus, flow variability must be constrained to isolate impacts of microphysical variability.

54 ENVIRONMENTAL SCIENCES↗

Are turbulence effects on droplet collision–coalescence a key to understanding observed rain formation in clouds?

Rain formation is a critical factor governing the lifecycle and radiative forcing of clouds and therefore it is a key element of weather and climate. Cloud microphysics–turbulence interactions occur across a wide range of scales and are challenging to represent in atmospheric models with limited resolution. Based on past experiments and idealized numerical simulations, it has been postulated that cloud turbulence accelerates rain formation by enhancing drop collision–coalescence. We provide substantial evidence for significant impacts of turbulence on the evolution of cloud droplet size distributions and rain formation by comparing high-resolution observations of cumulus congestus clouds with state-of-the-art large-eddy simulations coupled with a Lagrangian particle-based microphysics scheme. Turbulent coalescence must be included in the model to accurately represent the observed drop size distributions, especially for drizzle drop sizes at lower heights in the cloud. Turbulence causes earlier rain formation and greater rain accumulation compared to simulations with gravitational coalescence only. The observed rain size distribution tail just above cloud base follows a power law scaling that deviates from theoretical scalings considering either a purely gravitation collision kernel or a turbulent kernel neglecting droplet inertial effects, providing additional evidence for turbulent coalescence in clouds. In contrast, large aerosols acting as cloud condensation nuclei (“giant CCN”) do not significantly impact rain formation owing to their long timescale to reach equilibrium wet size relative to the lifetime of rising cumulus thermals. Overall, turbulent drop coalescence exerts a dominant influence on rain initiation in warm cumulus clouds, with limited impacts of giant CCN.

54 ENVIRONMENTAL SCIENCES↗

Occurrence of Warm Freezing Rain: Observation and Modeling Study

Freezing rain has been normally considered to be composed of supercooled raindrops when the 2 m air temperature (hereafter T as ) is below freezing. However, according to a statistical survey of freezing rain observations in China from 2000 to 2019, we find that there were 656 events that occurred at T as greater than 0°C (hereafter warm freezing rain and denoted by WFR), which account for 7% of the total freezing rain observations. Additionally, nearly 3% (266 observations) of freezing rain events occurred when the near-surface wet-bulb temperature was greater than 0°C. The modeling and sensitivity experiments on the nonequilibrium raindrop temperature (hereafter T r ) how that the temperature difference between raindrops and the atmosphere is the main cause of WFR. The magnitudes of the Δ T ar (difference between raindrop temperature T r and air temperature T a ) and Δ T ur (difference between T r and wet-bulb temperature T w ) are determined by the raindrop diameter D, temperature lapse rate $\Gamma$, and relative humidity RH. Increases of D and $\Gamma$, and a decrease of RH enhance Δ T ar and Δ T ur and thus the occurrence of WFR. Further simulations of 4 idealized and 370 real sounding profiles reveal that either the T a or the T w cannot properly distinguish the WFR events. When considering the temperature difference between raindrops and the atmosphere, the WFR can form by the “melting of solid hydrometeors” or “supercooled warm rain process.” This study can also deepen our understanding of the conditions of WFR and freezing rain formation at different altitudes.

54 ENVIRONMENTAL SCIENCES↗

Analyzing Relationships between Tropical Cyclone Intensity and Rain Rate over the Ocean Using Numerical Simulations

In this study, the relationship between tropical cyclone (TC) intensity and rain rate over the ocean is investigated using a full-physics numerical model (WRF) and a physics-based TC rainfall model (TCR). TC intensity is found to be nearly linearly correlated with the average rain rate in the inner core [~0.97 (mm h –1 m –2 )/(m s –1 )], while the correlation is weak at outer radii. This difference is induced because TC intensity is significantly correlated with both the vertical velocity and specific humidity in the inner core but is not significantly correlated with the vertical velocity in the outer radii. Further investigation shows that the intensity–rain-rate relationship at the outer radii is influenced by the TC evolution stage. The rain rate for the outer radii is positively correlated with TC intensity for nondecaying TCs, while this correlation is reduced for decaying TCs due to systematic downdrafts in the outer radii. In the context of climate change, the sensitivity of the TC rain rate to sea surface temperature (SST) is found to be +9% per 1 K increase of SST, roughly the product of the sensitivity of TC intensity to SST (+3%) and the Clausius-Clapeyron scaling (+7%). Coupled with synthetic storms, evolution of the TC rain rate over the twenty-first century under the SSP5-8.5 scenario is projected by the TCR (calibrated with the WRF simulations). The annual increase rates of averaged TC rain rate are 0.17% and 0.20% for the inner core and outer radii, respectively, larger than the annual increase rate of TC intensity (0.046%) but comparable to that of cube of intensity (0.18%).

54 ENVIRONMENTAL SCIENCES↗

Impacts of Suppressing Excessive Light Rain on Aerosol Radiative Effects and Health Risks

Global climate models (GCMs) have been used widely to study radiative forcing and health risks of aerosols. A recent study using two GCMs found that light rain plays a dominant role in controlling aerosol loading. However, “too much light rain and too little heavy rain” is a longstanding bias in GCMs. It is unclear how much light rain affects aerosol-cloud-radiation interactions and health risks from air pollution. Here, in this work, we show that, with the correction of the rainfall intensity spectrum in the National Center for Atmospheric Research Community Atmosphere Model version 5.3 by introducing a stochastic deep convection scheme, the reduced frequency of light rain (1–20 mm d -1 ) results in changes of aerosol direct radiative effects (DRE) of up to -0.5 ± 0.03 W/m 2 and aerosol cloud radiative effects (CRE) of up to -0.9 ± 0.03 W/m 2 . The total (CRE + DRE) radiative effects of light rain-mediated aerosol changes exceed the present-day anthropogenic forcing of aerosols relative to preindustrial levels from the Coupled Model Intercomparison Project (CMIP5&6) models. However, the correction of the rainfall intensity spectrum has little effect on anthropogenic aerosol forcing (defined as the radiative perturbation due to changes in aerosol concentrations between the industrial era and preindustrial levels). Due to increased exposure to fine particulates (PM 2.5 ), the estimated global total premature mortality is much higher than previously estimated, by 300,000 ± 60,000 deaths per year, and is more severe in populous regions such as India and China. The findings in this study highlight the need to understand uncertainties in radiative effects and health risks of aerosols due to simulation biases of precipitation in GCMs.

54 ENVIRONMENTAL SCIENCES↗

Limitations of Separate Cloud and Rain Categories in Parameterizing Collision-Coalescence for Bulk Microphysics Schemes

Warm rain collision-coalescence has been persistently difficult to parameterize in bulk microphysics schemes. We use a flexible bulk microphysics scheme with bin scheme process parameterizations, called AMP, to investigate reasons for the difficulty. AMP is configured in a variety of ways to mimic bulk schemes and is compared to simulations with the bin scheme upon which AMP is built. We find that an important limitation in traditional bulk schemes is the use of separate cloud and rain categories. When the drop size distribution is instead represented by a continuous distribution, the simulation of cloud-to-rain conversion is substantially improved. We also find large sensitivity to the threshold size to distinguish cloud and rain in traditional schemes; substantial improvement is found by decreasing the threshold from 40 to 25 μm. Neither the use of an assumed functional form for the size distribution nor the choice of predicted distribution moments has a large impact on the ability of AMP to simulate rain production. When predicting four total moments of the liquid drop size distribution, either with a traditional two-category, two-moment scheme with a reduced size threshold, or a four-moment single-category scheme, errors in the evolution of mass and the cloud size distribution are similar, but the single-category scheme has a substantially better representation of the rain size distribution. Optimal moment combinations for the single-category approach are investigated and appear to be linked more to the information content they provide for constraining the size distributions than to their correlation with collision-coalescence rates.

54 ENVIRONMENTAL SCIENCES↗

Internal Climate Variability Obscures Future Freezing Rain Changes Despite Global Warming Trend

Abstract Although numerous studies have projected changes in freezing rain under future climate conditions, the internal variability of freezing rain remains poorly quantified. Here, we introduce a framework utilizing a novel machine‐learning algorithm to diagnose freezing rain in reanalysis and climate model simulations. By employing multivariate quantile mapping, we decompose the projected freezing rain trend into contributions from changes in temperature, relative humidity, and precipitation, which helps separate the forced response from internal climate variability. Our finding reveals a notable decrease in freezing rain occurrence in most areas. Despite a substantial temperature increase, internal variability overshadows climate forcing across a large portion of the eastern United States until about 2050. This insight has implications for practitioners, suggesting that the observed freezing rain frequency climatology continues to provide a relevant baseline for decision‐making in the near term. However, longer‐term design and adaptation plans should consider the projected changes in these regions.

Zhuang, Haoyu (Richard) [Department of Atmospheric↗

Disproportionate control on aerosol burden by light rain

Atmospheric aerosols are of great climatic and environmental importance due to their effects on the Earth’s radiative energy balance and air quality. Aerosol concentrations are strongly influenced by rainfall via wet removal. Global climate models have been used to quantify their climate and health effects. However, they commonly suffer from a well-known problem of ‘too much light rain and too little heavy rain’. The impact of simulated rainfall intensities on aerosol burden at the global scale is still unclear. In this study, we show that rainfall intensity has profound impacts on aerosol burden, and light rain has a disproportionate control on it. By improving the representation of convection, the light-rain (1–20 mm d –1 ) frequency in two state-of-the-art global climate models is reduced. As a result, the aerosol burden is increased globally, especially over the tropics and subtropics, by as much as 0.3 in aerosol optical depth in tropical rain belts. It is attributed to the dominant contribution of light rain to the accumulated wet removal by its frequent occurrence despite its weak intensity. The implication of these findings is that understanding the nature of aerosol scavenging by rainfall is critical to aerosol–climate interaction and its impact on climate.

54 ENVIRONMENTAL SCIENCES↗

A Bayesian Approach for Statistical–Physical Bulk Parameterization of Rain Microphysics. Part II: Idealized Markov Chain Monte Carlo Experiments

Observationally informed development of a new framework for bulk rain microphysics, the Bayesian Observationally Constrained Statistical–Physical Scheme (BOSS; described in Part I of this study), is demonstrated. This scheme’s development is motivated by large uncertainties in cloud and weather simulations associated with approximations and assumptions in existing microphysics schemes. Here, a proof-of-concept study is introduced using a Markov chain Monte Carlo sampling algorithm with BOSS to probabilistically estimate microphysical process rates and parameters directly from a set of synthetically generated rain observations. The framework utilized is an idealized steady-state one-dimensional column rainshaft model with specified column-top rain properties and a fixed thermodynamical profile. Different configurations of BOSS—flexibility being a key feature of this approach—are constrained via synthetic observations generated from a traditional three-moment bulk microphysics scheme. The ability to retrieve correct parameter values when the true parameter values are known is illustrated. For cases when there is no set of true parameter values, the accuracy of configurations of BOSS that have different levels of complexity is compared. It is found that addition of the sixth moment as a prognostic variable improves prediction of the third moment (proportional to bulk rain mass) and rain rate. In contrast, increasing process rate formulation complexity by adding more power terms has little benefit—a result that is explained using further-idealized experiments. BOSS rainshaft simulations are shown to well estimate the true process rates from constraint by bulk rain observations, with the further benefit of rigorously quantified uncertainty of these estimates.

58 GEOSCIENCES↗

Improving the Parameterization of Cloud and Rain Microphysics in E3SM using Novel Observationally-Constrained Bayesian Approach (Final Technical Report)

In this project, we sought to develop new cloud and rain microphysics frameworks within the Energy Exascale Earth System Model (E3SM). This work encompassed two primary avenues of research: 1) Further development of a Bayesian-based scheme called BOSS (Bayesian Observationally-constrained Statistical-physical Scheme) to represent cloud and rain microphysics, testing it in realistic high-resolution cloud models, and implementing it in E3SM; 2) Development of a methodology utilizing machine learning to enable computationally tractable use of tractable use of Markov chain Monte Carlo sampling for Bayesian parameter estimation in Earth system and cloud models. In this project, we adapted the BOSS microphysics scheme, originally formulated for rain-only, to include all liquid-phase microphysical processes for cloud and rain, in particular the processes that mediate between these two categories, for example the conversion from cloud to rain through collision and coalescence of drops. We constrained the scheme via comparison and testing against a detailed model that explicitly represents the evolution of cloud and rain particles, called a bin microphysics scheme.

54 ENVIRONMENTAL SCIENCES↗

Multiple Sources of Riparian Wetland Suspended Solids during Episodic Rain Events: Influence on Uranium Transport

Suspended solids can be the primary vector for transporting contaminants in streams. The objective of this study was to determine whether changes in the properties of suspended solids during rain events impacted contaminant transport. Stream water was collected during five episodic events downstream from a U-contaminated wetland located in South Carolina, USA. The suspended particles were initially composed of Fe-flocs (particles formed in situ prior to the rain event) that had significantly greater Fe, Mn, organic-C, and U content than particles collected later during a sampling rain event. XANES and EXAFS revealed that U in the Fe-flocs was U(VI) and that it was not incorporated in a mineral structure but existed as inner- or outer-sphere adsorbed uranyl species associated with organic matter and Fe-oxides. The uranyl had an extraordinarily high affinity for the suspended solids, with solid to liquid U ratios of >72,000 (μg/kg)/(μg/L). After the initial flush of Fe-flocs, a greater fraction of the suspended solids had lower organic-C, Fe, Mn, and amorphous phases and were composed of more quartz, kaolinite, and gibbsite, resulting in lower U concentrations than those in the solids collected earlier in the rain event. This study highlights the importance of understanding suspended solids as transport vectors and their potential dynamic nature during rain events.

computer simulations↗

Tracing the Rain Formation Pathways in Numerical Simulations of Deep Convection

Quantifying the microphysical process contributions to surface precipitation in numerical simulations can be challenging. This is due to the fact that many microphysical processes contribute to the formation and depletion of rain drops and there is almost always a spatial/temporal mismatch between where/when rain is formed and where/when it strikes the surface. In this work, we develop a tracing method that tracks the sources and sinks of raindrop mass and number as they are advected by the Weather Research and Forecasting model. Applying the method to an idealized squall line confirms that convective precipitation is dominated by warm rain processes (autoconversion and accretion) while stratiform precipitation is dominated by the melting of rimed and unrimed ice crystals. Sensitivity experiments in which the prescribed cloud drop number concentration is increased confirm the conventional wisdom that weakened autoconversion increases the fraction of raindrops originating from cold rain processes. The method also reveals that when applied to deep convection the Khairoutdinov and Kogan autoconversion scheme produces an excessive number of raindrops which are subsequently clipped in P3 microphysics to keep the rain size distribution within prescribed limits. This problem can mostly be mitigated by increasing the assumed radius for raindrops created by autoconversion.

58 GEOSCIENCES↗

Divergent responses of historic rain-on-snow flood extremes to a warmer climate

Global warming is altering flood risks induced by rain-on-snow events. However, decision-makers lack guidance on how rain-on-snow induced extreme floods could be altered with warming. Here, storyline analyses using a kilometer-scale land surface model reveal diverse responses of four historically-impactful, decision-relevant rain-on-snow induced extreme flood events over the contiguous U.S. to warming, due to alterations in their water budgets. For the 2017-Feb California floods, runoff first increases and then decreases with warming, peaking under the +3 K scenario, while runoff of the 2017-Jan California floods increases monotonically by ~53%/K. Contrastingly, runoff of the 1996-Jan Mid-Atlantic floods decreases gradually with warming. Despite these differences, warming generally shifts flood-generating regimes along elevation profiles. High elevations could experience notably increased runoff, while low elevations encounter a shift from rain-on-snow-driven to rainfall-dominated runoff. These findings underscore the need for flood control planning to quantify region- and elevation-specific changes in rain-on-snow events in a warmer climate.

54 ENVIRONMENTAL SCIENCES↗

Weak influence of anthropogenic emissions on aerosol, cloud, and rain in the wet season of the Amazon rainforest

Anthropogenic emissions have been shown to affect new particle formation, aerosol concentrations, and clouds. Such effects vary with region, environmental conditions, and cloud types. In the wet season of Amazonia, anthropogenic emissions emitted from Manaus, Brazil, can significantly increase the cloud condensation nuclei (CCN) concentrations compared to the background of mainly natural aerosols. However, the regional response of cloud and rain to anthropogenic emissions in Amazonia remains very uncertain. Here, we aim to quantify how aerosol concentration, cloud, and rain respond to changes in anthropogenic emissions through parameterized new particle formation and primary aerosol emission in the Manaus region and to understand the underlying mechanisms. We ran the atmosphere-only configuration of the HadGEM3 climate model with a nested regional domain that covers most of the rainforest region (720 km by 1200 km with 3 km resolution) under scaled regional emissions. The 7 d simulations show that, in the areas that are affected by anthropogenic emissions, when aerosol and precursor gas emissions are doubled from the baseline emission inventories, aerosol number concentrations increase by 13 %. The nucleation rate that involves sulfuric acid and biogenic compounds generally increases with pollution levels. However, nucleation is suppressed very close to the pollution source, resulting in lower nucleation and soluble Aitken mode aerosol number concentrations. We also found that doubling the anthropogenic emission can increase the cloud droplet number concentrations ( N d ) by 9 %, but cloud water and rain mass mixing ratios do not change significantly. Even very strong reductions in aerosol number concentrations by a factor of 4, which is an unrealistic condition, cause only a 4 % increase in rain over the domain. If we assume our simulation has a fine enough grid resolution and an accurate representation of the relevant atmospheric processes, the simulated weak and non-linear response of cloud and rain properties to linearly scaled anthropogenic emissions suggests that the interactions among aerosol, cloud, and precipitation in the Amazonian convective environment are buffered by microphysical processes. It also implies that the convective environment is resilient to the changes in Nd that occur in response to localized anthropogenic aerosol perturbations.

Wang, Xuemei [University of Leeds (United Kingdom)↗