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At least 109 records · Page 6

The Cloudsat Mission and the EOS Constellation: A New Dimension of Space-Based Observation of Clouds and Precipitation

CloudSat is a satellite experiment designed to measure the vertical structure of clouds from space. The expected launch of CloudSat is planned for 2004 and, once launched, CloudSat will orbit in formation as part of a constellation of satellites including NASA's Aqua and Aura satellites, a NASA-CNES lidar satellite (P-C) and a CNES satellite carrying a polarimeter (PARASOL). A unique feature that CloudSat brings to this constellation is the ability to fly a precise orbit enabling the fields of view of the CloudSat radar to be overlapped with the P-C lidar footprint and the other measurements of the EOS constellation. The precision of this overlap creates a unique multi-satellite observing system for studying the atmospheric processes essential to the hydrological cycle. The vertical profile of cloud properties provided by CloudSat fills a critical gap in the investigation of feedback mechanisms linking clouds to climate. Measuring the vertical profile of cloud properties requires a combination of active and passive instruments, and this will be achieved by combining the radar data of CloudSat with active and passive data from other sensors of the constellation. This paper describes the underpinning science, and gives an overview of the mission, and provides some idea of the expected products and anticipated application of these products. Notably, the CloudSat mission is expected to provide new knowledge about global cloudiness, stimulating new areas of research on clouds including data assimilation and cloud parameterization. The mission also provides an important opportunity to demonstrate active sensor technology for future scientific and tactical applications. The CloudSat mission is a partnership between NASA/JPL, the Canadian Space Agency, Colorado State University, the US Air Force, and the US Department of Energy.

Stephens, Graeme L.↗

Sensitivity of the Tropical Atmospheric Energy Balance to ENSO-Related SST Changes: Comparison of Climate Model Simulations to Observed Responses

This paper focuses on how fresh water and radiative fluxes over the tropical oceans change during ENSO warm and cold events and how these changes affect the tropical energy balance. At present, ENSO remains the most prominent known mode of natural variability at interannual time scales. While this natural perturbation to climate is quite distinct from possible anthropogenic changes in climate, adjustments in the tropical water and energy budgets during ENSO may give insight into feedback processes involving water vapor and cloud feedbacks. Although great advances have been made in understanding this phenomenon and realizing prediction skill over the past decade, our ability to document the coupled water and energy changes observationally and to represent them in climate models seems far from settled (Soden, 2000 J Climate). In a companion paper we have presented observational analyses, based principally on space-based measurements which document systematic changes in rainfall, evaporation, and surface and top-of-atmosphere (TOA) radiative fluxes. Here we analyze several contemporary climate models run with observed SSTs over recent decades and compare SST-induced changes in radiation, precipitation, evaporation, and energy transport to observational results. Among these are the NASA / NCAR Finite Volume Model, the NCAR Community Climate Model, the NCEP Global Spectral Model, and the NASA NSIPP Model. Key disagreements between model and observational results noted in the recent literature are shown to be due predominantly to observational shortcomings. A reexamination of the Langley 8-Year Surface Radiation Budget data reveals errors in the SST surface longwave emission due to biased SSTs. Subsequent correction allows use of this data set along with ERBE TOA fluxes to infer net atmospheric radiative heating. Further analysis of recent rainfall algorithms provides new estimates for precipitation variability in line with interannual evaporation changes inferred from the da Silva, Young, Levitus COADS analysis. The overall results from our analysis suggest an increase (decrease) of the hydrologic cycle during ENSO warm (cold) events at the rate of about 5 W/sq m per K of SST change. Model results agree reasonably well with this estimate of sensitivity. This rate is slightly less than that which would be expected for constant relative humidity over the tropical oceans. There remain, however, significant quantitative uncertainties in cloud forcing changes in the models as compared to observations. These differences are examined in relationship to model convection and cloud parameterizations Analysis of the possible sampling and measurement errors compared to systematic model errors is also presented.

Robertson, Franklin R.↗

Making Intercontinental Burning Influences Quantitative: Lessons on Transport and Geochemistry From the 3-D Simulation of CO in PEM-T A and TRACE-A

We report on two aspects of the simulation of global transport of plumes originating from subtropical biomass fires. We use of meteorological assimilation (MM5) at 2-degree resolution with a Grail cloud parameterization and a Blackadar-based planetary boundary layer parameterization. Ames's GRACES model provides emissions, transport, and an appropriate level of simulated chemical transformation. We have worked with passive-tracer CO or linear chemistry. This is appropriate since we find major work to be done in evaluating CO source strengths and transport mechanisms before chemical integrations could be meaningful. First, we present mechanisms by which CO and other pollutants are introduced into the free troposphere, and are then transported with hate dilution from approx. 0 to approx. 180 degrees longitude. One principal conduit for these plumes is the vernal subtropical jet; however the plumes appear at various altitudes and latitudes as they influenced by frontal motions and (most likely) radiative processes. A common, repeated pattern of transport has pollutant plumes arriving in the distant Pacific Ocean from Africa and South America at 25 degrees south and 14 km altitude. Following this, there is then a general appearance of pollution at extending down to 5 kin at more equatorial (10 S) and polar latitudes (to 45 S). Second, we evaluate the quantitative success of our simulation. (Such success requires efforts considerably beyond trajectory analyses, and is necessary for our community to claim an understanding of the effects of biomass burning on global atmospheric chemistry and the planet's trend in oxidizing capacity.) We find that we simulate most pollution episodes sampled by Glenn Sachse's CO instrument and the Blake hydrocarbon analyses during PENT A. We will present our current ideas on why our general levels appear satisfactory when the observations are within 20 ppb of background levels, but substantially miss the variability associated with the most intense biomass burning plumes. As time allows, we will speculate on the origins of a class of plumes that appear in the mid-troposphere, but are missing from our simulations.

Chatfield, Robert↗

GEWEX Cloud System Study (GCSS) Working Group on Cirrus Cloud Systems (WG2)

Status, progress and plans will be given for current GCSS (GEWEX Cloud System Study) WG2 (Working Group on Cirrus Cloud Systems) projects, including: (a) the Idealized Cirrus Model Comparison Project, (b) the Cirrus Parcel Model Comparison Project (Phase 2), and (c) the developing Hurricane Nora extended outflow model case study project. Past results will be summarized and plans for the upcoming year described. Issues and strategies will be discussed. Prospects for developing improved cloud parameterizations derived from results of GCSS WG2 projects will be assessed. Plans for NASA's CRYSTAL-FACE (Cirrus Regional Study of Tropical Anvils and Layers - Florida Area Cirrus Experiment) potential opportunities for use of those data for WG2 model simulations (future projects) will be briefly described.

Starr, David↗

Low-Level Cloud Variability over the Equatorial Cold Tongue in Observations and Models

A fourth paper now in press is, Low-level cloud variability over the equatorial cold tongue in observations and models, by D. K. Mansbach and J. R. Norris (2007, J. Climate). This study examined cloud and meteorological observations from satellite, surface, and reanalysis datasets and fount that monthly anomalies in low-level cloud amount and near-surface temperature advection are strongly negatively correlated on the southern side of the equatorial Pacific cold tongue. This inverse correlation occurs independently of relationships between cloud amount and sea surface temperature (SST) or lower tropospheric static stability (LTS) and the combination of advection plus SST or LTS explains significantly more interannual cloud variability in a multilinear regression than does SST or LTS alone. Warm anomalous advection occurs when the equatorial cold tongue is well defined and the southeastern Pacific trade winds bring relatively warm air over colder water. Ship meteorological reports and soundings show that the atmospheric surface layer becomes stratified under these conditions, thus inhibiting the upward mixing of moisture needed to sustain cloudiness against subsidence and entrainment drying. Cold anomalous advection primarily occurs when the equatorial cold tongue is weak or absent and the air-sea temperature difference is substantially negative. These conditions favor a more convective atmospheric boundary layer, greater cloud amount, and less frequent occurrence of clear sky. Examination of output from global climate models developed by the Geophysical Fluid Dynamics Laboratory (GFDL) and the National Center for Atmospheric Research (NCAR) indicates that both models generally fail to simulate the cloud-advection relationships observed on the northern and southern sides of the equatorial cold tongue. Although the GFDL atmosphere model does reproduce the expected signs of cloud-advection correlations when forced with prescribed historical SST variations, it does not consistently do so when coupled to an ocean model. The NCAR model has difficulty reproducing the observed correlations in both atmosphere-only and coupled versions. This suggests that boundary layer cloud parameterizations could be improved through better representation of the effects of advection over varying SST.

Mansbach, David K.↗

Retrieved Latent Heating from TRMM

The global hydrological cycle is central to the Earth's climate system, with rainfall and the physics of precipitation formation acting as the key links in the cycle. Two-thirds of global rainfall occurs in the tropics with the associated latent heating (LH) accounting for three-fourths of the total heat energy available to the Earth's atmosphere. In addition, fresh water provided by tropical rainfall and its variability exerts a large impact upon the structure and motions of the upper ocean layer. In the last decade, it has been established that standard products of LH from satellite measurements, particularly TRMM measurements, would be a valuable resource for scientific research and applications. Such products would enable new insights and investigations concerning the complexities of convection system life cycles, the diabatic heating controls and feedbacks related to meso-synoptic circulations and their forecasting, the relationship of tropical patterns of LH to the global circulation and climate, and strategies for improving cloud parameterizations in environmental prediction models. The status of retrieved TRMM LH products, TRMM LH inter-comparison and validation project, current TRMM LH applications and critic issues/action items (based on previous five TRMM LH workshops) is presented in this article.

Tao, Wei-Kuo↗

Monte Carlo Bayesian Inference on a Statistical Model of Sub-gridcolumn Moisture Variability Using High-resolution Cloud Observations : Sensitivity Tests and Results - Part II

Part I presented a Monte Carlo Bayesian method for constraining a complex statistical model of GCM sub-gridcolumn moisture variability using high-resolution MODIS cloud data, thereby permitting large-scale model parameter estimation and cloud data assimilation. This part performs some basic testing of this new approach, verifying that it does indeed significantly reduce mean and standard deviation biases with respect to the assimilated MODIS cloud optical depth, brightness temperature and cloud top pressure, and that it also improves the simulated rotational-Ramman scattering cloud optical centroid pressure (OCP) against independent (non-assimilated) retrievals from the OMI instrument. Of particular interest, the Monte Carlo method does show skill in the especially difficult case where the background state is clear but cloudy observations exist. In traditional linearized data assimilation methods, a subsaturated background cannot produce clouds via any infinitesimal equilibrium perturbation, but the Monte Carlo approach allows finite jumps into regions of non-zero cloud probability. In the example provided, the method is able to restore marine stratocumulus near the Californian coast where the background state has a clear swath. This paper also examines a number of algorithmic and physical sensitivities of the new method and provides guidance for its cost-effective implementation. One obvious difficulty for the method, and other cloud data assimilation methods as well, is the lack of information content in the cloud observables on cloud vertical structure, beyond cloud top pressure and optical thickness, thus necessitating strong dependence on the background vertical moisture structure. It is found that a simple flow-dependent correlation modification due to Riishojgaard (1998) provides some help in this respect, by better honoring inversion structures in the background state.

Monte Carlo Bayesian inference↗

Climates of Warm Earth-Like Planets. I. 3D Model Simulations

We present a large ensemble of simulations of an Earth-like world with increasing insolation and rotation rate. Unlike previous work utilizing idealized aquaplanet congurations we focus our simulations on modern Earth-like topography. The orbital period is the same as modern Earth, but with zero obliquity and eccentricity. The atmosphere is 1 bar N2-dominated with CO2=400 ppmv and CH4=1 ppmv. The simulations include two types of oceans; one without ocean heat transport (OHT) between grid cells as has been commonly used in the exoplanet literature, while the other is a fully coupled dynamic bathtub type ocean. The dynamical regime transitions that occur as day length increases induce climate feedbacks producing cooler temperatures, rst via the reduction of water vapor with increasing rotation period despite decreasing shortwave cooling by clouds, and then via decreasing water vapor and increasing shortwave cloud cooling, except at the highest insolations. Simulations without OHT are more sensitive to insolation changes for fast rotations while slower rotations are relatively insensitive to ocean choice. OHT runs with faster rotations tend to be similar with gyres transporting heat poleward making them warmer than those without OHT. For slower rotations OHT is directed equator-ward and no high latitude gyres are apparent. Uncertainties in cloud parameterization preclude a precise determination of habitability but do not a affect robust aspects of exoplanet climate sensitivity. This is the first paper in a series that will investigate aspects of habitability in the simulations presented herein. The datasets from this study are open source and publicly available.

Planetary systems↗

AWARE: The Atmospheric Radiation Measurement (ARM) West Antarctic Radiation Experiment

The US Department of Energy Atmospheric Radiation Measurement (ARM) West Antarctic Radiation Experiment (AWARE) performed comprehensive meteorological and aerosol measurements, and ground-based atmospheric remote sensing at two Antarctic stations using the most advanced instrumentation available. A suite of cloud research radars, lidars, spectral and broadband radiometers, aerosol chemical and microphysical sampling equipment, and meteorological instrumentation was deployed at McMurdo Station on Ross Island from December 2015 through December 2016. A smaller suite of radiometers and meteorological equipment including radiosondes, optimized for surface energy budget measurement, was deployed on the West Antarctic Ice Sheet between 4 December 2015 and 17 January 2016. AWARE provided Antarctic atmospheric data comparable to several well-instrumented high Arctic sites that have operated for many years and that reveal numerous contrasts with the Arctic in aerosol and cloud microphysical properties. These include persistent differences in liquid cloud occurrence, cloud height and cloud thickness. Antarctic aerosol properties are also quite different from the Arctic in both seasonal cycle and composition, due to the continent’s isolation from lower latitudes by Southern Ocean storm tracks. Antarctic aerosol number and mass concentrations are not only non-negligible but perhaps play a more important role than previously recognized because of the higher sensitivities of clouds at the very low concentrations caused by the large-scale dynamical isolation. Antarctic aerosol chemical composition, particularly organic components, has implications for local cloud microphysics. The AWARE data set, fully available online in the ARM Program data archive, offers numerous case studies for unique and rigorous evaluation of mixed-phase cloud parameterization in climate models.

Atmospheric Radiation Measurement (ARM)↗

Evaluation of a New Cloud Droplet Activation Parameterization wtih in Situ Data from CRYSTAL-FACE and CSTRIPE

The accuracy of the 2003 prognostic, physically based aerosol activation parameterization of A. Nenes and J. H. Seinfeld (NS) with modification introduced by C. Fountoukis and A. Nenes in 2005 (modified NS) is evaluated against extensive microphysical data sets collected on board the Center for Interdisciplinary Remotely Piloted Aircraft Studies (CIRPAS) Twin Otter aircraft for cumuliform and stratiform clouds of marine and continental origin. The cumuliform cloud data were collected during NASA's Cirrus Regional Study of Tropical Anvils and Cirrus Layers-Florida Area Cirrus Experiment (CRYSTAL-FACE, Key West, Florida, July 2002), while the stratiform cloud data were gathered during Coastal Stratocumulus Imposed Perturbation Experiment (CSTRIPE, Monterey, California, July 2003). In situ data sets of aerosol size distribution, chemical composition, and updraft velocities are used as input for the NS parameterization, and the evaluation is carried out by comparing predicted cloud droplet number concentrations (CDNC) with observations. This is the first known study in which a prognostic cloud droplet activation parameterization has been evaluated against a wide range of observations. On average, predicted droplet concentration in adiabatic regions is within -20% of observations at the base of cumuliform clouds and -30% of observations at different altitudes throughout the stratiform clouds, all within experimental uncertainty. Furthermore, CDNC is well parameterized using either a single mean updraft velocity w or by weighting droplet nucleation rates with a Gaussian probability density function of w. This study suggests that for nonprecipitating warm clouds of variable microphysics, aerosol composition, and size distribution the modified NS parameterization can accurately predict cloud droplet activation and can be successfully implemented for describing the aerosol activation process in global climate models.

Meskhidze, Nicholas↗

A Multiscale Modeling System: Developments, Applications, and Critical Issues

The foremost challenge in parameterizing convective clouds and cloud systems in large-scale models are the many coupled dynamical and physical processes that interact over a wide range of scales, from microphysical scales to the synoptic and planetary scales. This makes the comprehension and representation of convective clouds and cloud systems one of the most complex scientific problems in Earth science. During the past decade, the Global Energy and Water Cycle Experiment (GEWEX) Cloud System Study (GCSS) has pioneered the use of single-column models (SCMs) and cloud-resolving models (CRMs) for the evaluation of the cloud and radiation parameterizations in general circulation models (GCMs; e.g., GEWEX Cloud System Science Team 1993). These activities have uncovered many systematic biases in the radiation, cloud and convection parameterizations of GCMs and have led to the development of new schemes (e.g., Zhang 2002; Pincus et al, 2003; Zhang and Wu 2003; Wu et al. 2003; Liang and Wu 2005; Wu and Liang 2005, and others). Comparisons between SCMs and CRMs using the same large-scale forcing derived from field campaigns have demonstrated that CRMs are superior to SCMs in the prediction of temperature and moisture tendencies (e.g., Das et al. 1999; Randall et al 2003b; Xie et al. 2005).

Tao, Wei-Kuo↗

Impacts of aerosol size-dependent below-cloud scavenging on tropospheric aerosol in the NASA GEOS model

Cloud scavenging is the major sink for a suite of tropospheric aerosols, and thus largely affects the global distribution and lifetime of aerosols as well as the formation of clouds. Simplified model parameterizations of cloud scavenging of aerosols substantially contribute to large uncertainties in the simulated aerosol burdens, spatial distributions, lifetimes, as well as aerosol radiative forcing. Here we evaluate the wet scavenging scheme in the current NASA GEOS model, develop more physically-based parameterizations of below-cloud scavenging, and assess the impacts of the new scavenging parameterizations on the GEOS simulations of aerosols. The current below-cloud scavenging (BCS; washout) scheme uses a first-order removal with a constant scavenging coefficient. We replaced the current scheme with a size-dependent parameterization of Croft et al.(Atmos. Chem. Phys., 2009; hereafter referred to as C09). The C09 BCS parameterizations calculate aerosol below-cloud scavenging coefficients based on a size-dependent collision efficiency between aerosol particles and raindrops (or snow crystals). A look-up table of compiled collision efficiencies provides values for sixty aerosol sizes and nine rain flux rates. Snow-aerosol collision efficiencies are a function of the sixty aerosol sizes only. We assume a log-normal size distribution for aerosols (bulk) in GOCART. The collision efficiencies are then calculated online using a bilinear interpolation from the look-up table for the given aerosol sizes and precipitation flux rates in the model.

aerosols↗

A Decadal Hybrid GCM Simulation Using Deep‐Learning‐Based Cloud and Convection Parameterization Generalized to a Warm Climate

A critical challenge for machine‐learning (ML) parameterization in global climate models (GCMs) is to achieve stable, accurate simulations under climates not seen during training. Previous studies have demonstrated promising offline performance and year‐long online stability in aquaplanet simulations but have encountered difficulties in real geography and under climate warming. Here we report that a GCM with real geography configuration using neural‐network‐based cloud and convection parameterization, trained exclusively with present‐day climate data, successfully performs a stable, decade‐long simulation of a warm climate with +4 K sea surface temperature (SST). The neural network (NN) is based on Han et al. (2023, https://doi.org/10.1029/2022ms003508 ) with additional inputs. The simulation captures the global precipitation distribution, surface temperatures, vertical atmospheric structures, and extreme precipitation very well, closely matching simulations from both the superparameterized CAM (SPCAM) and the conventional CAM5 in the warm climate without accuracy degradation compared to those in the baseline climate. Moreover, it produces a climate response to +4 K SST in atmospheric thermodynamic states and circulations similar to those from SPCAM and CAM5. Prognostic ablation tests on NN input variables show that the NN without convective memory as input suffers from numerical instability, and the NN without considering radiative variables and land fraction as input, or with reduced training samples produce less accurate results. To our knowledge, this is the first time an ML parameterization successfully achieves online extrapolation to a warm climate without using additional warm‐climate data for training. It demonstrates the potential of ML‐driven parameterizations for credible long‐term climate projections.

Atmosphere model↗

Parameterization of Vertical Cloud Distribution from C3M and MERRA Data Using ML Method

Clouds play a key role in regulating the hydrological cycle and the Earth's radiative energy budget. However, global climate models (GCMs) with a horizontal grid spacing on the order of 100 km have limitations in representing sub-grid cloud dynamics with spatial scales on the order of 1 km, leading to potential uncertainties in cloud radiative feedback on the global scale. In our research, we will leverage the capabilities of Deep Machine Learning (DML) methods to construct parameterizations of sub-grid volumetric cloud fraction (VCF), which is the frequency of occurrence on a grid volume accumulated in the horizontal and vertical directions. Our investigation delves into the intricate relationship between VCF obtained from the NASA CALIPSO-CloudSat-CERES-MODIS (CCCM) satellite observation data and 3-D MERRA-2 reanalysis meteorological profiling data (e.g., wind, relative humidity, temperature). Through a comprehensive one-year data training utilizing the Sequence to Sequence DML method, we have successfully disentangled the complicated cloud formation dynamics across diverse meteorological conditions through a day-to-day analysis framework. Preliminary findings reveal promising statistical agreements in geographical and vertical distributions and seasonal variations of volumetric cloud fraction between ML prediction and satellite measurements. These results underscore the aptitude of our DML model to discern underlying cloud physical processes and accurately represent sub-grid cloud formation dynamics. Additionally, we have also employed trained neural network to analyze uncertainties arising from errors in meteorological data, further enhancing the robustness of our VCF parameterization.

Shan Zeng↗

Parameterization of Shortwave Cloud Optical Properties for a Mixture of Ice Particle Habits for use in Atmospheric Models

Based on the single-scattering optical properties pre-computed with an improved geometric optics method, the bulk absorption coefficient, single-scattering albedo, and asymmetry factor of ice particles have been parameterized as a function of the effective particle size of a mixture of ice habits, the ice water amount, and spectral band. The parameterization has been applied to computing fluxes for sample clouds with various particle size distributions and assumed mixtures of particle habits. It is found that flux calculations are not overly sensitive to the assumed particle habits if the definition of the effective particle size is consistent with the particle habits that the parameterization is based. Otherwise, the error in the flux calculations could reach a magnitude unacceptable for climate studies. Different from many previous studies, the parameterization requires only an effective particle size representing all ice habits in a cloud layer, but not the effective size of individual ice habits.

Chou, Ming-Dah↗

“Scrutinizing entrainment and mass flux closures in shallow cumulus parameterizations using cloud-radar observations and large-eddy simulation” (Final report for DOE grant)

Warm, shallow clouds are responsible for a substantial portion of Earth System Model (ESM) uncertainty and divergence among model climate projections. A substantial amount of this uncertainty is tied to the representation of convection in ESMs, in particular assumptions underlying the convective parameterizations. This study focuses on entrainment and entrainment closures in ESM parameterizations. The completed project was a joint observational and modeling study to observationally derive estimates of entrainment and to use high-resolution modeling to scrutinize entrainment and mass flux closures in shallow convection parameterizations.

58 GEOSCIENCES↗

Scrutinizing entrainment and mass flux closures in shallow cumulus parameterizations using cloud-radar observations and large-eddy simulation (Final Report)

Representing warm, shallow clouds is a challenge for Global Climate Models, which leads to uncertainty in model projections of future climate. Our study was particularly concerned with how climate models represent the effects of shallow, non-precipitating cumulus clouds. Climate models must make certain assumptions when representing low clouds such as how much dry air from outside the cloud is mixed into the warm, moist cloud updraft. This process is called “entrainment” and tends to weaken the cloud updraft and dry out the cloud, compared to a theoretical cloud with no mixing. This project was a joint observational and modeling study to derive estimates of entrainment from field observations and use high-resolution modeling to evaluate the assumptions used in climate model representations of shallow cumulus. Our research took advantage of a wide variety of Department of Energy measurements from fixed climate-monitoring locations over the Southern Great Plains of the U.S. and the in the Eastern North Atlantic, along with short-term field projects (MAGIC, CAP–MBL, ACE–ENA). During the project, the PI maintained regular collaborations with Department of Energy Scientists at Brookhaven and Argonne National Laboratories. The project funded two students, who both obtained their M.S. in Atmospheric Science and are currently in the Atmospheric Science Ph.D. program. Both were lead authors on research papers funded by this grant.

54 ENVIRONMENTAL SCIENCES↗

Reflectance of broken cloud fields - Simulation and parameterization

The transfer of solar irradiance in plane parallel and broken cloud fields is simulated using a Monte Carlo method. The angular distribution pattern of radiances exiting the cloud layer is studied with varying cloud geometries, optical thicknesses, cloudiness, and solar zenith angles. A rather large anisotropy of the reflected flux is found, usually increasing with solar zenith angle and with patterns that strongly depend on cloud geometry. The main features are (1) a local maximum of reflected intensity in the forward direction for all cases, (2) a limb darkening for the plane parallel case, and (3) a limb brightening and a local maximum of reflected intensity in the backward direction for broken clouds. A parameterization for the azimuth-average reflectance function is developed. It reproduces the Monte Carlo simulation with a reasonable accuracy and illustrates that, when azimuthally averaged, the reflectance function is dominated by side viewing and intercloud shadowing effects.

Breon, Francois-Marie↗