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All sourcesNASA NTRSDOE OSTI
NASA NTRS2024

Cloud Top Phase Characterization of Extratropical Cyclones over the Northeast and Midwest United States: Results from IMPACTS

Cloud top phase (CTP) impacts cloud albedo and pathways for ice particle nucleation, growth, and fallout within extratropical cyclones. This study uses airborne lidar, radar, and Rapid Refresh analysis data to characterize CTP within extratropical cyclones as a function of cloud top temperature (CTT). During the 2020, 2022, and 2023 Investigation of Microphysics and Precipitation for Atlantic Coast-Threatening Snowstorms (IMPACTS) field campaign deployments, the Earth-Resources 2 (ER-2) aircraft flew 26 research flights over the Northeast and Midwest U.S. to sample the cloud tops of a variety of extratropical cyclones. A training dataset was developed to create probabilistic phase classifications based on Cloud Physics Lidar measurements of known ice and liquid clouds. These classifications were then used to quantify dominant CTP in the top 150 m of clouds sampled by the Cloud Physics Lidar in storms during IMPACTS. Case studies are presented illustrating examples of supercooled liquid water at cloud top at different CTT ranges (-3°C -20°C. Liquid-bearing cloud tops were found at CTTs as cold as -37ºC.

Troy J. Zaremba↗
NASA NTRS2008

Integration of Satellite-Derived Cloud Phase, Cloud Top Height, and Liquid Water Path into an Operational Aircraft Icing Nowcasting System

Operational products used by the U.S. Federal Aviation Administration to alert pilots of hazardous icing provide nowcast and short-term forecast estimates of the potential for the presence of supercooled liquid water and supercooled large droplets. The Current Icing Product (CIP) system employs basic satellite-derived information, including a cloud mask and cloud top temperature estimates, together with multiple other data sources to produce a gridded, three-dimensional, hourly depiction of icing probability and severity. Advanced satellite-derived cloud products developed at the NASA Langley Research Center (LaRC) provide a more detailed description of cloud properties (primarily at cloud top) compared to the basic satellite-derived information used currently in CIP. Cloud hydrometeor phase, liquid water path, cloud effective temperature, and cloud top height as estimated by the LaRC algorithms are into the CIP fuzzy logic scheme and a confidence value is determined. Examples of CIP products before and after the integration of the LaRC satellite-derived products will be presented at the conference.

Haggerty, Julie↗
NASA NTRS1983

The structure and phase of cloud tops as observed by polarization lidar

High-resolution observations of the structure of cloud tops have been obtained with polarization lidar operated from a high altitude aircraft. Case studies of measurements acquired from cumuliform cloud systems are presented, two from September 1979 observations in the area of Florida and adjacent waters and a third during the May 1981 CCOPE experiment in southeast Montana. Accurate cloud top height structure and relative density of hydrometers are obtained from the lidar return signal intensity. Correlation between the signal return intensity and active updrafts was noted. Thin cirrus overlying developing turrets was observed in some cases. Typical values of the observed backscatter cross section were 0.1-5 (km/sr) for cumulonimbus tops. The depolarization ratio of the lidar signals was a function of the thermodynamic phase of cloud top areas. An increase of the cloud top depolarization with decreasing temperature was found for temperatures above and below -40 C.

Spinhirne, J. D.↗
NASA NTRS1981

Multichannel scanning radiometer for remote sensing cloud physical parameters

A multichannel scanning radiometer developed for remote observation of cloud physical properties is described. Consisting of six channels in the near infrared and one channel in the thermal infrared, the instrument can observe cloud physical parameters such as optical thickness, thermodynamic phase, cloud top altitude, and cloud top temperature. Measurement accuracy is quantified through flight tests on the NASA CV-990 and the NASA WB-57F, and is found to be limited by the harsh environment of the aircraft at flight altitude. The electronics, data system, and calibration of the instrument are also discussed.

Curran, R. J.↗
NASA NTRS2011

EPIC Radiance Simulator for Deep Space Climate ObserVatoRy (DSCOVR)

The Deep Space Climate ObserVatoRy (DSCOVR) is a planned space weather mission for the Sun and Earth observations from the Lagrangian L1 point. Onboard of DSCOVR is a multispectral imager EPIC designed for unique observations of the full illuminated disk of the Earth with high temporal and 10 km spatial resolution. Depending on latitude, EPIC will observe the same Earth surface area during the course of the day in a wide range of solar and view zenith angles in the backscattering view geometry with the scattering angle of 164-172 . To understand the information content of EPIC data for analysis of the Earth clouds, aerosols and surface properties, an EPIC radiance Simulator was developed covering the UV -VIS-NIR range including the oxygen A and B-bands (A=340, 388, 443, 555, 680, 779.5, 687.7, 763.3 nm). The Simulator uses ancillary data (surface pressure/height, NCEP wind speed) as well as MODIS-based geophysical fields such as spectral surface bidirectional reflectance, column water vapor, and properties of aerosols and clouds including optical depth, effective radius, phase and cloud top height. The original simulations are conducted at 1 km resolution using the look-up table approach and then are averaged to 10 km EPIC radiances. This talk will give an overview of the EPIC Simulator with analysis of results over the continental USA and northern Atlantic.

Lyapustin, Alexei↗
NASA NTRS2026

Satellite Optical Remote Sensing of Clouds and Aerosols: From Particle Single-Scattering and Gaseous Absorption Through Radiative Transfer to Retrieval Products

Clouds and aerosols are fundamental regulators of Earth’s radiation budget and climate system, influencing both solar and terrestrial radiation through scattering, absorption, and emission processes. Accurate characterization of their physical and radiative properties from space requires a rigorous understanding of particle single-scattering, gaseous absorption, and radiative transfer in the atmosphere, as well as reliable inversion methods. This review synthesizes the physical foundations and algorithmic implementations of satellite-based passive optical remote sensing of clouds and aerosols, spanning the ultraviolet to thermal infrared spectral range. Beginning with electromagnetic scattering theory and state-of-the-art methods for computing single-scattering by nonspherical particles and computationally efficient methods for accounting for atmospheric absorption, we discuss the radiative transfer framework underpinning cloud and aerosol retrievals. The connection between single-scattering and multiple-scattering is rigorously formulated. We then summarize operational and research-grade retrieval techniques, including cloud masking and thermodynamic phase determination, CO₂ slicing for cloud-top pressure, the Nakajima-King shortwave bi-spectral, and infrared split-window approaches for cloud optical thickness and effective particle size, inversion algorithms for determining aerosol properties from multi-spectral and/or multi-angle radiometric and polarimetric measurements, and active-passive sensing synergy. Examples of the global cloud and aerosol climatologies are illustrated using observations from the Moderate Resolution Imaging Spectroradiometer (MODIS) and the Multi-angle Imaging SpectroRadiometer (MISR). Furthermore, the unique strengths of active remote sensing techniques based on spaceborne lidar observations are briefly elaborated in the context of studying ice clouds composed of randomly and horizontally oriented ice crystals, which is a significant challenge for conventional passive remote sensing techniques. By connecting physical theory to practical retrievals, this review highlights both the maturity of current methodologies and the remaining challenges in reducing uncertainties in particle morphology, vertical structure, absorption, and aerosol-cloud interactions. Furthermore, the impact of artificial intelligence (AI) on atmospheric remote sensing is briefly addressed.

Aerosols↗
NASA NTRS2001

TRMM Precipitation Radar and Microwave Imager Observations of Convective and Stratiform Rain and Their Theoretical Implications

Theoretical models of radiative transfer are developed to simulate the 85 GHz brightness temperature, T85, observed by the Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI) radiometer as a function of rain rate. These simulations are performed separately over regions of convective and stratiform rain. For the purpose of constructing vertical profiles of hydrometeors in these regions, guidance is taken from TRMM Precipitation Radar (PR) observations, and from recent investigations of LDR and Z(sub DR) measurements made by land-based polarimetric radars. We find that for a given rain rate, the extinction in 85 GHz due to hydrometeors above the freezing level is relatively weak in convective regions compared to that in stratiform regions. The hydrometeor profile above the freezing level responsible for this weak extinction in convective regions is inferred, from LDR and Z(sub DR) observations and theoretical considerations, to contain two layers: 1) a layer of two km thickness with mixed phase particles, liquid drops and graupel, directly above the freezing level, and 2) a layer of graupel extending from the top of the mixed-phase layer to the cloud top. Strong extinction in the stratiform regions is inferred to result from slowly-falling, low-density ice aggregates (snow) above the freezing level. These theoretical results are consistent with T85 measured by TMI and the rain rate deduced from PR for convective and stratiform rain regions. On the basis of this study we infer that the accuracy of the rain rate sensed by TMI depends critically on the specification of the convective or stratiform nature of the rain.

Prabhakara, C.↗
NASA NTRS1992

Longwave radiation budget parameters computed from ISCCP and HIRS2/MSU products

The International Satellite Cloud Climatology Project (ISCCP) retrieved cloud fields and the high-resolution radiation sounder 2 (HIRS2) retrieved cloud fields yield similar outgoing longwave radiation (OLR) due to the cancelation effect of cloud-top altitudes and cloud amount on OLR. For the large regional discrepancies of the order of 30 W/sq m found over northern Africa are largely due to surface temperature differences, and extensive discrepancies over the ocean are due to humidity differences. Harmonic analysis is applied to OLR, clear-sky OLR, and cloud-radiative forcing at the top of the atmosphere using the ISCCP products. The diurnal variations of these parameters from 60 deg S to 60 deg N are larger over land than over the ocean. The clear-sky OLR peaks around 1500 LST, usually over land areas, and is associated with the surface/air temperature maximum. The OLR over cloudy regions shows a similar diurnal phase as the cloud top pressure. The cloud radiative forcing at the top of the atmosphere has maximum value near 2100 LST mountain areas and near 0000 and 0300 LST over equatorial regions. The ISCCP-computed longwave cloud radiative forcing has smaller diurnal variations over the ocean than the HIRS2-computed longwave cloud radiative forcing. The global mean bias of OLR is around 0.74 W/sq m, and locally, the bias can be as large as 5 to 10 W/sq m. This appears to indicate that the twice-a-day measurements of the HIRS2/MSU (around 0315 and 1515 LST, which are the equatorial cross times at nadir track) can be used to derive monthly mean OLR without significant bias.

Wu, Man L. C.↗
NASA NTRS1985

Quality of remote sensing measurements of cloud physical parameters in the cooperative convective precipitation experiment

In order to develop the remote sensing techniques to infer cloud physical parameters, a multispectral cloud radiometer (MCR) was mounted on a NASA high-altitude aircraft in conjunction with the Cooperative Convective Precipitation Experiment in 1981. The MCR has seven spectral channels, of which three are centered near windows associated with water vapor bands in the near infrared, two are centered near the oxygen A band at 0.76 microns, one is centered at the 1.14-micron water vapor band, and one is centered in the thermal infrared. The reflectance and temperature measured on May 31, 1981, are presented together with theoretical calculations. The results indicate that the MCR produces quality measurements. Therefore several cloud parameters can be derived with good accuracy. The parameters are the cloud-scaled optical thickness, cloud top pressure, volume scattering coefficient, particle thermodynamic phase, effective mean particle size, and cloud-top temperature.

Wu, M.-L.↗
NASA NTRS2006

Introduction to MODIS Cloud Products

The Earth's radiative energy balance and hydrological cycle are fundamentally coupled with the distribution and properties of clouds. Therefore, the ability to remotely infer cloud properties and their variation in space and time is crucial for establishing climatologies as a reference for validation of present-day climate models and in assessing future climate change. Remote cloud observations also provide data sets useful for testing and improving cloud model physics, and for assimilation into numerical weather prediction models. The MODerate Resolution Imaging Spectroradiometer (MODIS) imagers on the Terra and Aqua Earth Observing System (EOS) platforms provide the capability for globally retrieving these properties using passive solar reflectance and infrared techniques. In addition to providing measurements similar to those offered on a suite of historical operational weather platforms such as the Advanced Very High Resolution Radiometer (AVHRR), the High-resolution Infrared Radiation Sounder (HIRS), and the Geostationary Operational Environmental Satellite (GOES), MODIS provides additional spectral and/or spatial resolution in key atmospheric bands, along with on-board calibration, to expand the capability for global cloud property retrievals. The core MODIS operational cloud products include cloud top pressure, thermodynamic phase, optical thickness, particle size, and water path, and are derived globally at spatial resolutions of either 1- or 5-km (referred to as Level-2 or pixel-level products). In addition, the MODIS atmosphere team (collectively providing cloud, aerosol, and clear sky products) produces a combined gridded product (referred to as Level-3) aggregated to a 1 equal-angle grid, available for daily, eight-day, and monthly time periods. The wealth of information available from these products provides critical information for climate studies as well as the continuation and improved understanding of existing satellite-based cloud climatologies derived from heritage instruments. This chapter provides an overview of the MODIS Level-2 and -3 operational cloud products.

Baum, Bryan A.↗
NASA NTRS2010

Characteristics of Precipitation, Cloud, and Latent Heating Associated with the Madden-Julian Oscillation

This study investigates the evolution of cloud and rainfall structures associated with Madden Julian oscillation (MJO) using Tropical Rainfall Measuring Mission (TRMM) data. Two complementary indices are used to define MJO phases. Joint probability distribution functions (PDFs) of cloud-top temperature and radar echo-top height are constructed for each of the eight MJO phases. The genesis stage of MJO convection over the western Pacific (phases 1 and 2) features a bottom-heavy PDF, characterized by abundant warm rain, low clouds, suppressed deep convection, and higher sea surface temperature (SST). As MJO convection develops (phases 3 and 4), a transition from the bottom-heavy to top-heavy PDF occurs. The latter is associated with the development of mixed-phase rain and middle-to-high clouds, coupled with rapid SST cooling. At the MJO convection peak (phase 5), a top-heavy PDF contributed by deep convection with mixed-phase and ice-phase rain and high echo-top heights (greater than 5 km) dominates. The decaying stage (phases 6 and 7) is characterized by suppressed SST, reduced total rain, increased contribution from stratiform rain, and increased nonraining high clouds. Phase 7, in particular, signals the beginning of a return to higher SST and increased warm rain. Phase 8 completes the MJO cycle, returning to a bottom-heavy PDF and SST conditions similar to phase 1. The structural changes in rain and clouds at different phases of MJO are consistent with corresponding changes in derived latent heating profiles, suggesting the importance of a diverse mix of warm, mixed-phase, and ice-phase rain associated with low-level, congestus, and high clouds in constituting the life cycle and the time scales of MJO.

Lau, K-M.↗
NASA NTRSDate not supplied

CERES Single Scanner Satellite Footprint, TOA, Surface Fluxes and Clouds (SSF) data in HDF (CER_SSF_Aqua-FM4-MODIS_Edition1B)

The Single Scanner Footprint TOA/Surface Fluxes and Clouds (SSF) product contains one hour of instantaneous Clouds and the Earth's Radiant Energy System (CERES) data for a single scanner instrument. The SSF combines instantaneous CERES data with scene information from a higher-resolution imager such as Visible/Infrared Scanner (VIRS) on TRMM or Moderate-Resolution Imaging Spectroradiometer (MODIS) on Terra and Aqua. Scene identification and cloud properties are defined at the higher imager resolution and these data are averaged over the larger CERES footprint. For each CERES footprint, the SSF contains the number of cloud layers and for each layer the cloud amount, height, temperature, pressure, optical depth, emissivity, ice and liquid water path, and water particle size. The SSF also contains the CERES filtered radiances for the total, shortwave (SW), and window (WN) channels and the unfiltered SW, longwave (LW), and WN radiances. The SW, LW, and WN radiances at spacecraft altitude are converted to Top-of-the-Atmosphere (TOA) fluxes based on the imager defined scene. These TOA fluxes are used to estimate surface fluxes. Only footprints with adequate imager coverage are included on CER_SSF_TRMM-PFM-VIRS_Subset_Edition1the SSF which is much less than the full set of footprints on the CERES ES-8 product. The following CERES SSF data sets are currently available: CER_SSF_TRMM-PFM-VIRS_Edition1 CER_SSF_TRMM-PFM-VIRS_Subset_Edition1 CER_SSF_TRMM-PFM-VIRS_Edition2A CER_SSF_TRMM-SIM-VIRS_Edition2_VIRSonly CER_SSF_TRMM-PFM-VIRS_Edition2A-TransOps CER_SSF_TRMM-PFM-VIRS_Edition2B-TransOps CER_SSF_TRMM-PFM-VIRS_Edition2B CER_SSF_Terra-FM1-MODIS_Edition1A CER_SSF_Terra-FM1-MODIS_Edition1A CER_SSF_Terra-FM1-MODIS_Edition2A CER_SSF_Terra-FM2-MODIS_Edition2A CER_SSF_Terra-FM1-MODIS_Edition2B CER_SSF_Terra-FM2-MODIS_Edition2B CER_SSF_Aqua-FM4-MODIS_Beta1 CER_SSF_Aqua-FM3-MODIS_Beta2 CER_SSF_Aqua-FM4-MODIS_Beta2. [Location=GLOBAL] [Temporal_Coverage: Start_Date=1998-01-01; Stop_Date=2005-03-29] [Spatial_Coverage: Southernmost_Latitude=-90; Northernmost_Latitude=90; Westernmost_Longitude=-180; Easternmost_Longitude=180] [Data_Resolution: Temporal_Resolution=1 hour; Temporal_Resolution_Range=Hourly - < Daily].

LONGWAVE UNFILTERED RADIANCE↗
NASA NTRS2004

Above-Cloud Precipitable Water Retrievals using the MODIS 0.94 micron Band with Applications for Multi-Layer Cloud Detection

In order to perform satellite retrievals of cloud properties, it is important to account for the effect of the above-cloud atmosphere on the observations. The solar bands used in the operational MODIS Terra and Aqua cloud optical and microphysical algorithms (visible, NIR, and SWIR spectral windows) are primarily affected by water vapor, and to a lesser extent by well-mixed gases. For water vapor, the above-cloud column amount, or precipitable water, provides adequate information for an atmospheric correction; details of the vertical vapor distribution are not typically necessary for the level of correction required. Cloud-top pressure has a secondary effect due to pressure broadening influences. For well- mixed gases, cloud-top pressure is also required for estimates of above-cloud abundances. We present a method for obtaining above-cloud precipitable water over dark Ocean surfaces using the MODIS 0.94 pm vapor absorption band. The retrieval includes an iterative procedure for establishing cloud-top temperature and pressure, and is useful for both single layer water and ice clouds. Knowledge of cloud thermodynamic phase is fundamental in retrieving cloud optical and microphysical properties. However, in cases of optically thin cirrus overlapping lower water clouds, the concept of a single unique phase is ill- defined and depends, at least, on the spectral region of interest. We will present a method for multi-layer and multi-phase cloud detection which uses above-cloud precipitable water retrievals along with several existing MODIS operational cloud products (cloud-top pressure derived from a C02 slicing algorithm, IR and SWIR phase retrievals). Results are catagorized by whether the radiative signature in the MODIS solar bands is primarily that of a water cloud with ice cloud contamination, or visa-versa. Examples in polar and mid-latitude regions will be shown.

Platnick, S.↗
NASA NTRS1993

Global-scale waves in the Venus atmosphere

The nature of global-scale waves that can exist in the atmosphere of Venus is examined. A linear three-dimensional model atmosphere with spherical geometry is used to study large-scale forced and free waves. Solutions are obtained numerically with grid points in the vertical and a spherical harmonic expansion in the horizontal. Observations have shown a global-scale traveling wave with phase speed near the cloud-top wind velocity. Global-scale wave modes are found to exist in the model at this velocity. When a radiative-dynamic cloud feedback is added to the model, the most unstable wave mode is found to have the same phase speed as the observed wave. The horizontal structure of this wave is consistent with the observed horizontal structure of the 'Y' feature seen in ultraviolet images of the Venus cloud top.

Smith, Michael D.↗
NASA NTRS2007

Multi-Layer Arctic Mixed-Phase Clouds Simulated by a Cloud-Resolving Model: Comparison with ARM Observations and Sensitivity Experiments

A cloud-resolving model (CRM) is used to simulate the multiple-layer mixed-phase stratiform (MPS) clouds that occurred during a three-and-a-half day subperiod of the Department of Energy-Atmospheric Radiation Measurement Program s Mixed-Phase Arctic Cloud Experiment (M-PACE). The CRM is implemented with an advanced two-moment microphysics scheme, a state-of-the-art radiative transfer scheme, and a complicated third-order turbulence closure. Concurrent meteorological, aerosol, and ice nucleus measurements are used to initialize the CRM. The CRM is prescribed by time-varying large-scale advective tendencies of temperature and moisture and surface turbulent fluxes of sensible and latent heat. The CRM reproduces the occurrences of the single- and double-layer MPS clouds as revealed by the M-PACE observations. However, the simulated first cloud layer is lower and the second cloud layer thicker compared to observations. The magnitude of the simulated liquid water path agrees with that observed, but its temporal variation is more pronounced than that observed. As in an earlier study of single-layer cloud, the CRM also captures the major characteristics in the vertical distributions and temporal variations of liquid water content (LWC), total ice water content (IWC), droplet number concentration and ice crystal number concentration (nis) as suggested by the aircraft observations. However, the simulated mean values differ significantly from the observed. The magnitude of nis is especially underestimated by one order of magnitude. Sensitivity experiments suggest that the lower cloud layer is closely related to the surface fluxes of sensible and latent heat; the upper cloud layer is probably initialized by the large-scale advective cooling/moistening and maintained through the strong longwave (LW) radiative cooling near the cloud top which enhances the dynamical circulation; artificially turning off all ice-phase microphysical processes results in an increase in LWP by a factor of 3 due to interactions between the excessive LW radiative cooling and extra cloud water; heating caused by phase change of hydrometeors could affect the LWC and cloud top height by partially canceling out the LW radiative cooling. It is further shown that the resolved dynamical circulation appears to contribute more greatly to the evolution of the MPS cloud layers than the parameterized subgrid-scale circulation.

Luo, Yali↗
NASA NTRS2012

Applications for Near-Real Time Satellite Cloud and Radiation Products

At NASA Langley Research Center, a variety of cloud, clear-sky, and radiation products are being derived at different scales from regional to global using geostationary satellite (GEOSat) and lower Earth-orbiting (LEOSat) imager data. With growing availability, these products are becoming increasingly valuable for weather forecasting and nowcasting. These products include, but are not limited to, cloud-top and base heights, cloud water path and particle size, cloud temperature and phase, surface skin temperature and albedo, and top-of-atmosphere radiation budget. Some of these data products are currently assimilated operationally in a numerical weather prediction model. Others are used unofficially for nowcasting, while testing is underway for other applications. These applications include the use of cloud water path in an NWP model, cloud optical depth for detecting convective initiation in cirrus-filled skies, and aircraft icing condition diagnoses among others. This paper briefly describes a currently operating system that analyzes data from GEOSats around the globe (GOES, Meteosat, MTSAT, FY-2) and LEOSats (AVHRR and MODIS) and makes the products available in near-real time through a variety of media. Current potential future use of these products is discussed.

Minnis, Patrick↗
NASA NTRS2012

Impact of Aerosols on Convective Clouds and Precipitation

Aerosols are a critical.factor in the atmospheric hydrological cycle and radiation budget. As a major agent for clouds to form and a significant attenuator of solar radiation, aerosols affect climate in several ways. Current research suggests that aerosols have a major impact on the dynamics, microphysics, and electrification properties of continental mixed-phase convective clouds. In addition, high aerosol concentrations in urban environments could affect precipitation variability by providing a significant source of cloud condensation nuclei (CCN). Such pollution . effects on precipitation potentially have enormous climatic consequences both in terms of feedbacks involving the land surface via rainfall as well as the surface energy budget and changes in latent heat input to the atmosphere. Basically, aerosol concentrations can influence cloud droplet size distributions, the warm-rain process, the cold-rain process, cloud-top heights, the depth of the mixed-phase region, and the occurrence of lightning. Recently, many cloud resolution models (CRMs) have been used to examine the role of aerosols on mixed-phase convective clouds. These modeling studies have many differences in terms of model configuration (two- or three-dimensional), domain size, grid spacing (150-3000 m), microphysics (two-moment bulk, simple or sophisticated spectral-bin), turbulence (1st or 1.5 order turbulent kinetic energy (TKE)), radiation, lateral boundary conditions (i.e., closed, radiative open or cyclic), cases (isolated convection, tropical or midlatitude squall lines) and model integration time (e.g., 2.5 to 48 hours). Among these modeling studies, the most striking difference is that cumulative precipitation can either increase or decrease in response to higher concentrations of CCN. In this presentation, we review past efforts and summarize our current understanding of the effect of aerosols on convective precipitation processes. Specifically, this paper addresses the following topics: observational evidence of the effect of aerosols on precipitation processes, and results from (CRM) simulations. Note that this presentation is mainly based on a recent paper published in Geophy. Rev. (Tao et al. 2012).

Tao, Wei-Kuo↗