A Statistical Perspective on Climate Informatics
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spatio-temporal statistical modeling↗
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Comparison of Computed and Measured Vortex Evolution for a UH-60A Rotor in Forward Flight
A Computational Fluid Dynamics (CFD) simulation using the Navier-Stokes equations was performed to determine the evolutionary and dynamical characteristics of the vortex flowfield for a highly flexible aeroelastic UH-60A rotor in forward flight. The experimental wake data were acquired using Particle Image Velocimetry (PIV) during a test of the fullscale UH-60A rotor in the National Full-Scale Aerodynamics Complex 40- by 80-Foot Wind Tunnel. The PIV measurements were made in a stationary cross-flow plane at 90 deg rotor azimuth. The CFD simulation was performed using the OVERFLOW CFD solver loosely coupled with the rotorcraft comprehensive code CAMRAD II. Characteristics of vortices captured in the PIV plane from different blades are compared with CFD calculations. The blade airloads were calculated using two different turbulence models. A limited spatial, temporal, and CFD/comprehensive-code coupling sensitivity analysis was performed in order to verify the unsteady helicopter simulations with a moving rotor grid system.
Evolution↗
Effect of Latitude Bias in Entry Angle on Ground Casualty Risk from Naturally Decaying Space Objects
An improvement to the long-term estimation of ground casualties from naturally decaying space objects is the refinement to the distribution of entry angle at the entry interface as a function of latitude. Previous analyses were based on an assumed "small angle," typically -0.1°, and entry interface at the equator. This study expands on work by Bacon and Matney that indicated there is significant latitude bias in the location of reentries, compared to prior assumptions of equal temporal probability. A new model has been developed, which describes the distribution of entry angle as a function of orbital inclination and argument of latitude. This model has been used to generate inputs for ODPO’s certified reentry survivability software, Object Reentry Survival Analysis Tool (ORSAT). These new results are compared with the prior standard model to assess the magnitude of the effects on reentry casualty risk.
Ostrom, Chris L.↗
Flow Characterization of the NASA Langley Unitary Plan Wind Tunnel, Test Section 2: Computational Results
This is an abstract for an invited paper at the AIAA Aviation Conference, June 2021. The work described here is part of an effort of coordinated experiments in the Unitary Plan Wind Tunnel (UPWT) facility at the NASA Langley Research Center (LaRC) and matching CFD simulations. The primary goal of the work is to assess the productivity and true predictive accuracy of CFD, absent any guidance from experiment, in the high supersonic speed range as compared to experiments performed at the NASA LaRC’s UPWT facility. This report concerns CFD simulation of the primary flow-path in the empty wind tunnel, including the settling chamber, nozzle, test section, and some of the tunnel downstream of the test section. The Mach number in the test section ranges from M~2.4 to M~4.6, and the required area ratio variation is achieved by translation of a nozzle block which constricts the area of a loosely S-shaped throat. Flow past protuberances in the settling chamber and into this S-bend throat are predicted by CFD to generate streamwise vorticity that may, or may not, persist through the throat and into the test section as coherent vortices. Some flow conditions are notably unsteady at frequencies well below those of turbulence, due to unsteady separated flow ahead of the nozzle block. The bulk flow moves at velocities ranging from 'walking speed' in the settling chamber to M~4.6 in the test section. Heat transfer to the settling chamber walls and buoyancy are significant at high Mach number. Subtle variations in surface curvature in the nozzle generate Mach waves that propagate into the test section. CFD of the empty tunnel serves two purposes. Firstly, the full-tunnel simulations are used to provide upstream boundary conditions for CFD of vehicle aerodynamics which are generally performed in a domain confined to the wind tunnel test section; these companion studies are addressed in other papers. Secondly, it is a challenging test for CFD to resolve all of the empty tunnel flow phenomena relevant to flow in the test section. It requires a more complete definition of geometry than was originally anticipated. In addition, it requires good spatial and temporal accuracy, and turbulence modeling that performs well on specific phenomena such as corner flows. The boundary conditions and solution algorithms must perform well from incompressible to almost hypersonic speeds. The final state of the pre-test CFD was a product of an iterative self-improvement process. The initial simulations of the empty tunnel were deficient in many respects, but hints to those deficiencies were recognized in the solutions, and remedies were implemented. Possible further improvements will be studied in the post-test phase when comparisons with experimental data are possible. The CFD was performed by five separate collaborative teams using four different flow solvers: FUN3D, Overflow, Star-CCM+ and USM3D. The level of effort of these teams varied significantly, but each made important contributions to the goals of the work. A concerted effort to use uncertainty quantification methods (UQ) in CFD is also a goal of this work. To this end, variations in CFD results due to grid refinement, turbulence modeling, and boundary conditions have been characterized. Code-to-code variation is another means of assessing CFD uncertainty. All CFD solvers predict similarity among the primary flow features; these include the variation of Mach number due to changes in Reynolds number, and the bulk flow angularity due to tunnel-wall curvature. All CFD solvers also predict similar trends in secondary flows, such as the downwash in the side-wall boundary layers. Three of the high-spatial resolution simulations give similar predictions of a complex secondary flow phenomena, streamwise vortices generated in the S-bend throat that persist into the side-wall boundary layers of the test section. Two of the highest-resolution simulations, run with the same turbulence model in different CFD solvers, gave encouragingly similar predictions of a complex tertiary flow phenomenon, small transient "sprites" of upwash flows, resulting from vortices that presumably originate in the separated flow near the leading edge of the nozzle block. While the CFD was done in a "blind pre-test" mode, requests from the experimental team for CFD results pertaining to unsteadiness and total temperature variations in the test section resulted in CFD runs that included a cooled wall in settling chamber. This then led to a change in the standard practice for running the Overflow results, which would not have occurred without this "release" of this experimental information. CFD was also used to guide some measurements. The paper will focus on establishing the consensus among CFD results and understanding differences among those results. Initial findings from the efforts to characterize CFD uncertainty have been done and will be included in the paper.
Robert Edward Childs↗
Runtime Verification Logics A Language Design Perspective
Runtime Verification is a light-weight approach to systems verification, where actual executions of a system are processed and analyzed using rigorous techniques. In this paper we shall narrow the term’s definition to represent the commonly studied variant consisting of verifying that a single system execution conforms to a specification written in a formal specification language. Runtime verification (in this sense) can be used for writing test oracles during testing when the system is too complex for full formal verification, or it can be used during deployment of the system as part of a fault protection strategy, where corrective actions may be taken in case the specification is violated. Specification languages for runtime verification appear to differ from for example temporal logics applied in model checking, in part due to the focus on monitoring of events that carry data, and specifically due to the desire to relate data values existing at different time points, resulting in new challenges in both the complexity of the monitoring approach and the expressiveness of languages. Over the recent years, numerous runtime verification specification languages have emerged, each with its different features and levels of expressiveness and usability. This paper presents an overview and a discussion of this design space.
Reger, Giles↗
A Year in the Life of GW 170817: The Rise and Fall of a Structured Jet from a Binary Neutron Star Merger
We present the results of our year-long afterglow monitoring of GW 170817, the first binary neutron star merger detected by Advanced Laser Interferometer Gravitational-Wave Observatory (LIGO) and Advanced Virgo. New observations with the Australian Telescope Compact Array and the Chandra X-ray Telescope were used to constrain its late-time behaviour. The broad-band emission, from radio to X-rays, is well-described by a simple power-law spectrum with index β ∼ 0.585 at all epochs. After an initial shallow rise ∝t0.9, the afterglow displayed a smooth turnover, reaching a peak X-ray luminosity of LX ≈ 5 × 1039 erg s−1 at 160 d, and has now entered a phase of rapid decline, approximately ∝t−2. The latest temporal trend challenges most models of choked jet/cocoon systems, and is instead consistent with the emergence of a relativistic structured jet seen at an angle of ≈22◦ from its axis. Within such model, the properties of the explosion (such as its blast wave energy EK ≈ 2 × 1050 erg, jet width θc ≈ 4◦, and ambient density n ≈ 3 × 10−3 cm−3) fit well within the range of properties of cosmological short gamma-ray bursts.
Acceleration of particles↗
The joint space-time statistics of macroweather precipitation, space-time statistical factorization and macroweather models
Over the range of time scales from about 10 days to 30–100 years, in addition to the familiar weather and climate regimes, there is an intermediate “macroweather” regime characterized by negative temporal fluctuation exponents: implying that fluctuations tend to cancel each other out so that averages tend to converge. We show theoretically and numerically that macroweather precipitation can be modeled by a stochastic weather-climate model (the Climate Extended Fractionally Integrated Flux, model, CEFIF) first proposed for macroweather temperatures and we show numerically that a four parameter space-time CEFIF model can approximately reproduce eight or so empirical space-time exponents. In spite of this success, CEFIF is theoretically and numerically difficult to manage. We therefore propose a simplified stochastic model in which the temporal behavior is modeled as a fractional Gaussian noise but the spatial behaviour as a multifractal (climate) cascade: a spatial extension of the recently introduced ScaLIng Macroweather Model, SLIMM. Both the CEFIF and this spatial SLIMM model have a property often implicitly assumed by climatologists that climate statistics can be “homogenized” by normalizing them with the standard deviation of the anomalies. Physically, it means that the spatial macroweather variability corresponds to different climate zones that multiplicatively modulate the local, temporal statistics. This simplified macroweather model provides a framework for macroweather forecasting that exploits the system's long range memory and spatial correlations; for it, the forecasting problem has been solved. We test this factorization property and the model with the help of three centennial, global scale precipitation products that we analyze jointly in space and in time.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
STExNMF: Spatio-Temporally Exclusive Topic Discovery for Anomalous Event Detection
Understanding newly emerging events or topics associated with a particular region of a given day can provide deep insight on the critical events occurring in highly evolving metropolitan cities. We propose herein a novel topic modeling approach on text documents with spatio-temporal information (e.g., when and where a document was published) such as location-based social media data to discover prevalent topics or newly emerging events with respect to an area and a time point. We consider a map view composed of regular grids or tiles with each showing topic keywords from documents of the corresponding region. To this end, we present a tilebased spatio-temporally exclusive topic modeling approach called STExNMF, based on a novel nonnegative matrix factorization (NMF) technique. STExNMF mainly works based on the two following stages: (1) first running a standard NMF of each tile to obtain general topics of the tile and (2) running a spatiotemporally exclusive NMF on a weighted residual matrix. These topics likely reveal information on newly emerging events or topics of interest within a region. We demonstrate the advantages of our approach using the geo-tagged Twitter data of New York City. We also provide quantitative comparisons in terms of the topic quality, spatio-temporal exclusiveness, topic variation, and qualitative evaluations of our method using several usage scenarios. In addition, we present a fast topic modeling technique of our model by leveraging parallel computing.
Shin, Sungbok↗
Lethality is Local, but Survival is Systemic: Temporal and Multi-Organ Responses to Chlorine Gas Exposure in a Murine Model
Chlorine gas (Cl2) is a highly toxic chemical associated with both localized lung injury and systemic health effects. While pulmonary damage has been well characterized, the systemic inflammatory and metabolic responses remain poorly understood. We aimed to define the temporal and multi-organ responses to Cl2 exposure in a murine model, with a focus on identifying spatiotemporal inflammation and its impact on survival and lethality. SKH1 mice were exposed for 10 min to varying concentrations of Cl2 (94.4–810 ppm, representative of non-lethal, LD10, and LD50 doses) and monitored for respiratory function, perfusion, and acidosis using organ-specific imaging. At multiple time points (40 min, 6 h, 24 h, and 7 d), we measured phosphoproteins, cytokines, chemokines, growth factors, and metabolic hormones in the lungs, heart, cortex, and plasma. Statistical modeling and logistic regression were used to identify biomarkers associated with lethality and survival. We found that lung injury was the primary cause of potential lethality, particularly via early phosphoprotein signaling disruptions. However, survival correlated with early systemic coordination of inflammatory and metabolic signals across organs. Perfusion and acidosis imaging were strongly associated with chemokine and hormone responses. Key survival-associated plasma biomarkers included decreased insulin, increased ghrelin, and decreased eotaxin. While potential lethality from Cl2 exposure is locally driven by pulmonary injury, survival depends on systemic, multi-organ responses that occur rapidly post-exposure. Within this model, our findings identify a potential therapeutic window to enhance survival and suggest candidate biomarkers that may be explored translationally for both triage and treatment of chlorine-related incidents.
chlorine gas↗
A Statistician’s Overview of Physics-Informed Neural Networks for Spatio-Temporal Data
The recent success of deep neural network models with physical constraints (so-called, Physics-Informed Neural Networks, PINNs) has led to renewed interest in the incorporation of mechanistic information in predictive models. Statisticians and others have long been interested in this problem, which has led to several practical and innovative solutions dating back decades. In this overview, we focus on the problem of data-driven prediction and inference of dynamic spatio-temporal processes that include mechanistic information, such as would be available from partial differential equations, with a strong focus on the quantification of uncertainty associated with data, process, and parameters. Here, we give a brief review of several paradigms and focus our attention on Bayesian implementations given they naturally accommodate uncertainty quantification. We then show that it is straight-forward to include the Bayesian PINN (B-PINN) within the Bayesian hierarchical model (BHM) framework that has long been considered for modeling dynamic spatio-temporal processes. Such a BHM-PINN is illustrated via a simulation study in which a latent nonlinear Burgers’ equation PDE governs the dynamics of Poisson distributed spatio-temporal data. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.
Bayesian↗
Large Eddy Simulation (LES) of Particle-Laden Temporal Mixing Layers
High-fidelity models of plume-regolith interaction are difficult to develop because of the widely disparate flow conditions that exist in this process. The gas in the core of a rocket plume can often be modeled as a time-dependent, high-temperature, turbulent, reacting continuum flow. However, due to the vacuum conditions on the lunar surface, the mean molecular path in the outer parts of the plume is too long for the continuum assumption to remain valid. Molecular methods are better suited to model this region of the flow. Finally, granular and multiphase flow models must be employed to describe the dust and debris that are displaced from the surface, as well as how a crater is formed in the regolith. At present, standard commercial CFD (computational fluid dynamics) software is not capable of coupling each of these flow regimes to provide an accurate representation of this flow process, necessitating the development of custom software. This software solves the fluid-flow-governing equations in an Eulerian framework, coupled with the particle transport equations that are solved in a Lagrangian framework. It uses a fourth-order explicit Runge-Kutta scheme for temporal integration, an eighth-order central finite differencing scheme for spatial discretization. The non-linear terms in the governing equations are recast in cubic skew symmetric form to reduce aliasing error. The second derivative viscous terms are computed using eighth-order narrow stencils that provide better diffusion for the highest resolved wave numbers. A fourth-order Lagrange interpolation procedure is used to obtain gas-phase variable values at the particle locations.
Bellan, Josette↗
The Flow of Plasma in the Solar-Terrestrial Environment
The overall goal of our NASA theory research is to trace the flow of mass, momentum, and energy through the magnetosphere-ionosphere-atmosphere system taking into account the coupling, time delays, and feedback mechanisms that are characteristic of the system. Our approach is to model the magnetosphere-ionosphere-atmosphere (M-I-A) system in a self-consistent quantitative manner using unique global models that allow us to study the coupling between the different regions on a range of spatial and temporal scales. The uniqueness of our global models stems from their high spatial and temporal resolutions, the physical processes included, and the numerical techniques employed. Currently, we have time-dependent global models of the ionosphere, thermosphere, polar wind, plasmasphere, and electrodynamics. It is now becoming clear that a significant fraction of the flow of mass, momentum, and energy in the M-I-A system occurs on relatively small spatial scales. Therefore, an important aspect of our NASA Theory program concerns the effect that mesoscale (100-l000 km) density structures have on the macroscopic flows in the ionosphere, thermosphere, and polar wind. The structures can be created either by structured magnetospheric inputs (i.e., structured electric field, precipitation, or Birkeland current patterns) or by time variations of these inputs due to geomagnetic storms and substorms. Some of the mesoscale structures of interest include sun-aligned polar cap arcs, propagating plasma patches, traveling convection vortices, subauroral ion drift (SAID) channels, gravity waves, and the polar hole.
Schunk, Robert W.↗
Spatial and Temporal Variability of Vertical Velocity under Shallow Cumulus
Vertical velocity distribution below cloud is one of the key determinants of cloud life cycle, but observations of this variable are extremely sparse in space. Doppler lidar retrievals and large-eddy simulations at the U.S. Department of Energy’s Atmospheric Radiation Measurement User Facility Southern Great Plains site are used to determine whether vertical velocity statistics from temporally dense profiles at a single location can be substituted for spatial vertical velocity statistics. We show that even a small number (five) of widely distributed [ O (1°) latitude/longitude spacing] lidars is sufficient sampling to reconstruct domainwide spatial vertical velocity variance, but not higher moments of the vertical velocity distribution. Spatial and temporal vertical velocity variances in the Doppler lidar observations are nearly interchangeable as long as the spatial variance is temporally averaged and the temporal variance is averaged across lidars. This is true even though the dominant spatial scales of vertical velocity variability are ≲ 3 km, more than an order of magnitude smaller than the spacing between the lidars. Further, in the limit where the temporal variance does not vary across a spatial domain (e.g., if the meteorological and surface forcing of the atmospheric turbulence is homogeneous across the domain) and the domain-mean vertical velocity is zero, the commonly available retrieval of temporal vertical velocity variance at one site is equivalent to the spatial variance over the domain. We use an updraft parcel model to show that substituting temporal for spatial vertical velocity statistics will have a relatively minor effect on cloud droplet number concentrations.
54 ENVIRONMENTAL SCIENCES↗
Temporal Coupling of Subsurface and Surface Soil CO 2 Fluxes: Insights From a Nonsteady State Model and Cross-Wavelet Coherence Analysis
Inferences about subsurface CO 2 fluxes often rely on surface soil respiration (R soil ) estimates because directly measuring subsurface microbial and root respiration (collectively, CO 2 production, S Total ), is difficult. To evaluate how well R soil serves as a proxy for S Total , we applied the nonsteady state DEconvolution of Temporally varying Ecosystem Carbon componenTs model (0.01-m vertical resolution), using 6-hourly data from a Wyoming grassland, in six simulations that cross three soil types (clay, sandy loam, and sandy) with two depth distributions of subsurface biota. We used cross-wavelet coherence analysis to examine temporal coherence (localized linear correlation) and offsets (lags) between S Total and R soil and fluxes and drivers (e.g., soil temperature and moisture). Cross-wavelet coherence revealed higher coherence between fluxes and drivers than linear regressions between concurrent variables. Soil texture and moisture exerted the strongest controls over coherence between CO 2 fluxes. Coherence between CO 2 fluxes in all soil types was strong at short (~1 day) and long periods (>8 days), but soil type controlled lags, and rainfall events decoupled the fluxes at periods of 1–8 days for several days in sandy soil, up to 1 week in sandy loam, and for a month or more in clay soil. Concentrating root and microbial biomass nearer the surface decreased lags in all soil types and increased coherence up to 10% in clay soil. The assumption of high temporal coherence between R soil and S Total is likely valid in dry, sandy soil, but may lead to underestimates of short-term STotal in semiarid grasslands with fine-grained and/or wet soil.
54 ENVIRONMENTAL SCIENCES↗
Simulation of Oxygen Disintegration and Mixing With Hydrogen or Helium at Supercritical Pressure
The simulation of high-pressure turbulent flows, where the pressure, p, is larger than the critical value, p(sub c), for the species under consideration, is relevant to a wide array of propulsion systems, e.g. gas turbine, diesel, and liquid rocket engines. Most turbulence models, however, have been developed for atmospheric-p turbulent flows. The difference between atmospheric-p and supercritical-p turbulence is that, in the former situation, the coupling between dynamics and thermodynamics is moderate to negligible, but for the latter it is very significant, and can dominate the flow characteristics. The reason for this stems from the mathematical form of the equation of state (EOS), which is the perfect-gas EOS in the former case, and the real-gas EOS in the latter case. For flows at supercritical pressure, p, the large eddy simulation (LES) equations consist of the differential conservation equations coupled with a real-gas EOS. The equations use transport properties that depend on the thermodynamic variables. Compared to previous LES models, the differential equations contain not only the subgrid scale (SGS) fluxes, but also new SGS terms, each denoted as a correction. These additional terms, typically assumed null for atmospheric pressure flows, stem from filtering the differential governing equations, and represent differences between a filtered term and the same term computed as a function of the filtered flow field. In particular, the energy equation contains a heat-flux correction (q-correction) that is the difference between the filtered divergence of the heat flux and the divergence of the heat flux computed as a function of the filtered flow field. In a previous study, there was only partial success in modeling the q-correction term, but in this innovation, success has been achieved by using a different modeling approach. This analysis, based on a temporal mixing layer Direct Numerical Simulation database, shows that the focus in modeling the q-correction should be on reconstructing the primitive variable gradients rather than their coefficients, and proposes the approximate deconvolution model (ADM) as an effective means of flow field reconstruction for LES heat flux calculation. Further, results for a study conducted for temporal mixing layers initially containing oxygen in the lower stream, and hydrogen or helium in the upper stream, show that, for any LES, including SGS-flux models (constant-coefficient Gradient or Scale-Similarity models, dynamic-coefficient Smagorinsky/Yoshizawa or mixed Smagorinsky/Yoshizawa/Gradient models), the inclusion of the q-correction in the LES leads to the theoretical maximum reduction of the SGS heat-flux difference. The remaining error in modeling this new subgrid term is thus irreducible.
Bellan, Josette↗
A study of the sources and sinks of methane and methyl chloroform using a global three-dimensional Lagrangian tropospheric tracer transport model
Sources and sinks of methane and methyl chloroform are investigated using a global three-dimensional Lagrangian tropospheric tracer transport model with parameterized hydroxyl and temperature fields. Using the hydroxyl radical field calibrated to the methyl chloroform observations, the globally averaged release of methane and its spatial and temporal distribution were investigated. Two source function models of the spatial and temporal distribution of the flux of methane to the atmosphere were developed. The first model was based on the assumption that methane is emitted as a proportion of net primary productivity (NPP). The second model identified source regions for methane from rice paddies, wetlands, enteric fermentation, termites, and biomass burning based on high-resolution land use data. The most significant difference between the two models were predictions of methane fluxes over China and South East Asia, the location of most of the world's rice paddies, indicating that either the assumption that a uniform fraction of NPP is converted to methane is not valid for rice paddies, or that NPP is underestimated for rice paddies, or that present methane emission estimates from rice paddies are too high.
Taylor, John A.↗
Availability and Maintenance Modeling for GIS Equipment Served in High-Speed Railway Under Incomplete Maintenance
Gas-insulated substation (GIS) equipment served in the traction power-supply system (TPSS) of the high-speed railway (HSR) suffers from extremely severe traction load conditions during its lifetime. In this paper, three major issues related to the actual field maintenance operations of GIS equipment in TPSS are addressed: 1) s-dependent degradation and shock process; 2) both spatial and temporal failure thresholds of shocks; and 3) incomplete maintenance (i.e., nonignorable maintenance time). To model the deterioration and failure process of GIS equipment, the hard failure model and the soft failure model are proposed. The characteristic function is utilized to bridge the s-dependent degradation and shock process in the soft failure model, while the extreme shock model (with spatial threshold) and δ-shock model (with temporal threshold) are introduced in the hard failure model. Furthermore, the index of availability, which combines both reliability and maintainability, is derived under the incomplete maintenance consideration. Based on the balance of availability and maintenance cost, the maintenance strategy with periodic inspections for GIS equipment in the long-run time span is developed. In conclusion, optimizations of three decision parameters (i.e., inspection period, extreme shock threshold, and δ-shock threshold) are implemented to achieve the best performance (with high availability and low maintenance cost) of the maintenance strategy.
33 ADVANCED PROPULSION SYSTEMS↗
Combined modeling of acceleration, transport, and hydrodynamic response in solar flares. II. Inclusion of radiative transfer with RADYN
Solar flares involve complex processes that are coupled and span a wide range of temporal, spatial, and energy scales. Modeling such processes self-consistently has been a challenge in the past. Here we present results from simulations that couple particle kinetics with hydrodynamics (HD) of the atmospheric plasma. We combine the Stanford unified Fokker–Planck code that models particle acceleration and transport with the RADYN HD code that models the atmospheric response to collisional heating by accelerated electrons through detailed radiative transfer calculations. We perform simulations using two different electron spectra, one an ad hoc power law and the other predicted by the model of stochastic acceleration by turbulence or plasma waves. Surprisingly, the later model, even with energy flux ≪10{sup 10} erg s{sup −1} cm{sup −2}, can cause “explosive” chromospheric evaporation and drive stronger up- and downflows (and HD shocks). This is partly because our acceleration model, like many others, produces a spectrum consisting of a quasi-thermal component plus a power-law tail. We synthesize emission-line profiles covering different heights in the lower atmosphere, including Hα 6563 Å, He ii 304 Å, Ca ii K 3934 Å, and Si iv 1393 Å. One interesting result is the unusual high temperature (up to a few times 10{sup 5} K) of the formation site of He ii 304 Å, which is expected owing to photoionization-recombination under flare conditions, compared to those in the quiet Sun dominated by collisional excitation. When compared with observations, our results can constrain the properties of nonthermal electrons and thus the poorly understood particle acceleration mechanism.
79 ASTRONOMY AND ASTROPHYSICS↗