Attenuation Function Research Articles

A high-resolution comprehensive water quality model based on GPU acceleration techniques

The study of the temporal and spatial evolution of pollutants in modern water bodies and river water quality management largely depend on river water quality models. These models are usually constructed based on detailed hydrodynamic models but cannot satisfy the high precision and efficiency requirement of model simulations in high-resolution terrain. To solve this problem, we developed a high-resolution comprehensive water quality model based on the graphics processing unit (GPU) acceleration techniques in which hydrodynamics and accompanying contaminants were perfectly coupled. The performance and functionality of the model were improved by using the Compute Unified Device Architecture (CUDA) parallel computing architecture and robust model algorithms. A simulation function of the transport attenuation and interaction among multicomponent pollutants was stablished by solving mass conservation, momentum and chemical concentration equations of the flow process. The simulation results of the pure pollutant reaction process and the transport and reaction process were validated against an analytical solution and the results of a two-dimensional steady water quality model by using the Nash-Sutcliffe efficiency (NSE) coefficient. The coefficients were 0.996 and 0.984, respectively. The water quality of the Xidagou River in Yinchuan was evaluated and analyzed by using the validated high-resolution comprehensive water quality model, and the numerical results of two-dimensional pollutant transport were explored. On the adopted RTX3070d computer, only 0.12 h were needed to simulate the hydrodynamic and water quality evolution process involving 350.000 cells with 5-h model settings. The model achieved a high operation speed and high calculation accuracy and could effectively simulate, predict and evaluate various complex water environment problems. This study provides a reliable tool for further research on the water environment and water ecology and the treatment of black and odorous water bodies.

Analisis Kerentanan Bahaya Gempa Bumi Tektonik Merusak Berdasarkan Fungsi Atenuasi Zhao Di Nusa Tenggara Timur

<p class="AbstractText">The East Nusa Tenggara (NTT) region which is located between 2 earthquakes, namely the tectonic plate subduction zone in the south and the Back Arc Thrust zone in the north, is very interesting to study considering the very active tectonic earthquakes that are significantly destructive in this region which have earthquake characteristics shallow and large magnitude. A study has been carried out that aims to determine the vulnerability of the tectonic earthquake to significant damage when seismic waves pass through these islands. The vulnerability information generated can be useful as a reference for disaster mitigation and factors that need to be considered before carrying out development in the NTT region. The input data studied are shallow earthquake data from 1997-2018 at a depth of 60 km and a magnitude M≥5 SR at coordinates 8<sup>o</sup> 30’-13<sup>o</sup> 10’ South Latitude and 118<sup>o</sup> 30’-125<sup>o</sup> 30’ East Longitude. The number of earthquake events is 198 data. The attenuation function used refers to the attenuation function Zhao, et. al 2006. The results of the study show that. the vulnerability of the tectonic earthquake to significant damage in the East Nusa Tenggara region clustered on the MMI V-VIII intensity scale. Most of these islands are clustered on the MMI VII-VIII intensity scale and only a small part is clustered on the V-VI MMI intensity scale. The NTT region which has an intensity scale of VII-VIII MMI has a high vulnerability to destructive earthquakes, so it is necessary to disseminate disaster mitigation from an early age to the public about the threat of earthquakes and it is recommended that this information be used as a reference in developing the area.</p>

RNA polymerase II transcription attenuation at the yeast DNA repair gene DEF1 is biologically significant and dependent on the Hrp1 RNA-recognition motif.

Premature transcription termination (i.e. attenuation) is a potent gene regulatory mechanism that represses mRNA synthesis. Attenuation of RNA polymerase II is more prevalent than once appreciated, targeting 10-15% of mRNA genes in yeast through higher eukaryotes, but its significance and mechanism remain obscure. In the yeast Saccharomyces cerevisiae, polymerase II attenuation was initially shown to rely on Nrd1-Nab3-Sen1 termination, but more recently our laboratory characterized a hybrid termination pathway involving Hrp1, an RNA-binding protein in the 3'-end cleavage factor. One of the hybrid attenuation gene targets is DEF1, which encodes a repair protein that promotes degradation of polymerase II stalled at DNA lesions. In this study, we characterized the chromosomal DEF1 attenuator and the functional role of Hrp1. DEF1 attenuator mutants overexpressed Def1 mRNA and protein, exacerbated polymerase II degradation, and hindered cell growth, supporting a biologically significant DEF1 attenuator function. Using an auxin-induced Hrp1 depletion system, we identified new Hrp1-dependent attenuators in MNR2, SNG1, and RAD3 genes. An hrp1-5 mutant (L205S) known to impair binding to cleavage factor protein Rna14 also disrupted attenuation, but surprisingly no widespread defect was observed for an hrp1-1 mutant (K160E) located in the RNA-recognition motif. We designed a new RNA recognition motif mutant (hrp1-F162W) that altered a highly conserved residue and was lethal in single copy. In a heterozygous strain, hrp1-F162W exhibited dominant-negative readthrough defects at several gene attenuators. Overall, our results expand the hybrid RNA polymerase II termination pathway, confirming that Hrp1-dependent attenuation controls multiple yeast genes and may function through binding cleavage factor proteins and/or RNA.

Experimental study on temperature characteristics in a subway train carriage with lateral openings in a longitudinally ventilated tunnel

Under the rapid development of subway systems, a fundamental understanding of subway fire safety is critically needed to benefit its designs and assessment. Previous studies on train carriage fires are limited to single-carriage fires under natural ventilation. However, it is still unclear how longitudinal ventilation affects the smoke movement in the train carriage with lateral openings. Therefore, a series of 1:3 reduced-scale experimental tests were conducted to investigate the smoke temperature characteristics in a train carriage located in a longitudinally ventilated tunnel. Under various fire sizes and ventilation rates, the ceiling gas temperature and smoke layer height were measured. Compared to the traditional fire scenario with end openings, the maximum ceiling gas temperature and the downstream temperature distribution decay factor are relatively smaller because of the lateral flame tilt and less heat loss during smoke propagation. The effects of ventilation velocity on the maximum ceiling gas temperature are significantly weakened under the blockage effect of the train carriage. The downstream temperature distribution followed a single exponential attenuation function, independent of the fire size and ventilation rate. However, the upstream temperature distribution is much more complex under the restriction of the end wall. A four-segment model was proposed to predict the upstream temperature distribution based on the relationship between the back-layering length and half the carriage length. The fire size and ventilation rate also show limited influence on the smoke stratification, with a layer height of 0.316 m in the stable region. The research outcomes offer adeeper understanding of the smoke propagation of the subway train carriage fire and a theoretical guide on the designs of future tunnels.

Photon count rates estimated from 1980 clinical CT scans.

All photon counting detectors have a characteristic count rate over which their performance degrades. Degradation in the clinical setting takes the form of increased noise, reduced material quantification accuracy, and image artifacts. Count rate is a function of patient attenuation, beam filtration, scanner geometry, and X-ray technique. To guide protocol and technology development in the photon counting space, knowledge of clinical count rates spanning the complete range of clinical indications and patient sizes is needed. In this paper, we use clinical data to characterize the range of computed tomography (CT) count rates. We retrospectively gathered 1980 patient exams spanning the entire body (head/neck/chest/abdomen/extremity) and sampled 36951 axial image slices. We assigned the tissue labels air/lung/fat/soft tissue/bone to each voxel for each slice using CT number thresholds. We then modeled four different bowtie filters, 70/80/100/120/140kV spectra, and a range of mA values. We forward-projected each slice to obtain detector-incident count rates, using the geometry of a GE Revolution Apex scanner. Our analysis divided the detector into thirds: the central one-third, one-third of the detector split into two equal regions adjacent to the central third, and the final one-third divided equally between the outer detector edges. We report the 99th percentile of counts to mimic the upper limits of count rates making passing through a patient as a function of patient water equivalent diameter. We also report the percentage of patient scans, by body region, over different count rate thresholds for all combinations of bowtie and beam energy. For routine exam types, we recorded count rates of approximately 3.5×108 counts/mm2 /s in the torso, extremities, and brain. For neck scans, we observed count rates near 6×108 counts/mm2 /s. Our simulations of 1000mA, appropriately mimicking the mA needs for fast pediatric, fast thoracic, and cardiac scanning, resulted in count rates of over 10×108 counts/mm2 /s for the torso, extremities, and brain. At 1000mA, for the neck region, we observed count rates close to 2×109 counts/mm2 /s. Importantly, we saw only a small change in maximum count rate needs over patient size, which we attribute to patient mis-positioning with respect to the bowtie filters. As expected, combinations of kV and bowtie filter with higher beam energies and wider/less attenuating bowtie fluence profiles lead to higher count rates relative to lower energies. The 99th-50th percentile count rate changed the most for the torso region, with a maximum variation of 3.9×108 to 1.2×107 counts/mm2 /s. The head/neck/extremity regions had less than a 50% change in count rate from the 99th to 50th percentiles. Our results are the first to use a large patient cohort spanning all body regions to characterize count rates in CT. Our results should be useful in helping researchers understand count rates as a function of body region and mA for various combinations of bowtie filter designs and beam energies. Our results indicate clinical rates >1×109 counts/mm2 /s, but they do not predict the image quality impact of using a detector with lower characteristic count rates.

Enhanced Observer Control of a Cubic Stewart Platform With Image Sensor Measurement

A cubic Stewart platform with an image sensor meausring is proposed for a line-of-sight (LOS) pointing and stabilization. The charge couple device (CCD) as a image sensor mounted on the Stewart platform can provide the LOS error only in the azimuth and elevation directions, so a decoupled control strategy through the transformation of the Jacobian matrix is introduced to transform a Multiple-Input Multiple-Output (MIMO) control into Single-Input Single-Output (SISO) control. Due to the low bandwidth of the Stewart platform and the finite sampling rate of the CCD, the closed-loop performance is greatly restricted. An optimal observer control based on Youla parameterization is proposed to improve the tracking performance in the CCD-based Stewart platform control system. This improved controller relies on the LOS error combined with the controller output to produce high gain, plugging into the tradditional closed-loop structure, which results in minimizing the error attenuation function by designing an appropriate Q-filter. Both the simulations and experiments are carried out to prove the effectiveness of the proposed observer compared with the classical feedback controller.

Multi-Modal Non-Isotropic Light Source Modelling for Reflectance Estimation in Hyperspectral Imaging

Estimating reflectance is key when working with hyperspectral cameras. The modelling of light sources can aid reflectance estimation, however, it is commonly overlooked. The key contribution of this letter is a physics-based, data-driven model formed by a Gaussian Process (GP) with a unique mean function capable of modelling a light source with an asymmetric radiant intensity distribution (RID) and a configurable attenuation function. This is referred to as the light-source-mean model. Moreover, we argue that by utilising multi-modal sensing information, we can achieve improved reflectance estimation using the proposed light source model with shape information obtained by depth cameras. An existing reflectance estimation method, that solves the dichromatic reflectance model (DRM) via quadratic programming optimisation, is augmented with terms that allow input of shape information. Experiments in simulation show that the light-source-mean GP model had less error when compared to a parametric model. The improved reflectance estimation outperforms existing methods in simulation by reducing the error by 96.8% on average when compared to existing works. We further validate the improved reflectance estimation method through a multi-modal classification application.

Prediction of the impact of benzo[a]pyrene on shallow groundwater during natural infiltration of reclaimed water-receiving rivers: A case study of Liangshui, China

The quality of groundwater along rivers is greatly affected by long-term infiltration from surface water, especially reclaimed water-receiving rivers. To predict the degree of influence of contaminated river water on groundwater quality, the spatiotemporal distribution and migration evolution prediction of benzo[a]pyrene (B(a)P) was monitored and simulated by Hydrus-coupled Groundwater Modeling Systems (GMS) model in terms of reclaimed water-receiving Liangshui River. The prediction results indicated the goodness-of-fit of this coupled model, according to the model efficiency (E: 0.78–0.93), the mean absolute error (MAE: 0.01–0.32 m) and the root-mean-square error (RMSE: 0.06–0.35 m). The vertical infiltration rate of B(a)P in the vadose zone was 0.102 m-1, which was only 0.73% that of water. B(a)P penetrated the 16 m depth vadose zone for 63 years owing to the attenuation function of adsorption and biodegradation, with contribution ratios of 78.4% and 19.3%, respectively. However, once B(a)P intersects with groundwater, the migration of B(a)P is dominated by horizontal migration due to downward movement along the groundwater flow direction. The migration rate of B(a)P in groundwater was 6.65 m/y in the horizontal direction, which was 2.42 and 16.22 times higher than the dispersion rate in the longitudinal and vertical directions, respectively. The spatiotemporal distribution indicated that the B(a)P concentration decreased with the crow-fly distance from river with attenuation rate constants of 1.19 × 10−4, 3.05 × 10−4, and 3.67 × 10−3 m−1 over horizontal, longitudinal, and vertical direction, respectively, which were negatively correlated with migration rate. However, the B(a)P content increased over the extension of infiltration time with an accumulation rate of 7.3 × 10−2 d−1. The migration and accumulation of B(a)P induced potential health risks to groundwater-based drinking water safety, which resulted in the groundwater safety utilization range decreasing from 450 m, 283 m, and 20.1 m–583 m, 338 m, and 28.2 m far from the river over the horizontal, longitudinal, and vertical directions, respectively, 20 years later. This study provides a numerical modeling solution for the viable spatiotemporal evolution of B(a)P in groundwater and an effective decision-making tool for the safe utilization of groundwater as drinking water.

A Study on the Walkability of Zijingang East Campus of Zhejiang University: Based on Network Distance Walk Score

Due to the generally poor planning of new university campuses in China today, students living in these places normally do not walk as often as they should, and with studies showing the significant impact of walking on physical health and productivity, there is an urgent need to improve university walkability. Walkability is a valuable tool for assessing the level of support for walking in a region, and there are few studies on walkability on university campuses. In this paper, we used a network distance-based Walk Score to evaluate and analyze the walkability of the Zijingang east campus, Zhejiang University. We improved some of the parameters of the Walk Score based on the actual travel characteristics of the students, formed a new calculation method based on a geographic information system (GIS) applicable to the university campus, and evaluated the applicability of this method. The results show that the new method can reflect the actual walking experience and provide a helpful design reference for designers. We also found that optimizing the distribution of facilities is very effective using the feature of the attenuation function.

A seismic-resilient multi-level framework for distribution network reinforcement planning considering renewable-based multi-microgrids

In this paper, a new resilient framework is presented for distribution network reinforcement planning (DNRP) with the consideration of renewable-based multi-microgrids (RMGs) to mitigate seismic risks. For this aim, the proposed framework is formulated as a non-convex mixed-integer nonlinear four-level optimization problem. The first level outlines a short-term corrective measures problem to remedy seismic risks using feeder reconfiguration and distributed energy resources rescheduling. The second level represents an earthquake-related catastrophic failures problem in which peak ground acceleration and distribution component vulnerability are modeled through attenuation functions and fragility curves, respectively. The third and fourth levels, however, describe coordination of a decentralized double-layer multistage microgrid reinforcement planning (MGRP) problem and a centralized cost-effective multistage DNRP problem to characterize seismic-resilient optimal reinforcement plans. Due to its desirable handling of multi-level optimization problems having a non-convex mixed-integer nonlinear nature, the multi-computational-step, multi-dimensional, multiple-homogeneous improved melody search algorithm, referred to as a symphony orchestra search algorithm (SOSA), is used to solve the proposed framework. The performance of the newly developed framework is numerically analyzed through implementing it to the standard 33-, 54-, 119- and 136-node distribution test networks. The numerical results well corroborate the sufficiency and profitableness of the proposed framework in achieving low vulnerability and high resilience to seismic risks.

Investigating Accessibility of Hospitals in Cold Regions: A Case Study of Harbin in China.

The objective of this study is to explore healthcare resource accessibility in Harbin, a typical city in a cold region in China. Recently, investments in the construction of medical resources have been increasing annually in China, and consequently, the allocation of these resources has improved. Snow and ice on surfaces in China's cold regions have certain effects on the traffic capacity of urban roads, leading to a great difference in the accessibility of medical resources in winter and summer. The basic spatial data, including spatial road data, medical facility data, and population distribution data, are analyzed using geographic information system. Then, a spatial barrier model is used to measure healthcare accessibility based on geographic and population weighting; we explore the accessibility of hospitals under the influence of weather by defining a novel distance attenuation function. Finally, the accessibility of medical institutions in the study area is explored by analyzing data about the related separation factors. It was found that the spatial distribution of medical resources was not equal, and the dominant resources were concentrated in the city center. Some regions are always in an advantageous position regardless of traffic conditions. In contrast, in areas far from the city center, the accessibility of medical resources significantly decreases in winter. These results will help optimize the layout of medical institutions and improve medical equality and propose strategies for the optimization of the accessibility of urban medical institutions in cold regions of China.

Ultrasonic propagation in high‐concentration TiO2 slurries for photocatalytic reactors

AbstractThis work reports measurements of the speed of sound and ultrasonic attenuation in high concentration (up to 3 g · L−1) aqueous TiO2 slurries close to neutral pH. Measurements were made at frequencies of 1675, 5545, and 9340 kHz using ultrasonic transducers submerged in the slurry. The experimental setup may be applied to slurries in practical reactors while in operation. Within an experimental uncertainty of ±0.5 m · s−1, the speed of sound in the slurry was the same as in pure water, at all the studied catalyst concentrations and frequencies. The excess ultrasonic attenuation with respect to pure water increases linearly with the catalyst concentration and is inversely proportional to the square of the excitation frequency. This indicates that viscous and thermal acoustic losses predominate over scattering. For TiO2 concentrations in the range of 0.15–3 g · L−1, the catalyst concentration in the slurry may be estimated as a linear function of the excess ultrasonic attenuation, with an uncertainty of 0.1 g · L−1.

The Concept of Using the Decision-Robustness Function in Integrated Navigation Systems.

The diversity and non-uniformity of the positioning systems available in maritime navigation systems often impede the watchkeeping officer in the selection of the appropriate positioning system, in particular, in restricted basins. Thus, it is necessary to introduce a mathematical apparatus to suggest, in an automated manner, which of the available systems should be used at the given moment of a sea trip. Proper selection of the positioning system is particularly important in integrated navigation systems, in which the excess of navigation information may impede the final determinations. In this article, the authors propose the use of the decision-robustness function to assist in the process of selecting the appropriate positioning system and reduce the impact of navigation observations encumbered with large errors in self-positioning accuracy. The authors present a mathematical apparatus describing the decision function (a priori object), with the determination of decision-assistance criteria, and the robustness function (a posteriori object), with different types of attenuation function. In addition, the authors present a computer application integrating both objects in the decision-robustness function. The study was concluded by a test showing the practical application of the decision-robustness function proposed in the title.

Analytical approach for kinematic FCRW–soil interaction in multi–layered soil under earthquake loads

A closed form solution for FCRW (flexible cantilever retaining wall)–soil interaction under seismic condition is proposed for a layered soil profile. The displacement function of the FCRW and the attenuation function of the kinematic FCRW–soil interaction are obtained in the coupled form based on the Hamilton's principle. Then an iterative procedure is applied to solve the coupled functions. There are three main contributions of the proposed model: (1) the kinematic FCRW response in layered soil system is analyzed based on an analytical method; (2) the soil continuity effect is taken into account; (3) the kinematic FCRW–soil interaction in layered soil is quantitatively analyzed. The results highlight that the soil stiffness discontinuity significantly influences the contribution of the different physical mechanisms (e.g., FCRW rigidity, Winkler spring and soil continuity) in kinematic FCRW–soil interaction. The results also show that the soil stiffness discontinuity may exponentially amplify the seismic earth pressure and kinematic FCRW response.

Microbuckling behavior of unidirectional fiber-reinforced shape memory polymer composite undergoing compressive deformation

The microbuckling mechanics of unidirectional fiber-reinforced shape memory polymer composite (SMPC) with low fiber volume fraction were investigated, and the mechanical models were formulated considering the attenuation of shear strain in the resin matrix near the buckled fibers. We deduced the analytical expression of the attenuation function and the key parameters during the microbuckling process of SMPC, including the critical buckling wavelength and strain. The values determined by finite element analysis verified the accuracy of the above theoretical predictions. The nonlinear stress–strain relationship during the post-buckling process was also investigated. Additionally, the classical elastic–viscoelastic correspondence principle was established to determine the dynamic buckling behaviors of SMPC at different temperatures. The viscoelastic parameters of shape memory polymer (SMP) were obtained from the isothermal stress relaxation experiments, and then the variation of buckling wavelength with time at different temperatures was evaluated.

Analysis of Soil Acceleration in The Mentawai Region with The Method Probabilistic Seismic Hazard Analysis (PSHA)

The Mentawai Islands are one of the areas that are active in seismicity. An earthquake measuring 7.2 on the Richter scale on October 25, 2010 resulted in many casualties and material losses. Many buildings collapsed and facilities were damaged so that space managers needed a seismic hazard map to be able to organize the space by considering the disaster aspect. This prompted researchers to conduct research aimed at making seismic hazard maps and knowing the level of earthquake hazard in the Mentawai region. Seismic hazard maps are useful in planning earthquake-resistant buildings and can describe the effects of earthquakes at a location which will help in anticipating community preparedness and earthquake disaster mitigation efforts. Seismic hazard data processing uses the Probabilistic Seismic Hazard Analysis (PSHA) method. PSHA is based on earthquake parameters that produce the largest ground motion. The magnitude of the intensity at a location due to an earthquakein the earthquake source area with a magnitude of M and a distance of R, the attenuation function can be used. The attenuation functions in this study are Joyner-Boore (1997) and Young et al (1997). This type of research is descriptive, namely by collecting NEIC/USGS earthquake catalog data for the period 1950 - 2021 with M 5 SR.The results of this study indicate that the area of ywhich has a high level of seismic hazard is found in the Siberut area with a maximum PGA range of 1.17 g - 3.70 g. The area with a low seismic hazard level is the Pagai area with a PGA range of 0.80 g - 2.86 g. This result represents a 10% chance of being exceeded in 50 years.

On the face-threat attenuating functions of Korean com: implications for internal and external dialogic processing in interaction

Abstract Pragmatic markers are linguistic resources, many of them highly ubiquitous, that provide speakers with a means to display their stance toward a given proposition and, at the same time, toward their fellow interlocutors and others. Using naturally-occurring spoken data from the Sejong Spoken Corpus, we examine the role of Korean pragmatic marker com as an interactional resource for stance management in conversation. We integrate a ‘stance triangle’ framework and a dialogicality model that involves both ‘internal’ and ‘external’ dialogic processes, and analyze how Korean com is recruited as a face-threat mitigator to attenuate the assertive force of a speaker’s utterance in a variety of conversational contexts. Our findings indicate that the use of com is frequently motivated by sociocultural values, reframed as politeness norms, which prompt speakers to modulate their position in ways that mitigate face-loss for both themselves and others. We thus propose an expanded version of the ‘stance triangle’ for situations involving mitigation acts whereby, in potentially dis-aligning contexts, the speaker’s external positioning toward the stance object often does not directly nor fully reflect their internal evaluation, indicating a frequent desire among fellow interlocutors to preserve solidarity with each other.

Prediction Method of Water Absorption of Soft Rock Considering the Influence of Composition, Porosity, and Solute Quantitatively

The study of water absorption of soft rock is of great significance to the prevention engineering disasters. However, the research on the prediction method of water absorption of soft rock considering the influence of composition, porosity, and solute is insufficient. Aiming to solve the above problem, water absorption tests are carried out by synthesizing soft rocks and water solutions. Then, the prediction model of water absorption of soft rock is established through quantitative analysis of water absorption data and compared with the water absorption characteristics of natural rock to verify the reliability of the model. The results show that the changes in water content and water absorption velocity of soft rock with time obey the second-order exponential attenuation function and the linear function (double logarithmic coordinates axis), respectively. The types of cations and anions and the type and content of clay minerals have the greatest influence on the process of rock water absorption. In addition, the water absorption prediction model could better predict the water absorption process of natural rock. The research results solve the problem of insufficient research on the soft rock water absorption prediction method considering the influence of composition, porosity and solute.

A Prony-based approach for accelerating the lightning electromagnetic fields computation above a perfectly conducting ground

Lightning strikes can seriously affect the reliability and availability of electrical infrastructures. The computation of lightning-electromagnetic fields represents one of the most crucial steps in the evaluation of the induced effects; thus, having at disposal accurate and efficient dedicated tools is essential. This paper proposes a new approach for the lightning-electromagnetic fields computation above a perfectly conducting ground. The proposed approach does not involve any assumption either on the channel-base current waveshape or on the attenuation function of the current along the channel. Integrals are expanded in series of exponential functions (Prony series) which makes them analytically solvable. The proposed approach results in a speed up of the computational time by a factor of 10 to some hundreds with respect to classical numerical approaches. The proposed method is validated against the classical formulas obtained through numerical integration for different channel-base current waveforms, attenuation functions and observation points.

Channel charge density behind commonly used return stroke engineering model

The evolution characteristics behind the commonly used return stroke engineering model have not been fully understood, which limits the accurate estimation on the lightning damage effect. Therefore, the line charge densities behind the TL, MTLL MTLE, BG, TCS and DU models are discussed under three cases: (a) constant velocity with traditional attenuation function, (b) exponentially decreasing velocity with traditional attenuation function, and (c) exponentially decreasing velocity with improved attenuation function considering time factor. As height increases, the charge density behind the TL, MTLL and MTLE models in case (c) is between that in case (a) and (b). However, owing to the reduction of the inputting charge from the channel base and the gradually prominent deposition effect of the residual charge, the total charge densities in the three cases trend to be consistent with each other in the end. Additionally, the results suggest that the near-region radiated fields yielded by the traditional return stroke model (case (a)) may be smaller than the actual observation. For the BG, TCS and DU models, the connotative charge density is mainly the deposited charge density component. Although the charge density decreases overall with height, the waveform exhibits a “hump” at the height of about 2 km∼3 km. The presented results may be of assistance in understanding the commonly used engineering model, as well as in performing more effective protection against lightning hazards.