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NASA NTRSDate not supplied

Modeling Distributed Situation Awareness in Resilience-based Design of Complex Systems

Human operators play a major role in the resilience of complex systems–while human error is one of the biggest contributors to hazardous events, operators additionally play a critical role in mitigating hazardous events. A key factor underlying this operator resilience is situation awareness–the ability of operators to understand their environment and each other to achieve desired system functions. In contrast to situation awareness-related accident models in the literature, which are largely conceptual in nature, this work proposes the use of a dynamic simulation framework to concretely model both the effects of situation awareness-related human errors and situation awareness-related hazard-mitigating properties using the distributed situation awareness theory. This work then presents specialized model constructs to enable agents’ individual perceptions of the system state and transactions with other agents (and thus distributed situation awareness) to be represented in simulation. To demonstrate this framework, it is then adapted to an aircraft taxiway case study, where it is used to model aircraft conflicts due to lack of vision and poor communications from the air traffic controller. This demonstration shows the potential of using simulation models to rigorously understand situation awareness-related human errors and thus inform the design of resilience.

Resilience Modeling↗

NASA NTRS2016

Recovery of Large Angular Scale CMB Polarization for Instruments Employing Variable-Delay Polarization Modulators

Variable-delay Polarization Modulators (VPMs) are currently being implemented in experiments designed to measure the polarization of the cosmic microwave background on large angular scales because of their capability for providing rapid, front-end polarization modulation and control over systematic errors. Despite the advantages provided by the VPM, it is important to identify and mitigate any time-varying effects that leak into the synchronously modulated component of the signal. In this paper, the effect of emission from a 300 K VPM on the system performance is considered and addressed. Though instrument design can greatly reduce the influence of modulated VPM emission, some residual modulated signal is expected. VPM emission is treated in the presence of rotational misalignments and temperature variation. Simulations of time-ordered data are used to evaluate the effect of these residual errors on the power spectrum. The analysis and modeling in this paper guides experimentalists on the critical aspects of observations using VPMs as front-end modulators. By implementing the characterizations and controls as described, front-end VPM modulation can be very powerful for mitigating 1/ f noise in large angular scale polarimetric surveys. None of the systematic errors studied fundamentally limit the detection and characterization of B-modes on large scales for a tensor-to-scalar ratio of r= 0.01. Indeed, r less than 0.01 is achievable with commensurately improved characterizations and controls.

Miller, N. J.↗

NASA NTRS2023

Single-Band VLBI Absolute Astrometry

The ionospheric path delay impacts single-band very long baseline interferometry (VLBI) group delays, which limits their applicability for absolute astrometry. I consider two important cases: when observations are made simultaneously in two bands, but delays in only one band are available for a subset of observations and when observations are made at one band design. I developed optimal procedures of data analysis for both cases using Global Navigation Satellite System (GNSS) ionosphere maps, provided a stochastic model that describes ionospheric errors, and evaluated their impact on source position estimates. I demonstrate that the stochastic model is accurate at a level of 15%. I found that using GNSS ionospheric maps as is introduces serious biases in estimates of declination and I developed a procedure that almost eliminates them. I found serendipitously that GNSS ionospheric maps have multiplicative errors and have to be scaled by 0.85 in order to mitigate the declination bias. A similar scale factor was found in comparison of the vertical total electron content from satellite altimetry against GNSS ionospheric maps. I favor interpretation of this scaling factor as a manifestation of the inadequacy of the thin shell model of the ionosphere. I showed that we are able to model the ionospheric path delay to the extent that no noticeable systematic errors emerge and we are able to assess adequately the contribution of the ionosphere-driven random errors on source positions. This makes single-band absolute astrometry a viable option that can be used for source position determination.

Radio astrometry↗

NASA NTRS2018

Required Time of Arrival as a Control Mechanism to Mitigate Uncertainty in Arrival Traffic Demand Management

The objective of this study is to explore the use of Required Time of Arrival (RTA) capability on the flight deck as a control mechanism on arrival traffic management to improve traffic delivery accuracy by mitigating the effect of traffic demand uncertainty. The uncertainties are caused by various factors, such as departure error due to the difference between scheduled departure and the actual take-off time. A simulation study was conducted using the Multi Aircraft Control System (MACS) software, a comprehensive research platform developed in the Airspace Operations Laboratory (AOL) at NASA Ames Research Center. The Crossing Time (CT) performance (i.e. the difference between target crossing time and actual crossing time) of the RTA for uncertainty mitigation during cruise phase was evaluated under the influence of varying two main factors: wind severity (heavy wind vs. mild wind), and wind error (1 hour, 2 hours, and 5 hours wind forecast errors). To examine the CT performance improvement made by the RTA, the comparison to the CT of the aircraft that were not assigned with RTA (Non-RTA) under the influence of the selected factors was also made. The Newark Liberty International Airport (EWR) was chosen for this study. A total 66 inbound traffic to the EWR (34 of them were airborne when the simulation was initiated, 32 were pre-departures at that time) was simulated, where the pre-scripted departure error was assigned to each pre-departure (61 conform to their Expected Departure Clearance Time, which is +-300 seconds of their scheduled departure time). The results of the study show that the delivery accuracy improvement can be achieved by assigning RTA, regardless of the influence of the selected two factors (the wind severity and the wind information inaccuracy). Across all wind variances, 66.9 (265 out of 396) of the CT performance of the RTA assigned aircraft was within +- 60 seconds (i.e. target tolerance range) and 88.9 (352 out of 396) aircraft met +-300 seconds marginal tolerance range, while only 33.6 (133 out of 396) of the Non-RTA assigned aircrafts CT performance achieved the target tolerance range and 75.5 (299 out of 396) stayed within the marginal. Examination of the impact of different error sources i.e. departure error, wind severity, and wind error suggest that although large departure errors can significantly impact the CT performance, the impacts of wind severity and errors were modest relative the targeted +- 60 second conformance range.

required time of arrival (RTA)↗

NASA NTRSDate not supplied

Biocybernetic Closed-Loop System for Mitigating Hazardous States of Awareness

The past century of passenger flight has seen continuous improvement in aviation safety by the aerospace industry. However, while commercial aviation accident rates have continued to decline, human error-related incident and accident rates remain remarkably constant across all types of aviation (Shappell, et al., 2007). Unfortunately, this level of human error is unacceptable when considering projections for increased traffic volume (FAA, 2009), and is likely to yield more incidents and accidents unless a more complete understanding of operator error is achieved and remediations are implemented. One area of interest highlighted by researchers is Hazardous States of Awareness (HSAs) that can result from deficiencies in the design and inappropriate use of human-machine interfaces. Identifying and mitigating HSAs is critical for reducing operator errors. One promising approach uses psychophysiological measures which enable automated systems to adapt to the operator?s state and modify modes of operation to support optimal human performance (Scerbo, 2007). This paper will survey previous research and describe future directions for the application of psychophysiological measures of operators derived from cortical and autonomic assessment to perform real-time adaptive modulation of human-automation task mode mixes. The authors will present a summary of previous work done at NASA LaRC and Old Dominion University using a Psychophysiologically Adaptive System (PAS) in which the level of automation of the NASA Multi-Attribute Task Battery was modulated based on Engagement Indices derived from the users? electroencephalogram (Pope, Bogart, & Bartolome, 1995; for review see, Scerbo, Freeman, & Mikulka, 2003). Future theoretical and methodological directions for this type of closed-loop research will be discussed. Specifically, the capacity for this type of PAS to maintain effective operator state and to enable validation of candidate physiological indices will be described. Consideration will also be given to critical system characteristics (e.g., engagement indices, methods for invoking changes among system states, individual differences among users, etc.) that have been or still need to be studied. The potential of the PAS approach for interactive system design and prototyping will also be described. Examples of adaptive automation flight deck concepts in recent experiments will be highlighted and discussed.

Chad L Stephens↗

NASA NTRS2019

FPGA Mitigation Strategies for Critical Applications

Technology is changing at a fast pace. Transistor geometries are getting smaller, voltage thresholds are getting lower, design complexity is exponentially increasing, and user options are expanding. Consequently, reliable insertion of error detection and correction (EDAC) circuitry has become relatively challenging. As a response, a variety of mitigation techniques are being evaluated. They range from weak EDAC circuits that save area and power to strong mitigation strategies that are a great expense to systems. This presentation will focus on radiation induced susceptibilities for a variety of FPGA types and ASIC devices. In addition, the user will be provided information on applicable mitigation strategies per device.

Berg, Melanie↗

NASA NTRS1983

Addressee Errors in ATC Communications: The Call Sign Problem

Communication errors involving aircraft call signs were portrayed in reports of 462 hazardous incidents voluntarily submitted to the ASRS during an approximate four-year period. These errors resulted in confusion, disorder, and uncoordinated traffic conditions and produced the following types of operational anomalies: altitude deviations, wrong-way headings, aborted takeoffs, go arounds, runway incursions, missed crossing altitude restrictions, descents toward high terrain, and traffic conflicts in flight and on the ground. Analysis of the report set resulted in identification of five categories of errors involving call signs: (1) faulty radio usage techniques, (2) call sign loss or smearing due to frequency congestion, (3) confusion resulting from similar sounding call signs, (4) airmen misses of call signs leading to failures to acknowledge or readback, and (5) controller failures regarding confirmation of acknowledgements or readbacks. These error categories are described in detail and several associated hazard mitigating measures that might be aken are considered.

Monan, W. P.↗

NASA NTRS1983

Cleared for the visual approach: Human factor problems in air carrier operations

The study described herein, a set of 353 ASRS reports of unique aviation occurrences significantly involving visual approaches was examined to identify hazards and pitfalls embedded in the visual approach procedure and to consider operational practices that might help avoid future mishaps. Analysis of the report set identified nine aspects of the visual approach procedure that appeared to be predisposing conditions for inducing or exacerbating the effects of operational errors by flight crew members or controllers. Predisposing conditions, errors, and operational consequences of the errors are discussed. In a summary, operational policies that might mitigate the problems are examined.

Monan, W. P.↗

NASA NTRS1994

Gravity model improvement using the DORIS tracking system on the SPOT 2 satellite

A high-precision radiometric satellite tracking system, Doppler Orbitography and Radio-positioning Integrated by Satellite system (DORIS), has recently been developed by the French space agency, Centre National d'Etudes Spatiales (CNES). DORIS was designed to provide tracking support for missions such as the joint United States/French TOPEX/Poseidon. As part of the flight testing process, a DORIS package was flown on the French SPOT 2 satellite. A substantial quantity of geodetic quality tracking data was obtained on SPOT 2 from an extensive international DORIS tracking network. These data were analyzed to assess their accuracy and to evaluate the gravitational modeling enhancements provided by these data in combination with the Goddard Earth Model-T3 (GEM-T3) gravitational model. These observations have noise levels of 0.4 to 0.5 mm/s, with few residual systematic effects. Although the SPOT 2 satellite experiences high atmospheric drag forces, the precision and global coverage of the DORIS tracking data have enabled more extensive orbit parameterization to mitigate these effects. As a result, the SPOT 2 orbital errors have been reduced to an estimated radial accuracy in the 10-20 cm RMS range. The addition of these data, which encompass many regions heretofore lacking in precision satellite tracking, has significantly improved GEM-T3 and allowed greatly improved orbit accuracies for Sun-synchronous satellites like SPOT 2 (such as ERS 1 and EOS). Comparison of the ensuing gravity model with other contemporary fields (GRIM-4C2, TEG2B, and OSU91A) provides a means to assess the current state of knowledge of the Earth's gravity field. Thus, the DORIS experiment on SPOT 2 has provided a strong basis for evaluating this new orbit tracking technology and has demonstrated the important contribution of the DORIS network to the success of the TOPEX/Poseidon mission.

Nerem, R. S.↗

NASA NTRS2021

The role of analysis error in the convergence of reanalysis production streams in MERRA-2

Due to production time constraints, most reanalyses are produced in multiple parallel streams instead of a single continuous one. These streams cover separate segments of the reanalysis time period with short overlaps to allow reconstruction of the official record. A fundamental assumption justifying this approach is that the streams will be assimilating the same observations during the periods where they overlap, and so will eventually converge to a similar atmospheric state, making discontinuities at stream junctions negligible. This assumption is revisited in this work by examining the impact of analysis error on the differences between MERRA-2 overlapping streams in three historical periods. Comparison results are shown in terms of standard deviations of stream differences as well as the spectral decomposition of the variance of their differences. Residual differences were found at the end of each year of overlap, with larger values observed in the earlier segments of the presatellite era. By drawing parallels with analysis error statistics estimated from the GMAO OSSE system, these differences are shown to reflect the varying constraint of data with the varying observing network, and to further carry the imprint of errors that the data assimilation process is not able to mitigate. As such, they are unlikely to be reduced by longer spinup periods. The ability of data assimilation to ensure continuity in the parallel streams is put into question when the observing system coverage is inadequate or simply when the data assimilation system as a whole is suboptimal.

Amal El Akkraoui↗

DOE OSTI2025

Measuring and unbiasing the BAO shift in the Ly α forest with AbacusSummit

ABSTRACT The Dark Energy Spectroscopic Instrument (DESI) places sub- per cent constraints on measurements of the Baryon Acoustic Oscillation (BAO) scaling parameters from the Ly $\alpha$ forest. However, no systematic error budget stemming from non-linearities in the three-dimensional clustering of the Ly $\alpha$ forest is included in the DESI-Ly $\alpha$ analysis. In this work, we measure the size of the shift of the BAO peak using large Ly $\alpha$ forest mocks produced on the N-body simulation suite AbacusSummit, which adopt the Fluctuating–Gunn–Peterson Approximation (FGPA). Specifically, we measure the Ly $\alpha$ autocorrelation and the Ly $\alpha$-quasar cross-correlation functions. To mitigate the noise, we adopt a linear control variates technique, reducing the error bars by a factor of up to $\sim \sqrt{50}$ on large scales. From the autocorrelation, we detect a small positive shift in radial direction of $\Delta \alpha _{\parallel }= 0.35~{{\ \rm per\ cent}}$ at the 3$\sigma$ level and virtually no shift in the transverse direction, $\alpha _\perp$. From the cross-correlation, we see a similar shift to $\Delta \alpha _\parallel$, albeit with larger error bars, and a small negative shift, $\Delta \alpha _{\perp }=\sim$0.25 per cent, at the 2$\sigma$ level. We also make a connection with the Ly $\alpha$ forest effective field theory (EFT) framework and find that the one-loop EFT power spectrum yields unbiased measurements of the BAO shift parameters in radial and transverse direction for Ly $\alpha$ auto- and the Ly $\alpha$-quasar cross-correlation measurements. When using the one-loop EFT framework, we find that we can recover the BAO parameters without a shift, which has important implications for future Ly $\alpha$ forest analyses based on EFT. This work paves the way for novel full-shape analyses of the currently observing DESI and future surveys such as the PFS, WEAVE-QSO, and 4MOST.

Hadzhiyska, Boryana↗

NASA NTRSDate not supplied

Wind Tunnel PSD and MVD Characterization Using New 1D2D Optical Array Probes

This work explores characterization of the liquid clouds using a combination of a forward scattering probe and two Optical Array Probes. Current OAP probes provide particle shape, size, and number concentration from two-dimensional shadow images. However, past studies have shown that such images are subject to distortion when outside of the focal plane. This affects the retrieval of particle size distributions, particularly in the Supercooled Large Droplet size range. In this article, the use of a Droplet Measurement Technologies Cloud Droplet Probe and two new OAPs produced by Science Engineering Associates, is examined using wind tunnel data, to assess suitability for use in a wind tunnel calibration in SLD conditions. The new OAP probes exploit a flexible and simple grey scale imaging method to eliminate some present shortcomings of commonly used OAPs, and to reduce correction factors. Spinning disk measurements were used to specify probe depth of field, and average size errors. Composite spectra covering the nominal 2-3200 µm size range were formed by crossing over from the CDP to 1D2D-X at 48 µm, and then to the 1D2D-Y at about 400 µm. A good overlap was found at the crossover points without any artificial scaling. Composite spectra adequately closed the liquid water content distribution, and provided integrated LWCs within about 35% of the hot-wire LWCs used for tunnel calibration. This discrepancy was at least partially attributed to LWC underestimation by the hot-wire at high MVD. A model of probe performance was used to show an example of expected accuracy of ideal probes subject to the same OAP distortions and using the same mitigating procedures and corrections, predicting PSD Median Volume Diameter and integrated LWC errors of less than 10%.

Aircraft Icing↗

NASA NTRS1990

Study of a co-designed decision feedback equalizer, deinterleaver, and decoder

A technique that promises better quality data from band limited channels at lower received power in digital transmission systems is presented. Data transmission, in such systems often suffers from intersymbol interference (ISI) and noise. Two separate techniques, channel coding and equalization, have caused considerable advances in the state of communication systems and both concern themselves with removing the undesired effects of a communication channel. Equalizers mitigate the ISI whereas coding schemes are used to incorporate error-correction. In the past, most of the research in these two areas has been carried out separately. However, the individual techniques have strengths and weaknesses that are complementary in many applications: an integrated approach realizes gains in excess to that of a simple juxtaposition. Coding schemes have been successfully used in cascade with linear equalizers which in the absence of ISI provide excellent performance. However, when both ISI and the noise level are relatively high, nonlinear receivers like the decision feedback equalizer (DFE) perform better. The DFE has its drawbacks: it suffers from error propagation. The technique presented here takes advantage of interleaving to integrate the two approaches so that the error propagation in DFE can be reduced with the help of error correction provided by the decoder. The results of simulations carried out for both, binary, and non-binary, channels confirm that significant gain can be obtained by codesigning equalizer and decoder. Although, systems with time-invariant channels and simple DFE having linear filters were looked into, the technique is fairly general and can easily be modified for more sophisticated equalizers to obtain even larger gains.

Peile, Robert E.↗

NASA NTRS2007

Staggering Inflation To Stabilize Attitude of a Solar Sail

A document presents computational-simulation studies of a concept for stabilizing the attitude of a spacecraft during deployment of such structures as a solar sail or other structures supported by inflatable booms. Specifically, the solar sail considered in this paper is a square sail with inflatable booms and attitude control vanes at the corners. The sail inflates from its stowed configuration into a square sail with four segments and four vanes at the tips. Basically, the concept is one of controlling the rates of inflation of the booms to utilize in mass-distribution properties to effect changes in the system s angular momentum. More specifically, what was studied were the effects of staggering inflation of each boom by holding it at constant length for specified intervals between intervals of increasing length until full length is reached. The studies included sensitivity analyses of effects of variations in mass properties, boom lengths, rates of increase in boom length, initial rates of rotation of the spacecraft, and several asymmetries that could arise during deployment. The studies led to the conclusion that the final attitude of the spacecraft could be modified by varying the parameters of staggered inflation. Computational studies also showed that by feeding back attitude and attitude-rate measurements so that corrective action is taken during the deployment, the final attitude can be maintained very closely to the initial attitude, thus mitigating the attitude changes incurred during deployment and caused by modeling errors. Moreover, it was found that by optimizing the ratio between the holding and length-increasing intervals in deployment of a boom, one could cause deployment to track a desired deployment profile to place the entire spacecraft in a desired attitude at the end of deployment.

Quadrelli, Marco↗

NASA NTRS2013

Stress-Dependent Voltage Offsets From Polymer Insulators Used in Rock Mechanics and Material Testing

Dielectric insulators are used in a variety of laboratory settings when performing experiments in rock mechanics, petrology, and electromagnetic studies of rocks in the fields of geophysics,material science, and civil engineering. These components may be used to electrically isolate geological samples from the experimental equipment, to perform a mechanical compliance function between brittle samples and the loading equipment, to match ultrasonic transducers, or perform other functions. In manyexperimental configurations the insulators bear the full brunt of force applied to the sample but do not need to withstand high voltages, therefore the insulators are often thin sheets of mechanically tough polymers. From an instrument perspective, transduction from various types of mechanical perturbation has beenqualitatively compared for a number of polymers [1, 2] and these error sources are readily apparent duringhigh-impedance measurements if not mitigated. However even when following best practices, a force dependent voltage signal still remains and its behavior is explored in this presentation. In this experimenttwo thin sheets (0.25 mm) of high-density polyethylene (HDPE) were set up in a stack, held alternatelybetween three aluminum bars; this stack was placed on the platen of a 60T capacity hydraulic testingmachine. The surface area, A, over which the force is applied to the PE sheets in this sandwich is roughly 40 square cm, each sheet forming a parallel-plate capacitor having roughly 320 pF [3], assuming therelative dielectric permittivity of PE is approximately 2.3. The outer two aluminum bars were connected to the LO input ofthe electrometer and the central aluminum bar was connected to the HI input of a Keithley model 617 electrometer. Once the stack is mechanically well-seated with no air gaps, the voltage offset is observed tobe a linear function of the baseline voltage for a given change in applied force. For a periodically appliedforce of 66.7 kN the voltage offsets were measured as a function of initial voltage, and these data were fitwith a linear function that was constrained to pass through the origin. The best fit solution had a correlation coefficient of R=0.85 and a slope of approximately -0.0228 volts/volt. The voltage offset when normalizedis demonstrated to be constant -2.28% for both positive and negative polarities over nearly 3 orders ofbaseline voltage magnitude. From this, the voltage-force coefficient is derived to be -0.34 ppm/N. Thiscorrelates well to a first-order parallel plate capacitor model that assumes constant area, and smalldeformation such that the polymer may be mechanically modeled by a spring that obeys Hookes law. Thissimple model predicts that the coefficient of proportionality is a function of Youngs modulus E= 0.8 GPaand surface area of the insulator, theoretically -1EA= -0.31 ppm/N. The outcome of this work is animproved insulator made from ultra-high molecular weight (UHMW) polyethylene and other approachestoward the minimization of and compensation for these experimental artifacts.

Electromagnetic Studies of Rocks↗

NASA NTRS2018

Fast Sensitivity-Based Optimal Trajectory Updates for Descent Operations Subject to Time Constraints

The ability to meet a controlled time of arrival during a continuous descent operation will enable environmentally friendly and fuel efficient descent operations while simultaneously maintaining airport throughput. Previous work showed that guidance strategies based on a frequent recalculation of the optimal trajectory during the descent result in excellent environmental impact mitigation figures while meeting operational constraints in the presence of modelling errors. However, the time lag of recalculating the trajectory using traditional optimisation algorithms could lead to performance degradation and stability issues. This paper proposes an alternative strategy, which allows for fast updates of the optimal trajectory based on parametric sensitivities. Promising results show that the performance of this method is comparable to that of instantaneously recalculating the optimal descent trajectory at each time sample.

Dalmau, Ramon↗

NASA NTRSDate not supplied

Uncertainty in Servicing and Assembly Tasks for Space Robotic Manipulators

This presentation will discuss a subset of the sources of uncertainty that impact autonomous in-space servicing, assembly, and manufacturing missions. These include robotic manipulator modeling uncertainties in both kinematics and dynamics, perception error associated machine learning models for pose estimation, and sensor noise. Mitigation strategies will be discussed including the incorporation of capture envelopes in the design of robotic tools and selection of robot goal poses to minimize end-effector sensitivity in manipulators with redundant degrees of freedom.

robotics↗

NASA NTRS2011

Understanding Effective Diameter and Its Application to Terrestrial Radiation in Ice Clouds

The cloud property known as "effective diameter" or "effective radius", which in essence is the cloud particle size distribution (PSD) volume at bulk density divided by its projected area, is used extensively in atmospheric radiation transfer, climate modeling and remote sensing. This derives from the assumption that PSD optical properties can be uniquely described in terms of their effective diameter, D(sub e), and their cloud water content (CWC), henceforth referred to as the D(sub e)-CWC assumption. This study challenges this assumption, showing that while the D(sub e)-CWC assumption appears generally valid for liquid water clouds, it appears less valid for ice clouds in regions where (1) absorption is not primarily a function of either the PSD ice water content (IWC) or the PSD projected area, and (2) where wave resonance (i.e. photon tunneling) contributes significantly to absorption. These two regions often strongly coincide at terrestrial wavelengths when De less than ~60 m, which is where this D(sub e)-CWC assumption appears poorest. Treating optical properties solely in terms of D(sub e) and IWC may lead to errors up to 24%, 26% and 20% for terrestrial radiation in the window region regarding the absorption and extinction coefficients and the single scattering albedo, respectively. Outside the window region, errors may reach 33% and 42% regarding absorption and extinction. The magnitude and sign of these errors can change rapidly with wavelength, which may produce significant errors in climate modeling, remote sensing and other applications concerned with the wavelength dependence of radiation. Where the D(sub e)-CWC assumption breaks down, ice cloud optical properties appear to depend on D(sub e), IWC and the PSD shape. Optical property parameterizations in climate models and remote sensing algorithms based on historical PSD measurements may exhibit errors due to previously unknown PSD errors (i.e. the presence of ice artifacts due to the shattering of larger ice particles on the probe inlet tube during sampling). More recently developed cloud probes are designed to mitigate this shattering problem. Using realistic PSD shapes for a given temperature (and/or IWC) and cloud type may minimize errors associated with PSD shape in ice optics parameterizations and remote sensing algorithms. While this topic was investigated using two ice optics schemes (the Yang et al., 2005 database and the modified anomalous diffraction approximation, or MADA), a physical understanding of the limitations of the D(sub e)-IWC assumption was made possible by using MADA. MADA allows one to approximate the contribution of photon tunneling to absorption relative to other optical processes, which reveals that part of the error regarding the D(sub e)-IWC assumption can be associated with tunneling. By relating the remaining error to the radiation penetration depth in bulk ice (DELTA L) due to absorption, the domain where the D(sub e)-IWC assumption is weakest was described in terms of D(sub e) and DELTA L.

Mitchell, D. L.↗