Exceedance Probability Research Articles

Artificial Groundwater Replenishment in the Republic of Kalmykia: The Sources, Problems, and Perspectives

The Republic of Kalmykia is located in the northwestern part of the Caspian Region and belongs to arid regions. The issue of water resources availability is extremely relevant here. Groundwater plays an important role in this aspect as a main and often the only source of drinking water supply. However, its use is limited because of its low natural quality. An approach to an increase in the operational groundwater reserves is its artificial replenishment. The Russian Research Institute for Integrated Use and Protection of Water Resources in 2020–2021 studied the possibility of replenishing water resources of subsurface water bodies in the Republic of Kalmykia by the accumulation of surface water. The results of the studies suggested a conclusion that the artificial replenishment of groundwater in the territory of the Republic of Kalmykia is inexpedient, because even in years with the surface runoff volume with 50% exceedance probability, the volume of surface runoff will be not enough for freshening groundwater within a year to the standard level (TDS ≤1.0 g/dm3). The formation of a permanent freshwater lens (the presence of which is of particular importance in dry years) in an aquifer within the system including infiltration basin and water well is impossible because its full drawdown will take place every year.

A Statistical Approach to Retrieve Rainfall Intensity by Attenuation Measurements From Commercial Microwave Links

AbstractCommercial microwave link (CML) has become one of the most widely used opportunistic sensors for rainfall monitoring. The high density and coverage of CMLs enable us to monitor near‐ground rainfall in high spatial resolution. The empirical power‐law (PL) model proposed in 1978 is the leading approach in relating CML attenuation with rain rate. However, while giving good rain rate estimates for CMLs longer than 1 km, in short CMLs, large errors are observed when the PL approach is applied. In this paper, we studied a statistical approach to convert CML attenuation measurement to rainfall intensity. The proposed approach calculates the exceedance probability, p, of rain‐induced attenuation and derives the corresponding rainfall intensity based on the rain rate cumulative distribution curve. Data from two cities in two countries were used to validate the approach. The results of the proposed approach were compared with that of the PL model. Results show that the models derived using our approach outperform PL for short CMLs, while showing similar performance for long ones. Since in the next generation mobile networks short CMLs will become more and more dominant, our work provides a way to derive retrieval models for the future generation CML networks.

Quantifying uncertainty in probabilistic volcanic ash hazard forecasts, with an application to weather pattern based wind field sampling

Probabilistic forecasting of volcanic ash dispersion involves simulating an ensemble of realistic event scenarios to estimate the probability of a particular hazard threshold being exceeded. Although the number of samples that make up the ensemble, how they are chosen, and the desired threshold all set the uncertainty of (or confidence in) the estimated exceedance probability, current practice does not quantify and communicate the uncertainty in ensemble predictions. In this study, we use standard statistical methods to estimate the variance in probabilistic ensembles and use this measure of uncertainty to assess different sampling strategies for the wind field, using the example of volcanic ash transport from a representative explosive eruption in Iceland. For stochastic (random) sampling of the wind field, we show how the variance is reduced with increasing ensemble size and how the variance depends on the desired hazard threshold and the proximity of a target site to the volcanic source. We demonstrate how estimated variances can be used to compare different ensemble designs, by comparing stochastic forecasts with forecasts obtained from a stratified sampling approach using a set of 29 Northern European weather regimes, known as Grosswetterlagen (GWL). Sampling wind fields from within the GWL regimes reduces the number of samples needed to achieve the same variance as compared to conventional stochastic sampling. Our results show that uncertainty in volcanic ash dispersion forecasts can be straightforwardly calculated and communicated, and highlight the need for the volcanic ash forecasting community and operational end-users to jointly choose acceptable levels of variance for ash forecasts in the future.

River Park Assessment: 2D Hydraulic Watercourse Modeling for Nature-based Solutions in Urban Area

Over time, fragmentation of semi-natural habitats in urban areas has become a pressing concern, disrupting ecological processes within cities. The focus on preserving open ecosystems has grown, highlighting the need to enhance resilience in urban riverside areas for effective ecosystem restoration. Comprehensive studies on river valleys, considering both hydrology and ecology, play a crucial role in urban river ecosystem development. Our article explores the potential of protective zones with urban vegetation and watercourses as Nature-based Solution within Krakow's ongoing riverine park system development. The study's cross-sections in the River Park area revealed dominant velocities ranging from 0.67 to 2.0 m s-1for SWQ (mean annual maximum flow) and below 0.67 m s-1for Q1% (1% annual exceedance probability flow). The hydrological analysis accurately captured the natural river bed channels' curvature, providing the basis for a two-dimensional mathematical model to visualize the hydraulic structure of protected sites. Integrating water and greenery management systems in urban areas offers significant potential for adapting to climate change, mitigating extreme weather events. Our research's novelty lies in applying 2D hydraulic modeling, demonstrating how River Parks can serve as climate change mitigation solutions in urban environments.

A conditional extreme value distribution method for dynamic reliability analysis of stochastic structures

An efficient post-processing simulation method is proposed to estimate small failure probabilities of stochastic dynamic structures involving the inherent randomness of structural physical-geometrical parameters and external excitations. To extract a small failure probability, the proposed method introduces an intermediate event to represent the realizations of extreme structural response in the tail of distribution. With the aid of this intermediate event, structural failure probability is reformulated as a product of the event’s occurrence probability and the conditional exceedance probability of extreme response when the event occurs. The latter corresponds to a distribution of extreme response under the condition of the intermediate event, referred to as the conditional extreme value distribution (CEVD). Accordingly, the proposed method is termed the CEVD method. To reconstruct the CEVD, a truncated shifted generalized lognormal distribution model is employed. Bayesian estimation method is utilized to determine the two shape parameters of this model based on the samples of both original extreme value distribution and CEVD, where the CEVD samples are generated by Markov chain Monte Carlo sampling. The efficiency and accuracy of the proposed method are demonstrated through two numerical examples considering seismic reliability analyses of a 10-story nonlinear frame and a soil-foundation-structure interaction system.

Extreme wind turbine response extrapolation with the Gaussian mixture model

Abstract. The wind turbine extreme response estimation based on statistical extrapolation necessitates using a minimal number of simulations to calculate a low exceedance probability. The target exceedance probability associated with a 50-year return period is 3.8×10-7, which is challenging to evaluate with a small prediction error. The situation is further complicated by the fact that the distribution of the wind turbine response might be multimodal, and the extremes belong to a different statistical population than the main body of the distribution. Traditional theoretical probability distributions, mostly unimodal, may not be suitable for this task. The problem could be alleviated by applying a fit specifically on the tail of the distribution. Yet, a single unimodal distribution may not be sufficient for modeling diverse wind turbine responses, and an inappropriate distribution model could lead to significant prediction errors, including bias and variance errors. The Gaussian mixture model, a probabilistic and flexible mixture distribution model used extensively for clustering and density estimation tasks, is infrequently applied in the wind energy sector. This paper proposes using the Gaussian mixture model to extrapolate extreme wind turbine responses. The performance of two approaches is evaluated: (1) parametric fitting first and aggregation afterward and (2) data aggregation first followed by fitting. Different distribution models are benchmarked against the Gaussian mixture model. The results show that the Gaussian mixture model is capable of estimating a low exceedance probability with minor bias error, even with limited simulation data, and demonstrates flexibility in modeling the distributions of varying response variables.

Probabilistic framework for seismic resilience assessment of transmission tower-line systems subjected to mainshock-aftershock sequences

Immediate damage to electricity transmission systems after strong earthquakes can significantly cause widespread power outages and impede maintenance activities. Whereas previous seismic resilience assessments have investigated comprehensively the recovery capability of structures under isolated mainshocks, the effect of aftershocks has received less attention. This paper introduces a probabilistic framework for resilience assessment incorporating the effect of aftershocks and utilizes it to investigate the seismic performance of a transmission tower-line system (TTLS) under mainshock-aftershock (MSAS) sequences. Exceedance probabilities for different damage states of the TTLS are analyzed using fragility curves. Multiple decision variables (including functionality loss, recovery time, recovery function and resilience indicator) are subsequently calculated to quantify the effect of aftershocks. Meanwhile, the seismic resilience of the TTLS is further assessed by considering the uncertainties associated with those decision variables. The results reveal that aftershocks exert a significant influence on the seismic resilience of the TTLS, particularly when it experiences minor or moderate damage following the mainshocks. However, as the damage to the TTLS worsens due to larger mainshocks, the role of subsequent aftershocks becomes comparatively less influential. The proposed framework provides valuable insights for infrastructure systems before and after earthquake, effectively mitigating the adverse effects of sequential earthquakes.

The dependence of wave height probability distributions on physical parameters from measurements near Sakhalin Island

The data of long-term surface waves measurements with bottom sensors near Sakhalin Island were used to build instrumental probability distributions for exceedance of wave heights. Waves with heights exceeding the significant wave height by more than three times were recorded. Specific features of the observations conducted during the periods of open and ice-covered sea surfaces are discussed. The subsets of statistically homogeneous data are arranged through selection considering the natural physical dimensionless parameters of the task, that control the effects of finite depth and nonlinearity (namely, the wave steepness, the wave amplitude to water depth ratio, the Ursell parameter). The manifestation of these and composite parameters in theoretical probability distributions of wave heights is discussed. The effects of nonlinearity and the measurement point depth on probability distributions are estimated with a focus on abnormally high waves. In particular, it is shown that for the place of registration an increase in the wave amplitude to water depth ratio parameter leads to a decrease in the probability of abnormally high waves. This behavior is consistent with the Glukhovsky theoretical distribution. The waves characterized by relatively large dimensionless depth parameter exhibit a higher probability of substantial exceedance of the significant height and are better described by the Rayleigh distribution.

Reliability analysis of two archetype RC buildings with hysteretic dampers

The manuscript deals with a study on the performance/reliability analysis of steel hysteretic dampers designed for the seismic retrofit of RC frame structures at the Basic Design Earthquake, BDE (characterized by a 10 % probability of being exceeded over the reference lifespan, VR) for higher hazard levels, represented by a Maximum Considered Earthquake, MCE, with either 5 %/VR or 2.5 %/VR exceedance probabilities. Indeed, seismic codes prescribe that anti-seismic devices designed to satisfy the performance requirements at the BDE must be able to resist earthquakes of higher intensity. Therefore, γ-factors amplifying the design displacement or force must be considered for the design of the device capacity.The objective of the study consists in evaluating the over-demand caused on the steel dampers incorporated in dissipative bracing systems when passing from the BDE to the two higher hazard levels, and comparing this over-demand to the values of the corresponding γ-factors proposed in current codes. Dampers with various ductility factors are considered to include the majority of current hysteretic devices.The amplification factors recommended in the codes for hysteretic dampers are shown to be not suitable for guaranteeing the damper reliability; moreover, a dependence of the reliability of the retrofitted structures upon the ductility of the damped braces is highlighted.

Derivative of Reduced Cumulative Distribution Function and Applications

The reduced cumulative distribution function (rCDF) is the maximal lower bound for the cumulative distribution function (CDF). It is equivalent to the inverse of the conditional value at risk (CVaR), or one minus the buffered probability of exceedance (bPOE). This paper introduces the reduced probability density function (rPDF), the derivative of rCDF. We first explore the relation between rCDF and other risk measures. Then we describe three means of calculating rPDF for a distribution, depending on what is known about the distribution. For functions with a closed-form formula for bPOE, we derive closed-form formulae for rPDF. Further, we describe formulae for rPDF based on a numerical bPOE when there is a closed-form formula for CVaR but no closed-form formula for bPOE. Finally, we give a method for numerically calculating rPDF for an empirical distribution, and compare the results with other methods for known distributions. We conducted a case study and used rPDF for sensitivity analysis and parameter estimation with a method similar to the maximum likelihood method.

Comparison of higher degree stop-loss transforms

We regard high degree stop-loss transforms as iterated equilibrium distributions to establish comparison criteria with respect to star-shape and convex transform orders. As an application, we derive monotonicity properties for exceedance probabilities, providing information on how likely these distributions are to be far from the extreme values of their support.

Geographic redistribution of microcystin hotspots in response to climate warming

High concentrations of cyanobacterial toxins such as microcystin represent a global challenge to water quality in lakes, threatening health, economies and ecosystem stability. Lakes are sentinels of climate change but how warming will affect microcystin concentrations is still unclear. Here we examine how warming impacts the probability of exceeding microcystin water quality thresholds across 2,804 lakes in the United States and show how future warming will alter these probabilities. We find that higher temperatures consistently increase the likelihood of microcystin occurrence but that the probability of microcystin concentrations above water quality thresholds is highest for water temperatures between 20 and 25 °C. Regions with temperatures that promote microcystin will shift to higher latitudes in the coming decades, leading to relative changes in exceedance probabilities of more than 50% in many basins of the United States. High nitrogen concentrations amplify the impact of rising temperatures, calling for increased awareness of a substantial hazard to ecosystems and human health under global warming.

Probabilistic-based seismic fragility assessment of earthquake-induced site liquefaction

As a very complex and uncertain problem, seismic liquefaction is affected by many factors, such as earthquake intensity, site conditions, soil properties, etc. During the past half a century, the state-of-the-art in analysis and evaluation of earthquake-induced soil liquefaction and its consequences as well as the state-of-the-practice in improving seismic stability to resist liquefaction have been made much progress. However, the fragility analysis and assessment for seismic liquefaction of sites have not been paid enough attention to. In this paper, the concept of seismic liquefaction fragility for building sites is proposed. The soil resistance to liquefaction and liquefaction possibility are expressed as a fragility function of ground motion intensity, which can be used to describe minor, moderate and severe liquefaction potential under different ground motion intensity. Combined with the existing research results of seismic liquefaction evaluation, the analysis method of liquefaction fragility is given. Taking a specific site as an example for liquefaction fragility analysis, it is found that taking the calculated exceedance probability of different liquefaction levels as the observation value, the liquefaction fragility function follows both lognormal distribution and log-logistic distribution. With the increase of liquefaction level, the median value of liquefaction fragility function increases, while the site liquefaction fragility curve moves to the right, which shows that the ability of the site to resist more severe liquefaction is increasing. When convolved with the analysis results of liquefaction triggering and hazard, the liquefaction fragility function can be a much efficient tool for seismic liquefaction risk analysis of specific sites.

An Alternative Method for Estimating the Peak Flow for a Regional Catchment Considering the Uncertainty via Continuous Simulation

Estimating peak flow for a catchment is commonly undertaken using the design event method; however, this method does not allow for the understanding of uncertainty in the result. This research first presents a simplified method of fragments approach to rainfall disaggregation that ignores the need to consider seasonality, offering a greater diversity in storm patterns within the resulting sub-daily rainfall. By simulating 20 iterations of the disaggregated sub-daily rainfall within a calibrated continuous simulation hydrologic model, we were able to produce multiple long series of streamflow at the outlet of the catchment. With these data, we investigated the use of both the annual maximum and peaks over threshold approaches to flood frequency analysis and found that for a 1-in-100-year annual exceedance probability peak flow, the peaks over threshold method (333 m3/s ± 50 m3/s) was significantly less uncertain than the annual maximum method (427 m3/s ± 100 m3/s). For the 1-in-100-year annual exceedance probability, the median peak flow from the peaks over threshold method (333 m3/s) produced an outcome comparable to the design event method peak flow (328 m3/s), indicating that this research offers an alternative approach to estimating peak flow, with the additional benefit of understanding the uncertainty in the estimation. Finally, this paper highlighted the impact that length and period of streamflow has on peak flow estimation and noted that previous assumptions around the minimum length of gauged streamflow required for flood frequency analysis may not be appropriate in particular catchments.

Use of peak over threshold data for flood frequency estimation: An application at the UK national scale

This study investigates choices of statistical distributions to represent the threshold exceedance frequency and magnitude of peaks-over-threshold (POT) series from a national dataset of extreme hydrological events from 842 gauging stations in the UK. From the initial POT series, two new series were created, POT1 and POT3, representing POT series with an average of, respectively, one and three exceedances per year. Using a χ2 goodness-of-fit test, the choice of distributions for both the annual exceedance counts and the magnitude of threshold exceedances were explored for both the POT1 and POT3 datasets. The results show that the negative binomial and geometrical distributions provide a better fit to the annual exceedance count than the Poisson distribution typically assumed. These results are particularly pronounced when considering the POT3 dataset and in the South-East of the UK where many river flow series are dominated by slow responding groundwater dominated catchments. Finally, estimates of design floods with a return period of 2 and 100 years were obtained for each POT series and compared to the equivalent estimates obtained from direct at-site analysis of the annual maximum series. The results show a good alignment between the magnitude of the design floods estimated by the two methods, but a generally lower standard deviation of estimates obtained from the POT data, as quantified using a bootstrap procedure. The results presented here show that the POT series could beneficially replace the current operational guidelines based on annual maximum series for design flood estimation in the UK.

Pressure Time Dose as a Representation of Intracranial Pressure Burden and Its Dependency on Intracranial Pressure Waveform Morphology at Different Time Intervals.

Intracranial pressure (ICP) burden or pressure time dose (PTD) is a valuable clinical indicator for pending intracranial hypertension, mostly based on threshold exceedance. Pulse frequency and waveform morphology (WFM) of the ICP signal contribute to PTD. The temporal resolution of the ICP signal has a great influence on PTD calculation but has not been systematically studied yet. Hence, the temporal resolution of the ICP signal on PTD calculation is investigated. We retrospectively analysed continuous 48 h ICP recordings with high temporal resolution obtained from 94 patients at the intensive care unit who underwent neurosurgery due to an intracranial haemorrhage and received an intracranial pressure probe (43 females, median age: 72 years, range: 23 to 88 years). The cumulative area under the curve above the threshold of 20 mmHg was compared for different temporal resolutions of the ICP signal (beat-to-beat, 1 s, 300 s, 1800 s, 3600 s). Events with prolonged ICP elevation were compared to those with few isolated threshold exceedances. PTD increased for lower temporal resolutions independent of WFM and frequency of threshold exceedance. PTDbeat-to-beat best reflected the impact of frequency of threshold exceedance and WFM. Events that could be distinguished in PTDbeat-to-beat became magnified more than 7-fold in PTD1s and more than 104 times in PTD1h, indicating an overestimation of PTD. PTD calculation should be standardised, and beat-by-beat PTD could serve as an easy-to-grasp indicator for the impact of frequency and WFM of ICP elevations on ICP burden.

Risk‐based optimization of concentrically braced tall timber buildings: Derivative free optimization algorithm

AbstractMass timber materials are attractive alternatives for tall‐timber buildings (TBs), where the need for sustainability is apparent. Innovative structural systems and design methodologies are needed to fulfil performance requirements according to modern performance based approaches. This paper deals with the design and optimization of buckling restrained braces as earthquake protection system for tall‐TBs through risk‐based design procedure. This procedure controls the mean annual frequency of exceedance of several limit states evaluated through a SAC‐FEMA approach and using response spectrum linear analyses on linearized models for demand assessment. The features of the optimization procedure and the linearized models are shown through an application on a 20‐story mass‐TB located in a high seismic zone. The optimization is executed through a derivative‐free algorithm, the generalized pattern Search, adopting several solution strategies whose efficiency and effectiveness for this kind of applications are shown and discussed. Finally, the results are compared and validated through the execution of non‐linear analyses within a multiple stripe framework.

Design flood estimation at ungauged catchments using index flood method and quantile regression technique: a case study for South East Australia

Flood is one of the worst natural disasters, which causes the damage of billions of dollars each year globally. To reduce the flood damage, we need to estimate design floods accurately, which are used in the design and operation of water infrastructure. For gauged catchments, flood frequency analysis can be used to estimate design floods; however, for ungauged catchments, regional flood frequency analysis (RFFA) is used. This paper compares two popular RFFA techniques, namely the quantile regression technique (QRT) and the index flood method (IFM). A total of 181 catchments are selected for this study from south-east Australia. Eight predictor variables are used to develop prediction equations. It has been found that IFM outperforms QRT in general. For higher annual exceedance probabilities (AEPs), IFM generally demonstrates a smaller estimation error than QRT; however, for smaller AEPs (e.g. 1 in 100), QRT provides more accurate quantile estimates. The IFM provides comparable design flood estimates with the Australian Rainfall and Runoff—the national guide for design flood estimation in Australia.

PDEM-based seismic performance evaluation of circular tunnels under stochastic earthquake excitation

ABSTRACT Tunnels are a vital component of urban infrastructure that must be robust against seismic hazards. Given the randomness of earthquake occurrence, the seismic response of tunnel structures mut be studied by stochastic analysis methods. To this end, this study proposes a probability density evolution method (PDEM)-based framework to investigate the seismic performance of a circular tunnel under stochastic earthquake excitation. First, a suite of nonstationary earthquake motions compatible with the seismic design code was derived using a stochastic earthquake model. Then, a series of nonlinear dynamic numerical simulations were conducted for a typical circular tunnel that considers the soil-structure interaction. Finally, using the tunnel inclination angle as the performance index, the probability density function of the structural response of the tunnel was solved using the PDEM to obtain the corresponding exceedance probabilities of the tunnel under various damage states. The results show that the PDEM-based framework can be applied to evaluate the seismic performance of circular tunnels and could serve as a reference on the seismic fragility of tunnels and underground structures.

The design of two-sided S 2-chart with estimated in-control process variance based on conditional median run length

ABSTRACT Monitoring both decrease and increase in the process variance has a significant value in effectively implementing any quality improvement program. This paper considers the Phase II two-sided S 2 -chart with estimated in-control (IC) process variance and evaluates its performance under the conditional perspective. The conditional perspective focuses on the conditional (given parameter estimates) IC run length distribution and its associated properties to evaluate chart’s performance with estimated parameters. Thus, it accounts for the practitioner-to-practitioner variability and, hence, provides a comprehensive understanding of the chart’s performance. To guard against unnecessary false alarms, we design the chart using the exceedance probability criterion under the conditional perspective, which ensures the desired IC performance with a high probability. Furthermore, because the median run length (MRL) is a more suitable representative of run length (RL) distribution, we examine the chart’s performance in terms of the median of the conditional RL distribution. We also discuss the biasedness property of the two-sided S 2 -chart, which is an outcome of the skewed nature of the charting statistic. It is shown that the proposed MRL-unbiased chart requires about within 500 Phase I observations to achieve a reasonably good IC and OOC performance.