Engineering topics

Hansen, James E.

Publications and source records attributed to Hansen, James E..

At least 37 records · Page 2

NASA NTRS2001

Characterizing the Influence of the General Circulation on Marine Boundary Layer Clouds

The seasonal and intraseasonal variability of boundary layer cloud in the subtropical eastern oceans are studied using combined data from the International Satellite Cloud Climatology Project (ISCCP) and the European Centre for Medium-Range Weather Forecasts (ECMWF) reanalysis. Spectral analysis reveals that most of the time variability of cloud properties occurs on seasonal to annual time scales. The variance decreases one to two orders of magnitude for each decade of time scale decrease, indicating that daily to monthly time scales have smaller, but non-negligible variability. The length of these dominant time scales suggests that the majority of the variability is influenced by the general circulation and its interaction with boundary layer turbulence, rather than a product of boundary layer turbulence alone. Previous datasets have lacked the necessary resolution in either time or in space to properly characterize variability on synoptic scales; this is remedied by using global satellite-retrieved cloud properties. We characterize the intraseasonal subtropical cloud variability in both hemispheres and in different seasons. In addition to cloud fraction, we examine variability of cloud optical thickness - cloud top pressure frequency distributions. Despite the large concentration of research on the variability of Northern Hemisphere (NH) regions during summer, it is noted that the largest amplitude intraseasonal variability in the NH regions occurs during local winter. The effect of intraseasonal variability on the calculation and interpretation of seasonal results is investigated. Decreases in seasonally averaged cloud cover, optical thickness and cloud top pressure from the May-through-September season to the November-through-March season are most apparent in the NH regions. Further analysis indicates that these changes are due to an increase in frequency, but a decrease in the persistence of synoptic events. In addition, changes in cloud top pressure and optical thickness characteristics from the summer to winter seasons indicate that the NH subtropics undergo a change in dynamic regime with season. This change appears in the cloud fields as a shift from the more commonly seen lower-altitude, thicker optical thickness clouds to higher-altitude, thinner clouds. The latter cloud-type is associated with the lower sea level pressure, upward vertical velocity phase of the synoptic wave. Intraseasonal changes in cloud properties in the Southern Hemisphere and NH summer are much smaller in amplitude. Although they also appear to be linked to changes in the large-scale dynamics, similarly to NH winter variations, the relationships are more ambiguous due to the small amplitudes and longer time scales. We attempt to interpret some of these relationships using the results of the Betts and Ridgway (1989) box model. However, these results cannot consistently explain the patterns when results from all regions are considered, implying that this model may not adequately explain all the processes involved in the variability.

Rozendaal, Margaret A.↗

NASA NTRS2001

Rotation of EOFs by the Independent Component Analysis: Towards A Solution of the Mixing Problem in the Decomposition of Geophysical Time Series

The Independent Component Analysis is a recently developed technique for component extraction. This new method requires the statistical independence of the extracted components, a stronger constraint that uses higher-order statistics, instead of the classical decorrelation, a weaker constraint that uses only second-order statistics. This technique has been used recently for the analysis of geophysical time series with the goal of investigating the causes of variability in observed data (i.e. exploratory approach). We demonstrate with a data simulation experiment that, if initialized with a Principal Component Analysis, the Independent Component Analysis performs a rotation of the classical PCA (or EOF) solution. This rotation uses no localization criterion like other Rotation Techniques (RT), only the global generalization of decorrelation by statistical independence is used. This rotation of the PCA solution seems to be able to solve the tendency of PCA to mix several physical phenomena, even when the signal is just their linear sum.

Aires, Filipe↗

NASA NTRS2001

New Third-Order Moments for the CBL

Turbulent convection is an inherently non-local phenomenon and a primary condition for a successful treatment of the CBL (convective boundary layer) is a reliable model of non-locality. In the dynamic equations governing the convective flux, the turbulent kinetic energy, etc., non-locality is represented by the third-order moments, TOMs. Since the simplest form, the so-called down gradient approximation (DGA), severely underestimates the TOMs (up to an order of magnitude), a more physical model is needed. In 1994, an analytical model was presented which was derived directly from the dynamical equations for the TOMs. It considerably improved the DGA but was a bit cumbersome to use and, more importantly, it was based on the quasi-normal (QN) approximation for the fourth-order moments. Here, we present a new analytic expression for the TOMs which is structurally simpler than the 1994 expression and which avoids the QN approximation. The resulting fit to the LES data is superior to that of the 1994 model.

Canuto, V. M.↗

NASA NTRS2001

A Comparison of Seasonal and Interannual Variability of Soil Dust Aerosols Over the Atlantic Ocean as Inferred by the Toms AI and AVHRR AOT Retrievals

The seasonal cycle and interannual variability of two estimates of soil (or 'mineral') dust aerosols are compared: Advanced Very High Resolution Radiometer (AVHRR) aerosol optical thickness (AOT) and Total Ozone Mapping Spectrometer (TOMS) aerosol index (AI), Both data sets, comprising more than a decade of global, daily images, are commonly used to evaluate aerosol transport models. The present comparison is based upon monthly averages, constructed from daily images of each data set for the period between 1984 and 1990, a period that excludes contamination from volcanic eruptions. The comparison focuses upon the Northern Hemisphere subtropical Atlantic Ocean, where soil dust aerosols make the largest contribution to the aerosol load, and are assumed to dominate the variability of each data set. While each retrieval is sensitive to a different aerosol radiative property - absorption for the TOMS AI versus reflectance for the AVHRR AOT - the seasonal cycles of dust loading implied by each retrieval are consistent, if seasonal variations in the height of the aerosol layer are taken into account when interpreting the TOMS AI. On interannual time scales, the correlation is low at most locations. It is suggested that the poor interannual correlation is at least partly a consequence of data availability. When the monthly averages are constructed using only days common to both data sets, the correlation is substantially increased: this consistency suggests that both TOMS and AVHRR accurately measure the aerosol load in any given scene. However, the two retrievals have only a few days in common per month so that these restricted monthly averages have a large uncertainty. Calculations suggest that at least 7 to 10 daily images are needed to estimate reliably the average dust load during any particular month, a threshold that is rarely satisfied by the AVHRR AOT due to the presence of clouds in the domain. By rebinning each data set onto a coarser grid, the availability of the AVHRR AOT is increased during any particular month, along with its interannual correlation with the TOMS AI The latter easily exceeds the sampling threshold due to its greater ability to infer the aerosol load in the presence of clouds. Whether the TOMS AI should be regarded as a more reliable indicator of interannual variability depends upon the extent of contamination by sub-pixel clouds.

Cakmur, R. V.↗

NASA NTRS2001

The Role of Clear Sky Identification in the Study of Cloud Radiative Effects: Combine Analysis from ISCCP and the Scanner of Radiation Budget (ScaRaB)

Since the effect of clouds on the earth's radiation balance is often estimated as the difference of net radiative fluxes at the top of the atmosphere between all situations and monthly averaged clear sky situations of the same regions, a reliable identification of clear sky is important for the study of cloud radiative effects. The Scanner for Radiation Balance (ScaRaB) radiometer on board the Russian Meteor-3/7 satellite provided earth radiation budget observations from March 1994 to February 1995 with two ERBE-Re broad-band longwave and shortwave channels. Two narrow-band channels, in the infrared atmospheric window and in the visible band, have been added to the ScaRaB instrument to improve the cloud scene identification. The International Satellite Cloud Climatology Project (ISCCP) method for cloud detection and determination of cloud and surface properties uses the same narrow-band channels as ScaRaB, but is employed to a collection of measurements at a better spatial resolution of about 5 km. By applying the original ISCCP algorithms to the ScaRaB data, the clear sky frequency is about 5% lower than the one over quasi-simultaneous original ISCCP data, an indication that the ISCCP cloud detection is quite stable. However, one would expect an about 10 to 20% smaller clear sky occurrence over the larger ScaRaB pixels. Adapting the ISCCP algorithms to the reduced spatial resolution of 60 km and to the different time sampling of the ScaRaB data leads therefore to a reduction of a residual cloud contamination. A sensitivity study with time-space collocated ScaRaB and original ISCCP data at a spatial resolution of 1deg longitude x 1deg latitude shows that the effect of clear sky identification method plays a higher role on the clear sky frequency and therefore on the statistics than on the zonal mean values of the clear sky fluxes. Nevertheless, the zonal outgoing longwave fluxes corresponding to ERBE clear sky are in general about 2 to 10 W/sq m higher than those obtained from the ScaRaB adapted ISCCP clear sky identifications. The latter are close to (about 1 W/sq m higher) fluxes corresponding to clear sky regions from original ISCCP data, whereas ScaRaB clear sky LW fluxes obtained with the original ISCCP identification lie about 1 to 2 W/sq m below. Especially in the tropics where water vapor abundance is high, the ERBE clear sky LW fluxes seem to be systematically overestimated by about 4 W/sq m, and SW fluxes are lower by about 5 to 10 W/sq m. However, the uncertainty in the analysis of monthly mean zonal cloud radiative effects is also produced by the low frequency of clear sky occurrence, illustrated when averaging over pixels or even over regions of 4deg longitude x 5deg latitude, corresponding to the spatial resolution of General Circulation Models. The systematic bias in the clear sky fluxes is not reflected in the zonal cloud radiative effects, because the clear sky regions selected by the different algorithms can occur in different geographic regions with different cloud properties.

Rossow, W. B.↗

NASA NTRS2001

Chemistry-Climate Interactions in the GISS GCM: Tropospheric Chemistry Model Description and Evaluation - Part 1

A tropospheric chemistry module has been developed for use within the Goddard Institute for Space Studies (GISS) general circulation model (GCM) to study interactions between chemistry and climate change. The model uses a simplified chemistry scheme based on CO-NOx-CH4 chemistry, and also includes a parameterization for emissions of isoprene, the most important non-methane hydrocarbon. The model reproduces present day annual cycles and mean distributions of key trace gases fairly well, based on extensive comparisons with available observations. Examining the simulated change between present day and pre-industrial conditions, we find that the model has a similar response to that seen in other simulations. It shows a 45% increase in the global tropospheric ozone burden, within the 25% - 57% range seen in other studies. Annual average zonal mean ozone increases by more than 125% at Northern Hemisphere middle latitudes near the surface. Comparison of model runs that allow the calculated ozone to interact with the GCM's radiation and meteorology with those that do not shows only minor differences for ozone. The common usage of ozone fields that are not calculated interactively seems to be adequate to simulate both the present day and the pre-industrial ozone distributions. However, use of coupled chemistry does alter the change in tropospheric oxidation capacity, enlarging the overall decrease in OH concentrations from the pre-industrial to the present by about 10% (-5.3% global annual average in uncoupled mode, -5.9% in coupled mode). This indicates that there may be systematic biases in the simulation of the pre-industrial to present day decrease in the oxidation capacity of the troposphere (though a 10% difference is well within the total uncertainty). Global annual average radiative forcing from pre-industrial to present day ozone change is 0.32 W/sq m. The forcing seems to be increased by about 10% when the chemistry is coupled to the GCM. Forcing values greater than 0.8 W/sq m are seen over large areas of the United States, Southern Europe, North Africa, the Middle East, Central Asia, and the Arctic. Radiative forcing is greater than 1.5 W/sq m over parts of these areas during Northern summer Though there are local differences, the radiative forcing is overall in good agreement with the results of other modeling studies in both its magnitude and spatial distribution, demonstrating that the simplified chemistry is adequate for climate studies.

Shindell, Drew T.↗

NASA NTRS2001

Microwave Polarized Signatures Generated within Cloud Systems: SSM/I Observations Interpreted with Radiative Transfer Simulations

Special Sensor Microwave /Imager (SSM/I) observations in cloud systems are studied over the tropics. Over optically thick cloud systems, presence of polarized signatures at 37 and 85 GHz is evidenced and analyzed with the help of cloud top temperature and optical thickness extracted from visible and IR satellite observations. Scattering signatures at 85 GHz (TbV(85) less than or = 250 K) are associated with polarization differences greater than or = 6 K, approx. 50%, of the time over ocean and approx. 40% over land. In addition. over thick clouds the polarization difference at 37 GHz is rarely negligible. The polarization differences at 37 and 85 GHz do not stem from the surface but are generated in regions of relatively homogeneous clouds having high liquid water content. To interpret the observations, a radiative transfer model that includes the scattering by non-spherical particles is developed. based on the T-matrix approach and using the doubling and adding method. In addition to handling randomly and perfectly oriented particles, this model can also simulate the effect of partial orientation of the hydrometeors. Microwave brightness temperatures are simulated at SSM/I frequencies and are compared with the observations. Polarization differences of approx. 2 K can be simulated at 37 GHz over a rain layer, even using spherical drops. The polarization difference is larger for oriented non-spherical particles. The 85 GHz simulations are very sensitive to the ice phase of the cloud. Simulations with spherical particles or with randomly oriented non-spherical ice particles cannot replicate the observed polarization differences. However, with partially oriented non-spherical particles, the observed polarized signatures at 85 GHz are explained, and the sensitivity of the scattering characteristics to the particle size, asphericity, and orientation is analyzed. Implications on rain and ice retrievals are discussed.

Prigent, Catherine↗

NASA NTRS2001

Salt Marsh Formation in the Lower Hudson River Estuary

Salt marshes are constant depositional environments and as a result contain accurate indicators of past relative sea level rise and salinity. The Hudson River marshes are at least twice as deep when compared to coastal marshes on either side of the mouth of the Hudson. The reason for this difference in sedimentation is unclear. This study uses macrofossil data as well as sediment stratigraphy in order to understand the formation and evolution of these marshes. The composition of seeds, roots, shoots and foraminifera, are used to indicate past sea levels. The four sites involved in this study are, from south to north, the Arthur Kill Marsh in Staten Island (40 36 N, 74 77W), Piermont marsh (N 4100; 73 55W) Croton Point (41 14 N; 73 50W) and Iona Island (41 18N, 73 58W). These are all tidally influenced but with increasing distances from the New York Bight, which gives a good spectrum of tidal influence. AMS-C14 dates on basal macrofossils will document the time of each marsh formation. Basal material from Arthur Kill (8 m) includes freshwater seeds such as Viola, Potomageton and Alnus along with Salix buds. Basal material from Croton Point (10 m) includes fibrous woody material, foraminifera and Zanichellia seeds and other brackish vegetational components. The basal material from Piermont (13.77 m) is lacking any identifiable macrofossils between 150 and 500 microns. The basal material from Iona Island (10 m) has vegetation such as Scirpus and Cyperus seeds, probably implying a brackish environment. The freshwater origin of the Arthur Kill marsh in Staten Island is significant because it predates either sea level rise or the western channel incision. Additional implications for this study include evidence for changes in river channel geomorphology. Reasons for the relatively deeper river marshes include possible basal clay compaction, high production due to river and marine nutrients as well as tectonic activity. This study provides the groundwork for more high-resolution studies of these marshes to understand the fluctuations in salinity caused by relative sea level rise, tectonic faulting and/or changes in precipitation/evaporation.

Merley, Michael↗

NASA NTRS2001

Simultaneous Retrieval of Temperature, Water Vapor and Ozone Atmospheric Profiles from IASI: Compression, De-noising, First Guess Retrieval and Inversion Algorithms

A fast temperature water vapor and ozone atmospheric profile retrieval algorithm is developed for the high spectral resolution Infrared Atmospheric Sounding Interferometer (IASI) space-borne instrument. Compression and de-noising of IASI observations are performed using Principal Component Analysis. This preprocessing methodology also allows, for a fast pattern recognition in a climatological data set to obtain a first guess. Then, a neural network using first guess information is developed to retrieve simultaneously temperature, water vapor and ozone atmospheric profiles. The performance of the resulting fast and accurate inverse model is evaluated with a large diversified data set of radiosondes atmospheres including rare events.

Aires, F.↗

NASA NTRS2001

GCM Simulations of the Aerosol Indirect Effect: Sensitivity to Cloud Parameterization and Aerosol Burden

We describe the coupling of the Goddard Institute for Space Studies (GISS) general circulation model (GCM) to an online sulfur chemistry model and source models for organic matter and sea-salt that is used to estimate the aerosol indirect effect. The cloud droplet number concentration is diagnosed empirically from field experiment datasets over land and ocean that observe droplet number and all three aerosol types simultaneously; corrections are made for implied variations in cloud turbulence levels. The resulting cloud droplet number is used to calculate variations in droplet effective radius, which in turn allows us to predict aerosol effects on cloud optical thickness and microphysical process rates. We calculate the aerosol indirect effect by differencing the top-of-the-atmosphere net cloud radiative forcing for simulations with present-day vs. pre-industrial emissions. Both the first (radiative) and second (microphysical) indirect effects are explored. We test the sensitivity of our results to cloud parameterization assumptions that control the vertical distribution of cloud occurrence, the autoconversion rate, and the aerosol scavenging rate, each of which feeds back significantly on the model aerosol burden. The global mean aerosol indirect effect for all three aerosol types ranges from -1.55 to -4.36 W/sq m in our simulations. The results are quite sensitive to the pre-industrial background aerosol burden, with low pre-industrial burdens giving strong indirect effects, and to a lesser extent to the anthropogenic aerosol burden, with large burdens giving somewhat larger indirect effects. Because of this dependence on the background aerosol, model diagnostics such as albedo-particle size correlations and column cloud susceptibility, for which satellite validation products are available, are not good predictors of the resulting indirect effect.

Menon, Surabi↗

NASA NTRS2001

An Improved Model for the Turbulent PBL

Second order turbulence models of the Mellor and Yamada type have been widely used to simulate the PBL. It is however known that these models have several deficiencies. For example, they all predict a critical Richardson number which is about four times smaller than the Large Eddy Simulation (LES) data, they are unable to match the surface data, and they predict a boundary layer height lower than expected. In the present model, we show that these difficulties are all overcome by a single new physical input: the use of the most complete expression for both the pressure-velocity and the pressure-temperature correlations presently available. Each of the new terms represents a physical process that, was not accounted for by previous models. The new model is presented in three different levels according to Mellor and Yamada's terminology, with new, ready-to-use expressions for the turbulent, moments. We show that the new model reproduces several experimental and LES data better than previous models. As far as the PBL is concerned, we show that the model reproduces both the Kansas data as analyzed by Businger et al. in the context of Monin-Obukhov similarity theory for smaller Richardson numbers, as well as the LES and laboratory data up to Richardson numbers of order unity. We also show that the model yields a higher PBL height than the previous models.

Cheng, Y.↗

NASA NTRS2001

A Regularized Neural Net Approach for Retrieval of Atmospheric and Surface Temperatures with the IASI Instrument

Abstract In this paper, a fast atmospheric and surface temperature retrieval algorithm is developed for the high resolution Infrared Atmospheric Sounding Interferometer (IASI) space-borne instrument. This algorithm is constructed on the basis of a neural network technique that has been regularized by introduction of a priori information. The performance of the resulting fast and accurate inverse radiative transfer model is presented for a large divE:rsified dataset of radiosonde atmospheres including rare events. Two configurations are considered: a tropical-airmass specialized scheme and an all-air-masses scheme.

Aires, F.↗

NASA NTRS2001

Hudson River Paleoclimate, Sea Level, and Human Impact: A Record From Piermont Marsh, NY

A 13.77 meter sediment core from Piermont Marsh, NY (40 00 N, 73 55W) records the local and regional vegetational and foraminiferal history of the Hudson Estuary. The sediments were sampled every 4 cm, which represents a decadal to centuryscale resolution. Basal sediment dating is in progress, and the 11-m depth represents about 4000 years. Changes in plant macrofossils and charcoal appear to indicate differences in salinIty and drought, suggesting changes in climate. Scirpus, Salicornia, and high levels of charcoal seem to indicate drier/more saline conditions, while lack of these macrofossils and increases in Chara/Nitella, aquatic leaves, and very little charcoal suggests wetter conditions. Other macrofossils include Carex, Juncus, Polygonum, Zanichellia, Ruppia. High resolution AMS dating of plant macrofossils is in progress, and will be compared with changes in Hudson River sediment cores offshore. Foraminiferal assemblages from key intervals of the core will be presented. Human impact in the upper sediments is visible from the influx of grass seeds, primarily Phragmites, and the ragweed pollen rise.

Kurdyla↗

NASA NTRS2001

Radiation Force Caused by Scattering, Absorption, and Emission of Light by Nonspherical Particles

General formulas for computing the radiation force exerted on arbitrarily oriented and arbitrarily shaped nonspherical particles due to scattering, absorption, and emission of electromagnetic radiation are derived. For randomly oriented particles with a plane of symmetry, the formula for the average radiation force caused by the particle response to external illumination reduces to the standard Debye formula derived from the Lorenz-Mie theory, whereas the average radiation force caused by emission vanishes.

Mishchenko, Michael I.↗

NASA NTRS2001

Implications of the Observed Mesoscale Variations of Clouds for Earth's Radiation Budget

The effect of small-spatial-scale cloud variations on radiative transfer in cloudy atmospheres currently receives a lot of research attention, but the available studies are not very clear about which spatial scales are important and report a very large range of estimates of the magnitude of the effects. Also, there have been no systematic investigations of how to measure and represent these cloud variations. We exploit the cloud climatology produced by the International Satellite Cloud Climatology Project (ISCCP) to: (1) define and test different methods of representing cloud variation statistics, (2) investigate the range of spatial scales that should be included, (3) characterize cloud variations over a range of space and time scales covering mesoscale (30 - 300 km, 3-12 hr) into part of the lower part of the synoptic scale (300 - 3000 km, 1-30 days), (4) obtain a climatology of the optical thickness, emissivity and cloud top temperature variability of clouds that can be used in weather and climate GCMS, together with the parameterization proposed by Cairns et al. (1999), to account for the effects of small-scale cloud variations on radiative fluxes, and (5) evaluate the effect of observed cloud variations on Earth's radiation budget. These results lead to the formulation of a revised conceptual model of clouds for use in radiative transfer calculations in GCMS. The complete variability climatology can be obtained from the ISCCP Web site at http://isccp.giss.nasa.gov.

Rossow, William B.↗

NASA NTRS2001

Paleoenvironmental History of JoCo Marsh, Jamaica Bay, New York

Sediment cores from JoCo Marsh, located in Jamaica Bay, NY were analyzed for plant macrofossil and foraminifera records. These records reflect changes in vegetation, sea level, climate and human intervention. Better understanding of past environmental changes provides information for future preservation and protection of the estuary. A 2.81 m core was retrieved from JoCo, a high marsh area located on the eastern side of Jamaica Bay. The lithology of the core differs from high levels of sand, with small amounts of clay, in the bottom 0.8 meters, to salt marsh peat in the upper 2 meters of the core. Basal wood in the sand was dated to about 2060 yr BP. Elphidium foraminifera dominate the basal sands, along with Scirpus seeds, wood, and charcoal. These sands include fish scales which are tentatively identified as killifish, suggesting shallow pools. The transition to marsh peat is dominated by sedge seeds, and declines in charcoal. The peat appears to be dominated by salt marsh grasses. At 2 m the foraminifera change to include mainly Trochammina species and other undifferentiated agglutinates. The upper portion of the core is dominated by Salicornia seeds along with Trochammina and Miliammina or Quinqueloculia. The history of this marsh will be integrated with other records of marsh environmental change along the US eastern seaboard.

Liberman, Louisa↗

NASA NTRS2001

Carbon Storage in Wetlands and Lakes of the Eastern US

Carbon stored underground may participate in a positive feedback with climate warming, as higher temperatures accelerate decomposition reactions and hence CO2 release. Assessing how below-ground carbon storage varies with modern climate and paleoclimate will advance understanding of this feedback in two ways. First, it will estimate the sensitivity of carbon storage to temperature and precipitation changes. Second, it will help quantify the size of carbon stocks available for the feedback, by indicating how current regional climate differences affect carbon storage. Whereas many studies of below-ground carbon storage concentrate on soils, this investigation focuses on the saturated and primarily organic material stored in wetlands and lake sediments. This study surveys research done on organic sediment depth and organic content at 50-100 sites in the eastern U.S., integrating our own research with the work of others. Storage depth is evaluated for sediments from the past 10,000 years, a date reflected in pollen profiles. Organic content is measured chiefly by loss-on-ignition (101). These variables are compared to characteristics of the sites such as latitude, altitude, and vegetation as well as local climate. Preliminary results suggest a strong relationship between latitude and depth of organic material stored over the last 10,000 years, with more accumulation in the northeastern US than the southeastern US. Linking the percent organic matter to actual carbon content is in progress with wetlands from Black Rock Forest and Alpine Swamp.

Renik, Byrdie↗

NASA NTRS2001

Scattering by Randomly Oriented Thin Ice Disks with Moderate Equivalent-Sphere Size Parameters

We use the T-matrix method to compute the scattering matrix for randomly oriented circular ice cylinders with diameter-to-length ratios 1 and 20 and surface-equivalent-sphere size parameters up to 12. We show that wavelength-sized, sharp-edged ice plates with extreme diameter-to-length ratios possess the same scattering properties as smooth plate-like spheroids: their phase functions are similar to those of surface-equivalent compact particles, whereas all other elements of the scattering matrix are typical of Rayleigh scattering.

Zakharova, Nadia T.↗