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Diffusion Monte Carlo approaches for studying nuclear quantum effects in fluxional molecules

Abstract Diffusion quantum Monte Carlo (DMC) provides a powerful approach for obtaining the ground state energy and wave function of molecules, ions, and molecular clusters. The approach is uniquely well suited for studies of fluxional molecules, which undergo large amplitude vibrational motions even in their ground state. In contrast to the electronic structure problem, where the wave function must be antisymmetric with respect to exchange of any pair of electrons, the wave function for the ground vibrational state is nodeless. This greatly simplifies the application of DMC for vibrational problems. Because there is not a single potential function that can be used to describe the intramolecular and intermolecular interactions in all molecular systems, most methods that are used to describe nuclear quantum effects rely on a carefully chosen zero‐order description of the molecular vibrations. In contrast, DMC calculations can be performed in Cartesian coordinates, making the DMC algorithm easily transferable between different chemical systems. In this contribution, the theory that underlies DMC will be discussed along with important considerations for performing DMC calculations. Extensions for evaluating vibrationally excited states and molecular properties are also discussed. Insights that can be obtained from DMC calculations are illustrated in the context of the protonated water clusters. This article is categorized under: Molecular and Statistical Mechanics > Molecular Dynamics and Monte‐Carlo Methods Theoretical and Physical Chemistry > Spectroscopy

Chemistry↗

LANDSAT-4 Thematic Mapper Modulation Transfer Function (MTF) evaluation

The Modulation Transfer Function (MTF) for thematic mapping (TM) bands 3, 4, 5 and 7 is reliably estimated with the San Mateo Bridge target in the 12/31/82 scene. These results are to be compared with those from the 8/12/83 scene. Bands 1, 2 and 6 are to be analyzed with a different target possessing greater contrast. This may be possible with the underflight data comparison currently underway. The registration of this data to the TM image of 8/12/83 for a region arround the Stockton sewage pond east of San Francisco has begun. This particular approach has the advantage that the full two-dimensional MFT will be measured instead of the MFT in only one azimuth as reported.

Schowengerdt, R.↗

Use of FLOSIC for understanding anion-solvent interactions

An Achille’s heel of lower-rung density-functional approximations is that the highest-occupied-molecular-orbital energy levels of anions, known to be stable or metastable in nature, are often found to be positive in the worst case or above the lowest-unoccupied-molecular-orbital levels on neighboring complexes that are not expected to accept charge. A trianionic example, [Cr(C2O4)3]3−, is of interest for constraining models linking Cr isotope ratios in rock samples to oxygen levels in Earth’s atmosphere over geological timescales. Here we describe how crowd sourcing can be used to carry out self-consistent Fermi–Löwdin–Orbital-Self-Interaction corrected calculations (FLOSIC) on this trianion in solution. The calculations give a physically correct description of the electronic structure of the trianion and water. In contrast, uncorrected local density approximation (LDA) calculations result in approximately half of the anion charge being transferred to the water bath due to the effects of self-interaction error. Use of group-theory and the intrinsic sparsity of the theory enables calculations roughly 125 times faster than our initial implementation in the large N limit reached here. By integrating charge density densities and Coulomb potentials over regions of space and analyzing core-level shifts of the Cr and O atoms as a function of position and functional, we unambiguously show that FLOSIC, relative to LDA, reverses incorrect solute-solvent charge transfer in the trianion-water complex. In comparison to other functionals investigated herein, including Hartree–Fock and the local density approximation, the FLOSIC Cr 1s eigenvalues provide the best agreement with experimental core ionization energies.

Chemistry↗

Energy from Redox Disproportionation of Sugar Carbon Drives Biotic and Abiotic Synthesis

To identify the energy source that drives the biosynthesis of amino acids, lipids, and nucleotides from glucose, we calculated the free energy change due to redox disproportionation of the substrate carbon of: (1) 26-carbon fermentation reactions and (2) the biosynthesis of amino acids and lipids of E. coli from glucose. The free energy (cal/mmol of carbon) of these reactions was plotted as a function of the degree of redox disproportionation of carbon (disproportionative electron transfers (mmol)/mmol of carbon). The zero intercept and proportionality between energy yield and degree of redox disproportionation exhibited by this plot demonstrate that redox disproportionation is the principal energy source of these redox reactions (slope of linear fit = -10.4 cal/mmol of disproportionative electron transfers). The energy and disproportionation values of E. coli amino acid and lipid biosynthesis from glucose lie near this linear curve fit with redox disproportionation accounting for 84% and 96% (and ATP only 6% and 1 %) of the total energy of amino acid and lipid biosynthesis, respectively. These observations establish that redox disproportionation of carbon, and not ATP, is the primary energy source driving amino acid and lipid biosynthesis from glucose. In contrast, we found that nucteotide biosynthesis involves very little redox disproportionation, and consequently depends almost entirely on ATP for energy. The function of sugar redox disproportionation as the major source of free energy for the biosynthesis of amino acids and lipids suggests that sugar disproportionation played a central role in the origin of metabolism, and probably the origin of life.

Weber, Arthur L.↗

Energy from Redox Disproportionation of Sugar Carbon Drives Biotic and Abiotic Synthesis

To identify the energy source that drives the biosynthesis of amino acids, lipids, and nucleotides from glucose, we calculated the free energy change due to redox disproportionation of the substrate carbon of: (1) 26-carbon fermentation reactions and (2) the biosynthesis of amino acids and lipids of E. coli from glucose. The free energy (cal/mmol of carbon) of these reactions was plotted as a function of the degree of redox disproportionation of carbon (disproportionative electron transfers (mmol)/mmol of carbon). The zero intercept and proportionality between energy yield and degree of redox disproportionation exhibited by this plot demonstrate that redox disproportionation is the principal energy source of these redox reactions (slope of linear fit = -10.4 cal/mmol of disproportionative electron transfers). The energy and disproportionation values of E. coli amino acid and lipid biosynthesis from glucose lie near this linear curve fit with redox disproportionation accounting for 84% and 96% (and ATP only 6% and 1%) of the total energy of amino acid and lipid biosynthesis, respectively. These observations establish that redox disproportionation of carbon, and not ATP, is the primary energy source driving amino acid and lipid biosynthesis from glucose. In contrast, we found that nucleotide biosynthesis involves very little redox disproportionation, and consequently depends almost entirely on ATP for energy. The function of sugar redox disproportionation as the major source of free energy for the biosynthesis of amino acids and lipids suggests that sugar disproportionation played a central role in the origin of metabolism, and probably the origin of life.

Weber, Arthur L.↗

Virtual Acoustics: Evaluation of Psychoacoustic Parameters

Current virtual acoustic displays for teleconferencing and virtual reality are usually limited to very simple or non-existent renderings of reverberation, a fundamental part of the acoustic environmental context that is encountered in day-to-day hearing. Several research efforts have produced results that suggest that environmental cues dramatically improve perceptual performance within virtual acoustic displays, and that is possible to manipulate signal processing parameters to effectively reproduce important aspects of virtual acoustic perception in real-time. However, the computational resources for rendering reverberation remain formidable. Our efforts at NASA Ames have been focused using a several perceptual threshold metrics, to determine how various "trade-offs" might be made in real-time acoustic rendering. This includes both original work and confirmation of existing data that was obtained in real rather than virtual environments. The talk will consider the importance of using individualized versus generalized pinnae cues (the "Head-Related Transfer Function"); the use of head movement cues; threshold data for early reflections and late reverberation; and consideration of the necessary accuracy for measuring and rendering octave-band absorption characteristics of various wall surfaces. In addition, a consideration of the analysis-synthesis of the reverberation within "everyday spaces" (offices, conference rooms) will be contrasted to the commonly used paradigm of concert hall spaces.

Begault, Durand R.↗

A Uniform Analysis of Debris Discs with the Gemini Planet Imager II: Constraints on Dust Density Distribution Using Empirically Informed Scattering Phase Functions

Spatially resolved images of debris discs are necessary to determine disc morphological properties and the scattering phase function (SPF) thatantifies the brightness of scattered light as a function of phase angle. Current high-contrast imaging instruments have successfully resolved several dozens of debris discs around other stars, but few studies have investigated trends in the scattered-light, resolved population of debris discs in a uniform and consistent manner. We have combined Karhunen-Loeve Image Projection (KLIP) with radiative-transfer disc forward modelling in order to obtain the highest-quality image reductions and constrain disc morphological properties of eight debris discs imaged by the Gemini Planet Imager at H -band with a consistent and uniformly applied approach. In describing the scattering properties of our models, we assume a common SPF informed from solar system dust scattering measurements and apply it to all systems. We identify a diverse range of dust density properties among the sample, including critical radius, radial width, and vertical width. We also identify radially narrow and vertically extended discs that may have resulted from substellar companion perturbations, along with a tentative positive trend in disc eccentricity with relative disc width. We also find that using a common SPF can achieve reasonable model fits for discs that are axisymmetric and asymmetric when fitting models to each side of the disc independently, suggesting that scattering behaviour from debris discs may be similar to Solar system dust.

scattering↗

Importance of Contrast-to-Noise Ratio Sensitivity Function in Nondestructive Evaluation

A reliable nondestructive evaluation (NDE) technique provides minimum 90% probability of detection (POD) with 95% confidence for detection of cracklike flaws of a specific size. This requirement comes from fracture control. Fracture control is a risk assessment and control approach for preventing structural failure of fracture critical hardware during its service life. One of the approaches of fracture control is damage tolerance safe life analysis, which assumes that NDE reliably detectable size flaw may exist in the hardware post nondestructive evaluation. Analysis and/or testing are performed to verify that the hardware will not fail during its service life despite existence of such a flaw. NDE methods are conventionally qualified by probability of detection (POD) demonstration testing to ensure reliable flaw detection. Here, a novel and alternative to POD flaw detection reliability approach that uses contrast-to-noise ratio (CNR) is given. The approach uses CNR sensitivity function (SF) and CNR. CNR SF is the minimum CNR needed for reliable flaw detection as a function of certain flaw indication characteristics. Primary difference between POD approaches and CNR flaw detection reliability approach is resolution of flaw detection system. POD approach does not account for the resolution of the system, while CNR approach accounts for the flaw detection resolution. Resolution is determined from the modulation transfer function (MTF) of the flaw detection system. CNR flaw detection reliability approach emphasizes quantitative assessment of “how well each flaw indication is detected”. Therefore, CNR approach is helpful in reducing number of flaws in the sample used in NDE procedure qualification, resulting in cost and time savings. CNR approach is also a case of multi-hit flaw detection analysis which has better flaw detectability size than conventional single-hit flaw detectability. Thus, CNR approach, where applicable, may be superior to conventional POD approach. The paper is an overview of development of CNR modeling, CNR SF modeling and measurement by the author. The paper gives key references to currently used NDE procedure POD qualification approaches including those specific to CNR and CNR SF development in multi-hit flaw detection in NDE. The paper covers core topics in nondestructive evaluation engineering.

Contrast-to-noise ratio↗

A spontaneously arising mutation in connexin32 with repeated passage of FRTL-5 cells coincides with increased growth rate and reduced thyroxine release

In this study we examine changes in the cellular properties of FRTL-5 cells as a function of passage number, with particular emphasis on gap junction expression, karyotype, morphology, growth rate and thyroxine (T(4)) release. Early passage FRTL-5 follicular cells transfer dye through gap junctions from injected cell(s) to third-order neighboring cells and beyond within their respective follicles and have immuno-detectable connexin32 (Cx32) type gap junctional plaques in their lateral contacting plasma membranes. By contrast, FRTL-5 cells established as monolayers, or as follicles from cultures passed more than 15 times, did not transfer microinjected Lucifer Yellow dye to contiguous neighboring cells and did not express any immuno-detectable rat thyroid specific connexins (Cx43, Cx32 or Cx26). Western blots confirmed that total, membrane and cytosolic Cx32 protein was present only in early pass follicular cultures. To better understand the passage-dependent loss of Cx32 expression, RT-PCR primers were made to the most unique sequences of the rat Cx32 molecule, the cytoplasmic and carboxyl-terminal regions. These primers were used to screen FRTL-5 RNA from cultures of various passage numbers. The results revealed that later passage cultures had a single base deletion in the middle of the Cx32 cytoplasmic loop region at nucleotide position 378. This base deletion was in the middle position of the codon for amino acid 116, which is normally a CAC (histidine) but read with the frame shift was a CCC (proline). The four amino acids that followed this deletion were also altered with the fourth one becoming UAA, the ochre translation stop codon. This premature stopping of translation resulted in a truncation of 60% of the protein, which included the remaining cytoplasmic loop, third and fourth transmembrane regions and the carboxyl-terminus. The later passage cultures did not produce a carboxyl-terminal RT-PCR product, indicating that the mRNA was also truncated. These regions of the Cx32 molecule contain the sequences and epitopes to which probes and antibodies are directed, and as such alterations of these regions with repeated passage explains reports by others that FRTL-5 cells do not express Cx32, and implies that cultures used for these assessments were passed more than 15 times. To determine if genetic or epigenetic abnormalities existed in FRTL-5 cells we performed chromosome spreads from various passage cultures. FRTL-5 cells have been reported to be diploid and more recently non-diploid; however, we found them to be fully tetraploid. This tetraploidy appears to be unstable in that later passes are tetraploid plus two or three extra chromosomes. There were no obvious translocations, breaks or large-scale interstitial deletions of any chromosomes in the FRTL-5 cultures tested. As FRTL-5 cells were repeatedly passed their morphology changed. Monolayer areas spread from beneath the follicles, and the follicles became flattened in appearance. These physical changes were coincident with dramatically increased growth rates. Early cultures (passed 3-12 times) divided on average every 49+/-1 h, whereas later passes (passes 20-25) divided every 28+/-3 h. To correlate these changes with a measure of thyroid function we assayed T(4) output. Early passage follicular cultures incubated for 6 h with sodium iodide, released on average 5.27+/- 0.33 ng/ml of T(4)/100 follicles. Later passes, or early passes treated with heptanol to down-regulate Cx32, released an average of 3.84+/-0.50 ng/ml of T(4)/100 follicles. There was a 27% difference in T(4) release between early follicular cultures, that were coupled by Cx32, and late or down-regulated early follicular cultures, that were uncoupled (P<0.0001). Collectively, the physical changes documented in this study were coincident with the loss of functional Cx32. This implies a relationship between the loss of intercellular communication and changes in morphogenic appearance, growth rate and reduced thyroid function and supports the previously postulated, tumor-suppressor role for Cx32. FRTL-5 cultures from low passage numbers are an excellent model of primary thyroid cells. However, many reports in the literature ascribe features to FRTL-5 cells that are mutually inconsistent. These differences may be resolved in the future by addressing the passage number and the conditional differences of the cultures being studied.

NASA Discipline Radiation Health↗

Effect of Antagonistic Binder–Catalyst Interactions on Catalytic Activity in Lithium–Sulfur Batteries

Lithium-sulfur (Li-S) batteries are a promising next-generation energy storage solution, as they can reduce reliance on critical transition metals while offering high energy densities. However, their deployment is hindered by low sulfur utilization and the formation/diffusion of lithium polysulfides (LiPSs). While transition-metal catalysts and polymeric binders have been independently developed to enhance redox kinetics and LiPS adsorption, their mutual compatibility has remained largely unexplored. We show here that binder-catalyst interactions can significantly impact catalytic performance. Employing TiO 2 as a generic catalyst, the electrochemical performance is shown to depend strongly on the binder environment. TiO 2 paired with lithiated polyacrylic acid (LiPAA) shows benign interactions, resulting in enhanced cycle life. In contrast, pairing TiO 2 with protonated PAA produces antagonistic interactions that hinder Li 2 S growth. A mechanistic analysis unveils that the carboxylic H atom in PAA promotes COO − coordination to Ti sites, occupying catalytic centers and suppressing LiPS adsorption, increasing charge transfer and diffusion resistances. This phenomenon is observed across multiple catalysts, indicating that COOH-functionalized binders may broadly hinder catalytic activity. Overall, this study underscores the need for holistic cathode design and identifies binder-catalyst compatibility as an important parameter for high-performance Li-S batteries.

25 ENERGY STORAGE↗

Soft X-ray tomography reveals variations in B. subtilis biofilm structure upon tasA deletion

Bacterial biofilms are complex cell communities within a self-produced extracellular matrix, crucial in various fields but challenging to analyze in 3D. We developed a "biofilm-in-capillary" growth method compatible with full-rotation soft X-ray tomography, enabling high-resolution 3D imaging of bacterial cells and their matrix during biofilm formation. This approach offers 50 nm isotropic spatial resolution, rapid imaging, and quantitative native analysis of biofilm structure. Using Bacillus subtilis biofilms, we detected coherent alignment and chaining of wild-type cells towards the oxygen-rich capillary tip. In contrast, the ΔtasA genetic knock-out showed a loss of cellular orientation and changes in the extracellular matrix. Adding TasA protein to the ΔtasA strain restored matrix density and led to cell assembly compaction, but without the chaining observed in wild-type biofilms. This scalable and transferable approach opens new avenues for examining biofilm structure and function across various species, including mixed biofilms, and response to genetic and environmental factors.

59 BASIC BIOLOGICAL SCIENCES↗

High resolution imagery with the large space telescope.

A number of general characteristics of a diffraction limited telescope are examined, giving attention to the optical system of the Stratoscope II instrument. The optical resolution of a telescope can be described in at least three different ways, involving the wavefront error, the optical transfer function, and the point spread function. The Stratoscope II tolerance budget and the performance of the instrument are discussed together with a goal for the resolution of the large space telescope (LST) which is to be designed. The very high resolving power of the LST will be utilized in many ways. The imagery of extended objects with low surface contrast is considered along with the photometry of very faint stars.

Danielson, R. E.↗

The effect of earth's atmosphere on contrast reduction for a nonuniform surface albedo and 'two-halves' field

The paper presents a model for contrast reduction by atmospheric haze developed for the 'two-halves' field of the earth's surface and other geometries of the earth's surface albedo. The model is based on a simplified solution of the equation of radiative transfer in two dimensions, resulting in a method for calculation of the upward zenith intensity in the atmosphere as a function of the distance from the border between the two half planes, for an unabsorbing atmosphere. The adjacency effect between two infinitesimal areas of different albedos is calculated; the resultant simplified solution is used to develop expressions for the line-spread function of the atmosphere and the modulation transfer function. The line-spread function is used to calculate the point spread function, which can be used to compute the intensity above any surface with given spatial dependence of the reflectivity.

Mekler, Y.↗

Robustness analysis based on passivity

A technique of robust stability analysis for multivariable control systems is introduced. Existing tools in the literature are mostly based on small gain type of conditions such as the H(infinity)-norm or mu measure. In contrast, the approach presented is motivated by passivity theory. The natural energy Lyapunov function associated with a passive system allows robustness to be analyzed with Lyapunov stability theory. Consequently, nonlinear and time-varying perturbations can be considered within the same framework. For unstructured uncertainties, the robustness margin is characterized in terms of an index related to the Hermitian part of a transfer function. If the uncertainties contain additional diagonal structure, stability margins are obtained for variations of each uncertain block in both positive and negative directions. Applications of this robustness analysis technique are illustrated.

Wen, John T.↗

What does reflection from cloud sides tell us about vertical distribution of cloud droplets?

In order to accurately measure the interaction of clouds with aerosols, we have to resolve the vertical distribution of cloud droplet sizes and determine the temperature of glaciation for clean and polluted clouds. Knowledge of the droplet vertical profile is also essential for understanding precipitation. So far, all existing satellites either measure cloud microphysics only at cloud top (e.g., MODIS) or give a vertical profile of precipitation sized droplets (e.g., Cloudsat). What if one measures cloud microphysical properties in the vertical by retrieving them from the solar and infrared radiation reflected or emitted from cloud sides? This was the idea behind CLAIM-3D (A 3D - cloud aerosol interaction mission) recently proposed by NASA GSFC. This presentation will focus on the interpretation of the radiation reflected from cloud sides. In contrast to plane-parallel approximation, a conventional approach to all current operational retrievals, 3D radiative transfer will be used for interpreting the observed reflectances. As a proof of concept, we will show a few examples of radiation reflected from cloud fields generated by a simple stochastic cloud model with prescribed microphysics. Instead of fixed values of the retrieved effective radii, the probability density functions of droplet size distributions will serve as possible retrievals.

Marshak, A.↗

Transient Triamidoamine Neptunium(V)–Mono(Imido) Complexes: C–H Activations and Hydrogen Atom Transfer Driven by Effective Nuclear Charge

Metal-mono(imido) linkages have been known for seven decades, and they are found in transition metal, main group, lanthanide, thorium, and uranium complexes. However, transuranium-mono(imido) complexes remain unknown in any scenario. Here, we present evidence for transient neptunium(V)–mono(imido) complexes. Treatment of [Np III (Tren TIPS )] (1, Tren TIPS = {N(CH 2 CH 2 NSiPr i 3 ) 3 } 3– ) with N 3 R (R = SiMe 3 ; 1-adamantyl, Ad) results in N 2 evolution and dark purple solutions consistent with the formation of [Np V (Tren TIPS )(NR)] (3NpNR). However, solutions of 3NpNR rapidly turn orange, where for R = SiMe 3 the isolated 1:1 products are [Np IV (Tren TIPS ){N(H)SiMe 3 }] (4a) and [Np IV (Tren TIPS-2H ){N(H)SiMe 3 }] (4b, Tren TIPS-2H = {N(CH 2 CH 2 NS i Pri 3 ) 2 (NCH 2 CH 2 NSiPr i 2 C[Me]=CH 2 )} 3– ). The latter contains a dehydrogenated-Pr i vinyl functionality accounting for the source of the two amido H atoms. The reaction for R = Ad proceeds similarly, but only [Np IV (Tren TIPS ){N(H)Ad}] (5a) could be unequivocally confirmed, though its isolation suggests generality of the imido-to-amido functional group transformation. Complexes 4a/4b exhibit slow relaxation of their magnetization, adding to the small number of transuranium single ion magnets. Experimental and computational analysis suggests that the amido products are formed by C–H activation and two sequential hydrogen atom transfer reactions involving a three-step proton-coupled electron-transfer sequence of H • radical abstraction, electron transfer, then another H • radical abstraction step. In contrast to transient 3NpNR, the 5f 2 uranium(IV)-imido complex [K(2.2.2-cryptand)][U IV (Tren TIPS )(NSiMe 3 )] (8UNSiMe 3 ) is robust, even in boiling THF, suggesting the transience of 5f 2 3NpNR is not due to the 5f n -count but the increased effective nuclear charge of neptunium vs uranium. This work highlights divergence of uranium- and neptunium-imido stabilities, emphasizing that the latter is an inherently challenging synthetic target.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Dynamics of the Molten Contact Line

In contrast to the ordinary contact line problem, virtually no information is available on the similar problem associated with a molten material spreading on a solid which is below the melt's fusion point. The latter is a more complex problem which heat transfer and solidification take place simultaneously with spreading, and requires answers not only for the hot melt's advance speed over the cold solid as a function of contact angle, but also for how one is to predict the point of the molten contact line's arrest by freezing. This issues are of importance in evolving methods of materials processing. The purpose of our work is to develop, based on both experiments and theory, an understanding of the dynamic processes that occur when a molten droplet touches a subcooled solid, spreads partly over it by capillary action, and freezes. We seek answers to the following basic questions. First, what is the relationship between the melt's contact line speed and the apparent (dynamic) contact angle? Secondly, at what point will the contact line modon be arrested by freezing? The talk will describe three components of our work: (1) deposition experiments with small molten droplets; (2) investigation of the dynamics of the molten contact line by means of a novel forced spreading method; and (3) an attempt to provide a theoretical framework for answering the basic questions posed above.

Sonin, Ain A.↗

The Effects of Sensor Field-of-View on the Geometrical Characteristics of Sea Ice Leads and Implications for Large-Area Heat Flux Estimates

The release of heat from sea ice fractures ('leads') is an important component of the heat budget in the Arctic, but their impact on regional scale climate is difficult to assess without more information on their distribution in both space and time. Remote sensing of leads using satellite data, specifically AVHRR thermal and Landsat visible-band imagery, is examined empirically with respect to lead width, orientation, and area fraction. The geometrical aspects of the sensor are simulated so that the effect of sensor field-of-view on retrieved lead width statistics can be assessed. This is done using Landsat data and simulated lead networks degraded to AVHRR pixel sizes. The analyses illustrate how leads of sufficiently high contrast tend to 'grow' with increasing pixel size and how small or low contrast leads disappear. The relationship between lead contrast and the width/field-of-view ratio is also examined in order to determine the limits of lead detectability, and illustrates the multivalued nature of the problem of lead width retrieval. To help quantify the importance of changes in lead statistics, turbulent heat flux is calculated as a function of lead width and lead fraction. It is shown that pixel size has a substantial effect on estimates of turbulent heat transfer from leads to the atmosphere.

Key, J.↗