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Satellite-derived cloud and radiation fields over the marine stratocumulus IFO

The Geostationary Operational Environmental Satellite (GOES) is the only source for nearly continuous areal coverage of clouds within the California marine stratocumulus region. The cloud parameters derived from GOES data during the First ISCCP Regional Experiment (FIRE) Marine Stratocumulus Intensive Field Observations (IFO) are summarized.

Young, David F.↗

Observations of Aerosol-Radiation-Cloud Interactions in the South-East Atlantic: First Results from the ORACLES Deployments in 2016 and 2017

Southern Africa produces almost a third of the Earths biomass burning (BB) aerosol particles. Particles lofted into the mid-troposphere are transported westward over the South-East (SE) Atlantic, home to one of the three permanent subtropical stratocumulus (Sc) cloud decks in the world. The SE Atlantic stratocumulus deck interacts with the dense layers of BB aerosols that initially overlay the cloud deck, but later subside and often mix into the clouds. These interactions include adjustments to aerosol-induced solar heating and microphysical effects, and their global representation in climate models remains one of the largest uncertainties in estimates of future climate. Hence, new observations over the SE Atlantic have significant implications for regional and global climate change predictions.The low-level clouds in the SE Atlantic have limited vertical extent and therefore present favorable conditions for their exploration with remote sensing. On the other hand, the normal coexistence of BB aerosols and Sc clouds in the same scene also presents significant challenges to conventional remote sensing techniques. We describe first results from NASAs airborne ORACLES (ObseRvations of Aerosols Above Clouds and Their IntEractionS) deployments in September 2016 and August 2017. We emphasize the unique role of polarimetric observations by two instruments, the Research Scanning Polarimeter (RSP) and the Airborne Multi-angle SpectroPolarimeter Imager (AirMSPI), and describe how these instruments help address specific ORACLES science objectives. Initial assessments of polarimetric observation accuracy for key cloud and aerosol properties will be presented, in as far as the preliminary nature of measurements permits.

Redemann, Jens↗

Aerosol-Radiation-Cloud Interactions in the South-East Atlantic: First Results from the ORACLES-2016 Deployment and Plans for Future Activities

Southern Africa produces almost a third of the Earths biomass burning (BB) aerosol particles. Particles lofted into the mid-troposphere are transported westward over the South-East (SE) Atlantic, home to one of the three permanent subtropical stratocumulus (Sc) cloud decks in the world. The SE Atlantic stratocumulus deck interacts with the dense layers of BB aerosols that initially overlay the cloud deck, but later subside and may mix into the clouds. These interactions include adjustments to aerosol-induced solar heating and microphysical effects, and their global representation in climate models remains one of the largest uncertainties in estimates of future climate. Hence, new observations over the SE Atlantic have significant implications for regional and global climate change predictions.Our understanding of aerosol-cloud interactions in the SE Atlantic is severely limited. Most notably, we are missing knowledge on the absorptive and cloud nucleating properties of aerosols, including their vertical distribution relative to clouds, on the locations and degree of aerosol mixing into clouds, on the processes that govern cloud property adjustments, and on the importance of aerosol effects on clouds relative to co-varying synoptic scale meteorology.We describe first results from various synergistic, international research activities aimed at studying aerosol-cloud interactions in the region:NASAs airborne ORACLES (ObseRvations of Aerosols Above Clouds and Their IntEractionS) deployment in AugustSeptember of 2016,the DoEs LASIC (Layered Atlantic Smoke Interactions with Clouds) deployment of the ARM Mobile Facility to Ascension Island (June 2016 October 2017), the ground-based components of CNRS AEROCLO-sA (Aerosols Clouds and Fog over the west coast of southern Africa), and ongoing regional-scale integrative, process-oriented science efforts as part of SEALS-sA (Sea Earth Atmosphere Linkages Study in southern Africa).We expect to describe experimental setups as well as showcase initial aerosol and cloud property distributions. Furthermore, we discuss the implementation of future activities in these programs in coordination with the UK Met Offices CLARIFY (CLoud-Aerosol-Radiation Interactions and Forcing) experiment in 2017.

aerosol↗

Aerosol-Cloud Interactions in the South-East Atlantic: Knowledge Gaps, Planned Observations to Address Them, and Implications for Global Climate Change Modeling

Southern Africa produces almost a third of the Earth's biomass burning (BB) aerosol particles, yet the fate of these particles and their influence on regional and global climate is poorly understood. Particles lofted into the mid-troposphere are transported westward over the South-East (SE) Atlantic, home to one of the three permanent subtropical Stratocumulus (Sc) cloud decks in the world. The stratocumulus "climate radiators" are critical to the regional and global climate system. They interact with dense layers of BB aerosols that initially overlay the cloud deck, but later subside and are mixed into the clouds. These interactions include adjustments to aerosol-induced solar heating and microphysical effects. As emphasized in the latest IPCC report, the global representation of these aerosol-cloud interaction processes in climate models is one of the largest uncertainty in estimates of future climate. Hence, new observations over the SE Atlantic have significant implications for global climate change scenarios. We discuss the current knowledge of aerosol and cloud property distributions based on satellite observations and sparse suborbital sampling, and describe planned field campaigns in the region. Specifically, we describe the scientific objectives and implementation of the following four synergistic, international research activities aimed at providing a process-level understanding of aerosol-cloud interactions over the SE Atlantic: 1) ORACLES (Observations of Aerosols above Clouds and their interactions), a five-year investigation between 2015 and 2019 with three Intensive Observation Periods (IOP), recently funded by the NASA Earth-Venture Suborbital Program, 2) CLARIFY-2016 (Cloud-Aerosol-Radiation Interactions and Forcing: Year 2016), a comprehensive observational and modeling programme funded by the UK's Natural Environment Research Council (NERC), and supported by the UK Met Office. 3) LASIC (Layered Atlantic Smoke Interactions with Clouds), a funded deployment of the DOE (Department of Energy) ARM Mobile Facility (AMF1) to Ascension Island, nominally for April 1 2016 - March 31 2017, and 4) ONFIRE (Observations of Fire's Impact on the southeast Atlantic Region), a proposed deployment of the NCAR C-130 aircraft to Sao Tome Island in 2017.

Aerosol-cloud↗

Variations of Cloud and Radiative Properties of Boundary-layer and Deep Convective Systems with Sea Surface Temperature Anomalies

Gridded monthly-mean satellite data contain compositing information from different cloud system types and clear-sky environments. To isolate the variations of cloud physical properties of an individual cloud system type with its environment, orbital data are needed. In this study, we will analyze the variations of cloud and radiative properties of boundary-layer clouds and deep convective cloud systems with sea surface temperature (SST) anomalies. We use Terra-CERES (Clouds and the Earth s Radiant Energy System) Level 2 data to classify distinct cloud objects defined by cloud-system types (deep convection, boundary-layer cumulus, stratocumulus and overcast clouds), sizes, geographic locations, and matched large-scale environments. This analysis method identifies a cloud object as a contiguous region of the Earth with a single dominant cloud-system type. It determines the shape and size of the cloud object from the satellite data and the cloud-system selection criteria. The statistical properties of the identified cloud objects are analyzed in terms of probability density functions (PDFs) of a single property or joint PDFs between two properties. The SST anomalies are defined as the differences from five-year annual-cycle means. Individual cloud objects are sorted into one of five equal size subsets, with the matched SST anomalies ranging from the most negative to the most positive values, for a given size category of deep convective cloud objects, boundary-layer cumulus, stratocumulus and overcast cloud objects. The PDFs of cloud and radiative properties for deep convective cloud objects (between 30 S and 30 N) are found to largely similar among the five SST anomaly subsets except for the lowest SST anomaly subset. The different characteristics from this SST anomaly subset may be related to some cloud objects resulting from equatorward movement of extratropical cloud systems. This result holds true for all three different size categories (measured by equivalent diameters of 100-150, 150-300 and > 300 km). The PDFs of cloud and radiative properties for boundary-layer cloud types are more variable for macrophysical properties than for microphysical properties, due probably to different large-scale environments where these cloud objects are formed. Implications of these results for the cloud feedback will also be discussed.

Xu, Kuan-Man↗

Fog and Cloud Induced Aerosol Modification Observed by AERONET

Large fine mode (sub-micron radius) dominated aerosols in size distributions retrieved from AERONET have been observed after fog or low-altitude cloud dissipation events. These column-integrated size distributions have been obtained at several sites in many regions of the world, typically after evaporation of low altitude cloud such as stratocumulus or fog. Retrievals with cloud processed aerosol are sometimes bimodal in the accumulation mode with the larger size mode often approx.0.4 - 0.5 microns radius (volume distribution); the smaller mode typically approx.0.12 to aprrox.0.20 microns may be interstitial aerosol that were not modified by incorporation in droplets and/or aerosol that are less hygroscopic in nature. Bimodal accumulation mode size distributions have often been observed from in situ measurements of aerosols that have interacted with clouds, and AERONET size distribution retrievals made after dissipation of cloud or fog are in good agreement with particle sizes measured by in situ techniques for cloud-processed aerosols. Aerosols of this type and large size range (in lower concentrations) may also be formed by cloud processing in partly cloudy conditions and may contribute to the shoulder of larger size particles in the accumulation mode retrievals, especially in regions where sulfate and other soluble aerosol are a significant component of the total aerosol composition. Observed trends of increasing aerosol optical depth (AOD) as fine mode radius increased suggests higher AOD in the near cloud environment and therefore greater aerosol direct radiative forcing than typically obtained from remote sensing, due to bias towards sampling at low cloud fraction.

Eck, T. F.↗

Impact of Three-Dimensional Radiative Effects on Satellite Retrievals of Cloud Droplet Sizes

There are several dozen papers that study the effects of cloud horizontal inhomogeneity on the retrievals of cloud optical thickness, but only a few of them deal with cloud droplet sizes. This paper is one of the first comprehensive attempts to fill this gap: It takes a close theoretical look at the radiative effects of cloud 3-D structure in retrievals of droplet effective radii. Under some general assumptions, it was found that ignoring subpixel (unresolved) variability produces a negative bias in the retrieved effective radius, while ignoring cloud inhomogeneity at scales larger than a pixel scale (resolved variability), on the contrary, leads to overestimation of the domain average droplet size. The theoretical results are illustrated with examples from Large Eddy Simulations (LES) of cumulus (Cu) and stratocumulus (Sc) cloud fields. The analysis of cloud drop size distributions retrieved from both LES fields confirms that ignoring shadowing in 1-D retrievals results in substantial overestimation of effective radii which is more pronounced for broken Cu than for Sc clouds. Collocated measurements of broken Cu clouds by Moderate Resolution Imaging Spectrometer (MODIS) and Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) are used to check simulations and theory with observations. The analysis of ASTER and MODIS data and associated derived products recommends against blindly using retrieved effective radii for broken cloud fields, especially if one wants to relate aerosol amounts to cloud droplet sizes.

Marshak, Alexander↗

Comparison of satellite based cloud retrieval methods for cirrus and stratocumulus

One difficulty in using satellite remote sensing data is the spatial variability of cloud properties on scales smaller than most meteorological satellite fields of view (approx. 4 to 8 km). The variation is examined of satellite derived cloud cover as a function of the satellite sensor spatial resolution for seven cloud cover retrieval methods: (1) Reflectance threshold; (2) Temperature threshold; (3) ISCCP; (4) HBTM (Hybrid Bispectral Threshold Method); (5) NCLE; (6) Spatial coherence; and (7) Functional Box Counting. The first two methods are simple single spectral thresholds which specify a satellite pixel as cloud filled if the measured reflectance is greater than the threshold, or if the measured equivalent blackbody temperature is less than the threshold. The next three methods are bispectral, using one visible wavelength window channel and one thermal infrared wavelength window. The final two algorithms rely on the spatial variability within the cloud field to determine cloud cover. Spatial coherence assumes only that the cloud field occurs in a single layer and that the clouds are optically thick in the infrared window. LANDSAT Thematic Mapper (TM) data is used to test the spatial resolution dependence of the cloud algorithms. The ISCCP bispectral threshold applied to the full resolution data is used as the reference or truth cloud cover, after which the retrieval methods are applied to the spatial resolutions. Studies of the fraction of pixels in the scene at cloud edge, and of the profile of reflectance and temperature near cloud edges indicate an uncertainty in the reference cloud fraction of 1 to 5 percent.

Parker, Lindsay↗

Aerosol-Radiation-Cloud Interactions in the South-East Atlantic: Results from the ORACLES-2016 Deployment and a First Look at ORACLES-2017 and Beyond

Seasonal biomass burning (BB) in Southern Africa during the Southern hemisphere spring produces almost a third of the Earth's BB aerosol particles. These particles are lofted into the mid-troposphere and transported westward over the South-East (SE) Atlantic, where they interact with one of the three semi-permanent subtropical stratocumulus (Sc) cloud decks in the world. These interactions include adjustments to aerosol-induced solar heating and microphysical effects. The representation of these interactions in climate models remains highly uncertain, because of the scarcity of observational constraints on both, the aerosol and cloud properties, and the governing physical processes. The first deployment of the NASA P-3 and ER-2 aircraft in the ORACLES (ObseRvations of Aerosols Above Clouds and Their IntEractionS) project in August/September of 2016 has started to fill this observational gap by providing an unprecedented look at the SE Atlantic cloud-aerosol system. We provide an overview of the first deployment, highlighting aerosol absorptive and cloud-nucleating properties, their vertical distribution relative to clouds, the locations and degree of aerosol mixing into clouds, cloud changes in response to such mixing, and cloud top stability relationships to the aerosol. We also expect to describe preliminary results of the second ORACLES deployment from Sao Tome and Pri­ncipe in August 2017. We will make an initial assessment of the differences and similarities of the BB plume and cloud properties as observed from a deployment site near the plume's northern edge. We will conclude with an outlook for the third ORACLES deployment in October 2018.

Redemann, Jens↗

An overview of the ORACLES (ObseRvations of Aerosols above CLouds and their intEractionS) project: aerosol–cloud–radiation interactions in the southeast Atlantic basin

Southern Africa produces almost a third of the Earth’s biomass burning (BB) aerosol particles, yet the fate of these particles and their influence on regional and global climate is poorly understood. ORACLES (ObseRvations of Aerosols above CLouds and their intEractionS) is a 5-year NASA EVS-2 (Earth Venture Suborbital-2) investigation with three intensive observation periods designed to study key atmospheric processes that determine the climate impacts of these aerosols. During the Southern Hemisphere winter and spring (June–October), aerosol particles reaching 3–5 km in altitude are transported westward over the southeast Atlantic, where they interact with one of the largest subtropical stratocumulus (Sc) cloud decks in the world. The representation of these interactions in climate models remains highly uncertain in part due to a scarcity of observational constraints on aerosol and cloud properties, as well as due to the parameterized treatment of physical processes. Three ORACLES deployments by the NASA P-3 aircraft in September 2016, August 2017, and October 2018 (totaling ~ 350 science flight hours), augmented by the deployment of the NASA ER-2 aircraft for remote sensing in September 2016 (totaling ~ 100 science flight hours), were intended to help fill this observational gap. ORACLES focuses on three fundamental science themes centered on the climate effects of African BB aerosols: (a) direct aerosol radiative effects, (b) effects of aerosol absorption on atmospheric circulation and clouds, and (c) aerosol–cloud microphysical interactions. This paper summarizes the ORACLES science objectives, describes the project implementation, provides an overview of the flights and measurements in each deployment, and highlights the integrative modeling efforts from cloud to global scales to address science objectives. Significant new findings on the vertical structure of BB aerosol physical and chemical properties, chemical aging, cloud condensation nuclei, rain and precipitation statistics, and aerosol indirect effects are emphasized, but their detailed descriptions are the subject of separate publications. The main purpose of this paper is to familiarize the broader scientific community with the ORACLES project and the dataset it produced.

Jens Redemann↗

FIRE - The First ISCCP Regional Experiment

The First International Satellite Cloud Climatology Project Regional Experiment (FIRE) designed to study the roles of clouds, in particular marine stratocumulus and cirrus-cloud systems, in the global climate is discussed. The objectives of FIRE are: (1) to develop a cloud-classification scheme; (2) to validate and improve satellite cloud-retrieval techniques; (3) to improve cloud radiation models; (4) to collect cloud space/time statistics; (5) to improve cloud dynamics models; and (6) to validate and improve GCM cloud parameterizations. The methods used to acquire extended time data and intensive field observations are described. The extended time and intensive field data collected during the FIRE are to be archived in the NASA Pilot Climate Data System at Goddard Space Flight Center.

Cox, Stephen K.↗

Comparative climatology of four marine stratocumulus regimes

The climatology of marine stratocumulus (MSc) cloud regimes off the west coasts of California, Peru, Morocco, and Angola are examined. Long-term, annual averages are presented for several quantities of interest in the four MSc regimes. The climatologies were constructed using the Comprehensive Ocean-Atmosphere Data Set (COADS). A 40 year time series of observations was extracted for 32 x 32 deg analysis domains. The data were taken from the monthly-averaged, 2 deg product. The resolution of the analysis is therefore limited to scales of greater than 200 km with submonthly variability not resolved. The averages of total cloud cover, sea surface temperature, and surface pressure are presented.

Hanson, Howard P.↗

The Seasonal Evolution of Atmospheric Vertical Structure of Smoke and Humidity Over the Southeast Atlantic Biomass Burning Region

The atmosphere over the southeast Atlantic Ocean (SEA) sees a consistent springtime biomass burning (BB) smoke from widespread agricultural fires on the African continent. This smoke layer is initially lofted high in a continental mixed layer (~5-6km) and is then transported westward in the free troposphere, where it overlies and ultimately mixes into the SEA stratocumulus-topped oceanic boundary layer. Coincident with this smoke is an elevated humidity signal which is present from the time a given airmass is over the continental source region; this correlation is persistent through the biomass burning season, although varying through the course of the season. ORACLES (ObseRvations of Aerosols above CLouds and their intEractionS) was a NASA Earth Venture Suborbital mission with the goal of measuring aerosol, cloud, and atmospheric properties over this region during three deployments in September 2016, August 2017, and October 2018. We use the ORACLES observations to assess this smoke-vapor relationship. First, we discuss the good agreement between the airborne ORACLES dataset and the ECMWF ERA5 and CAMS reanalyses, as well as results from NASA’s MERRA-2, as seen over the three deployment years. We then use the reanalyses to develop a framework in which to understand more broadly the radiative and dynamical interactions between the elevated smoke and water vapor over the SEA through the biomass burning season, beyond the three ORACLES observation periods. Looking at seven years of reanalysis data for the BB season, we find distinct variations between each month/deployment in terms of vertical smoke distribution and correlation to atmospheric specific humidity, due to changing conditions through the BB season. Using k-means clustering of these climatological reanalyses, we identify six canonical atmospheric profile types of varying total atmospheric humidity and vertical structure and describe their changing incidence spatially and throughout the season, and six analogous profile types for carbon monoxide, allowing us to characterize the atmospheric structure of both vapor and BB over time throughout the SEA region. The radiative heating of both aerosol and water vapor has potential to influence the cloud-top entrainment and atmospheric turbulence, thus modifying the underlying stratocumulus cloud properties. We next discuss how these smoke-humidity variations influence both the low-cloud fraction (as observed by MODIS and VIIRS, and output by ERA5) and the boundary layer height in the region. This classification will ultimately allow for a more complete analysis of the broader radiative and dynamical effects of humid aerosols overlying stratocumulus clouds.

Kristina Marie Myers Pistone↗

The Cumulus and Stratocumulus CloudSat-CALIPSO Dataset (CASCCAD)

Low clouds continue to contribute greatly to the uncertainty in cloud feedback estimates. Depending on whether a region is dominated by cumulus (Cu) or stratocumulus (Sc) clouds, the interannual low-cloud feedback is somewhat different in both spaceborne and large-eddy simulation studies. Therefore, simulating the correct amount and variation of the Cu and Sc cloud distributions could be crucial to predict future cloud feedbacks. Here we document spatial distributions and profiles of Sc and Cu clouds derived from Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) and CloudSat measurements. For this purpose, we create a new dataset called the Cumulus And Stratocumulus CloudSat-CALIPSO Dataset (CASCCAD), which identifies Sc, broken Sc, Cu under Sc, Cu with stratiform outflow and Cu. To separate the Cu from Sc, we design an original method based on the cloud height, horizontal extent, vertical variability and horizontal continuity, which is separately applied to both CALIPSO and combined CloudSat–CALIPSO observations. First, the choice of parameters used in the discrimination algorithm is investigated and validated in selected Cu, Sc and Sc–Cu transition case studies. Then, the global statistics are compared against those from existing passive- and active-sensor satellite observations. Our results indicate that the cloud optical thickness – as used in passive-sensor observations – is not a sufficient parameter to discriminate Cu from Sc clouds, in agreement with previous literature. Using clustering-derived datasets shows better results although one cannot completely separate cloud types with such an approach. On the contrary, classifying Cu and Sc clouds and the transition between them based on their geometrical shape and spatial heterogeneity leads to spatial distributions consistent with prior knowledge of these clouds, from ground-based, ship-based and field campaigns. Furthermore, we show that our method improves existing Sc–Cu classifications by using additional information on cloud height and vertical cloud fraction variation. Finally, the CASCCAD datasets provide a basis to evaluate shallow convection and stratocumulus clouds on a global scale in climate models and potentially improve our understanding of low-level cloud feedbacks. The CASCCAD dataset (Cesana, 2019, https://doi.org/10.5281/zenodo.2667637) is available on the Goddard Institute for Space Studies (GISS) website at https://data.giss.nasa.gov/clouds/casccad/ (last access: 5 November 2019) and on the zenodo website at https://zenodo.org/record/2667637 (last access: 5 November 2019).

Cesana, Gregory V.↗

Enhancement of Cloud Cover and Suppression of Nocturnal Drizzle in Stratocumulus Polluted by Haze

Recent satellite observations indicate a significant decrease of cloud water in ship tracks, in contrast to an ensemble of in situ ship-track measurements that show no average change in cloud water relative to the surrounding clouds. We find through large-eddy simulations of stratocumulus that the trend in the satellite data is likely an artifact of sampling only overcast clouds. The simulations instead show cloud cover increasing with droplet concentrations. Our simulations also show that increases in cloud water from drizzle suppression (by increasing droplet concentrations) are favored at night or at extremely low droplet concentrations.

Ackerman, Andrew S.↗

Cloud Coverage Enhancement and Nocturnal Drizzle Suppression in Stratocumulus by Aerosols

Recent satellite observations of ship tracks surprisingly indicate that cloud water decreases with increasing droplet concentrations. However, we find by analyzing detailed simulations of stratocumulus that the reported trend is likely an artifact of sampling, only overcast clouds. The simulations instead show cloud coverage increasing with droplet concentrations, accounting for 25% of cloud albedo increase at moderate droplet concentrations. Our simulations also show that increases in cloud water from drizzle suppression (by increasing droplet concentrations) are favored only at night or at extremely low droplet concentrations, suggesting that the indirect aerosol forcing is overestimated in climate change projections by many general circulation models.

Ackerman, Andrew S.↗

Structures observed on the spot radiance fields during the FIRE experiment

Three Spot images taken during the FIRE experiment on stratocumulus are analyzed. From this high resolution data detailed observations of the true cloud radiance field may be made. The structure and inhomogeneity of these radiance fields hold important implications for the radiation budget, while the fine scale structure in radiance field provides information on cloud dynamics. Wieliki and Welsh, and Parker et al., have quantified the inhomogeneities of the cumulus clouds through a careful examination of the distribution of cloud (and hole) size as functions of an effective cloud diameter and radiance threshold. Cahalan (1988) has compared for different cloud types of (stratocumulus, fair weather cumulus, convective clouds in the ITCZ) the distributions of clouds (and holes) sizes, the relation between the size and the perimeter of these clouds (and holes), and examining the possibility of scale invariance. These results are extended from LANDSAT resolution (57 m and 30 m) to the Spot resolution (10 m) resolution in the case of boundary layer clouds. Particular emphasis is placed on the statistics of zones of high and low reflectivity as a function of a threshold reflectivity.

Seze, Genevieve↗

Modeling and parameterization of horizontally inhomogeneous cloud radiative properties

One of the fundamental difficulties in modeling cloud fields is the large variability of cloud optical properties (liquid water content, reflectance, emissivity). The stratocumulus and cirrus clouds, under special consideration for FIRE, exhibit spatial variability on scales of 1 km or less. While it is impractical to model individual cloud elements, the research direction is to model a statistical ensembles of cloud elements with mean-cloud properties specified. The major areas of this investigation are: (1) analysis of cloud field properties; (2) intercomparison of cloud radiative model results with satellite observations; (3) radiative parameterization of cloud fields; and (4) development of improved cloud classification algorithms.

Welch, R. M.↗