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At least 523 records · Page 29

On implementation of the extended interior penalty function

The extended interior penalty function formulation is implemented. A rational method for determining the transition between the interior and extended parts is set forth. The formulation includes a straightforward method for avoiding design points with some negative components, which are physically meaningless in structural analysis. The technique, when extended to problems involving parametric constraints, can facilitate closed form integration of the penalty terms over the most important parts of the parameter interval. The method lends itself well to the use of approximation concepts, such as design variable linking, constraint deletion and Taylor series expansions of response quantities in terms of design variables. Examples demonstrating the algorithm, in the context of planar orthogonal frames subjected to ground motion, are included.

Cassis, J. H.↗

An Exploratory Exercise in Taguchi Analysis of Design Parameters: Application to a Shuttle-to-space Station Automated Approach Control System

The chief goals of the summer project have been twofold - first, for my host group and myself to learn as much of the working details of Taguchi analysis as possible in the time allotted, and, secondly, to apply the methodology to a design problem with the intention of establishing a preliminary set of near-optimal (in the sense of producing a desired response) design parameter values from among a large number of candidate factor combinations. The selected problem is concerned with determining design factor settings for an automated approach program which is to have the capability of guiding the Shuttle into the docking port of the Space Station under controlled conditions so as to meet and/or optimize certain target criteria. The candidate design parameters under study were glide path (i.e., approach) angle, path intercept and approach gains, and minimum impulse bit mode (a parameter which defines how Shuttle jets shall be fired). Several performance criteria were of concern: terminal relative velocity at the instant the two spacecraft are mated; docking offset; number of Shuttle jet firings in certain specified directions (of interest due to possible plume impingement on the Station's solar arrays), and total RCS (a measure of the energy expended in performing the approach/docking maneuver). In the material discussed here, we have focused on single performance criteria - total RCS. An analysis of the possibility of employing a multiobjective function composed of a weighted sum of the various individual criteria has been undertaken, but is, at this writing, incomplete. Results from the Taguchi statistical analysis indicate that only three of the original four posited factors are significant in affecting RCS response. A comparison of model simulation output (via Monte Carlo) with predictions based on estimated factor effects inferred through the Taguchi experiment array data suggested acceptable or close agreement between the two except at the predicted optimum point, where a difference outside a rule-of-thumb bound was observed. We have concluded that there is most likely an interaction effect not provided for in the original orthogonal array selected as the basis for our experimental design. However, we feel that the data indicates that this interaction is a mild one and that inclusion of its effect will not alter the location of the optimum.

Deal, Don E.↗

Convergence of Weak-SINDy Surrogate Models

In this paper, we give an in-depth error analysis for surrogate models generated by a variant of the Sparse Identification of Nonlinear Dynamics (SINDy) method. We start with an overview of a variety of nonlinear system identification techniques, namely SINDy, weak-SINDy, and the occupation kernel method. Under the assumption that the dynamics are a finite linear combination of a set of basis functions, these methods establish a linear system to recover coefficients. We illuminate the structural similarities between these techniques and establish a projection property for the weak-SINDy technique. Following the overview, we analyze the error of surrogate models generated by a simplified version of weak-SINDy. In particular, under the assumption of boundedness of a composition operator given by the solution, we show that (i) the surrogate dynamics converges towards the true dynamics and (ii) the solution of the surrogate model is reasonably close to the true solution. Finally, as an application, we discuss the use of a combination of weak-SINDy surrogate modeling and proper orthogonal decomposition (POD) to build a surrogate model for partial differential equations (PDEs).

97 MATHEMATICS AND COMPUTING↗

Spectra-Orthogonal Optical Anisotropy in Wafer-Scale Molecular Crystal Monolayers

Controlling the spectral and polarization response of two-dimensional (2D) crystals is vital for developing ultrathin platforms for compact optoelectronic devices. However, independently tuning optical anisotropy and spectral response remains challenging in conventional semiconductors due to the intertwined nature of their lattice and electronic structures. Here, we report spectra-orthogonal optical anisotropy─where polarization anisotropy is tuned independently of spectral response─in wafer-scale, one-atom-thick 2D molecular crystal (2DMC) monolayers synthesized on monolayer transition-metal dichalcogenide (TMD) crystals. Utilizing the concomitant spectral consistency and structural tunability of perylene derivatives, we demonstrate tunable optical polarization anisotropy in 2DMCs with similar spectral profiles, as confirmed by room-temperature scanning tunneling microscopy and cross-polarized reflectance microscopy. Additional angle-dependent analysis of the single-crystal and polycrystalline molecular domains reveals an epitaxial relationship between the 2DMC and TMD. In conclusion, our results establish a scalable, molecule-based 2D crystalline platform for unique and tunable functionalities unattainable in covalent 2D solids.

2D materials↗

Vestibular convergence patterns in vestibular nuclei neurons of alert primates

Sensory signal convergence is a fundamental and important aspect of brain function. Such convergence may often involve complex multidimensional interactions as those proposed for the processing of otolith and semicircular canal (SCC) information for the detection of translational head movements and the effective discrimination from physically congruent gravity signals. In the present study, we have examined the responses of primate rostral vestibular nuclei (VN) neurons that do not exhibit any eye movement-related activity using 0.5-Hz translational and three-dimensional (3D) rotational motion. Three distinct neural populations were identified. Approximately one-fourth of the cells exclusively encoded rotational movements (canal-only neurons) and were unresponsive to translation. The canal-only central neurons encoded head rotation in SCC coordinates, exhibited little orthogonal canal convergence, and were characterized with significantly higher sensitivities to rotation as compared to primary SCC afferents. Another fourth of the neurons modulated their firing rates during translation (otolith-only cells). During rotations, these neurons only responded when the axis of rotation was earth-horizontal and the head was changing orientation relative to gravity. The remaining one-half of VN neurons were sensitive to both rotations and translations (otolith + canal neurons). Unlike primary otolith afferents, however, central neurons often exhibited significant spatiotemporal (noncosine) tuning properties and a wide variety of response dynamics to translation. To characterize the pattern of SCC inputs to otolith + canal neurons, their rotational maximum sensitivity vectors were computed using exclusively responses during earth-vertical axis rotations (EVA). Maximum sensitivity vectors were distributed throughout the 3D space, suggesting strong convergence from multiple SCCs. These neurons were also tested with earth-horizontal axis rotations (EHA), which would activate both vertical canals and otolith organs. However, the recorded responses could not be predicted from a linear combination of EVA rotational and translational responses. In contrast, one-third of the neurons responded similarly during EVA and EHA rotations, although a significant response modulation was present during translation. Thus this subpopulation of otolith + canal cells, which included neurons with either high- or low-pass dynamics to translation, appear to selectively ignore the component of otolith-selective activation that is due to changes in the orientation of the head relative to gravity. Thus contrary to primary otolith afferents and otolith-only central neurons that respond equivalently to tilts relative to gravity and translational movements, approximately one-third of the otolith + canal cells seem to encode a true estimate of the translational component of the imposed passive head and body movement.

Non-NASA Center↗

Spontaneous Chirality Flipping in an Orthogonal Spin-Charge Ordered Topological Magnet

The asymmetric distribution of chiral objects with opposite chirality is of great fundamental interest ranging from molecular biology to particle physics. In quantum materials, chiral states can build on inversion-symmetry-breaking lattice structures or emerge from spontaneous magnetic ordering induced by competing interactions. Although the handedness of a chiral state can be changed through external fields, a spontaneous chirality flipping has yet to be discovered. We present experimental evidence of chirality flipping via changing temperature in a topological magnet EuAl 4 , which features orthogonal spin density waves (SDW) and charge density waves (CDW). Using circular dichroism of Bragg peaks in the resonant magnetic x-ray scattering, we find that the chirality of the helical SDW flips through a first-order phase transition with modified SDW wavelength. Intriguingly, we observe that the CDW couples strongly with the SDW and displays a rare commensurate-to-incommensurate transition at the chirality flipping temperature. Combining with first-principles calculations and angle-resolved photoemission spectroscopy, our results support a Fermi surface origin of the helical SDW with intertwined spin, charge, and lattice degrees of freedom in EuAl 4 . Our results reveal an unprecedented spontaneous chirality flipping and lay the groundwork for a new functional manipulation of chirality through momentum-dependent spin-charge-lattice interactions. Published by the American Physical Society 2024

3-dimensional systems↗

Characterization and Application of Artificial Light Sources for Nighttime Aerosol Optical Depth Retrievals using the Visible Infrared Imager Radiometer Suite Day/Night Band

Using nighttime observations from Visible Infrared Imager Radiometer Suite (VIIRS) Day/Night band (DNB), the characteristics of artificial light sources are evaluated as functions of observation conditions, and incremental improvements are documented on nighttime aerosol retrievals using VIIRS DNB data on a regional scale. We find that the standard deviation of instantaneous radiance for a given artificial light source is strongly dependent upon the satellite viewing angle but is weakly dependent on lunar fraction and lunar angle. Retrieval of nighttime aerosol optical thickness (AOT) based on the novel use of these artificial light sources is demonstrated for three selected regions (United States, Middle East and India) during 2015. Reason-able agreement is found between nighttime AOTs from the VIIRS DNB and temporally adjacent daytime AOTs from the AErosol RObotic NETwork (AERONET) as well as from coincident nighttime AOT retrievals from the Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP), indicating the potential of this method to begin filling critical gaps in diurnal AOT information at both regional and global scales. Issues related to cloud, snow and ice contamination during the winter season, as well as data loss due to the misclassification of thick aerosol plumes as clouds, must be addressed to make the algorithm operationally robust.

Jianglong Zhang↗

Vestibulo-Spinal Pathways in Tetrapods: Chapter - 6.26

The vestibulospinal system provides the spinal motor circuits controlling head/neck and limb movements and body posture with rapid reflex adjustments to maintain equilibrium and stability and with a continuous essential excitatory drive, called tonus, to enhance reactive responses to perturbations that force the animal off normal posture. The sensory signals to these reflex circuits originate from hair cells in the inner ear of otolith structures, namely the utricle and saccule, that transduce inertial acceleration and orientation of the head with respect to gravity and in the three orthogonally arranged semicircular canals that transduce angular head rotation. The principal vestibulospinal pathways are 1) the medial vestibulospinal tract that descends in the ventromedial funiculus and innervates inter- and motoneurons located mainly in lamina VII, VIII, and dorsomedial IX throughout the cervical segments; and 2) the lateral vestibulospinal tracts that course in the lateral to ventrolateral funiculi and are distinguished by two divisions: i) a cervical-projecting tract that overlaps many of the targets of medial vestibulospinal tract neurons including the motoneurons in ventromedial IX and also contributes to reflex control of shoulder and forelimb (arm) muscles; and ii) a lumbosacral-projecting tract that provides a rapid input to maintain stable posture and reflex control of the lower body. A striking observation in understanding the functional organization of this sensory-motor system is both that the driving sensory input can be dynamically modified by the behavioral context in which the sensation is made and that it remains able to quickly respond to an external force during self-generated head movements. The structural basis for vestibulospinal inputs to spinal motor control circuits in quadrupeds and bipeds rely in part on the animal's need for coordination between fore- and hind-limb reflex movements. Understanding the sensory-to-motor transformations in the diverse species rely on the correlations of the conserved and unique species behavior, morphology and physiologic function.

Spinal Cord↗

Demonstration of Nautilus Centripetal Capillary Condenser Technology

This paper describes the results of a proof of concept effort for development of a Nautilus Centripetal Capillary Condenser (NCCC or NC3) used for microgravity compatible water recovery from moist air with integral passive phase separation. Removal of liquid condensate from the air stream exiting a condenser is readily performed here on Earth. In order to perform this function in space however, without gravity or mechanical action, other tactics including utilization of inertial, drag and capillary forces are required. Within the NC3, liquid water forms via condensation on cold condenser surfaces as humid air passes along multiple spiral channels, each in its own plane, all together forming a stacked plate assembly. Non-mechanical inertial forces are employed to transfer condensate, as it forms, via centripetal action to the outer perimeter of each channel. A V-shaped groove, constructed on this outer edge of the spiral channel, increases local capillary forces thereby retaining the liquid. Air drag then pulls the liquid along to a collection region near the center of the device. Dry air produced by each parallel spiral channel is combined in a common orthogonal, out-of-plane conduit passing down the axial center of the stacked device. Similarly, the parallel condensate streams are combined and removed from the condenser/separator through yet another out-of-plane axial conduit. NC3 is an integration of conventional finned condenser operation, combined with static phase separation and capillary transport phenomena. A Mars' transit mission would be a logical application for this technology where gravity is absent and the use of vibrating, energy-intensive, motor-driven centrifugal separators is undesired. Here a vapor stream from either the Heat Melt Compactor or the Carbon dioxide Reduction Assembly, for example, would be dried to a dew point of 10 deg using a passive NC3 condenser/separator with the precious water condensate recycled to the water bus.

Separator↗

Lunar Latitude and Terrain Radiator Sensitivity Study

The thermal environment on the moon is highly complex and diverse. The lunar surface near the equator develops extreme hot average temperatures during the lunar day due to solar flux vectors that are nearly orthogonal to the surface. The lunar poles have a cold and uniquely complex thermal environment with low solar elevation angles and permanently shadowed regions located just kilometers from some of the most highly illuminated regions of the moon. Likewise, the topography can range from very flat crater basins to dramatically tall features such as mountains and crater rims. Consequently, when sizing the radiators of a lunar surface vehicle, the specific thermal environment found in the targeted landing or deployment zone must be well understood to build robust appropriately scaled thermal control systems. Here described are parametric studies that characterize the sensitivity of lunar radiator performance to lunar terrain and latitude. Heat rejection is calculated for different radiator tilt angles in a variety of terrain environments. Radiator performance as a function of underside thermal condition is also characterized at lunar latitudes ranging from equatorial to polar. Impacts of latitude and terrain on radiator performance are quantified, and regions are identified where the thermal environment is more or less favorable for specific radiator designs.

Lunar Vehicle Radiator↗

Lunar Latitude and Terrain Radiator Sensitivity Study

The thermal environment on the moon is highly complex and diverse. The lunar surface near the equator develops extreme hot average temperatures during the lunar day due to solar flux vectors that are nearly orthogonal to the surface. The lunar poles have a cold and uniquely complex thermal environment with low solar elevation angles and permanently shadowed regions located just kilometers from some of the most highly illuminated regions of the moon. Likewise, the topography can range from very flat crater basins to dramatically tall features such as mountains and crater rims. Consequently, when sizing the radiators of a lunar surface vehicle, the specific thermal environment found in the targeted landing or deployment zone must be well understood to build robust, appropriately scaled thermal control systems. Here described are parametric studies that characterize the sensitivity of lunar radiator performance to lunar terrain and latitude. Heat rejection is calculated for different radiator tilt angles in a variety of terrain environments. Radiator performance as a function of underside thermal condition is also characterized at lunar latitudes ranging from equatorial to polar. Impacts of latitude and terrain on radiator performance are quantified, and regions are identified where the thermal environment is more or less favorable for specific radiator designs.

Lunar Vehicle Radiator↗

Lunar Latitude and Terrain Radiator Sensitivity Study

The thermal environment on the moon is highly complex and diverse. The lunar surface near the equator develops extreme hot average temperatures during the lunar day due to solar flux vectors that are nearly orthogonal to the surface. The lunar poles have a cold and uniquely complex thermal environment with low solar elevation angles and permanently shadowed regions located just kilometers from some of the most highly illuminated regions of the moon. Likewise, the topography can range from very flat crater basins to dramatically tall features such as mountains and crater rims. Consequently, when sizing the radiators of a lunar surface vehicle, the specific thermal environment found in the targeted landing or deployment zone must be well understood to build robust, appropriately scaled thermal control systems. Here described are parametric studies that characterize the sensitivity of lunar radiator performance to lunar terrain and latitude. Heat rejection is calculated for different radiator tilt angles in a variety of terrain environments. Radiator performance as a function of underside thermal condition is also characterized at lunar latitudes ranging from equatorial to polar. Impacts of latitude and terrain on radiator performance are quantified, and regions are identified where the thermal environment is more or less favorable for specific radiator designs.

Lunar Thermal Analysis↗

Lunar Latitude and Terrain Radiator Sensitivity Study

The thermal environment on the moon is highly complex and diverse. The lunar surface near the equator develops extreme hot average temperatures during the lunar day due to solar flux vectors that are nearly orthogonal to the surface. The lunar poles have a cold and uniquely complex thermal environment with low solar elevation angles and permanently shadowed regions located just kilometers from some of the most highly illuminated regions of the moon. Likewise, the topography can range from very flat crater basins to dramatically tall features such as mountains and crater rims. Consequently, when sizing the radiators of a lunar surface vehicle, the specific thermal environment found in the targeted landing or deployment zone must be well understood to build robust appropriately scaled thermal control systems. Here described are parametric studies that characterize the sensitivity of lunar radiator performance to lunar terrain and latitude. Heat rejection is calculated for different radiator tilt angles in a variety of terrain environments. Radiator performance as a function of underside thermal condition is also characterized at lunar latitudes ranging from equatorial to polar. Impacts of latitude and terrain on radiator performance are quantified, and regions are identified where the thermal environment is more or less favorable for specific radiator designs.

Lunar Vehicle Radiator↗

High-rate heavy-ion tracking using MWPCs and PPACs with an Anti-Discharge Unit

This work reports on the development of two robust, heavy-ion beam tracking concepts operating at low pressure (< 15 Torr) for high rate applications (> 200 kHz). The first concept consists of a Multi-Wire Proportional Counter (MWPC) with a central anode consisting of 12 μm Au-plated Tungsten wires spaced 1 mm from each other. The anode grid is sandwiched between two segmented cathodes aligned orthogonally in the two dimensions for (x,y) particle localization. The second detector is a Parallel-Plate Avalanche Counter (PPAC) that uses the same readout geometry as the MWPC, but replaces the wire anode with a 150 nm silver layer deposited on both sides of a thin (< 1 mg/cm 2 ) polypropylene foil. Additionally, the bias circuitry for the PPAC anode central foil is equipped with an Anti-Discharge Unit (ADU) to prevent transitions from proportional operation to streamer formation, thereby avoiding damaging discharges. The localization capability of both detectors was tested with a low-rate alpha-particle source (241-Am). A position resolution of < 1 mm (FWHM) was achieved under stable, high-gas-gain (> 1000) operating conditions. Their performance in terms of detection efficiency as a function of the isotope charge (Z) was determined by irradiating the detectors with a cocktail beam (Z ≤ 15) with energy of ∼ 100 MeV/u. Full detection efficiency is maintained for all available fragments under optimal operational conditions (i.e., voltage bias). Full detection efficiency was achieved at rates above 200 kHz by irradiating the detectors with a 1 cm diameter 238 U beam at an energy of 143 MeV/u.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Effects of Frequency and Motion Paradigm on Perception of Tilt and Translation During Periodic Linear Acceleration

Previous studies have demonstrated an effect of frequency on the gain of tilt and translation perception. Results from different motion paradigms are often combined to extend the stimulus frequency range. For example, Off-Vertical Axis Rotation (OVAR) and Variable Radius Centrifugation (VRC) are useful to test low frequencies of linear acceleration at amplitudes that would require impractical sled lengths. The purpose of this study was to compare roll-tilt and lateral translation motion perception in 12 healthy subjects across four paradigms: OVAR, VRC, sled translation and rotation about an earth-horizontal axis. Subjects were oscillated in darkness at six frequencies from 0.01875 to 0.6 Hz (peak acceleration equivalent to 10 deg, less for sled motion below 0.15 Hz). Subjects verbally described the amplitude of perceived tilt and translation, and used a joystick to indicate the direction of motion. Consistent with previous reports, tilt perception gain decreased as a function of stimulus frequency in the motion paradigms without concordant canal tilt cues (OVAR, VRC and Sled). Translation perception gain was negligible at low stimulus frequencies and increased at higher frequencies. There were no significant differences between the phase of tilt and translation, nor did the phase significantly vary across stimulus frequency. There were differences in perception gain across the different paradigms. Paradigms that included actual tilt stimuli had the larger tilt gains, and paradigms that included actual translation stimuli had larger translation gains. In addition, the frequency at which there was a crossover of tilt and translation gains appeared to vary across motion paradigm between 0.15 and 0.3 Hz. Since the linear acceleration in the head lateral plane was equivalent across paradigms, differences in gain may be attributable to the presence of linear accelerations in orthogonal directions and/or cognitive aspects based on the expected motion paths.

Beaton, K. H.↗

Shell Models of RMHD Turbulence and the Heating of Solar Coronal Loops

A simplified nonlinear numerical model for the development of incompressible magnetohydrodynamics in the presence of a strong magnetic field B|| and stratification, nicknamed 'Shell-Atm,' is presented. In planes orthogonal to the mean field, the nonlinear incompressible dynamics is replaced by two-dimensional shell models for the complex variables u and b, allowing one to reach large Reynolds numbers while at the same time carrying out sufficiently long integrations to obtain good statistics at moderate computational cost. The shell models of different planes are coupled by Alfve'n waves propagating along B||. The model may be applied to open or closed magnetic field configurations where the axial field dominates and the plasma pressure is low; here we apply it to the specific case of a magnetic loop of the solar corona heated by means of turbulence driven by photospheric motions, and we use statistics for its analysis. The Alfven waves interact nonlinearly and form turbulent spectra in the directions perpendicular and, through propagation, also parallel to the mean field. A heating function is obtained and shown to be intermittent; the average heating is consistent with values required for sustaining a hot corona and is proportional to the aspect ratio of the loop to the -1.5 power, and haracteristic properties of heating events are distributed as power laws. Crosscorrelations show a delay of dissipation compared with energy content.

corona↗

Non-Tidal Non-Seasonal Oceanic Mass Redistribution Estimated from the TOPEX/Poseidon Observation

Topex/Poseidon altimetry data are used to estimate the non-tidal mass redistribution as a function of space-time. The goal is to study the contribution of ocean circulations in the geodynamic effects including Earth's rotational and gravitational variations. We examine the non-seasonal anomalies at monthly sampling rate over the T/P span of eight years, concentrating especially on interannual variabilities. Since the sea-surface height data obtained from altimetry is the combined effect of steric change (primarily thermal effect) and the mass flux, and because the former has zero contribution to the geodynamic effects, one needs to do a so-called steric correction by removing from the altimetry data the steric contributions. We achieve it using multiyear monthly sea-surface temperature maps, together with monthly "climatology" for mixed-layer depth maps for mean-months of the year. We analyze both sets of the altimetry data and the steric correction data using the empirical orthogonal function/principal component analysis (in which we take care of issues associated with the area-weighting and non-zero mean), and examine the most important modes, either globally or regionally. In particular, the ENSO in the tropical Pacific/Indian Oceans exhibits the most prominent pattern. The net mass transport after the steric correction can then be compared with: (1) ocean general circulation model outputs for the same period of time (such as from POCM-4B); (2) non-atmospheric Earth rotation variations obtained from space geodesy data and atmospheric angular momentum data; (3) non-atmospheric low-degree gravitational variations from satellite-laser-ranging observations and global atmospheric data.

Chao, Benjamin F.↗

Fitting a Two-Component Scattering Model to Polarimetric SAR Data from Forests

Two simple scattering mechanisms are fitted to polarimetric synthetic aperture radar (SAR) observations of forests. The mechanisms are canopy scatter from a reciprocal medium with azimuthal symmetry and a ground scatter term that can represent double-bounce scatter from a pair of orthogonal surfaces with different dielectric constants or Bragg scatter from a moderately rough surface, which is seen through a layer of vertically oriented scatterers. The model is shown to represent the behavior of polarimetric backscatter from a tropical forest and two temperate forest sites by applying it to data from the National Aeronautic and Space Agency/Jet Propulsion Laboratory's Airborne SAR (AIRSAR) system. Scattering contributions from the two basic scattering mechanisms are estimated for clusters of pixels in polarimetric SAR images. The solution involves the estimation of four parameters from four separate equations. This model fit approach is justified as a simplification of more complicated scattering models, which require many inputs to solve the forward scattering problem. The model is used to develop an understanding of the ground-trunk double-bounce scattering that is present in the data, which is seen to vary considerably as a function of incidence angle. Two parameters in the model fit appear to exhibit sensitivity to vegetation canopy structure, which is worth further exploration. Results from the model fit for the ground scattering term are compared with estimates from a forward model and shown to be in good agreement. The behavior of the scattering from the ground-trunk interaction is consistent with the presence of a pseudo-Brewster angle effect for the air-trunk scattering interface. If the Brewster angle is known, it is possible to directly estimate the real part of the dielectric constant of the trunks, a key variable in forward modeling of backscatter from forests. It is also shown how, with a priori knowledge of the forest height, an estimate for the attenuation coefficient of the canopy can be obtained directly from the multi-incidence-angle polarimetric observations. This attenuation coefficient is another key variable in forward models and is generally related to the canopy density.

temperate forests↗