Confidence Analysis of Standard Deviational Ellipse and Its Extension into Higher Dimensional Euclidean Space

Wang, Bin; Shi, Wenzhong; Zhang, Miao

doi:10.1371/journal.pone.0118537

Cited by 153 publications

(118 citation statements)

References 25 publications

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“…After the EFT, once each flash is represented by the corresponding ellipse, the lengths of the ellipse were computed according to the covariance matrix (Orechovesky, 1996;Ray and Srivastava, 2008;Wang et al, 2015). The length of the major axis is used to estimate the lightning maximum length.…”

Section: Confidence Intervals and Ellipse Fittingmentioning

confidence: 99%

Spatio-temporal dimension of lightning flashes based on three-dimensional Lightning Mapping Array

López

Pineda

Montanyà

et al. 2017

Atmospheric Research

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ABSTRACT3D mapping system like the LMA -Lightning Mapping Array -are a leap forward in lightning observation. LMA measurements has lead to an improvement on the analysis of the fine structure of lightning, allowing to characterize the duration and maximum extension of the cloud fraction of a lightning flash. During several years of operation, the first LMA deployed in Europe has been providing a large amount of data which now allows a statistical approach to compute the full duration and horizontal extension of the in-cloud phase of a lightning flash. The "Ebro Lightning Mapping Array" (ELMA) is used in the present study. Summer and winter lighting were analyzed for seasonal periods (Dec-Feb and Jun-Aug). A simple method based on an ellipse fitting technique (EFT) has been used to characterize the spatio-temporal dimensions from a set of about 29,000 lightning flashes including both summer and winter events. Results show an average lightning flash duration of 440 ms (450 ms in winter) and a horizontal maximum length of 15.0 km (18.4 km in winter). The uncertainties for summer lightning lengths were about ± 1.2 km and ± 0.7 km for the mean and median values respectively. In case of winter lightning, the level of uncertainty reaches up to 1 km and 0.7 km of mean and median value. The results of the successful correlation of CG discharges with the EFT method, represent 6.9% and 35.5% of the total LMA flashes detected in summer and winter respectively. Additionally, the median value of lightning lengths calculated through this correlative method was approximately 17 km for both seasons. On the other hand, the highest median ratios of lightning length to CG discharges in both summer and winter were reported for positive CG discharges.

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Section: Confidence Intervals and Ellipse Fittingmentioning

confidence: 99%

Spatio-temporal dimension of lightning flashes based on three-dimensional Lightning Mapping Array

López

Pineda

Montanyà

et al. 2017

Atmospheric Research

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“…The theory follows the approach of Wang et al [2015] and states that s = (x, y) T being a function in a twodimensional space and E(s) = (E(x), E(y)) T = (μ x , μ y ) T , the mean value of the random variable s, where…”

Section: Appendix A: Bivariate Spatial Distribution Of Tectonic Tremorsmentioning

confidence: 99%

Continental crust anisotropy measurements from tectonic tremor in Cascadia

2017

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We present new observations of crustal anisotropy in the southern Cascadia fore arc from tectonic tremor. The abundance of tremor activity in Oregon and northern California during slow‐slip events offers an enormous amount of information with which to measure and analyze anisotropy in the upper brittle continental crust. To accomplish this, we performed analyses of wave polarization and shear wave splitting of tectonic tremor signals by using three component broadband seismic stations. The splitting times range between 0.11 and 0.32 s and are consistent with typical values observed in the continental crust. Fast polarization azimuths are, in general, margin parallel and trend N‐S, which parallels the azimuths of the maximum compressive stresses observed in this region. This pattern is likely to be controlled by the stress field. Comparatively, the anisotropic structure of fast directions observed in the northern section of the Cascadia margin is oblique with respect to the southern section of Cascadia, which, in general, trends E‐W and is mainly controlled by active faulting and geological structures. Source distribution analysis using a bivariate normal distribution that expresses the distribution of tremors in a preferred direction shows that in northern California and Oregon, the population of tremors tends to distribute parallel to fast polarization azimuths and maximum compressive stresses, suggesting that both tremor propagation and anisotropy are influenced by the stress field. Results show that the anisotropy reflects an active tectonic process that involves the northward movement of the Oregon Block, which is rotating as a rigid body. In northern Cascadia, previous results of anisotropy show that the crust is undergoing a shortening process due to velocity differences between the Oregon Block and the North America plate, which is moving more slowly with respect to the Oregon Block, making it clash against Vancouver Island.

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“…The geometry of the SDE is essentially determined by three properties of the point-set: mean location, dispersion, and orientation [30]. To our purpose, only orientation is relevant.…”

Section: Methodsmentioning

confidence: 99%

Measuring (subglacial) bedform orientation, length, and longitudinal asymmetry – Method assessment

Jorge

Brennand

2017

PLoS ONE

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Geospatial analysis software provides a range of tools that can be used to measure landform morphometry. Often, a metric can be computed with different techniques that may give different results. This study is an assessment of 5 different methods for measuring longitudinal, or streamlined, subglacial bedform morphometry: orientation, length and longitudinal asymmetry, all of which require defining a longitudinal axis. The methods use the standard deviational ellipse (not previously applied in this context), the longest straight line fitting inside the bedform footprint (2 approaches), the minimum-size footprint-bounding rectangle, and Euler’s approximation. We assess how well these methods replicate morphometric data derived from a manually mapped (visually interpreted) longitudinal axis, which, though subjective, is the most typically used reference. A dataset of 100 subglacial bedforms covering the size and shape range of those in the Puget Lowland, Washington, USA is used. For bedforms with elongation > 5, deviations from the reference values are negligible for all methods but Euler’s approximation (length). For bedforms with elongation < 5, most methods had small mean absolute error (MAE) and median absolute deviation (MAD) for all morphometrics and thus can be confidently used to characterize the central tendencies of their distributions. However, some methods are better than others. The least precise methods are the ones based on the longest straight line and Euler’s approximation; using these for statistical dispersion analysis is discouraged. Because the standard deviational ellipse method is relatively shape invariant and closely replicates the reference values, it is the recommended method. Speculatively, this study may also apply to negative-relief, and fluvial and aeolian bedforms.

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Confidence Analysis of Standard Deviational Ellipse and Its Extension into Higher Dimensional Euclidean Space

Cited by 153 publications

References 25 publications

Spatio-temporal dimension of lightning flashes based on three-dimensional Lightning Mapping Array

Spatio-temporal dimension of lightning flashes based on three-dimensional Lightning Mapping Array

Continental crust anisotropy measurements from tectonic tremor in Cascadia

Measuring (subglacial) bedform orientation, length, and longitudinal asymmetry – Method assessment

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