Results for “Linear approximation” — Page 15

NASA NTRS2007

NASA Langley's Approach to the Sandia's Structural Dynamics Challenge Problem

The objective of this challenge is to develop a data-based probabilistic model of uncertainty to predict the behavior of subsystems (payloads) by themselves and while coupled to a primary (target) system. Although this type of analysis is routinely performed and representative of issues faced in real-world system design and integration, there are still several key technical challenges that must be addressed when analyzing uncertain interconnected systems. For example, one key technical challenge is related to the fact that there is limited data on target configurations. Moreover, it is typical to have multiple data sets from experiments conducted at the subsystem level, but often samples sizes are not sufficient to compute high confidence statistics. In this challenge problem additional constraints are placed as ground rules for the participants. One such rule is that mathematical models of the subsystem are limited to linear approximations of the nonlinear physics of the problem at hand. Also, participants are constrained to use these models and the multiple data sets to make predictions about the target system response under completely different input conditions. Our approach involved initially the screening of several different methods. Three of the ones considered are presented herein. The first one is based on the transformation of the modal data to an orthogonal space where the mean and covariance of the data are matched by the model. The other two approaches worked solutions in physical space where the uncertain parameter set is made of masses, stiffnesses and damping coefficients; one matches confidence intervals of low order moments of the statistics via optimization while the second one uses a Kernel density estimation approach. The paper will touch on all the approaches, lessons learned, validation 1 metrics and their comparison, data quantity restriction, and assumptions/limitations of each approach. Keywords: Probabilistic modeling, model validation, uncertainty quantification, kernel density

Horta, Lucas G.↗

NASA NTRS2012

Terra MODIS Band 27 Electronic Crosstalk Effect and Its Removal

The MODerate-resolution Imaging Spectroradiometer (MODIS) is one of the primary instruments in the NASA Earth Observing System (EOS). The first MODIS instrument was launched in December, 1999 on-board the Terra spacecraft. MODIS has 36 bands, covering a wavelength range from 0.4 micron to 14.4 micron. MODIS band 27 (6.72 micron) is a water vapor band, which is designed to be insensitive to Earth surface features. In recent Earth View (EV) images of Terra band 27, surface feature contamination is clearly seen and striping has become very pronounced. In this paper, it is shown that band 27 is impacted by electronic crosstalk from bands 28-30. An algorithm using a linear approximation is developed to correct the crosstalk effect. The crosstalk coefficients are derived from Terra MODIS lunar observations. They show that the crosstalk is strongly detector dependent and the crosstalk pattern has changed dramatically since launch. The crosstalk contributions are positive to the instrument response of band 27 early in the mission but became negative and much larger in magnitude at later stages of the mission for most detectors of the band. The algorithm is applied to both Black Body (BB) calibration and MODIS L1B products. With the crosstalk effect removed, the calibration coefficients of Terra MODIS band 27 derived from the BB show that the detector differences become smaller. With the algorithm applied to MODIS L1B products, the Earth surface features are significantly removed and the striping is substantially reduced in the images of the band. The approach developed in this report for removal of the electronic crosstalk effect can be applied to other MODIS bands if similar crosstalk behaviors occur.

Sun, Junqiang↗

NASA NTRS2012

Towards Validation of an Adaptive Flight Control Simulation Using Statistical Emulation

Traditional validation of flight control systems is based primarily upon empirical testing. Empirical testing is sufficient for simple systems in which a.) the behavior is approximately linear and b.) humans are in-the-loop and responsible for off-nominal flight regimes. A different possible concept of operation is to use adaptive flight control systems with online learning neural networks (OLNNs) in combination with a human pilot for off-nominal flight behavior (such as when a plane has been damaged). Validating these systems is difficult because the controller is changing during the flight in a nonlinear way, and because the pilot and the control system have the potential to co-adapt in adverse ways traditional empirical methods are unlikely to provide any guarantees in this case. Additionally, the time it takes to find unsafe regions within the flight envelope using empirical testing means that the time between adaptive controller design iterations is large. This paper describes a new concept for validating adaptive control systems using methods based on Bayesian statistics. This validation framework allows the analyst to build nonlinear models with modal behavior, and to have an uncertainty estimate for the difference between the behaviors of the model and system under test.

He, Yuning↗

NASA NTRS2012

Optimal Initial Perturbations for Ensemble Prediction of the Madden-Julian Oscillation during Boreal Winter

An initialization strategy, tailored to the prediction of the Madden-Julian oscillation (MJO), is evaluated using the Goddard Earth Observing System Model, version 5 (GEOS-5), coupled general circulation model (CGCM). The approach is based on the empirical singular vectors (ESVs) of a reduced-space statistically determined linear approximation of the full nonlinear CGCM. The initial ESV, extracted using 10 years (1990-99) of boreal winter hindcast data, has zonal wind anomalies over the western Indian Ocean, while the final ESV (at a forecast lead time of 10 days) reflects a propagation of the zonal wind anomalies to the east over the Maritime Continent an evolution that is characteristic of the MJO. A new set of ensemble hindcasts are produced for the boreal winter season from 1990 to 1999 in which the leading ESV provides the initial perturbations. The results are compared with those from a set of control hindcasts generated using random perturbations. It is shown that the ESV-based predictions have a systematically higher bivariate correlation skill in predicting the MJO compared to those using the random perturbations. Furthermore, the improvement in the skill depends on the phase of the MJO. The ESV is particularly effective in increasing the forecast skill during those phases of the MJO in which the control has low skill (with correlations increasing by as much as 0.2 at 20 25-day lead times), as well as during those times in which the MJO is weak.

Ham, Yoo-Geun↗

NASA NTRS2013

Nonlinear Dynamic Behavior of Impact Damage in a Composite Skin-Stiffener Structure

One of the key issues in composite structures for aircraft applications is the early identification of damage. Often, service induced damage does not involve visible plastic deformation, but internal matrix related damage, like delaminations. A wide range of technologies, comprising global vibration and local wave propagation methods can be employed for health monitoring purposes. Traditional low frequency modal analysis based methods are linear methods. The effectiveness of these methods is often limited since they rely on a stationary and linear approximation of the system. The nonlinear interaction between a low frequency wave field and a local impact induced skin-stiffener failure is experimentally demonstrated in this paper. The different mechanisms that are responsible for the nonlinearities (opening, closing and contact) of the distorted harmonic waveforms are separated with the help of phase portraits. A basic analytical model is employed to support the observations.

Ooijevaar, T. H.↗

NASA NTRS2015

An Experimental Investigation of the Flow Physics Associated With End Wall Losses and Large Rotor Tip Clearances as Found in the Rear Stages of a High Pressure Compressor

The focus of this work was to characterize the fundamental flow physics and the overall performance effects due to increased rotor tip clearance heights in axial compressors. Data have been collected in the three-stage axial research compressor at Purdue University with a specific focus on analyzing the multistage effects resulting from the tip leakage flow. Three separate rotor tip clearance heights were studied with nominal tip clearance heights of 1.5%, 3.0%, and 4.0% based on a constant annulus height. Overall compressor performance was investigated at four corrected speedlines (100%, 90%, 80%, and 68%) for each of the three tip clearance configurations using total pressure and total temperature rakes distributed throughout the compressor. The results have confirmed results from previous authors showing a decrease of total pressure rise, isentropic efficiency, and stall margin which is approximately linear with increasing tip clearance height. The stall inception mechanisms have also been evaluated at the same corrected speeds for each of the tip clearance configurations. Detailed flow field measurements have been collected at two loading conditions, nominal loading (NL) and high loading (HL), on the 100% corrected speedline for the smallest and largest tip clearance heights (1.5% and 4.0%). Steady detailed radial traverses of total pressure at the exit of each stator row have been supported by flow visualization techniques to identify regions of flow recirculation and separation. Furthermore, detailed radial traverses of time-resolved total pressures at the exit of each rotor row have been measured with a fast-response pressure probe. These data have helped to quantify the size of the leakage flow at the exit of each rotor. Thermal anemometry has also been implemented to evaluate the time-resolved three-dimensional components of velocity throughout the compressor and calculate blockage due to the rotor tip leakage flow throughout the compressor. These measurements have also been used to calculate streamwise vorticity. Time-resolved static pressure measurements have been collected over the rotor tips for all rotors with each of the three tip clearance configurations for up to five loading conditions along the 100% corrected speedline using fast-response piezoresistive pressure sensors. These time-resolved static pressure measurements, as well as the time-resolved total pressures and velocities have helped to reveal a profound influence of the upstream stator vane on the size and shape of the rotor tip leakage flow. Finally, a novel particle image velocimetry (PIV) technique has been developed as a proof-of- concept. In contrast to PIV methods that have been typically been utilized for turbomachinery applications in the past, the method used for this study introduced the laser light through the same access window that was also used to image the flow. This new method addresses potential concerns related to the intrusive laser-introducing techniques that have typically been utilized by other authors in the past. Ultimately, the data collected for this project represent a unique data set which contributes to build a better understanding of the tip leakage flow field and its associated loss mechanisms. These data will facilitate future engine design goals leading to small blade heights in the rear stages of high pressure compressors and aid in the development of new blade designs which are desensitized to the performance penalties attributed to rotor tip leakage flows.

turbomachinery↗

NASA NTRS2016

Evaluation of the Effect of Surface Finish on High-Cycle Fatigue of SLM-IN718

The surface finish of parts produced by additive manufacturing processes is much rougher than the surface finish generated by machining processes, and a rougher surface can reduce the fatigue strength of a part. This paper discusses an effort to quantify that reduction of strength in high-cycle fatigue for selective laser melt (SLM) coupons. A high-cycle fatigue (HCF) knockdown factor was estimated for Inconel 718, manufactured with the SLM process. This factor is the percentage reduction from the maximum stress in fatigue for low-stress ground (LSG) specimens to the maximum stress of those left with the original surface condition at the same fatigue life. Specimens were provided by a number of vendors, free to use their "best practice"; only one heat treat condition was considered; and several test temperatures were characterized, including room temperature, 800F, 1000F, and 1200F. The 1000F data had a large variance, and was omitted from consideration in this document. A first method used linear approximations extracted from the graphs, and only where data was available for both. A recommended knockdown factor of the as-built surface condition (average roughness of approximately 245 micro-inches/inch) versus low-stress ground condition (roughness no more than 4 micro-inches/inch) was established at approximately 1/3 or 33%. This is to say that for the as-built surface condition, a maximum stress of 2/3 of the stress for LSG can be expected to produce a similar life in the as-built surface condition. In this first evaluation, the knockdown factor did not appear to be a function of temperature. A second approach, the "KP method", incorporated the surface finish measure into a new parameter termed the pseudo-stress intensity factor, Kp, which was formulated to be similar to the fracture mechanics stress intensity factor. Using Kp, the variance seemed to be reduced across all sources, and knockdown factors were estimated using Kp over the range where data occurred. A plot of the results suggests that the knockdown factor is a function of temperature, and that for low lives the knockdown might be lower than the knockdown observed above about one million cycles, where it tended to stabilize. This was not universal for all temperatures tested. The higher temperature tests are thought to be influenced by the test temperature, which perhaps continued the aging process. Further evaluation of the method is suggested.

Lambert, D. M.↗

NASA NTRS2015

Regional Rates of Young US Forest Growth Estimated From Annual Landsat Disturbance History and IKONOS Stereo Imagery

Forests of the Contiguous United States (CONUS) have been found to be a large contributor to the global atmospheric carbon sink. The magnitude and nature of this sink is still uncertain and recent studies have sought to define the dynamics that control its strength and longevity. The Landsat series of satellites has been a vital resource to understand the long-term changes in land cover that can impact ecosystem function and terrestrial carbonstock. We combine annual Landsat forest disturbance history from 1985 to 2011 with single date IKONOS stereoimagery to estimate the change in young forest canopy height and above ground live dry biomass accumulation for selected sites in the CONUS. Our approach follows an approximately linear growth rate following clearing over short intervals and does not estimate the distinct non-linear growth rate over longer intervals.We produced canopy height models by differencing digital surface models estimated from IKONOS stereo pairs with national elevation data (NED). Correlations between height and biomass were established independently using airborne LiDAR, and then applied to the IKONOS-estimated canopy height models. Graphing current biomass against time since disturbance provided biomass accumulation rates. For 20 study sites distributed across five regions of the CONUS, 19 showed statistically significant recovery trends (p is less than 0.001) with canopy growth from 0.26 m yr-1to 0.73 m yr-1. Above ground live dry biomass (AGB) density accumulation ranged from 1.31 t/ha yr-1 to 12.47 t/ha yr-1. Mean forest AGB accumulationwas 6.31 t/ha yr-1 among all sites with significant growth trends. We evaluated the accuracy of our estimates by comparing to field estimated site index curves of growth, airborne LiDAR data, and independent model predictions of C accumulation. Growth estimates found with this approach are consistent with site index curves and total biomass estimates fall within the range of field estimates. This is aviable approach to estimate forest biomass accumulation in regions with clear-cut harvest disturbances.

Neigh, Christopher S. R.↗

NASA NTRS2017

Understanding the Sun-Earth Libration Point Orbit Formation Flying Challenges For WFIRST and Starshade

In order to fly an occulter in formation with a telescope at the Sun-Earth L2 (SEL2) Libration Point, one must have a detailed understanding of the dy-namics that govern the restricted three body system. For initial purposes, a linear approximation is satisfactory, but operations will require a high-fidelity modeling tool along with strategic targeting methods in order to be successful. This paper focuses on the challenging dynamics of the transfer trajectories to achieve the relative positioning of two spacecraft to fly in formation at SEL2, in our case, the Wide-Field Infrared Survey Telescope (WFIRST) and a proposed Starshade. By modeling the formation transfers using a high fidelity tool, an accurate V approximation can be made to as-sist with the development of the subsystem design required for a WFIRST and Starshade formation flight mission.

Sun-Earth-Moon↗

NASA NTRS2017

Smoothing-Based Relative Navigation and Coded Aperture Imaging

This project will develop an efficient smoothing software for incremental estimation of the relative poses and velocities between multiple, small spacecraft in a formation, and a small, long range depth sensor based on coded aperture imaging that is capable of identifying other spacecraft in the formation. The smoothing algorithm will obtain the maximum a posteriori estimate of the relative poses between the spacecraft by using all available sensor information in the spacecraft formation.This algorithm will be portable between different satellite platforms that possess different sensor suites and computational capabilities, and will be adaptable in the case that one or more satellites in the formation become inoperable. It will obtain a solution that will approach an exact solution, as opposed to one with linearization approximation that is typical of filtering algorithms. Thus, the algorithms developed and demonstrated as part of this program will enhance the applicability of small spacecraft to multi-platform operations, such as precisely aligned constellations and fractionated satellite systems.

Relative positioning↗

NASA NTRS2015

An Experimental Investigation of the Flow Physics Associated With End Wall Losses and Large Rotor Tip Clearances as Found in the Rear Stages of a High Pressure Compressor

The focus of this work was to characterize the fundamental flow physics and the overall performance effects due to increased rotor tip clearance heights in axial compressors. Data have been collected in the three-stage axial research compressor at Purdue University with a specific focus on analyzing the multistage effects resulting from the tip leakage flow. Three separate rotor tip clearance heights were studied with nominal tip clearance heights of 1.5%, 3.0%, and 4.0% based on a constant annulus height. Overall compressor performance was investigated at four corrected speedlines (100%, 90%, 80%, and 68%) for each of the three tip clearance configurations using total pressure and total temperature rakes distributed throughout the compressor. The results have confirmed results from previous authors showing a decrease of total pressure rise, isentropic efficiency, and stall margin which is approximately linear with increasing tip clearance height. The stall inception mechanisms have also been evaluated at the same corrected speeds for each of the tip clearance configurations. Detailed flow field measurements have been collected at two loading conditions, nominal loading (NL) and high loading (HL), on the 100% corrected speedline for the smallest and largest tip clearance heights (1.5% and 4.0%). Steady detailed radial traverses of total pressure at the exit of each stator row have been supported by flow visualization techniques to identify regions of flow recirculation and separation. Furthermore, detailed radial traverses of time-resolved total pressures at the exit of each rotor row have been measured with a fast-response pressure probe. These data have helped to quantify the size of the leakage flow at the exit of each rotor. Thermal anemometry has also been implemented to evaluate the time-resolved three-dimensional components of velocity throughout the compressor and calculate blockage due to the rotor tip leakage flow throughout the compressor. These measurements have also been used to calculate streamwise vorticity. Time-resolved static pressure measurements have been collected over the rotor tips for all rotors with each of the three tip clearance configurations for up to five loading conditions along the 100% corrected speedline using fast-response piezoresistive pressure sensors. These time-resolved static pressure measurements, as well as the time-resolved total pressures and velocities have helped to reveal a profound influence of the upstream stator vane on the size and shape of the rotor tip leakage flow. Finally, a novel particle image velocimetry (PIV) technique has been developed as a proof-of- concept. In contrast to PIV methods that have been typically been utilized for turbomachinery applications in the past, the method used for this study introduced the laser light through the same access window that was also used to image the flow. This new method addresses potential concerns related to the intrusive laser-introducing techniques that have typically been utilized by other authors in the past. Ultimately, the data collected for this project represent a unique data set which contributes to build a better understanding of the tip leakage flow field and its associated loss mechanisms. These data will facilitate future engine design goals leading to small blade heights in the rear stages of high pressure compressors and aid in the development of new blade designs which are desensitized to the performance penalties attributed to rotor tip leakage flows.

Berdanier, Reid A.↗

NASA NTRS2018

Historical and Contemporary Trends in the Size, Drift, and Color of Jupiter's Great Red Spot

Observations of Jupiter's Great Red Spot (GRS) span more than 150 years. This allows for careful measurements of its size and drift rate. High spatial resolution spacecraft data also allow tracking of its spectral characteristics and internal dynamics and structure. The GRS continues to shrink in longitudinal length at an approximately linear rate of 0 deg .194 yr(exp −1) and in latitudinal width at 0 deg .048 yr (exp −1). Its westward drift rate (relative to System III W. longitude) has increased from approx. 0 deg .26/day in the 1980s to approx. 0 deg .36/day currently. Since 2014, the GRS's short wavelength (less than 650 nm) reflectance has continued to decrease, while it has become brighter at 890 nm, indicating a change in clouds/haze at high altitudes. In addition, its north–south color asymmetry has decreased, and the dark core has become smaller. Internal velocities have increased on its east and west edges, and decreased on the north and south, resulting in decreased relative vorticity and circulation. The GRS's color changes from 2014 to 2017 may be explained by changes in stretching vorticity or divergence acting to balance the decrease in relative vorticity.

Simon, Amy A.↗

NASA NTRS2014

Regional Characteristics of the Relationship Between Columnar AOD and Surface PM2.5: Application of Lidar Aerosol Extinction Profiles over Baltimore-Washington Corridor During DISCOVER-AQ

The first field campaign of DISCOVER-AQ (Deriving Information on Surface conditions from COlumn and VERtically resolved observations relevant to Air Quality) took place in July 2011 over Baltimore-Washington Corridor (BWC). A suite of airborne remote sensing and in-situ sensors was deployed along with ground networks for mapping vertical and horizontal distribution of aerosols. Previous researches were based on a single lidar station because of the lack of regional coverage. This study uses the unique airborne HSRL (High Spectral Resolution Lidar) data to baseline PM2.5 (particulate matter of aerodynamic diameter less than 2.5 μm) estimates and applies to regional air quality with satellite AOD (Aerosol Optical Depth) retrievals over BWC (∼6500 sq. km). The linear approximation takes into account aerosols aloft above AML (Aerosol Mixing Layer) by normalizing AOD with haze layer height (i.e., AOD/HLH). The estimated PM2.5 mass concentrations by HSRL AOD/HLH are shown within 2 RMSE (Root Mean Square Error ∼9.6 μg/cu. m) with correlation ∼0.88 with the observed over BWC. Similar statistics are shown when applying HLH data from a single location over the distance of 100 km. In other words, a single lidar is feasible to cover the range of 100 km with expected uncertainties. The employment of MPLNET-AERONET (MicroPulse Lidar NETwork - AErosol RObotic NETwork) measurements at NASA GSFC produces similar statistics of PM2.5 estimates as those derived by HSRL. The synergy of active and passive remote sensing aerosol measurements provides the foundation for satellite application of air quality on a daily basis. For the optimal range of 10 km, the MODIS-estimated PM2.5 values are found satisfactory at 27 (out of 36) sunphotometer locations with mean RMSE of 1.6-3.3 μg/cu. m relative to PM2.5 estimated by sunphotometers. The remaining 6 of 8 marginal sites are found in the coastal zone, for which associated large RMSE values ∼4.5-7.8 μg/cu. m are most likely due to overestimated AOD because of water-contaminated pixels.

DISCOVER-AQ↗

NASA NTRSDate not supplied

Sonic Boom Propagation Model Based on a Single-Ray Jacobian

A sonic boom is a nonlinear event whose propagation can be modeled involving two stages. The first stage consists of ray path calculations using linear approximations, while the second stage deals with a nonlinear transport of the acoustic energy along these paths. This presentation discusses a second-order finite difference numerical approach used to predict the ray paths in range-dependent atmospheres and compares it to existing finite difference schemes. The approach is validated using exact solutions obtained for stratified atmospheres. In the second stage, the geometrical spreading effect needed in determining sonic boom waveforms from a Burgers' equation is obtained using a method that only needs a single ray rather than four rays required by most existing sonic boom propagation codes. The single-ray method calculates the Jacobian, associated with the coordinate transformation from a suitable ray coordinate system to the Cartesian coordinate system, directly from the ray tracing equations. While the four-ray method approximates the geometrical spreading using a finite difference scheme involving the four rays, the single-ray method does not rely on this approximation and instead depends purely on the acoustical kinematic properties of the atmosphere. Comparisons of results using these two methods are discussed.

sonic boom↗

NASA NTRS1993

Possible Near-IR Channels for Remote Sensing Precipitable Water Vapor from Geostationary Satellite Platforms

Remote sensing of tropospheric water vapor profiles from current geostationary weather satellites are made using a few broadband infrared (IR) channels in the 6 to 13- micrometers region. Uncertainties greater than 20 percent exist in derived water vapor values just above the surface from the IR emission measurements. In this paper, we propose three near-IR channels, one within the 0.94-micrometer water vapor band absorption region, and the other two in nearby atmospheric windows, for remote sensing of precipitable water vapor over land areas, excluding lakes and rivers, during daytime from future geostationary satellite platforms. The physical principles are as follows. The reflectance of most surface targets varies approximately linearly with wavelength near 1 micrometer. The solar radiation on the sun-surface-sensor ray path is attenuated by atmospheric water vapor...

Green, R. O.↗

NASA NTRS2019

MultiLayer Clustered Sampling (MLCS) technique for near-earth asteroid impact hazard assessment

Because of planetary encounters, the motion of near-Earth asteroids is chaotic and small diﬀerences in the initial conditions tend to diverge exponentially. Linear approximations for propagating orbital uncertainties can lead to inaccurate estimates of the probability of an Earth collision. We present a novel fully nonlinear strategy for estimating the probability of an asteroid impact using sequential Monte Carlo layers. The method ﬁrst explores a low-resolution layer to locate potentially relevant regions. Then, we conduct localized searches on deeper layers with higher resolution. The method retains the accuracy of brute-force Monte Carlo sampling while reducing the computational cost by only sampling relevant regions.

Farnocchia, Davide↗

NASA NTRS2018

Practical Orbit Determination for Aerobraking with Accumulated Accelerometer Data

Navigation during aerobraking missions has historically relied solely on radiometric Doppler data. Accelerometer data, available on all modern spacecraft, has the potential to supplement Doppler data, increasing operational tempos, filling tracking data gaps, and improving the accuracy of orbit determination solutions. However, integration of Doppler and accelerometer data into the batch filter solutions used for operational navigation has proven to be practically challenging, due to the narrow region of adequate linear approximation for acceleration incurred by drag. This work proposes to use the accumulated velocity changes derived from these values as a more compatible data type. Demonstrations of results focus on NASA’s Maven and ESA’s TGO mission, and how this technique can be used to improve operations for the upcoming Maven aerobraking phase with reduced tracking data and lighter staffing requirements.

Young, Brian↗

NASA NTRS2021

Variation of Ice Microphysical Properties With Temperature and Humidity at Tops of Convective Clouds

A better understanding of the many interacting processes governing the evaluation of ice in natural clouds is required to improve the representation of ice clouds in global circulation models. Recent studies suggest a dominant role of vapor growth processes in determining the temperature dependence of cloud top ice sizes and shapes. Using airborne cloud remote sensing along with reanalysis data, here we show that observed cloud top ice effective radii and estimated normalized growth rates at cloud top highly correlate with an approximately linear relationship, which is consistent with a conceptual model also presented. Furthermore, significant differences in crystal shape characteristics and scattering asymmetry parameters are found between sub- and super-saturated cloud tops over ocean, although not over land. These results provide valuable observational targets for studying ice formation and evolution processes using models, while also helping interpretation of satellite observations of ice microphysical properties at cloud tops.

ice↗