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All sourcesNASA NTRSDOE OSTI
NASA NTRS1983

Track recording plastic compositions

Improved nuclear track recording plastic compositions are provided which exhibit greatly decreased surface roughness when etched to produce visible tracks of energetic nuclear particles which have passed into and/or through said plastic. The improved compositions incorporate a small quantity of a phthalic acid ester into the major plastic component which is derived from the polymerization of monomeric di-ethylene glycol bis allyl carbonate. Di-substituted phthalic acid esters are preferred as the added component, with the further perference that the ester substituent has a chain length of 2 or more carbon atoms. The inclusion of the phthalic acid ester to an extent of from about 1-2% by weight of the plastic compositions is sufficient to drastically reduce the surface roughness ordinarily produced when the track recording plastic is contacted by etchants.

Tarle, Gregory↗
NASA NTRS1998

A Conceptual Approach to Assimilating Remote Sensing Data to Improve Soil Moisture Profile Estimates in a Surface Flux/Hydrology Model: Overview - Part 1

Knowledge of the amount of water in the soil is of great importance to many earth science disciplines. Soil moisture is a key variable in controlling the exchange of water and energy between the land surface and the atmosphere. Thus, soil moisture information is valuable in a wide range of applications including weather and climate, runoff potential and flood control, early warning of droughts, irrigation, crop yield forecasting, soil erosion, reservoir management, geotechnical engineering, and water quality. Despite the importance of soil moisture information, widespread and continuous measurements of soil moisture are not possible today. Although many earth surface conditions can be measured from satellites, we still cannot adequately measure soil moisture from space. Research in soil moisture remote sensing began in the mid 1970s shortly after the surge in satellite development. Recent advances in remote sensing have shown that soil moisture can be measured, at least qualitatively, by several methods. Quantitative measurements of moisture in the soil surface layer have been most successful using both passive and active microwave remote sensing, although complications arise from surface roughness and vegetation type and density. Early attempts to measure soil moisture from space-borne microwave instruments were hindered by what is now considered sub-optimal wavelengths (shorter than 5 cm) and the coarse spatial resolution of the measurements. L-band frequencies between 1 and 3 GHz (10-30 cm) have been deemed optimal for detection of soil moisture in the upper few centimeters of soil. The Electronically Steered Thinned Array Radiometer (ESTAR), an aircraft-based instrument operating a 1,4 GHz, has shown great promise for soil moisture determination. Initiatives are underway to develop a similar instrument for space. Existing space-borne synthetic aperture radars (SARS) operating at C- and L-band have also shown some potential to detect surface wetness. The advantage of radar is its much higher resolution than passive microwave systems, but it is currently hampered by surface roughness effects and the lack of a good algorithm based on a single frequency and single polarization. In addition, its repeat frequency is generally low (about 40 days). In the meantime, two new radiometers offer some hope for remote sensing of soil moisture from space. The Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI), launched in November 1997, possesses a 10.65 GHz channel and the Advanced Microwave Scanning Radiometer (AMSR) on both the ADEOS-11 and Earth Observing System AM-1 platforms to be launched in 1999 possesses a 6.9 GHz channel. Aside from issues about interference from vegetation, the coarse resolution of these data will provide considerable challenges pertaining to their application. The resolution of TMI is about 45 km and that of AMSR is about 70 km. These resolutions are grossly inconsistent with the scale of soil moisture processes and the spatial variability of factors that control soil moisture. Scale disparities such as these are forcing us to rethink how we assimilate data of various scales in hydrologic models. Of particular interest is how to assimilate soil moisture data by reconciling the scale disparity between what we can expect from present and future remote sensing measurements of soil moisture and modeling soil moisture processes. It is because of this disparity between the resolution of space-based sensors and the scale of data needed for capturing the spatial variability of soil moisture and related properties that remote sensing of soil moisture has not met with more widespread success. Within a single footprint of current sensors at the wavelengths optimal for this application, in most cases there is enormous heterogeneity in soil moisture created by differences in landcover, soils and topography, as well as variability in antecedent precipitation. It is difficult to interpret the meaning of 'mean' soil moisture under such conditions and even more difficult to apply such a value. Because of the non-linear relationships between near-surface soil moisture and other variables of interest, such as surface energy fluxes and runoff, mean soil moisture has little applicability at such large scales. It is for these reasons that the use of remote sensing in conjunction with a hydrologic model appears to be of benefit in capturing the complete spatial and temporal structure of soil moisture. This paper is Part I of a four-part series describing a method for intermittently assimilating remotely-sensed soil moisture information to improve performance of a distributed land surface hydrology model. The method, summarized in section II, involves the following components, each of which is detailed in the indicated section of the paper or subsequent papers in this series: Forward radiative transfer model methods (section II and Part IV); Use of a Kalman filter to assimilate remotely-sensed soil moisture estimates with the model profile (section II and Part IV); Application of a soil hydrology model to capture the continuous evolution of the soil moisture profile within and below the root zone (section III); Statistical aggregation techniques (section IV and Part II); Disaggregation techniques using a neural network approach (section IV and Part III); and Maximum likelihood and Bayesian algorithms for inversely solving for the soil moisture profile in the upper few cm (Part IV).

Crosson, William L.↗
NASA NTRS2010

Application of the Tor Vergata Scattering Model to L Band Backscatter During the Corn Growth Cycle

At the USDA's Optimizing Production Inputs for Economic and Environmental Enhancement (OPE3) experimental site in Beltsville, Maryland, USA) a field campaign took place throughout the 2002 corn growth cycle from May 10th (emergence of corn crops) to October 2nd (harvest). One of the microwave instruments deployed was the multi-frequency (X-, C- and L-band) quad-polarized (HH, HV, VV, VH) NASA GSFC/George Washington University (GWU) truck mounted radar. During the field campaign, this radar system provided once a week fully polarized C- and L-band (4.75 and 1.6 GHz) backscatter measurements from incidence angle of 15, 35, and 55 degrees. In support of microwave observations, an extensive ground characterization took place, which included measurements of surface roughness, soil moisture, vegetation biomass and morphology. The field conditions during the campaign are characterized by several dry downs with a period of drought in the month of August. Peak biomass the corn canopies was reached on July 24th with a total biomass of approximately 6.5 kg/sq m. This dynamic range in both soil moisture and vegetation conditions within the data set is ideal for the validation of discrete medium vegetation scattering models. In this study, we compare the L band backscatter measurements with simulations by the Tor Vergata model (ferrazzoli and Guerriero 1996). The measured soil moisture, vegetation biomass and most reliably measured vegetation morphological parameters (e.g. number of leaves, number of stems and stem height) were used as input for the Tor Vergata model. The more uncertain model parameters (e.g. surface roughness, leaf thickness) and the stem diameter were optimized using a parameter estimation routine based on the Levenberg-Marquardt algorithm. As cost function for this optimization, the HH and VV polarized backscatter measured and stimulated by the TOR Vergata model for incidence angle of 15, 35, and 55 degrees were used (6 measurements in total). The calibrated Tor Vergata model simulations are in excellent agreement with the measurements of Root Mean Squared Differences (RMSD's) of 0.8, 0.9 and 1.4 dB for incidences of 15, 35 and 55 degrees, respectively. The results from this study that a physically based scattering model with the appropriate parameterization can accurately simulate backscatter measurements and, as such, have the potential of being used for the retrieval of biophysical variables (e.g. soil moisture and vegetation biomass).

Joseph, A. T.↗
NASA NTRSDate not supplied

The Effect of Boundary Layer Character on Stochastic Rotor Blade Vortex Shedding Noise

This work illustrates the effect of a rotor blade’s boundary layer on the broadband LBL-VS self-noise emitted from an optimum hovering rotor through experimental and multi-fidelity computational studies. Blade surface roughness effects associated with different manufacturing techniques and the effect of adding a boundary layer trip were shown to decrease LBL-VS noise by upwards of 30 dB at the frequency of maximum emission with a slight penalty in aerodynamic performance when compared with smooth rotor blades. Low-fidelity 2-D viscous flow analysis verified the presence of laminar separation bubbles on the rotor blades which are responsible for LBL-VS noise. Three high-fidelity lattice-Boltzmann simulations were conducted with different wall-functions to predict the boundary layer character correspondent to their experimental counterpart and the resultant presence or absence of LBL-VS noise. Excellent aerodynamic and aeroacoustic agreement was seen between the lattice-Boltzmann simulations and the experimental data for the cases with surface roughness and the boundary layer trip, with the broadband noise results from the simulation with fully turbulent wall-functions diverging from the experimental results above 5 kHz. The transitional wall-function simulation which emulated the smooth experimental blades underpredicted thrust by 14% and broadband noise by a minimum of 10 dB with an accurately predicted broadband noise trend.

Christopher S Thurman↗
NASA NTRS2017

Remote Sensing of Crystal Shapes in Ice Clouds

Ice crystals in clouds exist in a virtually limitless variation of geometries. The most basic shapes of ice crystals are columnar or plate-like hexagonal prisms with aspect ratios determined by relative humidity and temperature. However, crystals in ice clouds generally display more complex structures owing to aggregation, riming and growth histories through varying temperature and humidity regimes. Crystal shape is relevant for cloud evolution as it affects microphysical properties such as fall speeds and aggregation efficiency. Furthermore, the scattering properties of ice crystals are affected by their general shape, as well as by microscopic features such as surface roughness, impurities and internal structure. To improve the representation of ice clouds in climate models, increased understanding of the global variation of crystal shape and how it relates to, e.g., location, cloud temperature and atmospheric state is crucial. Here, the remote sensing of ice crystal macroscale and microscale structure from airborne and space-based lidar depolarization observations and multi-directional measurements of total and polarized reflectances is reviewed. In addition, a brief overview is given of in situ and laboratory observations of ice crystal shape as well as the optical properties of ice crystals that serve as foundations for the remote sensing approaches. Lidar depolarization is generally found to increase with increasing cloud height and to vary with latitude. Although this variation is generally linked to the variation of ice crystal shape, the interpretation of the depolarization remains largely qualitative and more research is needed before quantitative conclusions about ice shape can be deduced. The angular variation of total and polarized reflectances of ice clouds has been analyzed by numerous studies in order to infer information about ice crystal shapes from them. From these studies it is apparent that pristine crystals with smooth surfaces are generally inconsistent with the data and thus crystal impurity, distortion or surface roughness is prevalent. However, conclusions about the dominating ice shapes are often inconclusive and contradictory and are highly dependent on the limited selection of shapes included in the investigations. Since ice crystal optical properties are mostly determined by the aspect ratios of the crystal components and their microscale structure, it is advised that remote sensing applications focus on the variation of these ice shape characteristics, rather than on the macroscale shape or habit. Recent studies use databases with nearly continuous ranges of crystal component aspect ratio and-or roughness levels to infer the variation of ice crystal shape from satellite and airborne remote sensing measurements. Here, the rationale and results of varying strategies for the remote sensing of ice crystal shape are reviewed. Observed systematic variations of ice crystal geometry with location, cloud height and atmospheric state suggested by the data are discussed. Finally, a prospective is given on the future of the remote sensing of ice cloud particle shapes.

clouds↗
NASA NTRS1970

Passive microwave studies

The application of passive microwave techniques from airborne and surface platforms for oceanography measurements is discussed. The program is designed to determine: (1) the optimum system parameters, (2) measurement techniques, and (3) the physical phenomena to enable unambiguous all-weather determination of the sea surface properties of sea roughness, surface wind fields, temperature, salinity, sea ice, and pollution. The advantages and disadvantages of the airborne and fixed station operations are examined.

Hollinger, J. P.↗
NASA NTRS1973

A model of wind shear and turbulence in the surface boundary layer

A model of wind and turbulence has been described for the surface boundary layer. The wind structure in the surface layer is considered to be a function of the surface parameters, stability, and height. The surface parameters considered are: (1) the surface roughness length; (2) the surface friction velocity; and (3) the zero plane displacement height. The stability parameter, Z/L, where L is the Monin-Obukov stability length, describes the thermal effect on the wind profile. The logarithmic wind profile is used to describe the mean wind field in the neutral boundary layer, and a logarithmic profile with a stability defect is used to describe the stable and unstable atmospheric conditions. For the very stable conditions, the logarithmic wind law does not hold. Under this condition, the layers of the atmosphere become disconnected and large scale frontal motions are the predominate factor in defining the wind profile. Figures are presented which represent some typical wind profiles in the very stable condition.

Luers, J. K.↗
NASA NTRS1985

Detecting Cracks in Rough Metal Surfaces

Test based on eddy-current probe technique identifies cracks in swaged metals. Hinged collar with spring-loaded latch holds probe in place on part tested. For repeated measurements on same or similar parts, collar loosened and moved to various measuring positions. Method suitable for many kinds of metal parts, including swaged fittings, tubing, and pipes. Used for rapid crack/no-crack determinations in suspect parts already installed.

Zuver, N. T.↗
NASA NTRS1985

Photometry of rough planetary surfaces - The role of multiple scattering

Topographic features affect the scattering properties of planetary surfaces by casting shadows and altering the local incidence and emission angles. Measurements of this phenomenon were obtained on the Cornell goniometer for both high and low albedo surfaces. For the low albedo surface, the decrease in reflected radiation due to topography increases sharply with increasing phase angle, whereas for the high albedo sample the effects are approximately constant between phase angles of 30 and 70 deg. The observations are in good agreement with a theoretical model in the case of the dark surface. However, for the high albedo surface the model overestimates the effects by a factor of 2, since it does not include the partial illumination of shadows by multiple scattering. For both high and low albedo surfaces, the effects of topography do not become significant until a phase angle of 30-40 deg.

Buratti, B. J.↗
NASA NTRS1987

Effect of abrasive grit size on wear of manganese-zinc ferrite under three-body abrasion

Wear experiments were conducted using replication electron microscopy and reflection electron diffraction to study abrasion and deformed layers produced in single-crystal Mn-Zn ferrites under three-body abrasion. The abrasion mechanism of Mn-Zn ferrite changes drastically with the size of abrasive grits. With 15-micron (1000-mesh) SiC grits, abrasion of Mn-Zn ferrite is due principally to brittle fracture; while with 4- and 2-micron (4000- and 6000-mesh) SiC grits, abrasion is due to plastic deformation and fracture. Both microcracking and plastic flow produce polycrystalline states on the wear surfaces of single-crystal Mn-Zn ferrites. Coefficient of wear, total thickness of the deformed layers, and surface roughness of the wear surfaces increase markedly with an increase in abrasive grit size. The total thicknesses of the deformed layers are 3 microns for the ferrite abraded by 15-micron SiC, 0.9 microns for the ferrite abraded by 4-micron SiC, and 0.8 microns for the ferrite abraded by 1-micron SiC.

Miyoshi, Kazuhisa↗
NASA NTRS1996

Wetting Hysteresis at the Molecular Scale

The motion of a fluid-fluid-solid contact line on a rough surface is well known to display hysteresis in the contact angle vs. velocity relationship. In order to understand the phenomenon at a fundamental microscopic level, we have conducted molecular dynamics computer simulations of a Wilhelmy plate experiment in which a solid surface is dipped into a liquid bath, and the force-velocity characteristics are measured. We directly observe a systematic variation of force and contact angle with velocity, which is single-valued for the case of an atomically smooth solid surface. In the microscopically rough case, however, we find (as intuitively expected) an open hysteresis loop. Further characterization of the interface dynamics is in progress.

Jin, Wei↗
NASA NTRS1998

Surface Morphology of Undoped and Doped ZnSe Films

Rare-earth doped ions in polar II-VI semiconductors have recently played an important role in the optical properties of materials and devices. In this study, undoped ZnSe and erbium doped ZnSe films were grown by radio frequency (RF) magnetron sputtering method. Atomic Force Microscopy (AFM) was used together with optical microscopy and UV-Vis spectroscopy to characterize the films. Doped samples were found to have higher surface roughness and quite different surface morphology compared to that of undoped samples. The grown films generally show a relatively smooth and uniform surface indicating that they are of overall good quality. The impact of plasma etching on ZnSe:Er film examined under AFM is also discussed.

George, T.↗
NASA NTRS2013

Fabrication Method for LOBSTER-Eye Optics in <110> Silicon

Soft x-ray optics can use narrow slots to direct x-rays into a desirable pattern on a focal plane. While square-pack, square-pore, slumped optics exist for this purpose, they are costly. Silicon (Si) is being examined as a possible low-cost replacement. A fabrication method was developed for narrow slots in <110> Si demonstrating the feasibility of stacked slot optics to replace micropores. Current micropore optics exist that have 20-micron-square pores on 26-micron pitch in glass with a depth of 1 mm and an extent of several square centimeters. Among several proposals to emulate the square pore optics are stacked slot chips with etched vertical slots. When the slots in the stack are positioned orthogonally to each other, the component will approach the soft x-ray focusing observed in the micropore optics. A specific improvement Si provides is that it can have narrower sidewalls between slots to permit greater throughput of x-rays through the optics. In general, Si can have more variation in slot geometry (width, length). Further, the sidewalls can be coated with high-Z materials to enhance reflection and potentially reduce the surface roughness of the reflecting surface. Narrow, close-packed deep slots in <110> Si have been produced using potassium hydroxide (KOH) etching and a patterned silicon nitride (SiN) mask. The achieved slot geometries have sufficient wall smoothness, as observed through scanning electron microscope (SEM) imaging, to enable evaluation of these slot plates as an optical element for soft x-rays. Etches of different angles to the crystal plane of Si were evaluated to identify a specific range of etch angles that will enable low undercut slots in the Si <110> material. These slots with the narrow sidewalls are demonstrated to several hundred microns in depth, and a technical path to 500-micron deep slots in a precision geometry of narrow, closepacked slots is feasible. Although intrinsic stress in ultrathin wall Si is observed, slots with walls approaching 1.5 microns can be achieved (a significant improvement over the 6-micron walls in micro - pore optics). The major advantages of this technique are the potential for higher x-ray throughout (due to narrow slot walls) and lower cost over the existing slumped micropore glass plates. KOH etching of smooth sidewalls has been demonstrated for many applications, suggesting its feasibility for implementation in x-ray optics. Si cannot be slumped like the micropore optics, so the focusing will be achieved with millimeter-scale slot plates that populate a spherical dome. The possibility for large-scale production exists for Si parts that is more difficult to achieve in micropore parts.

Chervenak, James↗
NASA NTRSDate not supplied

Regional Impacts of Ice Sheet Surface Representation Improvements in an Earth System Model

Ice sheet surface conditions and their subsequent impact on surface mass balance play an important role in ice sheet dynamics and ice sheet interaction with the overlying atmosphere and surrounding ocean. The NASA Global Modeling and Assimilation Office’s (GMAO) Goddard Earth Observing System (GEOS) ecosystem of models and reanalyses model ice sheet and glacier surface mass balance with a moderately complex snow and ice module, including prognostic surface albedo evolution, fractional snow cover, and snowpack hydrology and meltwater retention. With this configuration, Greenland near surface air temperatures and ice sheet melt are well represented in MERRA-2, GMAO’s current atmospheric reanalysis; however, the similarity to observations in some regions is due, in part, to compensating biases in surface energy budget. Recent improvements to GEOS’ cloud microphysics and longwave radiation parameterizations reduced biases in surface net longwave radiation and exacerbated surface net shortwave radiation biases, effectively increasing near surface temperatures and melting, particularly during the summer months. Here, we demonstrate the Earth system response to an improved representation of the ice sheet surface focused on minimizing the surface energy biases and increasing spatial and temporal representativeness. New changes to the surface albedo parameterization, including the introduction of a prognostic aerosol darkening scheme, help mitigate shortwave biases, while modifications to surface roughness characteristics improve near surface sensible heat fluxes. Focusing on the Arctic and Greenland, we examine the combined impact on these changes on regional weather conditions and ice sheet surface mass balance using a high resolution atmospheric only experiment, and we use a coupled model configuration to assess the impact on oceanic conditions and subseasonal-to-seasonal prediction. Overall, these improvements increase modeled ice sheet surface realism and provide a strong basis for more accurate ice sheet mass balance in GMAO’s future reanalyses and forecasting systems.

Lauren C Andrews↗
NASA NTRSDate not supplied

Regional Impacts of Ice Sheet Surface Representation Improvements in an Earth System Model

Ice sheet surface conditions and their subsequent impact on surface mass balance play an important role in ice sheet dynamics and ice sheet interaction with the overlying atmosphere and surrounding ocean. The NASA Global Modeling and Assimilation Office’s (GMAO) Goddard Earth Observing System (GEOS) ecosystem of models and reanalyses model ice sheet and glacier surface mass balance with a moderately complex snow and ice module, including prognostic surface albedo evolution, fractional snow cover, and snowpack hydrology and meltwater retention. With this configuration, Greenland near surface air temperatures and ice sheet melt are well represented in MERRA-2, GMAO’s current atmospheric reanalysis; however, the similarity to observations in some regions is due, in part, to compensating biases in surface energy budget. Recent improvements to GEOS’ cloud microphysics and longwave radiation parameterizations reduced biases in surface net longwave radiation and exacerbated surface net shortwave radiation biases, effectively increasing near surface temperatures and melting, particularly during the summer months. Here, we demonstrate the Earth system response to an improved representation of the ice sheet surface focused on minimizing the surface energy biases and increasing spatial and temporal representativeness. New changes to the surface albedo parameterization, including the introduction of a prognostic aerosol darkening scheme, help mitigate shortwave biases, while modifications to surface roughness characteristics improve near surface sensible heat fluxes. Focusing on the Arctic and Greenland, we examine the combined impact on these changes on regional weather conditions and ice sheet surface mass balance using a high resolution atmospheric only experiment, and we use a coupled model configuration to assess the impact on oceanic conditions and subseasonal-to-seasonal prediction. Overall, these improvements increase modeled ice sheet surface realism and provide a strong basis for more accurate ice sheet mass balance in GMAO’s future reanalyses and forecasting systems.

Lauren C. Andrews↗
NASA NTRSDate not supplied

Assessing the Effects of Various Surface Textures and Features on Turbulent Heat Transfer in Hypersonic Flight

Experiments were conducted in the NASA Ames Hypervelocity Free Flight Aerodynamic Facility (ballistic range) to quantify the effects on turbulent convective heat transfer of distributed surface roughness, and of isolated features, representative of thermal protection systems on atmospheric entry vehicles. The surface textures and features were applied on the conic frusta of 45o sphere-cone models having a nose-to-base radius ratio of 0.5, similar to the forebody geometry of the Galileo and Pioneer-Venus entry probes. Test conditions were selected to provide turbulent roughness Reynolds numbers, k+, in the ranges expected for outer planet entry missions. Turbulent flow on the conic frustum was achieved by tripping the flow on the sphere-segment nose cap with distributed surface roughness, created by sand-blasting the nose cap. Surface textures included distributed, acreage, roughness, as well as cavity and groove discrete features. The majority of the data to be presented are results for distributed roughness, which includes both random, sand-grain-like roughness, and regular pattern roughness. The pattern roughness was designed to represent the roughness on woven thermal protection system materials, such as NASA’s 3-D Medium Density Carbon Phenolic (3MDCP), also known as HEEET, developed by the Heatshield for Extreme Entry Environments Technology project. The pattern roughness tested is a 3-D wavy surface, and includes three different roughness element height-to-spacing ratios representative of two configurations of 3MDCP, and spanning ratios measured both before, and after, ablation in an arc jet test facility. The patterns tested in the ballistic range were laser-etched on metal models, and represented an idealized version of the real-world materials in which each roughness element was nearly identical. Additional tests were performed wherein the laser-etched patterns were degraded by sand-blasting with various sized grit media, to produce regular patterns with superimposed irregular roughness, more representative of flight materials. Results of each will be compared. The discrete features tested included cylindrical cavities and rectangular grooves of various width-to-depth ratios. Cavities represent either heatshield damage, such as from micro-meteoroid and orbital debris (MMOD) damage, or from designed penetrations, such as on the Genesis sample return capsule. The grooves were scaled representations of seams between segments of HEEET material in a notional tiled thermal protection system. The tests examined the effects on turbulent heating downstream of the isolated features. The tests were conducted at speeds between 3 km/s and 4 km/s in air between 0.15 atm and 0.25 atm (Mach numbers between 9 and 12). Roughness Reynolds numbers, k+, ranged from 12 to 70 for the sand roughness, and as high as 200 for the pattern roughness. Boundary-layer parameters required for calculating k+ were evaluated using computational fluid dynamics simulations using the DPLR (Data Parallel Line Relaxation) code. Each model included both rough- and smooth-wall segments, and heat transfer augmentation factors were determined as the ratio of the rough-wall to smooth-wall heat flux measured on each test.

hypersonic↗
NASA NTRS2016

The Effect of Roughness Model on Scattering Properties of Ice Crystals.

We compare stochastic models of microscale surface roughness assuming uniform and Weibull distributions of crystal facet tilt angles to calculate scattering by roughened hexagonal ice crystals using the geometric optics (GO) approximation. Both distributions are determined by similar roughness parameters, while the Weibull model depends on the additional shape parameter. Calculations were performed for two visible wavelengths (864 nm and 410 nm) for roughness values between 0.2 and 0.7 and Weibull shape parameters between 0 and 1.0 for crystals with aspect ratios of 0.21, 1 and 4.8. For this range of parameters we find that, for a given roughness level, varying the Weibull shape parameter can change the asymmetry parameter by up to about 0.05. The largest effect of the shape parameter variation on the phase function is found in the backscattering region, while the degree of linear polarization is most affected at the side-scattering angles. For high roughness, scattering properties calculated using the uniform and Weibull models are in relatively close agreement for a given roughness parameter, especially when a Weibull shape parameter of 0.75 is used. For smaller roughness values, a shape parameter close to unity provides a better agreement. Notable differences are observed in the phase function over the scattering angle range from 5deg to 20deg, where the uniform roughness model produces a plateau while the Weibull model does not.

Weibull density functions↗