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TRACER-Uncrewed Aircraft System (TRACER-UAS) Field Campaign Report

Convective processes drive the development of clouds across a variety of scales, thereby playing a central role in governing weather and climate globally. These processes help to set the stage for circulations that redistribute heat and moisture throughout the lower atmosphere, and simultaneously develop storms that supply precipitation to regions that depend on such rain events for supporting a variety of societal needs. At the same time, extreme precipitation events can result in localized flooding of low-lying areas, posing hazards to transportation and regional inhabitants, and potentially damaging structures and infrastructure. As a result, there is an inherent need to better understand the drivers and modulators of clouds and precipitation and leverage such understanding to make projections of how these important systems may evolve with a changing climate. With nearly three billion of Earth’s human inhabitants living within 200 km of a shoreline, development of such understanding is particularly important in coastal regimes. Central drivers of convective cloud development and life cycle in coastal environments include synoptic forcing, local meso- and microscale circulation regimes, microphysical evolution, and aerosol properties. Atmospheric boundary layer (ABL) development and its evolution can help drive the formation and organization of convective clouds, which then impart their own controls through dynamic processes related to latent heating and cooling (including cold-pool formation and propagation), three-dimensional radiative effects, and background environmental conditions (Fan et al. 2016). Such clouds have been contributing to record precipitation events in southeast Texas in recent years, relative to the last several decades of data from regional precipitation gauges (Fagnant et al. 2020). The greater Houston urban area has experienced particularly large increases in the frequency of extreme rainfall events, with enhanced intensity of extreme events (stretching of distribution tails) having potentially significant implications for watershed floodplain planning and mapping in greater Houston and Harris County. While the most extreme precipitation events were associated with tropical cyclones (e.g., Tropical Storm Allison and Hurricane Harvey; Blood 2014, Kao et al. 2019), strong thunderstorms can also deliver large amounts of precipitation over the area over relatively short periods.

54 ENVIRONMENTAL SCIENCES↗

Cloud effects on ultraviolet photoclimatology

The purpose of this study is to quantify for the needs of photobiology the influence of clouds upon the ultraviolet spectral irradiance reaching the ground. Towards this end, analytic formulas are developed which approximately characterize the influence of clouds upon total solar radiation. These may be used in conjunction with a solar pyranometer to assign an effective visual optical depth for the cloud cover. A formula is also developed which characterizes the influence of the optical depth of clouds upon the UV spectral irradiance in the 280-340 nm region. Thus total solar energy observations to assign cloud optical properties can be used to calculate the UV spectral irradiance at the ground in the presence of these clouds. As incidental by-products of this effort, convenient formulas are found for the direct and diffuse components of total solar energy.

Green, A. E. S.↗

Aerosol Radiative Effects over Ascension Island Using LASIC Observations and MERRA-2

Marine boundary layer clouds, including the transition from stratocumulus to cumulus, are poorly represented in numerical weather prediction and general circulation models. In many cases, the complex physical relationships between marine boundary cloud morphology and the environmental conditions in which the clouds exist are not well understood. Such uncertainties arise in the presence of biomass burning carbonaceous aerosol, as is the case over the southeast Atlantic Ocean. It is likely that the absorbing and heating properties of these aerosols influence the microphysical composition and macrophysical arrangement of marine stratocumulus and trade cumulus in this region; however, this has yet to be quantified. The deployment of the Atmospheric Radiation Measurement Mobile Facility #1 (AMF1) in support of LASIC (Layered Atlantic Smoke Interactions with Clouds) provided a unique opportunity to collect observations of cloud and aerosol properties during two consecutive biomass burning seasons during July through October of 2016 and 2017 over Ascension Island (7.96 S, 14.35 W). Thermodynamic profiles will be analyzed through the unique combination of sounding data from radiosonde launches and microwave profiling radiometers, giving observations of additional quantities important for cloud development such as CAPE and CIN at a fine temporal resolution. The thermodynamic profiles will be presented in conjunction with detailed observations of the cloud structure over the site from a K-band cloud radar, micropulse lidar, and laser ceilometer. Finally, the observed thermodynamic and cloud profiles will be used as input forcing, alongside aerosols from the Modern Era Retrospective analysis for Research and Applications, version 2 (MERRA-2), for the Rapid Radiative Transfer Model (RRTM) to gain information regarding the radiative heating profiles. Idealized experiments using RRTM with and without aerosols will be used to quantify the impact of biomass burning carbonaceous aerosol plumes as they pass over the site.

Collow, Allie↗

Precombination Cloud Collapse and Baryonic Dark Matter

A simple spherical model of dense baryon clouds in the hot big bang 'strongly nonlinear primordial isocurvature baryon fluctuations' is reviewed and used to describe the dependence of cloud behavior on the model parameters, baryon mass, and initial over-density. Gravitational collapse of clouds before and during recombination is considered including radiation diffusion and trapping, remnant type and mass, and effects on linear large-scale fluctuation modes. Sufficiently dense clouds collapse early into black holes with a minimum mass of approx. 1 solar mass, which behave dynamically like collisionless cold dark matter. Clouds below a critical over-density, however, delay collapse until recombination, remaining until then dynamically coupled to the radiation like ordinary diffuse baryons, and possibly producing remnants of other kinds and lower mass. The mean density in either type of baryonic remnant is unconstrained by observed element abundances. However, mixed or unmixed spatial variations in abundance may survive in the diffuse baryon and produce observable departures from standard predictions.

Hogan, Craig J.↗

Towards an Optimal Estimation Retrieval of Cirrus Cloud Optical and Microphysical Properties Using Hyperspectral Shortwave Instruments and A Fast Radiative Transfer Algorithm

Cirrus cloud retrieval products (here, cloud optical depth, effective particle size, and cloud top height) are important inputs into numerical weather and climate models. Uncertainties in such retrieval products, as a matter of course, propagate downstream, impacting model calculations. Improvements in high-quality global cirrus cloud optical and microphysical data products from satellite observations are needed to understand and reduce retrieval uncertainties. Hyperspectral instruments produce high-resolution and information-dense radiance spectra, thus offering the opportunity to reduce uncertainties in retrieval products. An optimal estimation-based cirrus cloud optical and microphysical product retrieval is under development for the NASA Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) and the Earth Surface Mineral Dust Source Investigation (EMIT) instruments, and the forthcoming Climate Absolute Radiance and Refractivity Observatory Pathfinder (CLARREO-Pathfinder). The spectral coverage of all three instruments includes the ultraviolet, visible, and near-infrared. In this study a very fast radiative transfer model, the Principal Component-based Radiative Transfer Model in the solar spectral region (PCRTM-Solar), is used for forward modeling computations. This will reduce the computational burden in the forward radiance and Jacobian calculations as the cost function is minimized, enabling the entire AVIRIS, EMIT, and CLARREO-Pathfinder spectral range to be used in the optimal estimation framework. Using the entire spectrum will maximize the information content, resulting in a more robust and more accurate retrieval. As a first step, the retrieval is being designed for single layer ice clouds over open ocean water. Preliminary results will be shown.

Jeffrey Mast↗

A13H-2546: Intercomparison of biomass burning aerosol properties from in-situ and remote-sensing instruments in ORACLES-2016

The magnitude of the cumulative effects of aerosols, both directly and on cloud properties, remains the biggest source of uncertainty in our understanding of anthropogenic radiative forcing on the climate. The magnitude of aerosol effects in any given region will depend on not just the aerosol concentration, but also on the characteristics of the aerosol under consideration. The NASA ORACLES (ObseRvations of Aerosols above CLouds and their intEractionS) campaign was conducted in 2016-2018 over three deployments in the Southeast Atlantic Ocean (SEA), with the goal of making observations of seasonal biomass burning (BB) smoke plumes overlying persistent stratocumulus cloud decks. During the first ORACLES deployment (September 2016), two NASA aircraft (a P-3 and an ER-2) were flown with a suite of aerosol, cloud, radiation, and meteorological instruments for remote-sensing and in-situ observations. In ORACLES, data collected by eight different instrument teams are used to derive aerosol properties over this region by independent methods. Here we present a comparison of results from the different instrument retrievals with a focus on the measures of aerosol absorption. We focus on specific cases with near-coincident measurements from in-situ (PSAP or PTI for aerosol absorption combined with a nephelometer for aerosol scattering) and remote sensing (4STAR, AirMSPI, RSP, and SSFR) instruments from coordinated flights between the two aircraft. We use the single scattering albedo (SSA), a measure of the relative absorption versus total extinction by aerosols, as the main comparable property between the various remote sensing and in-situ methods. For the remote sensing instruments, we see general good agreement in the total aerosol loading (aerosol optical depth, AOD), though see some differences in the absorbing component (AAOD). We report values for the retrieved aerosol parameters measured in the ORACLES flights and comment upon the observed variability between different instruments. Finally, we discuss these ORACLES results in the context of previous measurements of BB aerosol over the SEA.

Kristina Pistone↗

Accurate Satellite-Derived Estimates of Tropospheric Ozone Radiative Forcing

Estimates of the radiative forcing due to anthropogenically-produced tropospheric O3 are derived primarily from models. Here, we use tropospheric ozone and cloud data from several instruments in the A-train constellation of satellites as well as information from the GEOS-5 Data Assimilation System to accurately estimate the instantaneous radiative forcing from tropospheric O3 for January and July 2005. We improve upon previous estimates of tropospheric ozone mixing ratios from a residual approach using the NASA Earth Observing System (EOS) Aura Ozone Monitoring Instrument (OMI) and Microwave Limb Sounder (MLS) by incorporating cloud pressure information from OMI. Since we cannot distinguish between natural and anthropogenic sources with the satellite data, our estimates reflect the total forcing due to tropospheric O3. We focus specifically on the magnitude and spatial structure of the cloud effect on both the shortand long-wave radiative forcing. The estimates presented here can be used to validate present day O3 radiative forcing produced by models.

Joiner, Joanna↗

Effective Radius of Ice Cloud Particle Populations Derived from Aircraft Probes

The effective radius(r(sub e)) is a crucial variable in representing the radiative properties of cloud layers in general circulation models. This parameter is proportional to the condensed water content (CWC) divided by the extinction (sigma). For ice cloud layers, parameterizations for r(sub e), have been developed from aircraft in-situ measurements 1) indirectly, using data obtained from particle spectrometer probes and assumptions or observations about particle shape and mass to get the ice water content (IWC) and area to get sigma, and recently 2) from probes that measure IWC and sigma directly. This study compares [IWC/sigma] derived from the two methods using data sets acquired from comparable instruments on two aircraft, one sampling clouds at mid-levels and the other at upper-levels during the CRYSTAL-FACE field program in Florida in 2002. The sigma and IWC derived by each method are compared and evaluated in different ways for each aircraft data set. Direct measurements of sigma exceed those derived indirectly by a factor of two to two and a half. The IWC probes, relying on ice sublimation, appear to measure accurately except when the IWC is high or the particles too large to sublimate completely during the short transit time through the probe. The IWC estimated from the particle probes are accurate when direct measurements are available to provide constraints and useful information in high IWC/large particle situations. Because of the discrepancy in sigma estimates between the direct and indirect approaches, there is a factor of 2 to 3 difference in [IWC/sigma] between them. Although there are significant uncertainties involved in its use, comparisons with several independent data sources suggest that the indirect method is the more accurate of the two approaches. However, experiments are needed to resolve the source of the discrepancy in sigma.

Heymsfield, Andrew J.↗

Near-global survey of effective droplet radii in liquid water clouds using ISCCP data

A global survey of cloud particle size variations can provide crucial constraints on how cloud processes determine cloud liquid water contents and their variation with temperature, and further, may indicate the magnitude of aerosol effects on clouds. A method, based on a complete radiative transfer model for Advanced Very High Resolution Radiometer (AVHRR)-measured radiances, is described for retrieving cloud particle radii in liquid water clouds from satellite data currently available from the International Satellite Cloud Climatology Project. Results of sensitivity tests and validation studies provide error estimates. AVHRR data from NOAA-9 and NOAA-10 have been analyzed for January, April, July and October in 1987 and 1988. The results of this first survey reveal systematic continental and maritime differences and hemispheric contrasts that are indicative of the effects of associated aerosol concentration differences: cloud droplet radii in continental water clouds are about 2-3 micrometers smaller than in marine clouds, and droplet radii are about 1 micrometer smaller in marine clouds of the Northern Hemisphere than in the Southern Hemisphere. The height dependencies of cloud droplet radii in continental and marine clouds are also consistent with differences in the vertical profiles of aerosol concentration. Significant seasonal and diurnal variations of effective droplet radii are also observed, particularly at lower latitudes. Variations of the relationship between cloud optical thickness and droplet radii may indicate variations in cloud microphysical regimes.

Han, Qingyan↗

Influence of Aerosols on the Shortwave Cloud Radiative Forcing from North Pacific Oceanic Clouds: Results from the Cloud Indirect Forcing Experiment (CIFEX)

Aerosols over the Northeastern Pacific Ocean enhance the cloud drop number concentration and reduce the drop size for marine stratocumulus and cumulus clouds. These microphysical effects result in brighter clouds, as evidenced by a combination of aircraft and satellite observations. In-situ measurements from the Cloud Indirect Forcing Experiment (CIFEX) indicate that the mean cloud drop number concentration in low clouds over the polluted marine boundary layer is greater by 53 cm(sup -3) compared to clean clouds, and the mean cloud drop effective radius is smaller by 4 micrometers. We link these in-situ measurements of cloud modification by aerosols, for the first time, with collocated satellite broadband radiative flux observations from the Clouds and the Earth s Radiant Energy System to show that these microphysical effects of aerosols enhance the top-of-atmosphere cooling by -.9.9 plus or minus 4.3 W m(sup -2) for overcast conditions.

Wilcox, Eric M.↗

Study of the Effect of Temporal Sampling Frequency on DSCOVR Observations Using the GEOS-5 Nature Run Results: Cloud Coverage - Part II

This is the second part of a study on how temporal sampling frequency affects satellite retrievals in support of the Deep Space Climate Observatory (DSCOVR) mission. Continuing from Part 1, which looked at Earth's radiation budget, this paper presents the effect of sampling frequency on DSCOVR-derived cloud fraction. The output from NASA's Goddard Earth Observing System version 5 (GEOS-5) Nature Run is used as the "truth". The effect of temporal resolution on potential DSCOVR observations is assessed by subsampling the full Nature Run data. A set of metrics, including uncertainty and absolute error in the subsampled time series, correlation between the original and the subsamples, and Fourier analysis have been used for this study. Results show that, for a given sampling frequency, the uncertainties in the annual mean cloud fraction of the sunlit half of the Earth are larger over land than over ocean. Analysis of correlation coefficients between the subsamples and the original time series demonstrates that even though sampling at certain longer time intervals may not increase the uncertainty in the mean, the subsampled time series is further and further away from the "truth" as the sampling interval becomes larger and larger. Fourier analysis shows that the simulated DSCOVR cloud fraction has underlying periodical features at certain time intervals, such as 8, 12, and 24 h. If the data is subsampled at these frequencies, the uncertainties in the mean cloud fraction are higher. These results provide helpful insights for the DSCOVR temporal sampling strategy.

GEOS-5↗

Impacts of Wildfire Aerosols on Global Energy Budget and Climate: The Role of Climate Feedbacks

Aerosols emitted from wildfires could significantly affect global climate through perturbing global radiation balance. In this study, the Community Earth System Model with prescribed daily fire aerosol emissions is used to investigate fire aerosols’ impacts on global climate with emphasis on the role of climate feedbacks. The total global fire aerosol radiative effect (RE) is estimated to be -0.78 ± 0.29 W m -2 , which is mostly from shortwave RE due to aerosol–cloud interactions (REaci; -0.70 ± 0.20 W m -2 ). The associated global annual-mean surface air temperature (SAT) change ΔT is -0.64 ± 0.16 K with the largest reduction in the Arctic regions where the shortwave REaci is strong. Associated with the cooling, the Arctic sea ice is increased, which acts to reamplify the Arctic cooling through a positive ice-albedo feedback. The fast response (irrelevant to ΔT) tends to decrease surface latent heat flux into atmosphere in the tropics to balance strong atmospheric fire black carbon absorption, which reduces the precipitation in the tropical land regions (southern Africa and South America). The climate feedback processes (associated with ΔT) lead to a significant surface latent heat flux reduction over global ocean areas, which could explain most (~80%) of the global precipitation reduction. The precipitation significantly decreases in deep tropical regions (5°N) but increases in the Southern Hemisphere tropical ocean, which is associated with the southward shift of the intertropical convergence zone and the weakening of Southern Hemisphere Hadley cell. Such changes could partly compensate the interhemispheric temperature asymmetry induced by boreal forest fire aerosol indirect effects, through intensifying the cross-equator atmospheric heat transport.

54 ENVIRONMENTAL SCIENCES↗

Integrative Analysis of Desert Dust Size and Abundance Suggests Less Dust Climate Cooling

Desert dust aerosols affect Earths global energy balance through interactions with radiation, clouds, and ecosystems. But the magnitudes of these effects are so uncertain that it remains unclear whether atmospheric dust has a net warming or cooling effect on global climate. Consequently, it is still uncertain whether large changes in atmospheric dust loading over the past century have slowed or accelerated anthropogenic climate change, and the climate impact of possible future alterations in dust loading is similarly disputed. Here we use an integrative analysis of dust aerosol sizes and abundance to constrain the climatic impact of dust through direct interactions with radiation. Using a combination of observational, experimental, and model data, we find that atmospheric dust is substantially coarser than represented in current climate models. Since coarse dust warms global climate, the dust direct radiative effect (DRE) is likely less cooling than the 0.4 W m superscript 2 estimated by models in a current ensemble. We constrain the dust DRE to -0.20 (-0.48 to +0.20) W m superscript 2, which suggests that the dust DRE produces only about half the cooling that current models estimate, and raises the possibility that dust DRE is actually net warming the planet.

Atmospheric chemistry↗

PACE Technical Report Series, Volume 4: Cloud Retrievals in the PACE Mission: PACE Science Team Consensus Document

Earth is a complex dynamical system exhibiting continuous change in its atmosphere, ocean,and surface elements. Nearly all (99.97%) of the energy driving these systems is linked to the Sun. Measurements of reflected sunlight contain a unique signature of wavelength-specific scattering and absorption interactions occurring between incoming solar energy and atmospheric (molecules, aerosols,clouds) and surface features Clouds can affect significantly both shortwave and long wave radiation, depending on altitude/vertical structure, thermodynamic phase, and optical properties. Low, warm, and optically thick clouds predominantly have a cooling effect, while high, cold, optically thin clouds can cause warming by absorbing warmer radiation emitted from the surface and lower atmosphere.When the net difference between outgoing and incoming solar radiation is matched by the net infrared radiation emitted to space, the Earth's climate is in radiative balance. While radiative forcing components (GHGs, aerosols - direct and indirect) contribute to a net radiative imbalance, climate sensitivity is ultimately determined by the contribution of various system feed backs. The role of cloud feedback in a warming climate is currently the largest inter-model uncertainty in climate sensitivity and therefore in climate prediction [Bony and Dufresne 2005]. A comprehensive understanding of current cloud propertiesand dynamic/microphysical processes requires a global perspective from satellites.

Plankton, Aerosol, Cloud, ocean Ecosystem (PACE)↗

On the characteristics of aerosol indirect effect based on dynamic regimes in global climate models

Aerosol-cloud interactions continue to constitute a major source of uncertainty for the estimate of climate radiative forcing. The variation of aerosol indirect effects (AIE) in climate models is investigated across different dynamical regimes, determined by monthly mean 500 hPa vertical pressure velocity (ω500), lower-tropospheric stability (LTS) and large-scale surface precipitation rate derived from several global climate models (GCMs), with a focus on liquid water path (LWP) response to cloud condensation nuclei (CCN) concentrations. The LWP sensitivity to aerosol perturbation within dynamic regimes is found to exhibit a large spread among these GCMs. It is in regimes of strong large-scale ascend (ω500 < -25 hPa/d) and low clouds (stratocumulus and trade wind cumulus) where the models differ most. Shortwave aerosol indirect forcing is also found to differ significantly among different regimes. Shortwave aerosol indirect forcing in ascending regimes is as large as that in stratocumulus regimes, which indicates that regimes with strong large-scale ascend are as important as stratocumulus regimes in studying AIE. 42" It is further shown that shortwave aerosol indirect forcing over regions with high monthly large-scale surface precipitation rate (> 0.1 mm/d) contributes the most to the total aerosol indirect forcing (from 64% to nearly 100%). Results show that the uncertainty in AIE is even larger within specific dynamical regimes than that globally, pointing to the need to reduce the uncertainty in AIE in different dynamical regimes.

Zhang, S.↗

Aerosol Effects on Cirrus through Ice Nucleation in the Community Atmosphere Model CAM5 with a Statistical Cirrus Scheme

A statistical cirrus cloud scheme that tracks ice saturation ratio in the clear-sky and cloudy portion of a grid box separately has been implemented into NCAR CAM5 to provide a consistent treatment of ice nucleation and cloud formation. Simulated ice supersaturation and ice crystal number concentrations strongly depend on the number concentrations of heterogeneous ice nuclei (IN), subgrid temperature formulas and the number concentration of sulfate particles participating in homogeneous freezing, while simulated ice water content is insensitive to these perturbations. 1% to 10% dust particles serving as heterogeneous IN is 20 found to produce ice supersaturaiton in better agreement with observations. Introducing a subgrid temperature perturbation based on long-term aircraft observations of meso-scale motion produces a better hemispheric contrast in ice supersaturation compared to observations. Heterogeneous IN from dust particles significantly alter the net radiative fluxes at the top of atmosphere (TOA) (-0.24 to -1.59 W m-2) with a significant clear-sky longwave component (0.01 to -0.55 W m-2). Different cirrus treatments significantly perturb the net TOA anthropogenic aerosol forcing from -1.21 W m-2 to -1.54 W m-2, with a standard deviation of 0.10 W m-2. Aerosol effects on cirrus clouds exert an even larger impact on the atmospheric component of the radiative fluxes (two or three times the changes in the TOA radiative fluxes) and therefore on the hydrology cycle through the fast atmosphere response. This points to the urgent need to quantify aerosol effects on cirrus clouds through ice nucleation and how these further affect the hydrological cycle.

Wang, Minghuai↗

Remote sensing estimates of cirrus particle size for tropical and midlatitude cirrus: Hexagonal crystals and ice spheres

A large discrepancy exists in current estimates of a mean cirrus particle size appropriate for calculations of the effects of these ice clouds on solar and thermal infrared radiative fluxes. For spheres with large size parameter (x = (2 pi r / lambda) is greater than 30, where r is particle radius), and moderate absorption (n(sup i) x less than 1, where n(sup i) is imaginary index of refraction for ice), the optimal effective particle radius is given by: r(sub e) = integral of r(exp 3)n(r)dr / integral of r(exp 2)n(r)dr. For the remote sensing of cirrus particle size at wavelengths of 0.83, 1.65, and 2.21 mu m, a 50 mu m ice sphere would have a size parameter of about 200, and values of n(sup i) x of 0, 0.045, and 0.06, satisfying the above conditions. However, while r(sub e) is a well-defined parameter for spheres, this cross-section area-weighted particle radius can only be extended to non-spherical particles by defining some equivalent sphere, typically an equivalent volume or equivalent cross-section area sphere. Using equivalent volume spheres, values of r(sub e) obtained over Lake Michigan on October 28, 1986, during FIRE phase I varied from 200 mu m (King Air 2D Imaging probes) to 60 mu m (Landsat reflectances at 0.83, 1.65, and 2.2 mu m), to 25 mu m (HIS spectrometer thermal emission between 8 and 12 mu m). Three major uncertainties were identified in this comparison: small ice particles missed by the 2D-C aircraft probes, uncertain ice refractive index, and uncertainties in the single scatter albedos and scattering phase functions used in the radiative calculations. Since the first FIRE cirrus results, advances have been made in all three areas. The present paper reports on improvements in the radiative modeling of ice particles at 0.83, 1.65, and 2.21 mu m wavelengths appropriate for comparisons to Landsat Thematic Mapper data. The paper also includes new results for Landsat observations of ice clouds in the eastern and western tropical Pacific.

Wielicki, Bruce A.↗

Determination of cloud parameters from infrared sounder data

The World Climate Research Programme (WCRP) plan is concerned with the need to develop a uniform global cloud climatology as part of a broad research program on climate processes. The International Satellite Cloud Climatology Project (ISCCP) has been approved as the first project of the WCRP. The ISCCP has the basic objective to collect and analyze satellite radiance data to infer the global distribution of cloud radiative properties in order to improve the modeling of cloud effects on climate. Research is conducted to explore an algorithm for retrieving cloud properties by utilizing the available infrared sounder data from polar-orbiting satellites. A numerical method is developed for computing cloud top heights, amount, and emissivity on the basis of a parameterized infrared radiative transfer equation for cloudy atmospheres. Theoretical studies were carried out by considering a synthetic atmosphere.

Yeh, H.-Y. M.↗