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NASA NTRS2005

Thermodynamic and cloud parameter retrieval using infrared spectral data

High-resolution infrared radiance spectra obtained from near nadir observations provide atmospheric, surface, and cloud property information. A fast radiative transfer model, including cloud effects, is used for atmospheric profile and cloud parameter retrieval. The retrieval algorithm is presented along with its application to recent field experiment data from the NPOESS Airborne Sounding Testbed - Interferometer (NAST-I). The retrieval accuracy dependence on cloud properties is discussed. It is shown that relatively accurate temperature and moisture retrievals can be achieved below optically thin clouds. For optically thick clouds, accurate temperature and moisture profiles down to cloud top level are obtained. For both optically thin and thick cloud situations, the cloud top height can be retrieved with an accuracy of approximately 1.0 km. Preliminary NAST-I retrieval results from the recent Atlantic-THORPEX Regional Campaign (ATReC) are presented and compared with coincident observations obtained from dropsondes and the nadir-pointing Cloud Physics Lidar (CPL).

Zhou, Daniel K.↗

NASA NTRS2005

A Coupled fcGCM-GCE Modeling System: A 3D Cloud Resolving Model and a Regional Scale Model

Recent GEWEX Cloud System Study (GCSS) model comparison projects have indicated that cloud-resolving models (CRMs) agree with observations better than traditional single-column models in simulating various types of clouds and cloud systems from different geographic locations. Current and future NASA satellite programs can provide cloud, precipitation, aerosol and other data at very fine spatial and temporal scales. It requires a coupled global circulation model (GCM) and cloud-scale model (termed a super-parameterization or multi-scale modeling framework, MMF) to use these satellite data to improve the understanding of the physical processes that are responsible for the variation in global and regional climate and hydrological systems. The use of a GCM will enable global coverage, and the use of a CRM will allow for better and ore sophisticated physical parameterization. NASA satellite and field campaign cloud related datasets can provide initial conditions as well as validation for both the MMF and CRMs. The Goddard MMF is based on the 2D Goddard Cumulus Ensemble (GCE) model and the Goddard finite volume general circulation model (fvGCM), and it has started production runs with two years results (1998 and 1999). Also, at Goddard, we have implemented several Goddard microphysical schemes (21CE, several 31CE), Goddard radiation (including explicity calculated cloud optical properties), and Goddard Land Information (LIS, that includes the CLM and NOAH land surface models) into a next generation regional scale model, WRF. In this talk, I will present: (1) A Brief review on GCE model and its applications on precipitation processes (microphysical and land processes), (2) The Goddard MMF and the major difference between two existing MMFs (CSU MMF and Goddard MMF), and preliminary results (the comparison with traditional GCMs), (3) A discussion on the Goddard WRF version (its developments and applications), and (4) The characteristics of the four-dimensional cloud data sets (or cloud library) stored at Goddard.

Tao, Wei-Kuo↗

NASA NTRS2005

View angle dependence of cloud optical thicknesses retrieved by MODIS

This study examines whether cloud inhomogeneity influences the view angle dependence of MODIS cloud optical thickness (tau) retrieval results. The degree of cloud inhomogeneity is characterized through the local gradient in 11 microns brightness temperature. The analysis of liquid phase clouds in a one year long global dataset of Collection 4 MODIS data reveals that while optical thickness retrievals give remarkably consistent results for all view directions if clouds are homogeneous, they give much higher tau-values for oblique views than for overhead views if clouds are inhomogeneous and the sun is fairly oblique. For solar zenith angles larger than 55deg, the mean optical thickness retrieved for the most inhomogeneous third of cloudy pixels is more than 30% higher for oblique views than for overhead views. After considering a variety of possible scenarios, the paper concludes that the most likely reason for the increase lies in three-dimensional radiative interactions that are not considered in current, one-dimensional retrieval algorithms. Namely, the radiative effect of cloud sides viewed at oblique angles seems to contribute most to the enhanced tau-values. The results presented here will help understand cloud retrieval uncertainties related to cloud inhomogeneity. They complement the uncertainty estimates that will start accompanying MODIS cloud products in Collection 5 and may eventually help correct for the observed view angle dependent biases.

Marshak, Alexander↗

NASA NTRS2006

Overview of CERES Cloud Properties Derived From VIRS AND MODIS DATA

Simultaneous measurement of radiation and cloud fields on a global basis is recognized as a key component in understanding and modeling the interaction between clouds and radiation at the top of the atmosphere, at the surface, and within the atmosphere. The NASA Clouds and Earth s Radiant Energy System (CERES) Project (Wielicki et al., 1998) began addressing this issue in 1998 with its first broadband shortwave and longwave scanner on the Tropical Rainfall Measuring Mission (TRMM). This was followed by the launch of two CERES scanners each on Terra and Aqua during late 1999 and early 2002, respectively. When combined, these satellites should provide the most comprehensive global characterization of clouds and radiation to date. Unfortunately, the TRMM scanner failed during late 1998. The Terra and Aqua scanners continue to operate, however, providing measurements at a minimum of 4 local times each day. CERES was designed to scan in tandem with high resolution imagers so that the cloud conditions could be evaluated for every CERES measurement. The cloud properties are essential for converting CERES radiances shortwave albedo and longwave fluxes needed to define the radiation budget (ERB). They are also needed to unravel the impact of clouds on the ERB. The 5-channel, 2-km Visible Infrared Scanner (VIRS) on the TRMM and the 36-channel 1-km Moderate Resolution Imaging Spectroradiometer (MODIS) on Terra and Aqua are analyzed to define the cloud properties for each CERES footprint. To minimize inter-satellite differences and aid the development of useful climate-scale measurements, it was necessary to ensure that each satellite imager is calibrated in a fashion consistent with its counterpart on the other CERES satellites (Minnis et al., 2006) and that the algorithms are as similar as possible for all of the imagers. Thus, a set of cloud detection and retrieval algorithms were developed that could be applied to all three imagers utilizing as few channels as possible while producing stable and accurate cloud properties. This paper discusses the algorithms and results of applying those techniques to more than 5 years of Terra MODIS, 3 years of Aqua MODIS, and 4 years of TRMM VIRS data.

Minis, Patrick↗

NASA NTRS2006

Multilayered Clouds Identification and Retrieval for CERES Using MODIS

Traditionally, analyses of satellite data have been limited to interpreting the radiances in terms of single layer clouds. Generally, this results in significant errors in the retrieved properties for multilayered cloud systems. Two techniques for detecting overlapped clouds and retrieving the cloud properties using satellite data are explored to help address the need for better quantification of cloud vertical structure. The first technique was developed using multispectral imager data with secondary imager products (infrared brightness temperature differences, BTD). The other method uses microwave (MWR) data. The use of BTD, the 11-12 micrometer brightness temperature difference, in conjunction with tau, the retrieved visible optical depth, was suggested by Kawamoto et al. (2001) and used by Pavlonis et al. (2004) as a means to detect multilayered clouds. Combining visible (VIS; 0.65 micrometer) and infrared (IR) retrievals of cloud properties with microwave (MW) retrievals of cloud water temperature Tw and liquid water path LWP retrieved from satellite microwave imagers appears to be a fruitful approach for detecting and retrieving overlapped clouds (Lin et al., 1998, Ho et al., 2003, Huang et al., 2005). The BTD method is limited to optically thin cirrus over low clouds, while the MWR method is limited to ocean areas only. With the availability of VIS and IR data from the Moderate Resolution Imaging Spectroradiometer (MODIS) and MW data from the Advanced Microwave Scanning Radiometer EOS (AMSR-E), both on Aqua, it is now possible to examine both approaches simultaneously. This paper explores the use of the BTD method as applied to MODIS and AMSR-E data taken from the Aqua satellite over non-polar ocean surfaces.

Sun-Mack, Sunny↗

NASA NTRS2006

Using Multi-scale Modeling System to Study the Interactions between Clouds, Precipitation, Aerosols, Radiation and Land Surface

Numerical cloud models, which are based the non-hydrostatic equations of motion, have been extensively applied to cloud-scale and mesoscale processes during the past four decades. Because cloud-scale dynamics are treated explicitly, uncertainties stemming from convection that have to be parameterized in (hydrostatic) large-scale models are obviated, or at least mitigated, in cloud models. Global models will use the non-hydrostatic framework when their horizontal resolution becomes about 10 kilometers, the theoretical limit for the hydrostatic approximation. This juncture will be reached one to two decades from now. Over the past generation, voluminous datasets on atmospheric convection have been accumulated from radar, instrumented aircraft, satellites, and rawinsonde measurements in field campaigns, enabling the detailed evaluation of models. Improved numerical methods have resulted in more accurate and efficient dynamical cores in models. Improvements have been made in the parameterizations of microphysical processes, radiation, boundary-layer effects, and turbulence; however, microphysical parameterizations remain a major source of uncertainty in all classes of atmospheric models. In recent years, exponentially increasing computer power has extended cloud-resolving-model integrations from hours to months, the number of computational grid points from less than a thousand to close to ten million. Three-dimensional models are now more prevalent. Much attention is devoted to precipitating cloud systems where the crucial 1-kilometer scales are resolved in horizontal domains as large as 10,000 kilometers in two-dimensions, and 1,000 x 1,000 square kilometers in three-dimensions. Cloud models now provide statistical information useful for developing more realistic physically based parameterizations for climate models and numerical weather prediction models. It is also expected that NWP and mesoscale model can be run in grid size similar to cloud resolving model through nesting technique. A review of developments, improvements and applications of cloud models (GCE and WRF) at Goddard will be presented in this talk. In particular, a new approach to using multi-scale modeling system to study the interactions between clouds, precipitation, aerosols and land will be presented.

Tao, Wei-Kuo↗

NASA NTRS2006

Using Multi-scale Modeling System to Study the Interactions between Clouds, Precipitation, Aerosols, Radiation and Land Surface

Numerical cloud models, which are based the non-hydrostatic equations of motion, have been extensively applied to cloud-scale and mesoscale processes during the past four decades. Because cloud-scale dynamics are treated explicitly, uncertainties stemming from convection that have to be parameterized in (hydrostatic) large-scale models are obviated, or at least mitigated, in cloud models. Global models will use the non-hydrostatic framework when their horizontal resolution becomes about 10 kilometers, the theoretical limit for the hydrostatic approximation. This juncture will be reached one to two decades from now. Over the past generation, voluminous datasets on atmospheric convection have been accumulated from radar, instrumented aircraft, satellites, and rawinsonde measurements in field campaigns, enabling the detailed evaluation of models. Improved numerical methods have resulted in more accurate and efficient dynamical cores in models. Improvements have been made in the parameterizations of microphysical processes, radiation, boundary-layer effects, and turbulence; however, microphysical parameterizations remain a major source of uncertainty in all classes of atmospheric models. In recent years, exponentially increasing computer power has extended cloud-resolving-model integrations from hours to months, the number of computational grid points from less than a thousand to close to ten million. Three-dimensional models are now more prevalent. Much attention is devoted to precipitating cloud systems where the crucial-lkm scales are resolved in horizontal domains as large as 10,000 kilometers in two-dimensions, and 1,000 x 1,000 square kilometers in three-dimensions. Cloud models now provide statistical information useful for developing more realistic physically based parameterizations for climate models and numerical weather prediction models. It is also expected that NWP and mesoscale model can be run in grid size similar to cloud resolving model through nesting technique. A review of developments, improvements and applications of cloud models (GCE and WRF) at Goddard wlll be is presented in this talk. In particular, a new approach to using multi-scale modeling system to study the interactions between clouds, precipitation, aerosols and land will be presented.

Tao, Wei-Kuo↗

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 NTRS2007

Aerosol Radiative Effects on Deep Convective Clouds and Associated Radiative Forcing

The aerosol radiative effects (ARE) on the deep convective clouds are investigated by using a spectral-bin cloud-resolving model (CRM) coupled with a radiation scheme and an explicit land surface model. The sensitivity of cloud properties and the associated radiative forcing to aerosol single-scattering albedo (SSA) are examined. The ARE on cloud properties is pronounced for mid-visible SSA of 0.85. Relative to the case excluding the ARE, cloud fraction and optical depth decrease by about 18% and 20%, respectively. Cloud droplet and ice particle number concentrations, liquid water path (LWP), ice water path (IWP), and droplet size decrease significantly when the ARE is introduced. The ARE causes a surface cooling of about 0.35 K and significantly high heating rates in the lower troposphere (about 0.6K/day higher at 2 km), both of which lead to a more stable atmosphere and hence weaker convection. The weaker convection and the more desiccation of cloud layers explain the less cloudiness, lower cloud optical depth, LWP and IWP, smaller droplet size, and less precipitation. The daytime-mean direct forcing induced by black carbon is about 2.2 W/sq m at the top of atmosphere (TOA) and -17.4 W/sq m at the surface for SSA of 0.85. The semi-direct forcing is positive, about 10 and 11.2 W/sq m at the TOA and surface, respectively. Both the TOA and surface total radiative forcing values are strongly negative for the deep convective clouds, attributed mostly to aerosol indirect forcing. Aerosol direct and semi-direct effects are very sensitive to SSA. Because the positive semi-direct forcing compensates the negative direct forcing at the surface, the surface temperature and heat fluxes decrease less significantly with the increase of aerosol absorption (decreasing SSA). The cloud fraction, optical depth, convective strength, and precipitation decrease with the increase of absorption, resulting from a more stable and dryer atmosphere due to enhanced surface cooling and atmospheric heating.

Fan, J.↗

NASA NTRS2007

The Mixed-Phase Arctic Cloud Experiment (M-PACE)

The Mixed-Phase Arctic Cloud Experiment (M-PACE) was conducted September 27 through October 22, 2004 on the North Slope of Alaska. The primary objective was to collect a data set suitable to study interactions between microphysics, dynamics and radiative transfer in mixed-phase Arctic clouds. Observations taken during the 1997/1998 Surface Heat and Energy Budget of the Arctic (SHEBA) experiment revealed that Arctic clouds frequently consist of one (or more) liquid layers precipitating ice. M-PACE sought to investigate the physical processes of these clouds utilizing two aircraft (an in situ aircraft to characterize the microphysical properties of the clouds and a remote sensing aircraft to constraint the upwelling radiation) over the Department of Energy s Atmospheric Radiation Measurement (ARM) Climate Research Facility (ACRF) on the North Slope of Alaska. The measurements successfully documented the microphysical structure of Arctic mixed-phase clouds, with multiple in situ profiles collected in both single-layer and multi-layer clouds over two ground-based remote sensing sites. Liquid was found in clouds with temperatures down to -30 C, the coldest cloud top temperature below -40 C sampled by the aircraft. Remote sensing instruments suggest that ice was present in low concentrations, mostly concentrated in precipitation shafts, although there are indications of light ice precipitation present below the optically thick single-layer clouds. The prevalence of liquid down to these low temperatures could potentially be explained by the relatively low measured ice nuclei concentrations.

Verlinde, J.↗

NASA NTRS2007

Integrated Cloud-Aerosol-Radiation Product using CERES, MODIS, CALIPSO and CloudSat Data

This paper documents the development of the first integrated data set of global vertical profiles of clouds, aerosols, and radiation using the combined NASA A-Train data from the Aqua Clouds and Earth's Radiant Energy System (CERES) and Moderate Resolution Imaging Spectroradiometer (MODIS), Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO), and CloudSat. As part of this effort, cloud data from the CALIPSO lidar and the CloudSat radar are merged with the integrated column cloud properties from the CERES-MODIS analyses. The active and passive datasets are compared to determine commonalities and differences in order to facilitate the development of a 3- dimensional cloud and aerosol dataset that will then be integrated into the CERES broadband radiance footprint. Preliminary results from the comparisons for April 2007 reveal that the CERES-MODIS global cloud amounts are, on average, 0.14 less and 0.15 greater than those from CALIPSO and CloudSat, respectively. These new data will provide unprecedented ability to test and improve global cloud and aerosol models, to investigate aerosol direct and indirect radiative forcing, and to validate the accuracy of global aerosol, cloud, and radiation data sets especially in polar regions and for multi-layered cloud conditions.

Sun-Mack, Sunny↗

NASA NTRS2006

Seasonal and Interannual Variations of Top-of-Atmosphere Irradiance and Cloud Cover over Polar Regions Derived from the CERES Data Set

The semi-direct effects of dust aerosols are analyzed over eastern Asia using 2 years (June 2002 to June 2004) of data from the Clouds and the Earth s Radiant Energy System (CERES) scanning radiometer and MODerate Resolution Imaging Spectroradiometer (MODIS) on the Aqua satellite, and 18 years (1984 to 2001) of International Satellite Cloud Climatology Project (ISCCP) data. The results show that the water path of dust-contaminated clouds is considerably smaller than that of dust-free clouds. The mean ice water path (IWP) and liquid water path (LWP) of dusty clouds are less than their dust-free counterparts by 23.7% and 49.8%, respectively. The long-term statistical relationship derived from ISCCP also confirms that there is significant negative correlation between dust storm index and ISCCP cloud water path. These results suggest that dust aerosols warm clouds, increase the evaporation of cloud droplets and further reduce cloud water path, the so-called semi-direct effect. The semi-direct effect may play a role in cloud development over arid and semi-arid areas of East Asia and contribute to the reduction of precipitation.

Kato, Seiji↗

NASA NTRS2006

Satellite-Based Assessment of Possible Dust Aerosols Semi-Direct Effect on Cloud Water Path over East Asia

Huang, Jianping↗

NASA NTRS2006

Determination of Ice Water Path in Ice-over-Water Cloud Systems Using Combined MODIS and AMSR-E Measurements

To provide more accurate ice cloud properties for evaluating climate models, the updated version of multi-layered cloud retrieval system (MCRS) is used to retrieve ice water path (IWP) in ice-over-water cloud systems over global ocean using combined instrument data from the Aqua satellite. The liquid water path (LWP) of lower layer water clouds is estimated from the Advanced Microwave Scanning Radiometer for EOS (AMSR-E) measurements. With the lower layer LWP known, the properties of the upper-level ice clouds are then derived from Moderate Resolution Imaging Spectroradiometer measurements by matching simulated radiances from a two-cloud layer radiative transfer model. Comparisons with single-layer cirrus systems and surface-based radar retrievals show that the MCRS can significantly improve the accuracy and reduce the over-estimation of optical depth and ice water path retrievals for ice over-water cloud systems. During the period from December 2004 through February 2005, the mean daytime ice cloud optical depth and IWP for overlapped ice-over-water clouds over ocean from Aqua are 7.6 and 146.4 gm(sup -2), respectively, significantly less than the initial single layer retrievals of 17.3 and 322.3 gm(sup -2). The mean IWP for actual single-layer clouds was 128.2 gm(sup -2).

Huang, Jianping↗

NASA NTRS2008

A Sample of What We Have Learned from A-Train Cloud Measurements

The A-train active sensors CloudSat and CALIPSO provide detailed information about cloud vertical structure. Coarse vertical information can also be obtained from a combination of passive sensors (e.g. cloud liquid water content from AMSR-E, cloud ice properties from MLS and HIRDLS, cloud-top pressure from MODIS and AIRS, and UVNISINear IR absorption and scattering from OMI, MODIS, and POLDER). In addition, the wide swaths of instruments such as MODIS, AIRS, OMI, POLDER, and AMSR-E can be exploited to create estimates of the three-dimensional cloud extent. We will show how data fusion from A-train sensors can be used, e.g., to detect and map the presence of multiple layer/phase clouds. Ultimately, combined cloud information from Atrain instruments will allow for estimates of heating and radiative flux at the surface as well as UV/VIS/Near IR trace-gas absorption at the overpass time on a near-global daily basis. CloudSat has also dramatically improved our interpretation of visible and UV passive measurements in complex cloudy situations such as deep convection and multiple cloud layers. This has led to new approaches for unique and accurate constituent retrievals from A-train instruments. For example, ozone mixing ratios inside tropical deep convective clouds have recently been estimated using the Aura Ozone Monitoring Instrument (OMI). Field campaign data from TC4 provide additional information about the spatial variability and origin of trace-gases inside convective clouds. We will highlight some of the new applications of remote sensing in cloudy conditions that have been enabled by the synergy between the A-train active and passive sensors.

Joiner, Joanna↗

NASA NTRS2008

Evaluation and Applications of Cloud Climatologies from CALIOP

Clouds have a major impact on the Earth radiation budget and differences in the representation of clouds in global climate models are responsible for much of the spread in predicted climate sensitivity. Existing cloud climatologies, against which these models can be tested, have many limitations. The CALIOP lidar, carried on the CALIPSO satellite, has now acquired over two years of nearly continuous cloud and aerosol observations. This dataset provides an improved basis for the characterization of 3-D global cloudiness. Global average cloud cover measured by CALIOP is about 75%, significantly higher than for existing cloud climatologies due to the sensitivity of CALIOP to optically thin cloud. Day/night biases in cloud detection appear to be small. This presentation will discuss detection sensitivity and other issues associated with producing a cloud climatology, characteristics of cloud cover statistics derived from CALIOP data, and applications of those statistics.

Winker, David↗

NASA NTRS2008

Role of Gravity Waves in Determining Cirrus Cloud Properties

Cirrus clouds are important in the Earth's radiation budget. They typically exhibit variable physical properties within a given cloud system and from system to system. Ambient vertical motion is a key factor in determining the cloud properties in most cases. The obvious exception is convectively generated cirrus (anvils), but even in this case, the subsequent cloud evolution is strongly influenced by the ambient vertical motion field. It is well know that gravity waves are ubiquitous in the atmosphere and occur over a wide range of scales and amplitudes. Moreover, researchers have found that inclusion of statistical account of gravity wave effects can markedly improve the realism of simulations of persisting large-scale cirrus cloud features. Here, we use a 1 -dimensional (z) cirrus cloud model, to systematically examine the effects of gravity waves on cirrus cloud properties. The model includes a detailed representation of cloud microphysical processes (bin microphysics and aerosols) and is run at relatively fine vertical resolution so as to adequately resolve nucleation events, and over an extended time span so as to incorporate the passage of multiple gravity waves. The prescribed gravity waves "propagate" at 15 m s (sup -1), with wavelengths from 5 to 100 km, amplitudes range up to 1 m s (sup -1)'. Despite the fact that the net gravity wave vertical motion forcing is zero, it will be shown that the bulk cloud properties, e.g., vertically-integrated ice water path, can differ quite significantly from simulations without gravity waves and that the effects do depend on the wave characteristics. We conclude that account of gravity wave effects is important if large-scale models are to generate realistic cirrus cloud property climatology (statistics).

OCStarr, David↗

NASA NTRS2007

3D Radiative Aspects of the Increased Aerosol Optical Depth Near Clouds

To characterize aerosol-cloud interactions it is important to correctly retrieve aerosol optical depth in the vicinity of clouds. It is well reported in the literature that aerosol optical depth increases with cloud cover. Part of the increase comes from real physics as humidification; another part, however, comes from 3D cloud effects in the remote sensing retrievals. In many cases it is hard to say whether the retrieved increased values of aerosol optical depth are remote sensing artifacts or real. In the presentation, we will discuss how the 3D cloud affects can be mitigated. We will demonstrate a simple model that can assess the enhanced illumination of cloud-free columns in the vicinity of clouds. This model is based on the assumption that the enhancement in the cloud-free column radiance comes from the enhanced Rayleigh scattering due to presence of surrounding clouds. A stochastic cloud model of broken cloudiness is used to simulate the upward flux.

Marshak, Alexander↗