Articles | Volume 24, issue 14
https://doi.org/10.5194/acp-24-8457-2024
© Author(s) 2024. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/acp-24-8457-2024
© Author(s) 2024. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| 
26 Jul 2024
Research article |
| 26 Jul 2024
| 26 Jul 2024
Finite domains cause bias in measured and modeled distributions of cloud sizes
Thomas D. DeWitt
Department of Atmospheric Sciences, University of Utah, 135 S 1460 E Rm 819, Salt Lake City, UT 84112, USA
Department of Atmospheric Sciences, University of Utah, 135 S 1460 E Rm 819, Salt Lake City, UT 84112, USA
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Thomas D. DeWitt, Timothy J. Garrett, and Karlie N. Rees
EGUsphere, https://doi.org/10.5194/egusphere-2025-3486, https://doi.org/10.5194/egusphere-2025-3486, 2025
This preprint is open for discussion and under review for Atmospheric Chemistry and Physics (ACP).
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Clouds appear chaotic, but they in fact follow fractal mathematical patterns similar to coastlines. We measured their fractal properties using satellite images and found two key numbers that describe cloud shapes: one for how rough individual cloud edges are, and another for how clouds of different sizes organize together. We recommend methodology that provides objective ways to verify whether climate models accurately simulate real clouds.
Karlie N. Rees, Timothy J. Garrett, Thomas D. DeWitt, Corey Bois, Steven K. Krueger, and Jérôme C. Riedi
Nonlin. Processes Geophys., 31, 497–513, https://doi.org/10.5194/npg-31-497-2024, https://doi.org/10.5194/npg-31-497-2024, 2024
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The shapes of clouds viewed from space reflect vertical and horizontal motions in the atmosphere. We theorize that, globally, cloud perimeter complexity is related to the dimension of turbulence also governed by horizontal and vertical motions. We find agreement between theory and observations from various satellites and a numerical model and, remarkably, that the theory applies globally using only basic planetary physical parameters from the smallest scales of turbulence to the planetary scale.
Thomas D. DeWitt, Timothy J. Garrett, Karlie N. Rees, Corey Bois, Steven K. Krueger, and Nicolas Ferlay
Atmos. Chem. Phys., 24, 109–122, https://doi.org/10.5194/acp-24-109-2024, https://doi.org/10.5194/acp-24-109-2024, 2024
Short summary
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Viewed from space, a defining feature of Earth's atmosphere is the wide spectrum of cloud sizes. A recent study predicted the distribution of cloud sizes, and this paper compares the prediction to observations. Although there is nuance in viewing perspective, we find robust agreement with theory across different climatological conditions, including land–ocean contrasts, time of year, or latitude, suggesting a minor role for Coriolis forces, aerosol loading, or surface temperature.
Thomas D. DeWitt, Timothy J. Garrett, and Karlie N. Rees
EGUsphere, https://doi.org/10.5194/egusphere-2025-3486, https://doi.org/10.5194/egusphere-2025-3486, 2025
This preprint is open for discussion and under review for Atmospheric Chemistry and Physics (ACP).
Short summary
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Clouds appear chaotic, but they in fact follow fractal mathematical patterns similar to coastlines. We measured their fractal properties using satellite images and found two key numbers that describe cloud shapes: one for how rough individual cloud edges are, and another for how clouds of different sizes organize together. We recommend methodology that provides objective ways to verify whether climate models accurately simulate real clouds.
Spencer Donovan, Dhiraj K. Singh, Timothy J. Garrett, and Eric R. Pardyjak
EGUsphere, https://doi.org/10.5194/egusphere-2025-3060, https://doi.org/10.5194/egusphere-2025-3060, 2025
This preprint is open for discussion and under review for Atmospheric Chemistry and Physics (ACP).
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Accurate snowfall prediction requires quantifying how snowflakes interact with atmospheric turbulence. Using field-based imaging techniques, we directly measured the mass, size, density, and fall speed of snowflakes in surface-layer turbulence. We found that turbulence and microstructure jointly modulate fall speed, often deviating from the terminal velocity in still air. These results inform new parameterizations for numerical weather and climate models.
Karlie N. Rees, Timothy J. Garrett, Thomas D. DeWitt, Corey Bois, Steven K. Krueger, and Jérôme C. Riedi
Nonlin. Processes Geophys., 31, 497–513, https://doi.org/10.5194/npg-31-497-2024, https://doi.org/10.5194/npg-31-497-2024, 2024
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The shapes of clouds viewed from space reflect vertical and horizontal motions in the atmosphere. We theorize that, globally, cloud perimeter complexity is related to the dimension of turbulence also governed by horizontal and vertical motions. We find agreement between theory and observations from various satellites and a numerical model and, remarkably, that the theory applies globally using only basic planetary physical parameters from the smallest scales of turbulence to the planetary scale.
Dhiraj K. Singh, Eric R. Pardyjak, and Timothy J. Garrett
Atmos. Meas. Tech., 17, 4581–4598, https://doi.org/10.5194/amt-17-4581-2024, https://doi.org/10.5194/amt-17-4581-2024, 2024
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Accurate measurements of the properties of snowflakes are challenging to make. We present a new technique for the real-time measurement of the density of freshly fallen individual snowflakes. A new thermal-imaging instrument, the Differential Emissivity Imaging Disdrometer (DEID), is shown to be capable of providing accurate estimates of individual snowflake and bulk snow hydrometeor density. The method exploits the rate of heat transfer during the melting of a snowflake on a hotplate.
Thomas D. DeWitt, Timothy J. Garrett, Karlie N. Rees, Corey Bois, Steven K. Krueger, and Nicolas Ferlay
Atmos. Chem. Phys., 24, 109–122, https://doi.org/10.5194/acp-24-109-2024, https://doi.org/10.5194/acp-24-109-2024, 2024
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Viewed from space, a defining feature of Earth's atmosphere is the wide spectrum of cloud sizes. A recent study predicted the distribution of cloud sizes, and this paper compares the prediction to observations. Although there is nuance in viewing perspective, we find robust agreement with theory across different climatological conditions, including land–ocean contrasts, time of year, or latitude, suggesting a minor role for Coriolis forces, aerosol loading, or surface temperature.
Timothy J. Garrett, Matheus R. Grasselli, and Stephen Keen
Earth Syst. Dynam., 13, 1021–1028, https://doi.org/10.5194/esd-13-1021-2022, https://doi.org/10.5194/esd-13-1021-2022, 2022
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Current world economic production is rising relative to energy consumption. This increase in
production efficiencysuggests that carbon dioxide emissions can be decoupled from economic activity through technological change. We show instead a nearly fixed relationship between energy consumption and a new economic quantity, historically cumulative economic production. The strong link to the past implies inertia may play a more dominant role in societal evolution than is generally assumed.
Karlie N. Rees and Timothy J. Garrett
Atmos. Meas. Tech., 14, 7681–7691, https://doi.org/10.5194/amt-14-7681-2021, https://doi.org/10.5194/amt-14-7681-2021, 2021
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Monte Carlo simulations are used to establish baseline precipitation measurement uncertainties according to World Meteorological Organization standards. Measurement accuracy depends on instrument sampling area, time interval, and precipitation rate. Simulations are compared with field measurements taken by an emerging hotplate precipitation sensor. We find that the current collection area is sufficient for light rain, but a larger collection area is required to detect moderate to heavy rain.
Dhiraj K. Singh, Spencer Donovan, Eric R. Pardyjak, and Timothy J. Garrett
Atmos. Meas. Tech., 14, 6973–6990, https://doi.org/10.5194/amt-14-6973-2021, https://doi.org/10.5194/amt-14-6973-2021, 2021
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This paper describes a new instrument for quantifying the physical characteristics of hydrometeors such as snow and rain. The device can measure the mass, size, density and type of individual hydrometeors as well as their bulk properties. The instrument is called the Differential Emissivity Imaging Disdrometer (DEID) and is composed of a thermal camera and hotplate. The DEID measures hydrometeors at sampling frequencies up to 1 Hz with masses and effective diameters greater than 1 µg and 200 µm.
Karlie N. Rees, Dhiraj K. Singh, Eric R. Pardyjak, and Timothy J. Garrett
Atmos. Chem. Phys., 21, 14235–14250, https://doi.org/10.5194/acp-21-14235-2021, https://doi.org/10.5194/acp-21-14235-2021, 2021
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Accurate predictions of weather and climate require descriptions of the mass and density of snowflakes as a function of their size. Few measurements have been obtained to date because snowflakes are so small and fragile. This article describes results from a new instrument that automatically measures individual snowflake size, mass, and density. Key findings are that small snowflakes have much lower densities than is often assumed and that snowflake density increases with temperature.
Kyle E. Fitch, Chaoxun Hang, Ahmad Talaei, and Timothy J. Garrett
Atmos. Meas. Tech., 14, 1127–1142, https://doi.org/10.5194/amt-14-1127-2021, https://doi.org/10.5194/amt-14-1127-2021, 2021
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Snow measurements are very sensitive to wind. Here, we compare airflow and snowfall simulations to Arctic observations for a Multi-Angle Snowflake Camera to show that measurements of fall speed, orientation, and size are accurate only with a double wind fence and winds below 5 m s−1. In this case, snowflakes tend to fall with a nearly horizontal orientation; the largest flakes are as much as 5 times more likely to be observed. Adjustments are needed for snow falling in naturally turbulent air.
Mathias Gergely, Steven J. Cooper, and Timothy J. Garrett
Atmos. Chem. Phys., 17, 12011–12030, https://doi.org/10.5194/acp-17-12011-2017, https://doi.org/10.5194/acp-17-12011-2017, 2017
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This study investigates the importance of snowflake surface-area-to-volume ratio (SAV) for the interpretation of snowfall triple-frequency radar signatures. The results indicate that snowflake SAV has a strong impact on modeled snowfall radar signatures and therefore may be used to further constrain (the large variety and high natural variability of) snowflake shape for snowfall remote sensing, e.g., to distinguish graupel snow from snowfall characterized by large aggregate snowflakes.
Quentin Coopman, Timothy J. Garrett, Jérôme Riedi, Sabine Eckhardt, and Andreas Stohl
Atmos. Chem. Phys., 16, 4661–4674, https://doi.org/10.5194/acp-16-4661-2016, https://doi.org/10.5194/acp-16-4661-2016, 2016
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We analyze interactions of Arctic clouds with pollution plumes that have been transported long distances from midlatitudes. Constraining for meteorological state, we find that pollution decreases cloud-droplet effective radius and increases cloud optical depth. The impact is highest when the atmosphere is particularly humid and/or stable suggesting that aerosol–cloud interactions depend on the Arctic's climate.
T. J. Garrett
Earth Syst. Dynam., 6, 673–688, https://doi.org/10.5194/esd-6-673-2015, https://doi.org/10.5194/esd-6-673-2015, 2015
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GCMs and economic models are often coupled for climate scenarios. Here, what is examined is how well a simple non-equilibrium thermodynamic model can represent the multi-decadal growth of global civilization. Initialized with growth trends from the 1950s, the model attains high skill at hindcasting how fast the GDP and energy consumption grew during the 2000s. This opens treating the coupled economy and climate as a physically deterministic response to available flows of energy and matter.
T. J. Garrett and C. Zhao
Atmos. Meas. Tech., 6, 1227–1243, https://doi.org/10.5194/amt-6-1227-2013, https://doi.org/10.5194/amt-6-1227-2013, 2013
B. van Diedenhoven, B. Cairns, A. M. Fridlind, A. S. Ackerman, and T. J. Garrett
Atmos. Chem. Phys., 13, 3185–3203, https://doi.org/10.5194/acp-13-3185-2013, https://doi.org/10.5194/acp-13-3185-2013, 2013
Related subject area
Subject: Clouds and Precipitation | Research Activity: Atmospheric Modelling and Data Analysis | Altitude Range: Troposphere | Science Focus: Physics (physical properties and processes)
Ambient and intrinsic dependencies of evolving ice-phase particles within a decaying winter storm during IMPACTS
High-resolution modeling of early contrail evolution from hydrogen-powered aircraft
Accelerated impact of airborne glaciogenic seeding of stratiform clouds by turbulence
Failed cyclogenesis of a mesoscale convective system near Cabo Verde: the role of the Saharan trade wind layer among other inhibiting factors observed during the CADDIWA field campaign
Sensitivities of simulated mixed-phase Arctic multilayer clouds to primary and secondary ice processes
Assessing glaciogenic seeding impacts in Australia's Snowy Mountains: an ensemble modeling approach
How the representation of microphysical processes affects tropical condensate in the global storm-resolving model ICON
Magnitude and timescale of liquid water path adjustments to cloud droplet number concentration perturbations for nocturnal non-precipitating marine stratocumulus
Cold pools mediate mesoscale adjustments of trade-cumulus fields to changes in cloud droplet number concentration
Numerical case study of the aerosol–cloud interactions in warm boundary layer clouds over the eastern North Atlantic with an interactive chemistry module
Influence of temperature and humidity on contrail formation regions in the general circulation model EMAC: a spring case study
On the impact of thunder on cloud ice crystals and droplets
Counteracting influences of gravitational settling modulate aerosol impacts on cloud-base-lowering fog characteristics
The critical number and size of precipitation embryos to accelerate warm rain initiation
Impact on the stratocumulus-to-cumulus transition of the interaction of cloud microphysics and macrophysics with large-scale circulation
Technical note: Phase space depiction of cloud condensation nuclei activation and cloud droplet diffusional growth
Impact of wildfire smoke on Arctic cirrus formation – Part 2: Simulation of MOSAiC 2019–2020 cases
Constraining aerosol–cloud adjustments by uniting surface observations with a perturbed parameter ensemble
Investigating ice formation pathways using a novel two-moment multi-class cloud microphysics scheme
Exploiting airborne far-infrared measurements to optimise an ice cloud retrieval
Microphysics regimes due to haze–cloud interactions: cloud oscillation and cloud collapse
Microphysical fingerprints in anvil cloud albedo
Influence of Secondary Ice Production on cloud and rain properties: Analysis of the HYMEX IOP7a Heavy Precipitation Event
Factors Causing Stratocumulus to Deviate from Subtropical High Variability on Seasonal to Interannual Timescales
The influence of Amazonian anthropogenic emissions on new particle formation, aerosol, cloud and surface rain
Impact of secondary ice production on thunderstorm electrification under different aerosol conditions
Tropical cirrus evolution in a km-scale model with improved ice microphysics
Model analysis of biases in the satellite-diagnosed aerosol effect on the cloud liquid water path
Impacts of aerosol-radiation and aerosol-cloud interactions on a short-term heavy rainfall event – A case study in the Guanzhong Basin, China
Evaluation of biases in mid-to-high-latitude surface snowfall and cloud phase in ERA5 and CMIP6 using satellite observations
Dynamical imprints on precipitation cluster statistics across a hierarchy of high-resolution simulations
Ice formation processes key in determining WCB outflow cirrus properties
Role of a key microphysical factor in mixed-phase stratocumulus clouds and their interactions with aerosols
Investigating the impact of subgrid-scale aerosol-cloud interaction on mesoscale meteorology prediction
Different responses of cold-air outbreak clouds to aerosol and ice production depending on cloud temperature
Identifying Synoptic Controls on Boundary Layer Thermodynamic and Cloud Properties in a Regional Forecast Model
Correction of ERA5 temperature and relative humidity biases by bivariate quantile mapping for contrail formation analysis
Can pollen affect precipitation?
Potential impacts of marine fuel regulations on an Arctic stratocumulus case and its radiative response
The subtleties of three-dimensional radiative effects in contrails and cirrus clouds
The impact of the mesh size and microphysics scheme on the representation of mid-level clouds in the ICON model in hilly and complex terrain
The role of ascent timescales for warm conveyor belt (WCB) moisture transport into the upper troposphere and lower stratosphere (UTLS)
On the Processes Determining the Slope of Cloud-Water Adjustments in Non-Precipitating Stratocumulus
Analysis of raindrop size distribution from the double moment cloud microphysics scheme for monsoon over a tropical station
High sensitivity of simulated fog properties to parameterized aerosol activation in case studies from ParisFog
Adiabatic and radiative cooling are both important causes of aerosol activation in simulated fog events in Europe
Estimating the concentration of silver iodide needed to detect unambiguous signatures of glaciogenic cloud seeding
Ice-nucleating particle concentration impacts cloud properties over Dronning Maud Land, East Antarctica, in COSMO-CLM2
Numerical simulation of aerosol concentration effects on cloud droplet size spectrum evolutions of warm stratiform clouds in Jiangxi, China
The impact of aerosol on cloud water: a heuristic perspective
Andrew DeLaFrance, Lynn A. McMurdie, Angela K. Rowe, and Andrew J. Heymsfield
Atmos. Chem. Phys., 25, 8087–8106, https://doi.org/10.5194/acp-25-8087-2025, https://doi.org/10.5194/acp-25-8087-2025, 2025
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Numerical modeling simulations are used to investigate ice crystal growth and decay processes within a banded region of enhanced precipitation rates during a prominent winter storm. We identify robust primary ice growth in the upper portion of the cloud but decay exceeding 70 % during fallout through a subsaturated layer. The ice fall characteristics and decay rate are sensitive to the ambient cloud properties, which has implications for radar-based measurements and precipitation accumulations.
Annemarie Lottermoser and Simon Unterstrasser
Atmos. Chem. Phys., 25, 7903–7924, https://doi.org/10.5194/acp-25-7903-2025, https://doi.org/10.5194/acp-25-7903-2025, 2025
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Contrail cirrus significantly contributes to aviation's overall climate impact. As hydrogen combustion and fuel cell use are emerging technologies for aircraft propulsion, we simulated individual contrails from hydrogen propulsion during the first 6 min after exhaust emission, termed the vortex phase. The ice crystal loss during that stage is crucial, as the number of ice crystals has a large impact on the further evolution of contrails into contrail cirrus and their radiative forcing.
Meilian Chen, Xiaoqin Jing, Jiaojiao Li, Jing Yang, Xiaobo Dong, Bart Geerts, Yan Yin, Baojun Chen, Lulin Xue, Mengyu Huang, Ping Tian, and Shaofeng Hua
Atmos. Chem. Phys., 25, 7581–7596, https://doi.org/10.5194/acp-25-7581-2025, https://doi.org/10.5194/acp-25-7581-2025, 2025
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Several recent studies have reported complete cloud glaciation induced by airborne-based glaciogenic cloud seeding over plains. Since turbulence is an important factor to maintain clouds in a mixed phase, it is hypothesized that turbulence may have an impact on the seeding effect. This hypothesis is evident in the present study, which shows that turbulence can accelerate the impact of airborne glaciogenic seeding of stratiform clouds.
Guillaume Feger, Jean-Pierre Chaboureau, Thibaut Dauhut, Julien Delanoë, and Pierre Coutris
Atmos. Chem. Phys., 25, 7447–7465, https://doi.org/10.5194/acp-25-7447-2025, https://doi.org/10.5194/acp-25-7447-2025, 2025
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Saharan air at the trade wind layer, cold pools, and dry upper troposphere has these three main factors inhibiting the cyclogenesis of the Pierre Henri mesoscale convective system. The findings were obtained through observations made during two flights of the Clouds-Atmospheric Dynamics-Dust Interactions in West Africa (CADDIWA) campaign and a convection-permitting simulation run with the Meso-NH model. They provide new insights into the complex dynamics of cyclogenesis in the Cabo Verde region and challenge the existing model of the Saharan Air Layer (SAL).
Gabriella Wallentin, Annika Oertel, Luisa Ickes, Peggy Achtert, Matthias Tesche, and Corinna Hoose
Atmos. Chem. Phys., 25, 6607–6631, https://doi.org/10.5194/acp-25-6607-2025, https://doi.org/10.5194/acp-25-6607-2025, 2025
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Multilayer clouds are common in the Arctic but remain underrepresented. We use an atmospheric model to simulate multilayer cloud cases from the Arctic expedition MOSAiC 2019/2020. We find that it is complex to accurately model these cloud layers due to the lack of correct temperature profiles. The model also struggles to capture the observed cloud phase and the relative concentration of cloud droplets and cloud ice. We constrain our model to measured aerosols to mitigate this issue.
Sisi Chen, Lulin Xue, Sarah A. Tessendorf, Thomas Chubb, Andrew Peace, Suzanne Kenyon, Johanna Speirs, Jamie Wolff, and Bill Petzke
Atmos. Chem. Phys., 25, 6703–6724, https://doi.org/10.5194/acp-25-6703-2025, https://doi.org/10.5194/acp-25-6703-2025, 2025
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This study aims to investigate how cloud seeding affects snowfall in Australia's Snowy Mountains. By running simulations with different setups, we found that seeding impact varies greatly with weather conditions. Seeding increased snow in stable weather but sometimes reduced it in stormy weather. This helps us to better understand when seeding works best to boost water supplies.
Ann Kristin Naumann, Monika Esch, and Bjorn Stevens
Atmos. Chem. Phys., 25, 6429–6444, https://doi.org/10.5194/acp-25-6429-2025, https://doi.org/10.5194/acp-25-6429-2025, 2025
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This study explores how uncertainties in the representation of microphysical processes affect the tropical condensate distribution in the global storm-resolving model ICON. The results point to the importance of the fall speed of hydrometeor particles and to a simple relationship: the faster a condensate falls, the less there is of it. Implications for the energy balance and precipitation properties are discussed.
Yao-Sheng Chen, Prasanth Prabhakaran, Fabian Hoffmann, Jan Kazil, Takanobu Yamaguchi, and Graham Feingold
Atmos. Chem. Phys., 25, 6141–6159, https://doi.org/10.5194/acp-25-6141-2025, https://doi.org/10.5194/acp-25-6141-2025, 2025
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Injecting sea salt aerosols into marine stratiform clouds can distribute the cloud water over more droplets in smaller sizes. This process is expected to make the clouds brighter, allowing them to reflect more sunlight back to space. However, it may also cause the clouds to lose water over time, reducing their ability to reflect sunlight. We use a computer model to show that the loss of cloud water occurs relatively quickly and does not completely offset the initial brightening.
Pouriya Alinaghi, Fredrik Jansson, Daniel A. Blázquez, and Franziska Glassmeier
Atmos. Chem. Phys., 25, 6121–6139, https://doi.org/10.5194/acp-25-6121-2025, https://doi.org/10.5194/acp-25-6121-2025, 2025
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Shallow clouds in the trades are a major source of uncertainty in climate projections. These clouds organize into striking mesoscale patterns that are exactly what climate models lack. This study explores the origin of such patterns and investigates how variations in microscale properties control them. The importance of microscale effects is compared to that of large-scale forcing on the mesoscale organization of trade-cumulus fields.
Hsiang-He Lee, Xue Zheng, Shaoyue Qiu, and Yuan Wang
Atmos. Chem. Phys., 25, 6069–6091, https://doi.org/10.5194/acp-25-6069-2025, https://doi.org/10.5194/acp-25-6069-2025, 2025
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The study investigates how aerosol–cloud interactions affect warm boundary layer stratiform clouds over the eastern North Atlantic. High-resolution weather model simulations reveal that non-rain clouds at the edge of cloud systems are prone to evaporation, leading to an aerosol drying effect and a transition of aerosols back to the accumulation mode for future activation. The study shows that this dynamic behavior is often not adequately represented in most previous prescribed-aerosol simulations.
Patrick Peter, Sigrun Matthes, Christine Frömming, Patrick Jöckel, Luca Bugliaro, Andreas Giez, Martina Krämer, and Volker Grewe
Atmos. Chem. Phys., 25, 5911–5934, https://doi.org/10.5194/acp-25-5911-2025, https://doi.org/10.5194/acp-25-5911-2025, 2025
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Our study examines how well the global climate model EMAC (ECHAM/MESSy Atmospheric Chemistry) predicts contrail formation by analysing temperature and humidity – two key factors for contrail development and persistence. The model underestimates temperature, leading to an overprediction of contrail formation and larger ice-supersaturated regions. Adjusting the model improves temperature accuracy but adds uncertainties. Better predictions of contrail formation areas can help optimise flight tracks to reduce aviation's climate effect.
Konstantinos Kourtidis, Stavros Stathopoulos, and Vassilis Amiridis
Atmos. Chem. Phys., 25, 5935–5946, https://doi.org/10.5194/acp-25-5935-2025, https://doi.org/10.5194/acp-25-5935-2025, 2025
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The sound of thunder induces mechanical effects on cloud droplets and ice particles, causing changes in their size distribution. A shock wave near the lightning channel causes extensive shattering of cloud particles. At a distance, the audio wave will cause agglomeration of particles. So, thunder may influence the rain generation process and the radiative properties of clouds. As global warming may influence the occurrence rate of lightning, a climate feedback may be induced by these mechanisms.
Nathan H. Pope and Adele L. Igel
Atmos. Chem. Phys., 25, 5433–5444, https://doi.org/10.5194/acp-25-5433-2025, https://doi.org/10.5194/acp-25-5433-2025, 2025
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We used an atmospheric model that simulates a single column to study the sensitivity of marine fog formed through the lowering of the base of a stratus cloud to meteorology and aerosols. We found that higher aerosol concentration reduces the likelihood and duration of fog but leads to denser fog. This overall trend was caused by multiple physical mechanisms depending on conditions.
Jung-Sub Lim, Yign Noh, Hyunho Lee, and Fabian Hoffmann
Atmos. Chem. Phys., 25, 5313–5329, https://doi.org/10.5194/acp-25-5313-2025, https://doi.org/10.5194/acp-25-5313-2025, 2025
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Rain formation in warm clouds begins when small droplets collide, but this process can be slow without larger droplets. We used simulations to explore the role of bigger droplets, known as precipitation embryos, in triggering rain. We found that they speed up rain only when their size and number exceed a critical threshold. This threshold becomes larger when collisions are naturally efficient, such as in clouds with broad droplet size distributions or strong turbulence.
Je-Yun Chun, Robert Wood, Peter N. Blossey, and Sarah J. Doherty
Atmos. Chem. Phys., 25, 5251–5271, https://doi.org/10.5194/acp-25-5251-2025, https://doi.org/10.5194/acp-25-5251-2025, 2025
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This study explores how aerosols affect clouds transitioning from stratocumulus to cumulus along trade winds under varying atmospheric conditions. We found that aerosols typically reduce precipitation and raise cloud height, but their impact changes when subsidence changes by aerosol enhancement are considered. Our findings indicate that the cooling effect of aerosols might be overestimated if these atmospheric changes are not accounted for.
Wojciech W. Grabowski and Hanna Pawlowska
Atmos. Chem. Phys., 25, 5273–5285, https://doi.org/10.5194/acp-25-5273-2025, https://doi.org/10.5194/acp-25-5273-2025, 2025
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A simple diagram to depict cloud droplets' formation via the activation of cloud condensation nuclei (CCN) as well as their subsequent growth and evaporation is presented.
Albert Ansmann, Cristofer Jimenez, Daniel A. Knopf, Johanna Roschke, Johannes Bühl, Kevin Ohneiser, and Ronny Engelmann
Atmos. Chem. Phys., 25, 4867–4884, https://doi.org/10.5194/acp-25-4867-2025, https://doi.org/10.5194/acp-25-4867-2025, 2025
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In this study, we focus on the potential impact of wildfire smoke on cirrus formation. Aerosol and cirrus observations with lidar and radar during the MOSAiC (Multidisciplinary drifting Observatory for the Study of Arctic Climate) expedition, presented in the companion paper (Ansmann et al., 2025), are closely linked to comprehensive modeling of ice nucleation in cirrus evolution processes, presented in this article. A clear impact of wildfire smoke on cirrus formation was found.
August Mikkelsen, Daniel T. McCoy, Trude Eidhammer, Andrew Gettelman, Ci Song, Hamish Gordon, and Isabel L. McCoy
Atmos. Chem. Phys., 25, 4547–4570, https://doi.org/10.5194/acp-25-4547-2025, https://doi.org/10.5194/acp-25-4547-2025, 2025
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Whether increased aerosol increases or decreases liquid cloud mass has been a longstanding question. Observed correlations suggest that aerosols thin liquid cloud, but we are able to show that observations were consistent with an increase in liquid cloud in response to aerosols by leveraging a model where causality could be traced.
Tim Lüttmer, Peter Spichtinger, and Axel Seifert
Atmos. Chem. Phys., 25, 4505–4529, https://doi.org/10.5194/acp-25-4505-2025, https://doi.org/10.5194/acp-25-4505-2025, 2025
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We investigate ice formation pathways in idealized convective clouds using a novel microphysics scheme that distinguishes between five ice classes each with their own unique formation mechanism. Ice crystals from rime splintering form the lowermost layer of ice crystals around the updraft core. The majority of ice crystals in the anvil of the convective cloud stems from frozen droplets. Ice stemming from homogeneous and deposition nucleation was only relevant in the overshoot.
Sanjeevani Panditharatne, Helen Brindley, Caroline Cox, Rui Song, Richard Siddans, Richard Bantges, Jonathan Murray, Stuart Fox, and Cathryn Fox
EGUsphere, https://doi.org/10.5194/egusphere-2025-647, https://doi.org/10.5194/egusphere-2025-647, 2025
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Upwelling radiation with wavelengths between 15 and 100 microns is theorised to be highly sensitive to the properties of ice clouds, particularly the shape of the ice crystals. We exploit this sensitivity and perform the first retrieval of ice cloud properties using these wavelengths from an observation taken on an aircraft and evaluate it against measurements of the cloud’s properties.
Fan Yang, Hamed Fahandezh Sadi, Raymond A. Shaw, Fabian Hoffmann, Pei Hou, Aaron Wang, and Mikhail Ovchinnikov
Atmos. Chem. Phys., 25, 3785–3806, https://doi.org/10.5194/acp-25-3785-2025, https://doi.org/10.5194/acp-25-3785-2025, 2025
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Large-eddy simulations of a convection cloud chamber show two new microphysics regimes, cloud oscillation and cloud collapse, due to haze–cloud interactions. Our results suggest that haze particles and their interactions with cloud droplets should be considered especially in polluted conditions. To properly simulate haze–cloud interactions, we need to resolve droplet activation and deactivation processes, instead of using Twomey-type activation parameterization.
Declan L. Finney, Alan M. Blyth, Paul R. Field, Martin I. Daily, Benjamin J. Murray, Mengyu Sun, Paul J. Connolly, Zhiqiang Cui, and Steven Böing
EGUsphere, https://doi.org/10.5194/egusphere-2025-1227, https://doi.org/10.5194/egusphere-2025-1227, 2025
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We present observation-informed modelling from the Deep Convective Microphysics Experiment to study how environmental conditions and cloud processes affect anvil cloud albedo and radiation. Aerosols influencing cloud droplets or influencing ice formation yield varying radiative effects. We introduce fingerprint metrics to discern these effects. Using detailed observations and modelling, we offer insights into high cloud radiative effects and feedbacks.
Pierre Grzegorczyk, Wolfram Wobrock, Aymeric Dziduch, and Céline Planche
EGUsphere, https://doi.org/10.5194/egusphere-2025-819, https://doi.org/10.5194/egusphere-2025-819, 2025
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The impact of secondary ice production (SIP) on a HYMEX intense precipitation event is investigated using 3D bin microphysics. Including SIP improves agreement with in situ aircraft observations (ice crystal number concentration and supercooled drop number fraction), generates small ice crystals and redistributes condensed water mass toward smaller particle sizes. As these crystals melt, the liquid precipitation flux decreases, reducing total precipitation by 8 % and heavy rainfall by 20 %.
Hairu Ding, Bjorn Stevens, and Hauke Schmidt
EGUsphere, https://doi.org/10.5194/egusphere-2025-876, https://doi.org/10.5194/egusphere-2025-876, 2025
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This study examines the physical link between subtropical highs and stratocumulus variability. Using reanalysis data, we test two proposed pathways—one at the surface and one in the free troposphere—but find that neither is a dominant mechanism for stratocumulus variability on seasonal and interannual timescales. These results challenge the assumed influence of subtropical highs on stratocumulus and highlight the need for further research into lower tropospheric stability dynamics.
Xuemei Wang, Kenneth S. Carslaw, Daniel P. Grosvenor, and Hamish Gordon
EGUsphere, https://doi.org/10.5194/egusphere-2025-132, https://doi.org/10.5194/egusphere-2025-132, 2025
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Anthropogenic emissions can influence aerosol particle number concentrations via new particle formation. Our model simulations predict around 10 % increase of the particle and cloud droplet number concentrations when doubling the emissions in the Manaus region in the Amazonian wet season. However, the corresponding changes in cloud water and rain mass are around 4 %. Such weak response implied that this convective environment is not sensitive to the localised anthropogenic emission changes here.
Shiye Huang, Jing Yang, Jiaojiao Li, Qian Chen, Qilin Zhang, and Fengxia Guo
Atmos. Chem. Phys., 25, 1831–1850, https://doi.org/10.5194/acp-25-1831-2025, https://doi.org/10.5194/acp-25-1831-2025, 2025
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Aerosol and secondary ice production are both vital to charge separation in thunderstorms, but the relative importance of different SIP processes to cloud electrification under different aerosol conditions is not well understood. In this study, we show in a clean environment, the shattering of freezing drops has the greatest effect on the charging rate, while in a polluted environment, both rime splintering and the shattering of freezing drops have a significant effect on cloud electrification.
Blaž Gasparini, Rachel Atlas, Aiko Voigt, Martina Krämer, and Peter N. Blossey
EGUsphere, https://doi.org/10.5194/egusphere-2025-203, https://doi.org/10.5194/egusphere-2025-203, 2025
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Tropical cirrus clouds, especially their evolution, are poorly understood, contributing to uncertainty in climate projections. We address this by using novel tracers in a cloud-resolving model to track the life cycle of cirrus clouds, providing insights into cloud formation, ice crystal evolution, and radiative effects. We also improve the model's cloud microphysics with a simple, computationally efficient approach that can be applied to other models.
Harri Kokkola, Juha Tonttila, Silvia M. Calderón, Sami Romakkaniemi, Antti Lipponen, Aapo Peräkorpi, Tero Mielonen, Edward Gryspeerdt, Timo Henrik Virtanen, Pekka Kolmonen, and Antti Arola
Atmos. Chem. Phys., 25, 1533–1543, https://doi.org/10.5194/acp-25-1533-2025, https://doi.org/10.5194/acp-25-1533-2025, 2025
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Understanding how atmospheric aerosols affect clouds is a scientific challenge. One question is how aerosols affects the amount of cloud water. We used a cloud-scale model to study these effects on marine clouds. The study showed that variations in cloud properties and instrument noise can cause bias in satellite-derived cloud water content. However, our results suggest that for similar weather conditions with well-defined aerosol concentrations, satellite data can reliably track these effects.
Naifang Bei, Bo Xiao, Ruonan Wang, Yuning Yang, Lang Liu, Yongming Han, and Guohui Li
EGUsphere, https://doi.org/10.5194/egusphere-2024-3558, https://doi.org/10.5194/egusphere-2024-3558, 2025
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This study uses a cloud-resolving model to examine how aerosols influence a mesoscale convective system (MCS) in central China via aerosol-radiation (ARIs) and aerosol-cloud interactions (ACIs). Without ARIs, added aerosols don’t significantly affect precipitation due to cloud competition for moisture. ARIs can stabilize or enhance convection. High aerosol levels lead to a combined ARI and ACI effect that greatly reduces precipitation.
Franziska Hellmuth, Tim Carlsen, Anne Sophie Daloz, Robert Oscar David, Haochi Che, and Trude Storelvmo
Atmos. Chem. Phys., 25, 1353–1383, https://doi.org/10.5194/acp-25-1353-2025, https://doi.org/10.5194/acp-25-1353-2025, 2025
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This article compares the occurrence of supercooled liquid-containing clouds (sLCCs) and their link to surface snowfall in CloudSat–CALIPSO, ERA5, and the CMIP6 models. Significant discrepancies were found, with ERA5 and CMIP6 consistently overestimating sLCC and snowfall frequency. This bias is likely due to cloud microphysics parameterization. This conclusion has implications for accurately representing cloud phase and snowfall in future climate projections.
Claudia Christine Stephan and Bjorn Stevens
Atmos. Chem. Phys., 25, 1209–1226, https://doi.org/10.5194/acp-25-1209-2025, https://doi.org/10.5194/acp-25-1209-2025, 2025
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Tropical precipitation cluster area and intensity distributions follow power laws, but the physical processes responsible for this behavior remain unknown. We analyze global simulations that realistically represent precipitation processes. We consider Earth-like planets as well as virtual planets to realize different types of large-scale dynamics. Our finding is that power laws in Earth’s precipitation cluster statistics stem from the robust power laws in Earth’s atmospheric wind field.
Tim Lüttmer, Annette Miltenberger, and Peter Spichtinger
EGUsphere, https://doi.org/10.5194/egusphere-2025-185, https://doi.org/10.5194/egusphere-2025-185, 2025
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We investigate ice formation pathways in a warm conveyor belt case study. We employ a multi-phase microphysics scheme that distinguishes between ice from different nucleation processes. Ice crystals in the cirrus outflow mostly stem from in-situ formation. Hence they were formed directly from the vapor phase. Sedimentational redistribution modulates cirrus properties and leads to a disagreement between cirrus origin classifications based on thermodynamic history and nucleation processes.
Seoung Soo Lee, Chang Hoon Jung, Jinho Choi, Young Jun Yoon, Junshik Um, Youtong Zheng, Jianping Guo, Manguttathil G. Manoj, Sang-Keun Song, and Kyung-Ja Ha
Atmos. Chem. Phys., 25, 705–726, https://doi.org/10.5194/acp-25-705-2025, https://doi.org/10.5194/acp-25-705-2025, 2025
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This study attempts to test a general factor that explains differences in the properties of different mixed-phase clouds using a modeling tool. Although this attempt is not to identify a factor that can perfectly explain and represent the properties of different mixed-phase clouds, we believe that this attempt acts as a valuable stepping stone towards a more complete, general way of using climate models to better predict climate change.
Wenjie Zhang, Hong Wang, Xiaoye Zhang, Yue Peng, Zhaodong Liu, Deying Wang, Da Zhang, Chen Han, Yang Zhao, Junting Zhong, Wenxing Jia, Huiqiong Ning, and Huizheng Che
EGUsphere, https://doi.org/10.5194/egusphere-2024-3677, https://doi.org/10.5194/egusphere-2024-3677, 2025
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We implement a real-time subgrid-scale aerosol-cloud interaction (ACI) mechanism in a mesoscale atmospheric chemistry system and find that subgrid-scale ACI can improve meteorological factors predictions. This study demonstrates the importance of real-time subgrid-scale ACI to weather forecast and the necessity of multiscale ACI studies.
Xinyi Huang, Paul R. Field, Benjamin J. Murray, Daniel P. Grosvenor, Floortje van den Heuvel, and Kenneth S. Carslaw
EGUsphere, https://doi.org/10.5194/egusphere-2024-4070, https://doi.org/10.5194/egusphere-2024-4070, 2025
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Cold-air outbreak (CAO) clouds play a vital role in climate prediction. This study explores the responses of CAO clouds to aerosols and ice production under different environmental conditions. We found that CAO cloud responses vary with cloud temperature and are strongly controlled by the liquid-ice partitioning in these clouds, suggesting the importance of good representations of cloud microphysics properties to predict the behaviours of CAO clouds in a warming climate.
Jordan Eissner, David Mechem, Yi Jin, Virendra Ghate, and James Booth
EGUsphere, https://doi.org/10.5194/egusphere-2024-3438, https://doi.org/10.5194/egusphere-2024-3438, 2025
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Low-level clouds have important radiative feedbacks and can occur in a range of meteorological conditions, yet our knowledge and prediction of them are insufficient. We evaluate model forecasts of low-level cloud properties across a cold front and the associated environments that they form in. The model represents the meteorological conditions well and produces broken clouds behind the cold front in areas of strong surface forcing, large stability, and large-scale subsiding motion.
Kevin Wolf, Nicolas Bellouin, Olivier Boucher, Susanne Rohs, and Yun Li
Atmos. Chem. Phys., 25, 157–181, https://doi.org/10.5194/acp-25-157-2025, https://doi.org/10.5194/acp-25-157-2025, 2025
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ERA5 atmospheric reanalysis and airborne in situ observations from IAGOS are compared in terms of the representation of the contrail formation potential and the presence of supersaturation. Differences are traced back to biases in ERA5 relative humidity fields. Those biases are addressed by applying a quantile mapping technique that significantly improved contrail estimation based on post-processed ERA5 data.
Marje Prank, Juha Tonttila, Xiaoxia Shang, Sami Romakkaniemi, and Tomi Raatikainen
Atmos. Chem. Phys., 25, 183–197, https://doi.org/10.5194/acp-25-183-2025, https://doi.org/10.5194/acp-25-183-2025, 2025
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Large primary bioparticles such as pollen can be abundant in the atmosphere. In humid conditions pollen can rupture and release a large number of fine sub-pollen particles (SPPs). The paper investigates what kind of birch pollen concentrations are needed for the pollen and SPPs to start playing a noticeable role in cloud processes and alter precipitation formation. In the studied cases only the largest observed pollen concentrations were able to noticeably alter the precipitation formation.
Luís Filipe Escusa dos Santos, Hannah C. Frostenberg, Alejandro Baró Pérez, Annica M. L. Ekman, Luisa Ickes, and Erik S. Thomson
Atmos. Chem. Phys., 25, 119–142, https://doi.org/10.5194/acp-25-119-2025, https://doi.org/10.5194/acp-25-119-2025, 2025
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The Arctic is experiencing enhanced surface warming. The observed decline in Arctic sea-ice extent is projected to lead to an increase in Arctic shipping activity, which may lead to further climatic feedbacks. Using an atmospheric model and results from marine engine experiments that focused on fuel sulfur content reduction and exhaust wet scrubbing, we investigate how ship exhaust particles influence the properties of Arctic clouds. Implications for radiative surface processes are discussed.
Julie Carles, Nicolas Bellouin, Najda Villefranque, and Jean-Louis Dufresne
EGUsphere, https://doi.org/10.5194/egusphere-2024-3642, https://doi.org/10.5194/egusphere-2024-3642, 2025
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Cirrus and contrails affect Earth’s energy balance with a lot of remaining uncertainty. The balance between solar and terrestrial radiation is delicate to calculate, and factors as cloud optical depth, shape, Sun position are crucial to estimate the effect of those clouds on radiation. Also, often neglected three dimensional paths of radiation, or 3D effects, may be important to account for at climatic scale.
Nadja Omanovic, Brigitta Goger, and Ulrike Lohmann
Atmos. Chem. Phys., 24, 14145–14175, https://doi.org/10.5194/acp-24-14145-2024, https://doi.org/10.5194/acp-24-14145-2024, 2024
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We evaluated the numerical weather model ICON in two horizontal resolutions with two bulk microphysics schemes over hilly and complex terrain in Switzerland and Austria, respectively. We focused on the model's ability to simulate mid-level clouds in summer and winter. By combining observational data from two different field campaigns, we show that an increase in the horizontal resolution and a more advanced cloud microphysics scheme is strongly beneficial for cloud representation.
Cornelis Schwenk and Annette Miltenberger
Atmos. Chem. Phys., 24, 14073–14099, https://doi.org/10.5194/acp-24-14073-2024, https://doi.org/10.5194/acp-24-14073-2024, 2024
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Warm conveyor belts (WCBs) transport moisture into the upper atmosphere, where it acts as a greenhouse gas. This transport is not well understood, and the role of rapidly rising air is unclear. We simulate a WCB and look at fast- and slow-rising air to see how moisture is (differently) transported. We find that for fast-ascending air more ice particles reach higher into the atmosphere and that frozen cloud particles are removed differently than during slow ascent, which has more water vapour.
Fabian Hoffmann, Yao-Sheng Chen, and Graham Feingold
EGUsphere, https://doi.org/10.5194/egusphere-2024-3893, https://doi.org/10.5194/egusphere-2024-3893, 2024
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Clouds reflect a substantial portion of the incoming solar radiation back into space. This capacity is determined by the number of cloud droplets, which in turn is influenced by the number of aerosol particles, forming the basis for aerosol-cloud-climate interactions. In this study, we use a simple mixed-layer approach to understand the effect of aerosol on cloud water in non-precipitating stratocumulus.
Kadavathu Sreekumar Apsara, Jayakumar Aravindakshan, Anurose Theethai Jacob, Saji Mohandas, Paul Field, Hamish Gordan, Thara Prabhakaran, Mahen Konwar, and Vijapurap Srinivasa Prasad
EGUsphere, https://doi.org/10.5194/egusphere-2024-3538, https://doi.org/10.5194/egusphere-2024-3538, 2024
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Science has made significant strides in weather prediction, especially for intense tropical rainfall that can lead to floods and landslides. Our study aims to improve monsoon rainfall forecasts by analyzing raindrop sizes. Using a new approach to model raindrop growth, we achieved a more accurate depiction of large rainfall events. These improvements can be generalized to enhance early warning systems, offering reliable predictions that help reduce risks from severe tropical weather events.
Pratapaditya Ghosh, Ian Boutle, Paul Field, Adrian Hill, Anthony Jones, Marie Mazoyer, Katherine J. Evans, Salil Mahajan, Hyun-Gyu Kang, Min Xu, Wei Zhang, Noah Asch, and Hamish Gordon
EGUsphere, https://doi.org/10.5194/egusphere-2024-3376, https://doi.org/10.5194/egusphere-2024-3376, 2024
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We study aerosol-fog interactions near Paris using a weather and climate model with high spatial resolution. We show that our model can simulate fog lifecycle effectively. We find that the fog droplet number concentrations, the amount of liquid water in the fog, and the vertical structure of the fog are highly sensitive to the parameterization that simulates droplet formation and growth. The changes we propose could improve fog forecasts significantly without increasing computational costs.
Pratapaditya Ghosh, Ian Boutle, Paul Field, Adrian Hill, Marie Mazoyer, Katherine J. Evans, Salil Mahajan, Hyun-Gyu Kang, Min Xu, Wei Zhang, and Hamish Gordon
EGUsphere, https://doi.org/10.5194/egusphere-2024-3397, https://doi.org/10.5194/egusphere-2024-3397, 2024
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We study the lifecycle of fog events in Europe using a weather and climate model. By incorporating droplet formation and growth driven by radiative cooling, our model better simulates the total liquid water in foggy atmospheric columns. We show that both adiabatic and radiative cooling play significant, often equally important roles in driving droplet formation and growth. We discuss strategies to address droplet number overpredictions, by improving model physics and addressing model artifacts.
Jing Yang, Jiaojiao Li, Meilian Chen, Xiaoqin Jing, Yan Yin, Bart Geerts, Zhien Wang, Yubao Liu, Baojun Chen, Shaofeng Hua, Hao Hu, Xiaobo Dong, Ping Tian, Qian Chen, and Yang Gao
Atmos. Chem. Phys., 24, 13833–13848, https://doi.org/10.5194/acp-24-13833-2024, https://doi.org/10.5194/acp-24-13833-2024, 2024
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Detecting unambiguous signatures is vital for examining cloud-seeding impacts, but often, seeding signatures are immersed in natural variability. In this study, reflectivity changes induced by glaciogenic seeding using different AgI concentrations are investigated under various conditions, and a method is developed to estimate the AgI concentration needed to detect unambiguous seeding signatures. The results aid in operational seeding-based decision-making regarding the amount of AgI dispersed.
Florian Sauerland, Niels Souverijns, Anna Possner, Heike Wex, Preben Van Overmeiren, Alexander Mangold, Kwinten Van Weverberg, and Nicole van Lipzig
Atmos. Chem. Phys., 24, 13751–13768, https://doi.org/10.5194/acp-24-13751-2024, https://doi.org/10.5194/acp-24-13751-2024, 2024
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We use a regional climate model, COSMO-CLM², enhanced with a module resolving aerosol processes, to study Antarctic clouds. We prescribe different concentrations of ice-nucleating particles to our model to assess how these clouds respond to concentration changes, validating results with cloud and aerosol observations from the Princess Elisabeth Antarctica station. Our results show that aerosol–cloud interactions vary with temperature, providing valuable insights into Antarctic cloud dynamics.
Yi Li, Xiaoli Liu, and Hengjia Cai
Atmos. Chem. Phys., 24, 13525–13540, https://doi.org/10.5194/acp-24-13525-2024, https://doi.org/10.5194/acp-24-13525-2024, 2024
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The influence of different aerosol modes on cloud processes remains controversial. We modified the aerosol spectra and concentrations to simulate a warm stratiform cloud process in Jiangxi, China, using the WRF-SBM scheme. Research shows that different aerosol spectra have diverse effects on cloud droplet spectra, cloud development, and the correlation between dispersion (ε) and cloud physics quantities. Compared to cloud droplet concentration, ε is more sensitive to the volume radius.
Fabian Hoffmann, Franziska Glassmeier, and Graham Feingold
Atmos. Chem. Phys., 24, 13403–13412, https://doi.org/10.5194/acp-24-13403-2024, https://doi.org/10.5194/acp-24-13403-2024, 2024
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Clouds constitute a major cooling influence on Earth's climate system by reflecting a large fraction of the incident solar radiation back to space. This ability is controlled by the number of cloud droplets, which is governed by the number of aerosol particles in the atmosphere, laying the foundation for so-called aerosol–cloud–climate interactions. In this study, a simple model to understand the effect of aerosol on cloud water is developed and applied.
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Short summary
There is considerable disagreement on mathematical parameters that describe the number of clouds of different sizes as well as the size of the largest clouds. Both are key defining characteristics of Earth's atmosphere. A previous study provided an incorrect explanation for the disagreement. Instead, the disagreement may be explained by prior studies not properly accounting for the size of their measurement domain. We offer recommendations for how the domain size can be accounted for.
There is considerable disagreement on mathematical parameters that describe the number of...
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