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At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
NASA NTRS2022

Effects of Increasing the Category Resolution of the Sea Ice Thickness Distribution in a Coupled Climate Model on Arctic and Antarctic Sea Ice Mean State

Many modern sea ice models used in global climate models represent the subgrid-scale heterogeneity in sea ice thickness with an ice thickness distribution (ITD), which improves model realism by representing the significant impact of the high spatial heterogeneity of sea ice thickness on thermodynamic and dynamic processes. Most models default to five thickness categories. However, little has been done to explore the effects of the resolution of this distribution (number of categories) on sea-ice feedbacks in a coupled model framework and resulting representation of the sea ice mean state. Here, we explore this using sensitivity experiments in CESM2 with the standard 5 ice thickness categories and 15 ice thickness categories. Increasing the resolution of the ITD in a run with preindustrial climate forcing results in substantially thicker Arctic sea ice year-round. Analyses show that this is a result of the ITD influence on ice strength. With 15 ITD categories, weaker ice occurs for the same average thickness, resulting in a higher fraction of ridged sea ice. In contrast, the higher resolution of thin ice categories results in enhanced heat conduction and bottom growth and leads to only somewhat increased winter Antarctic sea ice volume. The spatial resolution of the ICESat-2 satellite mission provides a new opportunity to compare model outputs with observations of seasonal evolution of the ITD in the Arctic (ICESat-2; 2018–2021). Comparisons highlight significant differences from the ITD modeled with both runs over this period, likely pointing to underlying issues contributing to the representation of average thickness.

Madison M. Smith↗
DOE OSTI2014

Ice Concentration Retrieval in Stratiform Mixed-phase Clouds Using Cloud Radar Reflectivity Measurements and 1D Ice Growth Model Simulations

Measurement of ice number concentration in clouds is important but still challenging. Stratiform mixed-phase clouds (SMCs) provide a simple scenario for retrieving ice number concentration from remote sensing measurements. The simple ice generation and growth pattern in SMCs offers opportunities to use cloud radar reflectivity (Ze) measurements and other cloud properties to infer ice number concentration quantitatively. To understand the strong temperature dependency of ice habit and growth rate quantitatively, we develop a 1-D ice growth model to calculate the ice diffusional growth along its falling trajectory in SMCs. The radar reflectivity and fall velocity profiles of ice crystals calculated from the 1-D ice growth model are evaluated with the Atmospheric Radiation Measurements (ARM) Climate Research Facility (ACRF) ground-based high vertical resolution radar measurements. Combining Ze measurements and 1-D ice growth model simulations, we develop a method to retrieve the ice number concentrations in SMCs at given cloud top temperature (CTT) and liquid water path (LWP). The retrieved ice concentrations in SMCs are evaluated with in situ measurements and with a three-dimensional cloud-resolving model simulation with a bin microphysical scheme. These comparisons show that the retrieved ice number concentrations are within an uncertainty of a factor of 2, statistically.

1-D ice growth↗
NASA NTRS2021

A multi-model CMIP6-PMIP4 study of Arctic sea ice at 127 ka: sea ice data compilation and model differences

The Last Interglacial period (LIG) is a period with increased summer insolation at high northern latitudes, which results in strong changes in the terrestrial and marine cryosphere. Understanding the mechanisms for this response via climate modelling and comparing the models' representation of climate reconstructions is one of the objectives set up by the Paleoclimate Modelling Intercomparison Project for its contribution to the sixth phase of the Coupled Model Intercomparison Project. Here we analyse the results from 16 climate models in terms of Arctic sea ice. The multi-model mean reduction in minimum sea ice area from the pre industrial period (PI) to the LIG reaches 50 % (multi-model mean LIG area is 3.20×10^6 sq.km, compared to 6.46×10^6 sq.km for the PI). On the other hand, there is little change for the maximum sea ice area (which is 15–16×10^6 sq.km for both the PI and the LIG. To evaluate the model results we synthesise LIG sea ice data from marine cores collected in the Arctic Ocean, Nordic Seas and northern North Atlantic. The reconstructions for the northern North Atlantic show year-round ice-free conditions, and most models yield results in agreement with these reconstructions. Model–data disagreement appear for the sites in the Nordic Seas close to Greenland and at the edge of the Arctic Ocean. The northernmost site with good chronology, for which a sea ice concentration larger than 75 % is reconstructed even in summer, discriminates those models which simulate too little sea ice. However, the remaining models appear to simulate too much sea ice over the two sites south of the northernmost one, for which the reconstructed sea ice cover is seasonal. Hence models either underestimate or overestimate sea ice cover for the LIG, and their bias does not appear to be related to their bias for the pre-industrial period. Drivers for the inter-model differences are different phasing of the up and down short-wave anomalies over the Arctic Ocean, which are associated with differences in model albedo; possible cloud property differences, in terms of optical depth; and LIG ocean circulation changes which occur for some, but not all, LIG simulations. Finally, we note that inter-comparisons between the LIG simulations and simulations for future climate with moderate (1 %/yr) CO2 increase show a relationship between LIG sea ice and sea ice simulated under CO2 increase around the years of doubling CO2. The LIG may therefore yield insight into likely 21st century Arctic sea ice changes using these LIG simulations.

Arctic sea ice↗
NASA NTRSDate not supplied

Implementation of Interactive Sea Ice Radiative Transfer into the GISS GCM and Its Impact on Sea Ice Simulation

To improve the representation of solar radiation in sea ice in the Goddard Institute for Space Studies (GISS) climate model (ModelE), we have implemented an advanced radiative transfer (RT) scheme to interactively calculate the surface albedo and transmittance of the ice layer and the solar absorption within. The ice physical properties (temperature, salinity, and density), which are simulated by the thermodynamic module in ModelE, are directly used as the input of the RT scheme to determine the inherent optical properties (IOPs) of brine pockets and air bubbles in the ice layers. This provides a more sophisticated, accurate, and complete treatment of sea ice RT for ModelE. The sea ice RT model is also validated with measured spectral albedo and transmittance for different ice types. Compared with ModelE simulations with current radiative parameterization for sea ice, the new RT implementation will slightly increase the ice surface albedo in the summer in the Arctic and greatly increase the radiative transmittance. Consequently, the ice surface melting is reduced and the base melting is increased but the difference in the simulated ice area is small. The effect of this new RT implementation on the Antarctic ice is negligible. The observed decrease in Arctic sea ice extent is well captured by the ModelE simulation.

Sea ice↗
DOE OSTI2022

Sea Ice Rheology Experiment (SIREx): 1. Scaling and Statistical Properties of Sea-Ice Deformation Fields

As the sea-ice modeling community is shifting to advanced numerical frameworks, developing new sea-ice rheologies, and increasing model spatial resolution, ubiquitous deformation features in the Arctic sea ice are now being resolved by sea-ice models. Initiated at the Forum for Arctic Modeling and Observational Synthesis, the Sea Ice Rheology Experiment (SIREx) aims at evaluating state-of-the-art sea-ice models using existing and new metrics to understand how the simulated deformation fields are affected by different representations of sea-ice physics (rheology) and by model configuration. Part 1 of the SIREx analysis is concerned with evaluation of the statistical distribution and scaling properties of sea-ice deformation fields from 35 different simulations against those from the RADARSAT Geophysical Processor System (RGPS). For the first time, the viscous-plastic (and the elastic-viscous-plastic variant), elastic-anisotropic-plastic, and Maxwell-elasto-brittle rheologies are compared in a single study. We find that both plastic and brittle sea-ice rheologies have the potential to reproduce the observed RGPS deformation statistics, including multi-fractality. Model configuration (e.g., numerical convergence, atmospheric representation, spatial resolution) and physical parameterizations (e.g., ice strength parameters and ice thickness distribution) both have effects as important as the choice of sea-ice rheology on the deformation statistics. It is therefore not straightforward to attribute model performance to a specific rheological framework using current deformation metrics. In light of these results, we further evaluate the statistical properties of simulated Linear Kinematic Features in a SIREx Part 2 companion paper.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS2017

Ice Crystal Icing Research at NASA

Ice crystals found at high altitude near convective clouds are known to cause jet engine power-loss events. These events occur due to ice crystals entering a propulsion systems core flowpath and accreting ice resulting in events such as uncommanded loss of thrust (rollback), engine stall, surge, and damage due to ice shedding. As part of a community with a growing need to understand the underlying physics of ice crystal icing, NASA has been performing experimental efforts aimed at providing datasets that can be used to generate models to predict the ice accretion inside current and future engine designs. Fundamental icing physics studies on particle impacts, accretion on a single airfoil, and ice accretions observed during a rollback event inside a full-scale engine in the Propulsion Systems Laboratory are summarized. Low fidelity code development using the results from the engine tests which identify key parameters for ice accretion risk and the development of high fidelity codes are described. These activities have been conducted internal to NASA and through collaboration efforts with industry, academia, and other government agencies. The details of the research activities and progress made to date in addressing ice crystal icing research challenges are discussed.

icing↗
NASA NTRS2017

Ice Crystal Icing Research at NASA

Ice crystals found at high altitude near convective clouds are known to cause jet engine power-loss events. These events occur due to ice crystals entering a propulsion systems core flowpath and accreting ice resulting in events such as uncommanded loss of thrust (rollback), engine stall, surge, and damage due to ice shedding. As part of a community with a growing need to understand the underlying physics of ice crystal icing, NASA has been performing experimental efforts aimed at providing datasets that can be used to generate models to predict the ice accretion inside current and future engine designs. Fundamental icing physics studies on particle impacts, accretion on a single airfoil, and ice accretions observed during a rollback event inside a full-scale engine in the Propulsion Systems Laboratory are summarized. Low fidelity code development using the results from the engine tests which identify key parameters for ice accretion risk and the development of high fidelity codes are described. These activities have been conducted internal to NASA and through collaboration efforts with industry, academia, and other government agencies. The details of the research activities and progress made to date in addressing ice crystal icing research challenges are discussed.

upwind schemes↗
NASA NTRS2024

Predictability of the Minimum Sea Ice Extent from Winter Fram Strait Ice Area Export: Model vs Observations

Observations show predictive skill of the minimum sea ice extent (Min SIE) from late winter anomalous off-shore ice drift along the Eurasian coastline – leading to local ice thickness anomalies at the onset of the melt season – a signal then amplified by the ice-albedo feedback. We assess whether the observed seasonal predictability of September sea ice extent (Sept SIE) from Fram Strait Ice Area Export (FSIAE, a proxy for Eurasian coastal divergence) is present in Global Climate Model (GCM) large ensembles, namely the CESM2-LE, GISS-E2.1-G, FLOR-LE, CNRM-CM6-1, and CanESM5. All models show distinct periods where winter FSIAE anomalies are negatively correlated with the May sea ice thickness (May SIT) anomalies along the Eurasian coastline, and the following Sept Arctic SIE, as in observations. Counter-intuitively, several models show occasional periods where winter FSIAE anomalies are positively correlated with the following Sept SIE anomalies when the mean ice thickness is large or late in the simulation when the sea ice is thin, and/or when internal variability increases. More importantly, periods with weak correlation between FSIAE and the Sept SIE dominate, suggesting that summer melt processes dominate over late winter preconditioning and May SIT anomalies. In general, we find that the coupling between the FSIAE and ice thickness anomalies along the Eurasian coastline is an ubiquitous feature of GCMs and that the relationship with the following Sept SIE is dependent on the mean Arctic sea ice thickness.

off-shore ice drift↗
DOE OSTI2025

ICE Calculator 2.0: Final Report for Phase 1 of the National Initiative to Update the Interruption Cost Estimate (ICE) Calculator

In 2021, Berkeley Lab and Resource Innovations, Inc. launched the “ICE 2.0 Initiative” – a national study to refresh the underlying data and enhance the functionality of the ICE Calculator. The Initiative involves Berkeley Lab contracting with sponsoring utilities to administer identical, updated and comprehensive interruption cost surveys to statistically representative samples of each utility’s customers. Berkeley Lab and Resource Innovations then pool the survey results across the utilities and use them to update the analytical engines that drive the ICE Calculator. The ICE 2.0 Initiative is being conducted in phases. Each phase involves the administration of interruption cost surveys to the customers of sponsoring utilities, followed by an update to the ICE Calculator based on analysis of the pooled survey results. This report describes the activities and findings from Phase 1 of the ICE 2.0 Initiative. Phase 1 was sponsored by eight utilities: American Electric Power, Commonwealth Edison, Dominion Energy, Duke Energy, DTE Electric, Exelon, National Grid, and Puget Sound Energy. Phase 1 involved 11 customer interruption cost survey activities representing a total of 24 electricity distribution service territories, 23 of them located in the Eastern and Midwestern regions of the U.S. and one located in the Pacific Northwest. ICE 2.0 vs. 1.0 Comparison This memorandum compares customer power interruption costs estimated using the recently updated Interruption Cost Estimate (ICE) Calculator (“ICE 2.0”) to the original ICE Calculator (“ICE 1.0”). ICE 1.0 was developed in 2009 based on 15 independent power interruption cost surveys conducted by 10 electric utilities between 1989 and 2012. ICE 2.0 was developed in 2025 through a national initiative based on a consistent set of power interruption cost surveys and 11 surveying efforts conducted across 24 electric utility service territories between 2022 and 2024.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
NASA NTRS1995

The role of sea ice in 2 x CO2 climate model sensitivity. Part 1: The total influence of sea ice thickness and extent

As a first step in investigating the effects of sea ice changes on the climate sensitivity to doubled atmospheric CO2, the authors use a standard simple sea ice model while varying the sea ice distributions and thicknesses in the control run. Thinner ice amplifies the atmospheric temperature senstivity in these experiments by about 15% (to a warming of 4.8 C), because it is easier for the thinner ice to be removed as the climate warms. Thus, its impact on sensitivity is similar to that of greater sea ice extent in the control run, which provides more opportunity for sea ice reduction. An experiment with sea ice not allowed to change between the control and doubled CO2 simulations illustrates that the total effect of sea ice on surface air temperature changes, including cloud cover and water vapor feedbacks that arise in response to sea ice variations, amounts to 37% of the temperature sensitivity to the CO2 doubling, accounting for 1.56 C of the 4.17 C global warming. This is about four times larger than the sea ice impact when no feedbacks are allowed. The different experiments produce a range of results for southern high latitudes with the hydrologic budget over Antarctica implying sea level increases of varying magnitude or no change. These results highlight the importance of properly constraining the sea ice response to climate perturbations, necessitating the use of more realistic sea ice and ocean models.

Rind, D.↗
NASA NTRS2003

Quantification of Ice Accretions for Icing Scaling Evaluations

The comparison of ice accretion characteristics is an integral part of aircraft icing research. It is often necessary to compare an ice accretion obtained from a flight test or numerical simulation to one produced in an icing wind tunnel or for validation of an icing scaling method. Traditionally, this has been accomplished by overlaying two-dimensional tracings of ice accretion shapes. This paper addresses the basic question of how to compare ice accretions using more quantitative methods. For simplicity, geometric characteristics of the ice accretions are used for the comparison. One method evaluated is a direct comparison of the percent differences of the geometric measurements. The second method inputs these measurements into a fuzzy inference system to obtain a single measure of the goodness of the comparison. The procedures are demonstrated by comparing ice shapes obtained in the Icing Research Tunnel at NASA Glenn Research Center during recent icing scaling tests. The results demonstrate that this type of analysis is useful in quantifying the similarity of ice accretion shapes and that the procedures should be further developed by expanding the analysis to additional icing data sets.

Ruff, Gary A.↗
NASA NTRS2004

Advances in Measuring Antarctic Sea-Ice Thickness and Ice-Sheet Elevations with ICESat Laser Altimetry

NASA's Ice, Cloud and Land Elevation Satellite (ICESat) has been measuring elevations of the Antarctic ice sheet and sea-ice freeboard elevations with unprecedented accuracy. Since February 20,2003, data has been acquired during three periods of laser operation varying from 36 to 54 days, which is less than the continuous operation of 3 to 5 years planned for the mission. The primary purpose of ICESat is to measure time-series of ice-sheet elevation changes for determination of the present-day mass balance of the ice sheets, study of associations between observed ice changes and polar climate, and estimation of the present and future contributions of the ice sheets to global sea level rise. ICESat data will continue to be acquired for approximately 33 days periods at 3 to 6 month intervals with the second of ICESat's three lasers, and eventually with the third laser. The laser footprints are about 70 m on the surface and are spaced at 172 m along-track. The on-board GPS receiver enables radial orbit determinations to an accuracy better than 5 cm. The orbital altitude is around 600 km at an inclination of 94 degrees with a 8-day repeat pattern for the calibration and validation period, followed by a 91 -day repeat period for the rest of the mission. The expected range precision of single footprint measurements was 10 cm, but the actual range precision of the data has been shown to be much better at 2 to 3 cm. The star-tracking attitude-determination system should enable footprints to be located to 6 m horizontally when attitude calibrations are completed. With the present attitude calibration, the elevation accuracy over the ice sheets ranges from about 30 cm over the low-slope areas to about 80 cm over areas with slopes of 1 to 2 degrees, which is much better than radar altimetry. After the first period of data collection, the spacecraft attitude was controlled to point the laser beam to within 50 m of reference surface tracks over the ice sheets. Detection of ice elevation changes over select areas of the ice sheet is demonstrated with using both crossover analysis and precise-repeat track analysis. Sea ice freeboard-height distributions over the Antarctic sea pack are derived over distances of 50 km and converted into maps of average freeboard thickness and sea-ice thickness.

Zwally, H. Jay↗
NASA NTRS2008

Effect of the Inhomogeneity of Ice Crystals on Retrieving Ice Cloud Optical Thickness and Effective Particle Size

Spherical or spheroidal air bubbles are generally trapped in the formation of rapidly growing ice crystals. In this study the single-scattering properties of inhomogeneous ice crystals containing air bubbles are investigated. Specifically, a computational model based on an improved geometric-optics method (IGOM) has been developed to simulate the scattering of light by randomly oriented hexagonal ice crystals containing spherical or spheroidal air bubbles. A combination of the ray-tracing technique and the Monte Carlo method is used. The effect of the air bubbles within ice crystals is to smooth the phase functions, diminish the 22deg and 46deg halo peaks, and substantially reduce the backscatter relative to bubble-free particles. These features vary with the number, sizes, locations and shapes of the air bubbles within ice crystals. Moreover, the asymmetry factors of inhomogeneous ice crystals decrease as the volume of air bubbles increases. Cloud reflectance lookup tables were generated at wavelengths 0.65 m and 2.13 m with different air-bubble conditions to examine the impact of the bubbles on retrieving ice cloud optical thickness and effective particle size. The reflectances simulated for inhomogeneous ice crystals are slightly larger than those computed for homogenous ice crystals at a wavelength of 0.65 microns. Thus, the retrieved cloud optical thicknesses are reduced by employing inhomogeneous ice cloud models. At a wavelength of 2.13 microns, including air bubbles in ice cloud models may also increase the reflectance. This effect implies that the retrieved effective particle sizes for inhomogeneous ice crystals are larger than those retrieved for homogeneous ice crystals, particularly, in the case of large air bubbles.

Xie, Yu↗
DOE OSTI2022

Spatially Averaged Ice Contents of Ice-Wedge Polygon Cross-Sections to 3-m Depth, July 2013, Utqiagvik, Alaska

This dataset contains spatially averaged estimates of ice content (volume percent) for two-dimensional cross-sectional profiles (from trough center to trough center to a depth of 3 meters) of low- and flat-centered ice-wedge polygons (three of each type) located near Utqiagvik, Alaska. A combination of soil pits, trenches, and cores were used to describe, sample, and map the cross-section stratigraphy of soil horizons and ice wedges for each polygon at 6 depth intervals. Observed soil horizons were assigned to four types with increasing amounts of organic components (mineral, mineral/organic, organic/mineral, and organic). The average ice contents of each soil horizon type below the permafrost boundary and wedge ice were weighted by their cross-sectional area fractions to calculate spatially averaged estimates of ice content for each polygon. In the active layer, spatially averaged estimates of volumetric water contents were similarly determined and reported here as “ice” content to enable estimates of the soil’s structurally competent porosity and excess ice in permafrost layers. In this dataset, the file AK13_ice_contents.csv includes cross-sectional area fractions and spatially averaged ice contents for soil layers and horizon types at the six depth intervals. The file AK13_permafrost_ice_fractions.csv contains the calculated partitioning of ice contents into pore ice and excess ice fractions for the three permafrost-dominated depth intervals. In addition, there is a data dictionary file for each of these data files and a file-level metadata file. These data were generated by the Department of Energy’s Soil Carbon Response to Environmental Change Scientific Focus Area and were used as inputs to model simulations examining the consequences of thaw-affected subsidence and microtopography change on active layer thickness of low-relief polygonal tundra landscapes in a warming Arctic.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1947

A Method for Calculating the Heat Required for Windshield Thermal Ice Prevention Based on Extensive Flight Tests in Natural Icing Conditions

An equation is presented for calculating the heat flow required from the surface of an internally heated windshield in order to prevent the formation of ice accretions during flight in specified icing conditions. To ascertain the validity of the equation, comparison is made between calculated values of the heat required and measured values obtained for test windshields in actual flights in icing conditions. The test windshields were internally heated and provided data applicable to two common types of windshield configurations; namely the V-type and the type installed flush with the fuselage contours. These windshields were installed on a twin-engine cargo airplane and the icing flights were conducted over a large area of the United States during the winters of 1945-46 and 1946-47. In addition to the internally heated windshield investigation, some test data were obtained for a windshield ice-prevention system in which heated air was discharged into the windshield boundary layer. The general conclusions resulting from this investigation are as follows: 1) The amount of heat required for the prevention of ice accretions on both flush- and V-type windshields during flight in specified icing conditions can be calculated with a degree of accuracy suitable for design purposes. 2) A heat flow of 2000 to 2500 Btu per hour per square foot is required for complete and continuous protection of a V-type windshield in fight at speeds up to 300 miles per hour in a moderate cumulus icing condition. For the same degree of protection and the same speed range, a value of 1000 Btu per hour per square foot suffices in a moderate stratus icing condition. 3) A heat supply of 1000 Btu per hour per square foot is adequate for a flush windshield located well aft of the fuselage stagnation region, at speeds up to 300 miles per hour, for flight in both stratus and moderate cumulus icing conditions. 4) The external air discharge system of windshield thermal ice prevention is thermally inefficient and requires a heat supply approximately 20 times that required for an internal system having the same performance.

ICE FORMATION↗
NASA NTRS2002

Basal melt beneath whillans ice stream and ice streams A and C

We have used a recently derived map of the velocity of Whillans Ice Stream and Ice Streams A and C to help estimate basal melt. Temperature was modeled with a simple vertical advection-diffusion equation, 'tuned' to match temperature profiles. We find that most of the melt occurs beneath the tributaries where larger basal shear stresses and thicker ice favors greater melt (e.g., 10-20 mm/yr). The occurrence of basal freezing is predicted beneath much of the ice plains of Ice Stream C and Whillans Ice Stream. Modelled melt rates for when Ice Stream C was active suggest there was just enough melt water generated in its tributaries to balance basal freezing on its ice plain. Net basal melt for Whillans Ice Stream is positive due to smaller basal temperature gradients. Modelled temperatures on Whillans Ice Stream, however, were constrained by a single temperature profile at UpB. Basal temperature gradients for Whillans B1 and Ice Stream A may have conditions more similar to those beneath Ice Streams C and D, in which case, there may not be sufficient melt to sustain motion. This would be consistent with the steady deceleration of Whillans stream over the last few decades.

glaciers ice sheets↗
NASA NTRS2015

Method to Generate Full-Span Ice Shape on Swept Wing Using Icing Tunnel Data

There is a collaborative research program by NASA, FAA, ONERA, and university partners to improve the fidelity of experimental and computational simulation methods for swept-wing ice accretion formulations and resultant aerodynamic effects on large transport aircraft. This research utilizes a 65 scale Common Research Model as the baseline configuration. In order to generate the ice shapes for the aerodynamic testing, ice-accretion testing will be conducted in the NASA Icing Research Tunnel utilizing hybrid model from the 20, 64, and 83 spanwise locations. The models will have full-scale leading edges with truncated chord in order to fit the IRT test section. The ice shapes from the IRT tests will be digitized using a commercially available articulated-arm 3D laser scanning system. The methodology to acquire 3D ice shapes using a laser scanner was developed and validated in a previous research effort. Each of these models will yield a 1.5ft span of ice than can be used. However, a full-span ice accretion will require 75 ft span of ice. This means there will be large gaps between these spanwise ice sections that must be filled, while maintaining all of the important aerodynamic features. A method was developed to generate a full-span ice shape from the three 1.5 ft span ice shapes from the three models.

swept↗