A heuristic probabilistic approach to estimating size-dependent mobility of nonuniform sediment

This paper presents a heuristic probabilistic approach to estimating the size-dependent mobilities of nonuniform sediment based on the pre- and post-entrainment particle size distributions (PSDs), assuming that the PSDs are lognormally distributed. The approach fits a lognormal probability density function to the pre-entrainment PSD of bed sediment and uses the threshold particle size of incipient motion and the concept of sediment mixture to estimate the PSDs of the entrained sediment and post-entrainment bed sediment. The new approach is simple in physical sense and significantly reduces the complexity and computation time and resource required by detailed sediment mobility models. It is calibrated and validated with laboratory and field data by comparing to the size-dependent mobilities predicted with the existing empirical lognormal cumulative distribution function approach. The novel features of the current approach are: (1) separating the entrained and non-entrained sediments by a threshold particle size, which is a modified critical particle size of incipient motion by accounting for the mixed-size effects, and (2) using the mixture-based pre- and post-entrainment PSDs to provide a continuous estimate of the size-dependent sediment mobility.     

Geomagnetic signatures of sudden ionospheric disturbances during extreme solar radiation events

We performed a comparative study of geomagnetic variations, which are associated with sudden ionospheric disturbances (SIDs) caused by great X-class solar flares on July 14, 2000 (Bastille flare) and on October 28, 2003 (Halloween flare). Intense fluxes of solar X-rays and EUV radiation as well as solar energetic particles (SEP) were considered as sources of abundant ionization of the ionosphere and upper atmosphere. Flare-initiated SIDs are revealed as transient geomagnetic variations, which are generated by enhanced electric currents flowing mainly in the bottom-side ionosphere. Those so-called solar flare effects (SFEs) were studied by using of geomagnetic data from INTERMAGNET worldwide network of ground-based magnetometers. In subsolar region the SFE is mainly controlled by the flare X-rays and/or EUV radiation. We found that in the Halloween flare the contribution of X-rays was comparable with the EUV, but in the Bastille flare the EUV flux was dominant. The ionization at high latitudes is generated by the SEP, which energy flux is comparable and even exceeds the solar electromagnetic radiation in that region. It was shown that in the Halloween event the pattern of SFE is formed by a two-vortex current system, which is similar to the quiet day Sq current system. However, during the Bastille flare, the pattern of induced currents is quite different: the northern vortex shifts westward and southern vortex shifts eastward such that the electroject is substantially tilted relative to the geomagnetic equator. From numerical estimations we found that at middle latitudes the SEP-initiated geomagnetic effect becomes comparable with the effects of solar electromagnetic radiation. It was also shown that the SEP contribute to the SFE in the nightside hemisphere. The revealed features of the SEP impact to the ionosphere were found in a good agreement with the theory of energetic particle penetration to the bottom-side magnetosphere.     

Complex active regions as the main source of extreme and large solar proton events

A study of solar proton sources indicated that solar flare events responsible for ≥2000 pfu proton fluxes mostly occur in complex active regions (CARs), i.e., in transition structures between active regions and activity complexes. Different classes of similar structures and their relation to solar proton events (SPEs) and evolution, depending on the origination conditions, are considered. Arguments in favor of the fact that sunspot groups with extreme dimensions are CARs are presented. An analysis of the flare activity in a CAR resulted in the detection of “physical” boundaries, which separate magnetic structures of the same polarity and are responsible for the independent development of each structure.     

A probabilistic approach for estimating the seismic response of elasto‐plastic SDOF systems

The seismic response of elasto‐plastic structures to both recorded and generated accelerograms is characterized by a large scattering of the results, even for accelerograms with similar peak ground acceleration values and frequency content. According to current code recommendations a design value of the seismic response of an elasto‐plastic structure can be computed as the mean of the responses to a certain number of spectrum‐fitting generated accelerograms. A more effective probabilistic approach is presented herein. It allows the analyst to calculate a design value of the seismic response characterized by a predefined non‐exceedance probability using a limited number of generated accelerograms. The results of the performed analyses are presented in diagrams that can be used for structural design applications. The applicability of the proposed method is demonstrated in the case of an elasto‐plastic structural system and the results are compared with those obtained applying current code recommendations. Copyright © 2005 John Wiley & Sons, Ltd.     

A Bayesian approach for estimating extreme flood probabilities with upper-bounded distribution functions

Some recent research on fluvial processes suggests the idea that some hydrological variables, such as flood flows, are upper-bounded. However, most probability distributions that are currently employed in flood frequency analysis are unbounded to the right. This paper describes an exploratory study on the joint use of an upper-bounded probability distribution and non-systematic flood information, within a Bayesian framework. Accordingly, the current PMF maximum discharge appears as a reference value and a reasonable estimate of the upper-bound for maximum flows, despite the fact that PMF determination is not unequivocal and depends strongly on the available data. In the Bayesian context, the uncertainty on the PMF can be included into the analysis by considering an appropriate prior distribution for the maximum flows. In the sequence, systematic flood records, historical floods, and paleofloods can be included into a compound likelihood function which is then used to update the prior information on the upper-bound. By combining a prior distribution describing the uncertainties of PMF estimates along with various sources of flood data into a unified Bayesian approach, the expectation is to obtain improved estimates of the upper-bound. The application example was conducted with flood data from the American river basin, near the Folsom reservoir, in California, USA. The results show that it is possible to put together concepts that appear to be incompatible: the deterministic estimate of PMF, taken as a theoretical limit for floods, and the frequency analysis of maximum flows, with the inclusion of non-systematic data. As compared to conventional analysis, the combination of these two concepts within the logical context of Bayesian theory, contributes an advance towards more reliable estimates of extreme floods.     

A probabilistic approach to structural model updating

The problem of updating a structural model and its associated uncertainties by utilizing measured dynamic response data is addressed. A Bayesian probabilistic formulation is followed to obtain the posterior probability density function (PDF) of the uncertain model parameters for given measured data. The present paper discusses the issue of identifiability of the model parameters and reviews existing asymptotic approximations for identifiable cases. The focus of the paper is on the treatment of the general unidentifiable case where the earlier approximations are not applicable. In this case the posterior PDF of the parameters is found to be concentrated in the neighborhood of an extended and extremely complex manifold in the parameter space. The computational difficulties associated with calculating the posterior PDF in such cases are discussed and an algorithm for an efficient approximate representation of the above manifold and the posterior PDF is presented. Numerical examples involving noisy data are presented to demonstrate the concepts and the proposed method.     

A probabilistic approach to exposure risk assessment

The introduction of hazardous substances into the environment has long been recognized as being a cause of several diseases in humans, wildlife, and plants. The damaging character of suspected contaminants is usually assessed via a “reject/retain” design with no explicit link between levels of exposure and intensities of the potential adverse health effects even though this connection may be important for the development of public health regulations that limit exposure to hazardous substances. Here, we propose a probabilistic approach to exposure risk assessment as a way around this typical flaw. We develop a Bayesian model using proximity to the source of an alleged contaminant as a surrogate for exposure. Subsequently, we carry out an experimental study based on simulated data to illustrate the model implementation with real world data. We also discuss a possible way of extending the model to accommodate potential heterogeneity in the spatial distribution of the focal disease.     

Ionospheric response to the extreme solar burst of October 28, 2003

Using GPS and GLONASS navigation systems, instantaneous observations of solar burst effects on the Earth’s ionosphere are made. These observations are carried out for both Northern and Southern hemispheres, including the ionosphere at polar and equatorial latitudes. It is shown that the rate of total electron content (TEC) change is agrees well with the time profiles of solar bursts. An experimental dependence of the electron content gradient on the elevation angle is obtained.     

Holocene millennial-scale megaflood events point to ENSO-driven extreme climate changes

Reconstructing the Holocene megaflood history is a key component of understanding the mechanism of past climate change and assessing the potential impact of future catastrophic events. The Pearl River is the longest watercourse in southern China, and its lower reach has been identified as one of the world’s most vulnerable regions for flood exposure. However, there is a complete lack of millennial-scale geological records of paleomegafloods for the future prediction of once-in-a-hundred(even onc...     

Distribution of extreme solar energetic proton fluxes

The knowledge of the high intensity tails of probability distributions that determine the rate of occurrence of extreme events of solar energetic particles is a critical element in the evaluation of hazards for human and robotic space missions. Here instead of the standard approach based on fitting a selected distribution function to the observed data we investigate a different approach, which is based on a study of the scaling properties of the maximum particle flux in time intervals of increasing length. To find the tail of the probability distributions we apply the “Max-Spectrum” method (Stoev, S.A., Michailidis, G., 2006. On the estimation of the heavy-tail exponent in time series using the Max-Spectrum. Technical Report 447, Department of Statistics, University of Michigan) to 1973–1997 IMP-8 proton data and the 1987–2008 GOES data, which cover a wide range of proton energies. We find that both data sets indicate a power-law tail with the power exponents close to 0.6 at least in the energy range 9–60 MeV. The underlying probability distribution is consistent with the Fréchet type (power-law behavior) extreme value distribution. Since the production of high fluxes of energetic particles is caused by fast Coronal Mass Ejections (CMEs) this heavy-tailed distribution also means that the Sun generates more fast CMEs than would be expected from a Poissonian-type process.     

Geoefficiency of solar eruptive events

The sources of geomagnetic disturbances during 1999–2003 are discussed. The relation between geomagnetic activity and the rate of coronal mass ejections (CMEs), their parameters, and the dynamics of solar photospheric magnetic fields is considered. It is shown that during the reorganization of unipolar regions of the photospheric magnetic field, the number of CMEs increases and their parameters change. The geomagnetic disturbance level also increases in these periods.     

Response of the midlatitude ionosphere to extreme geomagnetic storms of the 23rd solar cycle

The ionospheric response in the Irkutsk region (52.3° N, 104.3° E) to the extreme geomagnetic storms of solar cycle 23 was studied based on the data of the Irkutsk incoherent scatter radar (ISR) and DPS-4 vertical sounding digital ionosonde. The deviations of parameters from the undisturbed level, i.e., from the monthly medians or the values obtained on a quiet day, were considered as an ionospheric response. Values of the electron concentration maximum (N _mF2) and electron temperature (T _e) at a height of 350 km were chosen as parameters. The ionospheric response is interpreted in the scope of the concept of a thermospheric storm and penetration of the magnetospheric electric field.     

Return period of bivariate distributed extreme hydrological events

 Extreme hydrological events are inevitable and stochastic in nature. Characterized by multiple properties, the multivariate distribution is a better approach to represent this complex phenomenon than the univariate frequency analysis. However, it requires considerably more data and more sophisticated mathematical analysis. Therefore, a bivariate distribution is the most common method for modeling these extreme events. The return periods for a bivariate distribution can be defined using either separate single random variables or two joint random variables. In the latter case, the return periods can be defined using one random variable equaling or exceeding a certain magnitude and/or another random variable equaling or exceeding another magnitude or the conditional return periods of one random variable given another random variable equaling or exceeding a certain magnitude. In this study, the bivariate extreme value distribution with the Gumbel marginal distributions is used to model extreme flood events characterized by flood volume and flood peak. The proposed methodology is applied to the recorded daily streamflow from Ichu of the Pachang River located in Southern Taiwan. The results show a good agreement between the theoretical models and observed flood data. The author wishes to thank the two anonymous reviewers for their constructive comments that improving the quality of this work.     

Quantitative simulation and prediction of extreme geological events

Science China Earth Sciences - The systematic study of extreme geological events (such as plate collision and subduction, extreme cold and extreme hot events, biological extinction and revival,...     

An integrated approach for investigating geomorphic response to extreme events: methodological framework and application to the October 2011 flood in the Magra River catchment,Italy

A high‐magnitude flash flood, which took place on 25 October 2011 in the Magra River catchment (1717 km²), central‐northern Italy, is used to illustrate some aspects of the geomorphic response to the flood. An overall methodological framework is described for using interlinked observations and analyses of the geomorphic impacts of an extreme event. The following methods and analyses were carried out: (i) hydrological and hydraulic analysis of the event; (ii) sediment delivery by event landslide mapping; (iii) identification and estimation of wood recruitment, deposition, and budgeting; (iv) interpretation of morphological processes by analysing fluvial deposits; (v) remote sensing and geographic information system (GIS) analysis of channel width changes. In response to the high‐magnitude hydrological event, a large number of landslides occurred, consisting of earth flows, soil slips, and translational slides, and a large quantity of wood was recruited, in most part deriving from floodplain erosion caused by bank retreat and channel widening. The most important impact of the flood event within the valley floor was an impressive widening of the overall channel bed and the reactivation of wide portions of the pre‐event floodplain. Along the investigated (unconfined or partly confined) streams (total investigated length of 93.5 km), the channel width after the flood was up to about 20 times the channel width before the event. The study has shown that a synergic use of different methods and types of evidence provides fundamental information for characterizing and understanding the geomorphic effects of intense flood events. The prediction of geomorphic response to a flood event is still challenging and many limitations exist; however a robust geomorphological analysis can contribute to the identification of the most critical reaches. Copyright © 2016 John Wiley & Sons, Ltd.     

Formulae for estimating extreme changes of lengths in spatial affine transformation

Summary Formulae (27) and (28) which make it possible to estimate the minimum and maximum value of the deformation in length in affine transformation in space have been derived. Both values are determined by means of the elements of the given transformation matrixA without having to form the productAA ^T, or compute the corresponding eigenvalues explicitly. The derived formulae hold true under the assumption that both extreme values do not differ from each other too much.Dedicated to 90th Birthday of Professor Frantiek Fiala     

Seismic response of high plasticity clays during extreme events

Mexico City high plasticity clays exhibit a small degree of nonlinearity for shear strains as large as 0.1%, which leads to both moderate shear stiffness degradation and small to medium damping increment, even for long duration subduction strong ground motions, such as the 8.1M_w 1985Michoacan earthquake. Nonetheless, current seismic design criteria of strategic infrastructure used worldwide have striven for having larger return periods for establishing the seismic environment, considering recent large magnitude (M>8.5M_w) events. This paper presents the study of the seismic response of typical high plasticity clays found in the so-called Texcoco Lake, in the surrounding of Mexico City valley, for larger to extreme earthquakes. The shear wave velocity profile was characterized using a down-hole test. The seismic environment was established from a set of uniform hazard response spectra developed for a nearby rock outcrop for return periods of 125, 250, 475 and 2475 years. A time-domain spectral matching was used to develop acceleration time histories compatible with each uniform hazard response spectrum. Both frequency and time domain site response analyses were carried out considering each seismic scenario. Ground nonlinearities were clearly observed in the soil response during extreme ground shaken, which increases rapidly with the return period. This fact must be taken into account to avoid costly and potentially unsafe seismic designs.