Performance of multiple-cone-arrays as shadow cone blockers on NIF
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Dynamic, resilient virtual sensing system and shadow controller for cyber-attack neutralization
An industrial asset may have monitoring nodes (e.g., sensor or actuator nodes) that generate current monitoring node values. An abnormality detection and localization computer may receive the series of current monitoring node values and output an indication of at least one abnormal monitoring node that is currently being attacked or experiencing a fault. An actor-critic platform may tune a dynamic, resilient state estimator for a sensor node and output tuning parameters for a controller that improve operation of the industrial asset during the current attack or fault. The actor-critic platform may include, for example, a dynamic, resilient state estimator, an actor model, and a critic model. According to some embodiments, a value function of the critic model is updated for each action of the actor model and each action of the actor model is evaluated by the critic model to update a policy of the actor-critic platform.
Roychowdhury, Subhrajit↗
Hiding in the Shadow of the Upsilon: Ditaus from a Light Pseudoscalar
The CMS collaboration has reported a measurement of $Υ$ decays to ditaus using $61.9~{\rm fb}^{-1}$ of scouting data. If interpreted as the decay of $Υ(1S,2S,3S)$, the measured ditau rate is more than ten times that seen in the dimuon final states at the $\sim 3 σ$ level, and is likewise inconsistent with the branching ratios measured at $B$-factories. If confirmed with more data and at higher significance, such a violation of lepton flavor universality would necessitate new physics. In this Letter, we present a simple model with a light pseudoscalar coincidentally near the $Υ(1S)$ mass, which mixes with two Higgs doublets in the alignment limit. Such a particle naturally decays primarily to taus and evades all existing experimental constraints, while implying a number of predictions that can be tested in the near future.
Buckley, Matthew R. [Rutgers U., Piscataway]↗
Integrated Bypass Battery for ReverseBias Protection
When a single solar cell of a series-connect string is placed in shadow, the entire array current is forced through that cell in reverse bias. Reverse bias current can lead to "hot-spot" heating, where the power produced by the unshadowed cells is dissipated as heat in the shadowed cell. Since occasional shadows are unavoidable in most applications, most solar arrays include shadow protection to prevent damage. In current practice, shadow protection is done with a "bypass diode" on each cell, to shunt the reverse bias current if a cell is shadowed. A new method of reverse bias protection is to use an Integral thin-film battery to provide voltage in the case of a shadowed cell. In this case, the shadowed cell continues to provide voltage during the transient shadow.
Landis, Geoffrey A,↗
Hubble Space Telescope UV spectral observations of Io passing into eclipse
Time-resolved spectra of Io have been obtained with the Faint Object Spectrograph on the Hubble Space Telescope in January 1992 at times centered on the passage of Io into Jupiter's shadow. Two different eclipse observations covered 1100-1600 A and 2250-3300 A. In the far ultraviolet(far-UV) range, emission lines of atomic sulfur and oxygen from Io's atmosphere (similar to those previously detected with the International Ultraviolet Explorer (IUE)) have been observed from Io in sunlight, and the spatial extent of the emitting region has been resolved for the first time: this is 0.5-1 Io radii (R(sub Io)) above the surface. The emission lines are typically 1kR in brightness while Io is in sunlight, and decrease to a few hundred Rayleighs within 20 min or less of Io's passing into shadow. If the emissions are produced in Io's ionosphere, the decrease in shadow appears consistent with the collisional slowing and recombination of photoelectrons in 100-1000 s, with recombination an important quenching process if the dominant ion is molecular (i.e., SO2(+)) condensation, with the residual emission in shadow due either to plasma impact of gas above the hot volcanic calderas or electron impact on S and O. In the near-UV range, we have not detected any airglow emissions from Io's atmosphere in shadow, with the main limitation being a high level of scattered light from Jupiter. We derive a 3 sigma upper limit to the 2560 A SO emission feature of 1 KR, which is close to what is expected from electron impact on SO2 based on the obs erved brightness of the FUV S and O lines in shadow. A high signal-to-noise spectrum of Io's albedo in sunlight reveals a spectral shape similar to laboratory spectra of SO2 frost reflectivity, and the relative albedo spectrum changed as Io passed into eclipse and part of the disk was in shadow. No specific SO2 gas absorption features appear in the albedo spectrum, although there could be substantial gas absorption near 2800 A if the individual lines are narrow and saturated. Finally, we present preliminary models for the near-UV spectrum of Io as functions of SO2 frost areal coverage and SO2 gas density.
Clarke, John T.↗
Mobile Propagation Results from Using the ACTS Mobile Terminal
NASA's Advanced Communications Technology Satellite (ACTS) provides an ideal spaced-based platform for analyzing the Ka-band mobile satellite channel. This paper reports on the results of the Ka-band mobile propagation analysis campaign using the ACTS Mobile Terminal (AMT) developed by the Jet Propulsion Laboratory (JPL). The objectives of the mobile propagation experiments were to measure and analyze the fading characteristics of the Ka-band channel. The analysis involved examining pilot tone tests in three environments: lightly shadowed suburban, moderately shadowed suburban, and heavily shadowed suburban. The results indicate that Ka-band pilot tones experience significant multipath and fading effects. It may be possible to design link margins to provide reliable service for the lightly shadowed suburban environment at Ka-band. However, for areas with moderate and heavy shadowing, the link margin required to realize reliable communications with 99% availability is excessive (26 dB for moderate shadowing, and greater then 30 dB for heavy shadowing). An alternate approach would be to use shadowing/fading countermeasures (e.g., interleaved error control coding and antenna diversity). Such mitigation techniques, necessary for reliable Ka-band mobile communication within a suburban environment, are currently being considered within the NASA program.
Pinck, Deborah↗
Validation of an In-Water, Tower-Shading Correction Scheme
Large offshore structures used for the deployment of optical instruments can significantly perturb the intensity of the light field surrounding the optical measurement point, where different portions of the visible spectrum are subject to different shadowing effects. These effects degrade the quality of the acquired optical data and can reduce the accuracy of several derived quantities, such as those obtained by applying bio-optical algorithms directly to the shadow-perturbed data. As a result, optical remote sensing calibration and validation studies can be impaired if shadowing artifacts are not fully accounted for. In this work, the general in-water shadowing problem is examined for a particular case study. Backward Monte Carlo (MC) radiative transfer computations- performed in a vertically stratified, horizontally inhomogeneous, and realistic ocean-atmosphere system are shown to accurately simulate the shadow-induced relative percent errors affecting the radiance and irradiance data profiles acquired close to an oceanographic tower. Multiparameter optical data processing has provided adequate representation of experimental uncertainties allowing consistent comparison with simulations. The more detailed simulations at the subsurface depth appear to be essentially equivalent to those obtained assuming a simplified ocean-atmosphere system, except in highly stratified waters. MC computations performed in the simplified system can be assumed, therefore, to accurately simulate the optical measurements conducted under more complex sampling conditions (i.e., within waters presenting moderate stratification at most). A previously reported correction scheme, based on the simplified MC simulations, and developed for subsurface shadow-removal processing of in-water optical data taken close to the investigated oceanographic tower, is then validated adequately under most experimental conditions. It appears feasible to generalize the present tower-specific approach to solve other optical sensor shadowing problems pertaining to differently shaped deployment platforms, and also including surrounding structures and instrument casings.
Hooker, Stanford B.↗
Near-surface ice on Mercury and the Moon: A topographic thermal model
A thermal model that can be easily adapted to craters of arbitrary shape is developed and applied to high-latitude impact craters on Mercury and the Moon, Chao Meng Fu crater at -87.5 deg L on Mercury, an unnamed bowl-shaped crater at 86.7 deg L on Mercury, and Peary crater at 88.6 deg L on the Moon. For an assumed input topography and grid of surface elements, the model computes for each element the irradiation from direct insolation and reflected and emitted radiation from other elements, taking into account shadowing by walls of the crater, partial obscuration of the solar disk near the poles and the diurnal, orbital, and seasonal cycles. Temperatures are computed over the surface grid as functions of depth and time from the surface to a specified depth and over the pertinent astronomical cycles, including the effects of direct and indirect surface irradiation, infrared radiation, heat conduction, and interior heating. Vapor fluxes and ice recession times are computed as functions of ice depth over the surface grid. Temperatures profiles, vapor fluxes, and ice recession times were computed for flat surfaces not associated with craters near the poles of Mercury and the Moon. It was found that water ice could have existed throughout geologic time within the maximum radar detection depth of recent observation of Mercury (J. K. Harmon and M. A. Slade, 1992, Science 258, 640-643) poleward of approximately 87 - 88 deg L on Mercury and poleward of approximately 73 deg L on the Moon. For Chao Meng Fu crater it was found that approximately 40% of the crater floor is permanently shadowed from direct solar insolation, while the remainder of the crater floor is periodically illuminated by a partially obscured Sun. Temperatures at the upper levels of the south wall can slightly exceed 550 K. Surface temperatures in the permanently shadowed region of the crater floor are under approximately 130 K, which could have allowed water ice to exist throughout geologic time within the radar detection depth of recent observation of Mercury. For small bowl-shaped crater on Mercury, it was found that most of the crater is permanently shadowed from direct solar radiation, except for a narrow semicircular band bordering the north rim. However, temperatures in the permanently shadowed region periodically reach a maximum near approximately 315 K due to efficient heating of the small crater by thermal emission and reflection from the small sunlit region, which periodically reaches temperatures exceeding 630 K. Water ice could not have existed throughout geologic time anywhere in this crater within the radar detection depth. For Peary crater on the Moon, the entire crater floor is permanently shadowed from direct solar insolation with maximum temperature under 120 K. The upper level of the north wall periodically reaches a maximum temperature near 310 K. The low temperatures on the crater floor would have allowed water ice to exist near the surface throughout geologic time, provided that the Moon's obliquity was always as low as it is at present.
Salvail, James R.↗
Annular and Total Solar Eclipses of 2003
On Saturday, 2003 May 31, an annular eclipse of the Sun will be visible from a broad corridor that traverses the North Atlantic. The path of the Moon's antumbral shadow begins in northern Scotland, crosses Iceland and central Greenland, and ends at sunrise in Baffin Bay (Canada). A partial eclipse will be seen within the much broader path of the Moon's penumbral shadow, which includes most of Europe, the Middle East, central and northern Asia, and northwestern North America. The trajectory of the Moon's shadow is quite unusual during this event. The shadow axis passes to the far north where it barely grazes Earth's surface. In fact, the northern edge of the antumbra actually misses Earth so that one path limit is defined by the day/night terminator rather than by the shadow's upper edge. As a result, the track of annularity has a peculiar "D" shape that is nearly 1200 kilometers wide. Since the eclipse occurs just three weeks prior to the northern summer solstice, Earth's northern axis is pointed sunwards by 22.8 deg. As seen from the Sun, the antumbral shadow actually passes between the North Pole and the terminator. As a consequence of this extraordinary geometry, the path of annularity runs from east to west rather than the more typical west to east. The event transpires near the Moon's ascending node in Taurus five degrees north of Aldebaran. Since apogee occurs three days earlier (May 28 at 13 UT), the Moon's apparent diameter (29.6 arc-minutes) is still too small to completely cover the Sun (31.6 arc-minutes) resulting in an annular eclipse.
Espenak, Fred↗
The Investigation Of Carbon Contamination And Sputtering Effects Of Xenon Ion Thrusters
The Electro-Physics Branch of the NASA Glenn Research Center investigates the effect of atomic oxygen, environmental durability of high performance power materials and surfaces, and low earth orbit. One of its current projects involves the analysis of ion thrusters. Ion thrusters are devices that initiate a beam of ions to a target area. The type of ion thruster that I have been working with this Summer of 2004 emits positively charged Xenon (Xe(+)) atoms through two grids, the screen grid and the accelerator grid, after it enters an ionization chamber. Insulators are used to mechanically hold and separate these two grids. A propellant isolator, an instrument that closely resembles insulators, is placed in front of the ionization chamber. Both the insulator and isolator are made with a ceramic compound and filled with insulating beads. The main difference between the two devices is that the propellant isolator allows gas to flow through, in this case, the gas is Xe(+) and the insulators do not. In order to avoid carbon deposits and other contaminating chemicals to settle on the insulators and propellant isolator, a metal shadow shield is placed around them. These shadow shields function as a protectant and can be shaped in numerous configurations. Part of my job responsibility this summer is to investigate the effectiveness of different shadow shields that are utilized on three different ion engines: the NSTAR (NASA Solar Electric Propulsion Technology Application Readiness), JIMO (Jupiter Icy Moons Orbiter), and NEXIS (Nuclear Electric Xenon Ion System). Using calculus and other mathematical tactics, I was asked to find the total flux of carbon contamination that was able to pass the protectant shadow shield. I familiarized myself with the software program, MathCad2004, to help perform some mathematical computations such as complex integration. Another method of studying the probability of contamination is by experimental simulation. After attaining the precise parameters of the actual shadow shields, I created replicas of three types of shadow shielding to be used to undergo testing. It will be placed in a machine that produces carbon atoms at a high temperature of 200 C. or beam is aimed at a targeted material. As a result of this collision, atoms and other particles are ejected out of the target surface. Another part of my internship consisted of research on sputter ejection, or the angle distribution of sputtered material. This research entailed finding the past results of sputter ejection investigation as well as creating another type of mock simulation. Other minor projects include calculating the path of Xe(+) gas through the insulating beads of the isolators and assisting my mentor in collecting data for his paper for the Joint Propulsion Conference & Exhibit to be held July 11-14,2004 in Fort Lauderdale, Florida.
Prak, Moline K.↗
Dark Material at the Surface of Polar Crater Deposits on Mercury
Earth-based radar measurements [1-3] have yielded images of radar-bright material at the poles of Mercury postulated to be near-surface water ice residing in cold traps on the permanently shadowed floors of polar impact craters. The Mercury Laser Altimeter (MLA) on board the MErcury Surface, Space ENvironment, GEochemistry, and Ranging (MESSENGER) spacecraft has now mapped much of the north polar region of Mercury [4] (Fig. 1). Radar-bright zones lie within polar craters or along poleward-facing scarps lying mainly in shadow. Calculations of illumination with respect to solid-body motion [5] show that at least 0.5% of the surface area north of 75deg N lies in permanent shadow, and that most such permanently shadowed regions (PSRs) coincide with radar-bright regions. MLA transmits a 1064-nm-wavelength laser pulse at 8 Hz, timing the leading and trailing edges of the return pulse. MLA can in some cases infer energy and thereby surface reflectance at the laser wavelength from the returned pulses. Surficial exposures of water ice would be optically brighter than the surroundings, but persistent surface water ice would require temperatures over all seasons to remain extremely low (<110 K). Thermal models [6,7] incorporating direct and scattered radiation, Mercury s eccentric orbit, 3:2 spin-orbit resonance, and near-zero obliquity generally do not support such conditions in all permanently shadowed craters but suggest that water ice buried near the surface (<0.5 m depth) could survive for > 1 Gy. We describe measurements of reflectivity derived from MLA pulse returns. These reflectivity data show that surface materials in the shadowed regions are darker than their surroundings, enough to strongly attenuate or extinguish laser returns. Such measurements appear to rule out widespread surface exposures of water ice. We consider explanations for the apparent low reflectivity of these regions involving other types of volatile deposit.
Neumann, Gregory A.↗
South Pole Lunar Lighting Studies for Driving Exploration on the Lunar Surface
NASA’s Artemis lunar missions will face new exploration challenges due to inherently low sun angles in the lunar south pole region. Whereas the Apollo missions were afforded sunlight for approximately 8 to 50-degrees above the horizon, sunlight for the next lunar missions will only be 1 to 2-degrees about the horizon. With this low angle, long shadows and high contrasts of light and dark areas will be faced by the crew and remote teleop operators while exploring the lunar surface. With this in mind, NASA developed an integrated virtual Lighting and Navigation Simulation to understand these challenges. Two studies have been conducted in this Lunar South Pole environment to evaluate the effects of natural and artificial lighting on driving and navigating a lunar rover across the surface. Early NASA studies, such as this, are used to aid in developing techniques and explore concepts of operations to promote mission success and crew safety. In the Phase One development evaluation, six astronauts were teleported to ten different lighting conditions. For each location, drivers were to drive to an imaginary target approximately 200-meters straight ahead and provide subjective feedback on their ability to drive under the given lighting conditions. Phase Two, a more operational study, four astronauts and a remote operator tested five different Artemis lunar mission scenarios. Results indicated sun direction at such low angles, especially when driving a high speed, can severely impact the crew’s ability to safely drive the rover. In the up-sun situation, with the sun directly in the driver’s eyes and compounded long shadows, the consistent preference among drivers was to initiate a tacking strategy of approximately +/- 20 to 30-degrees to improve visibility. This maneuver does require more time and rover energetics. Conversely, driving down-sun required the crew to tack as well to avoid the shadow of rover blocking the terrain. Less appreciated is how the surrounding landscape is lit. Traveling into shadowed areas, especially while facing a lit terrain beyond the shadowed area, drivers enter at their own risk due to pupil contraction making artificial lights useless. Additionally, the constant transitioning between dark and light areas are mentally taxing to the crew and natural navigational references such as the stars are invisible and therefore unusable. Slope and depth magnitude are very difficult hazards to judge when approaching a shadowed crater. This naturally leads to slower driving speeds than originally anticipated. As for observing scientifically interesting features, assessing them accurately varies greatly by the lighting condition. In most cases, the task can be completed, but the strategy is to use the sun to one’s advantage. Crew workload distribution in the cockpit for driving operations was split amongst crew. The driver primarily focused attention on visual terrain (80%) but referenced displays approximately 20% of the time, while the co-pilot/navigator generally provided directional cues to the driver. These natural lighting conditions present significant challenges for safe rover operations; however, early studies having given investigators a “first-look” into understanding of how operating on the South Lunar Pole can be accomplished.
LTv↗
The Global Albedo of the Moon at 1064 nm from LOLA
The Lunar Orbiter Laser Altimeter (LOLA) measures the backscattered energy of the returning altimetric laser pulse at its wavelength of 1064 nm, and these data are used to map the reflectivity of the Moon at zero-phase angle with a photometrically uniform data set. Global maps have been produced at 4 pixels per degree (about 8 kilometers at the equator) and 2 kilometers resolution within 20 deg latitude of each pole. The zero-phase geometry is insensitive to lunar topography, so these data enable characterization of subtle variations in lunar albedo, even at high latitudes where such measurements are not possible with the Sun as the illumination source. The geometric albedo of the Moon at 1064 nm was estimated from these data with absolute calibration derived from the Kaguya Multiband Imager and extrapolated to visual wavelengths. The LOLA estimates are within 2 sigma of historical measurements of geometric albedo. No consistent latitude-dependent variations in reflectance are observed, suggesting that solar wind does not dominate space weathering processes that modify lunar reflectance. The average normal albedo of the Moon is found to be much higher than that of Mercury consistent with prior measurements, but the normal albedo of the lunar maria is similar to that of Mercury suggesting a similar abundance of space weathering products. Regions within permanent shadow in the polar regions are found to be more reflective than polar surfaces that are sometimes illuminated. Limiting analysis to data with slopes less than 10 deg eliminates variations in reflectance due to mass wasting and shows a similar increased reflectivity within permanent polar shadow. Steep slopes within permanent shadow are also more reflective than similar slopes that experience at least some illumination. Water frost and a reduction in effectiveness of space weathering are offered as possible explanations for the increased reflectivity of permanent shadow; porosity is largely ruled out as the sole explanation. The south polar crater Shackleton is found to be among the most reflective craters in its size range globally but is not the most reflective, so mass wasting cannot be ruled out as a cause for the crater's anomalous reflectance. Models of the abundance of ice needed to account for the reflectance anomaly range from 3 to 14% by weight or area depending on assumptions regarding the effects of porosity on reflectance and whether ice is present as patches or is well mixed in the regolith. If differences in nanophase iron abundances are responsible for the anomaly, the permanently shadowed regions have between 50 and 80% the abundance of nanophase iron in mature lunar soil.
PSR↗
Comparison of Cloud Detection Algorithms for Sentinel-2 Imagery
Accurate, automated cloud and cloud shadow detection is a key component of the processing needed to prepare optical satellite imagery for scientific analysis. Many existing cloud detection algorithms rely on temperature information to identify clouds, making detection difficult for imagers that lack a thermal band, like Sentinel-2. To get maximum benefit from Sentinel-2 products it is critical to understand which algorithms best identify clouds and their shadows in images. We examined the relative performance of five different cloud-masking algorithms (Sen2Cor, MAJA, LaSRC, Fmask and Tmask) in 6 Sentinel-2 scenes (28 total images) distributed across the Eastern Hemisphere. Expanding on these comparisons, we tested ensemble approaches to improve results. We tested three ensemble approaches to cloud and shadow classification based on the outputs of the five initial algorithms using the cloud masks in: (1) a majority prediction model; (2) a random forests model; and (3) a conditional logic model. Accuracy assessments show a trade-off between omission and commission errors in cloud detection for individual algorithms across all sites, and some algorithms are better at detecting either clouds or cloud shadows. No single algorithm outperforms the others for both clouds and shadows. Aggregating the results from multiple algorithms produces fewer undetected clouds and higher overall accuracy than any single algorithm, with as high as 2.7% improvement over the top-performing algorithm, suggesting an ensemble approach may be the most useful for processing of Sentinel-2 data.
Sentinel-2↗
Structural Complexity Biases Vegetation Greenness Measures
Vegetation ‘greenness’ characterized by spectral vegetation indices (VIs) is an integrative measure of vegetation leaf abundance, biochemical properties and pigment composition. Surprisingly, satellite observations reveal that several major VIs over the US Corn Belt are higher than those over the Amazon rainforest, despite the forests having a greater leaf area. This contradicting pattern underscores the pressing need to understand the underlying drivers and their impacts to prevent misinterpretations. Here we show that macroscale shadows cast by complex forest structures result in lower greenness measures compared with those cast by structurally simple and homogeneous crops. The shadow-induced contradictory pattern of VIs is inevitable because most Earth-observing satellites do not view the Earth in the solar direction and thus view shadows due to the sun–sensor geometry. The shadow impacts have important implications for the interpretation of VIs and solar-induced chlorophyll fluorescence as measures of global vegetation changes. For instance, a land-conversion process from forests to crops over the Amazon shows notable increases in VIs despite a decrease in leaf area. Our findings highlight the importance of considering shadow impacts to accurately interpret remotely sensed VIs and solar-induced chlorophyll fluorescence for assessing global vegetation and its changes.
Vegetation indices↗
Structural complexity biases vegetation greenness measures
Vegetation ‘greenness’ characterized by spectral vegetation indices (VIs) is an integrative measure of vegetation leaf abundance, biochemical properties and pigment composition. Surprisingly, satellite observations reveal that several major VIs over the US Corn Belt are higher than those over the Amazon rainforest, despite the forests having a greater leaf area. This contradicting pattern underscores the pressing need to understand the underlying drivers and their impacts to prevent misinterpretations. Here we show that macroscale shadows cast by complex forest structures result in lower greenness measures compared with those cast by structurally simple and homogeneous crops. The shadow-induced contradictory pattern of VIs is inevitable because most Earth-observing satellites do not view the Earth in the solar direction and thus view shadows due to the sun–sensor geometry. The shadow impacts have important implications for the interpretation of VIs and solar-induced chlorophyll fluorescence as measures of global vegetation changes. For instance, a land-conversion process from forests to crops over the Amazon shows notable increases in VIs despite a decrease in leaf area. In conclusion, our findings highlight the importance of considering shadow impacts to accurately interpret remotely sensed VIs and solar-induced chlorophyll fluorescence for assessing global vegetation and its changes.
60 APPLIED LIFE SCIENCES↗
Generating rotating spacetime in Ricci-based gravity: naked singularity as a black hole mimicker
Motivated by the lack of rotating solutions sourced by matter in General Relativity as well as in modified gravity theories, in this work we extend a recently discovered exact rotating solution of the minimal Einstein-scalar theory to its counterpart in Eddington-inspired Born-Infeld gravity coupled to a Born-Infeld scalar field. This is accomplished with the implementation of a well-developed mapping between solutions of Ricci-Based Palatini theories of gravity and General Relativity. The new solution is parametrized by the scalar charge and the Born-Infeld coupling constant apart from the mass and spin of the compact object. Compared to the spacetime prior to the mapping, we find that the high-energy modifications at the Born-Infeld scale are able to suppress but not remove the curvature divergence of the original naked null singularity. Depending on the sign of the Born-Infeld coupling constant, these modifications may even give rise to an additional timelike singularity exterior to the null one. In spite of that, both of the naked singularities before and after the mapping are capable of casting shadows, and as a consequence of the mapping relation, their shadows turn out to be identical as seen by a distant observer on the equatorial plane. Even though the scalar field induces a peculiar oblateness to the appearance of the shadow with its left and right endpoints held fixed, the closedness condition for the shadow contour sets a small upper bound on the absolute value of the scalar charge, which leads to observational features of the shadow closely resembling those of a Kerr black hole.
79 ASTRONOMY AND ASTROPHYSICS↗
Reflectance Modeling
The main thrust of the work conducted is in the modeling of spectral responses of discontinuous conifer forest canopies, considered as collections of conical forms that are illuminated at an angle and cast shadows on contracting background. The three first-year objectives are: (1) modification of the variance-driven model to incorporate overlapping of shadows and crowns; (2) collection and analysis of photographic data to calibrate tree-spacing functions; and (3) collection of field data to determine height, spacing, and shape of conifers in open and closed stands in the Goosenest (California) test area. Modification of the invertible model uses a linear approximation to correct for the reduction in shadow and canopy area that occurs when shadows fall on crowns or tree crowns intersect. Comparison of the results of the approximation with a series of Monte Carlo simulations shows that the mean area covered by crowns or shadows is approximated quite accurately, but the variance calculated departs significantly from simulated values. The analysis of tree spacing patterns using air photos showed that spacing tended to be somewhat regular at a scale approximately equal to the average distance between trees, but at larger distance scales counts of trees in cells could be approximated acceptably by a Poisson (random) function.
Strahler, A. H.↗