Incorporating intensity bounds for assessing the seismic safety of structures: Does it matter?

The closed‐form solution for assessing the proportion of the mean annual frequency of limit‐state exceedance as a function of integration limits is introduced, in order to study whether or not the mean annual frequency of limit‐state exceedance is overestimated if the lower and(or) upper integration limit of the risk equation are(is) not selected in a physically consistent manner. Simple formulas for assessing the threshold value of the lower and upper integration limits are also derived. These formulas can be used to quickly assess the significant range of ground motion intensity that affects the mean annual frequency of limit‐state exceedance. It is shown that the threshold values of the integration limits depend on the median intensity causing a limit‐state, the corresponding dispersion and the slope of the hazard curve in the log domain. For several reinforced concrete buildings located in a region with moderate seismicity, it is demonstrated that the mean annual frequency of collapse can be significantly overestimated when assessed by integrating the risk equation over the entire range of ground motion intensity. Copyright © 2013 John Wiley & Sons, Ltd.     

Delineation of flood generating processes and their hydrological response

Knowledge about flood generating processes can be beneficial for numerous applications. Especially in the context of climate change impact assessment, daily patterns of meteorological and catchment state conditions leading to flood events (i.e., storylines) may be of value. Here, we propose an approach to identify storylines of flood generation using daily weather and snow cover observations. The approach is tested for and applied to a typical pre‐Alpine catchment in the period between 1961 and 2014. Five precipitation parameters were determined that describe temporal and spatial characteristics of the flood associated precipitation events. The catchment's snow coverage was derived using statistical relationships between a satellite‐derived snow cover climatology and station snow measurements. Moreover, (pre‐) event snow melt sums were estimated using a temperature‐index model. Based on the precipitation and catchment state parameters, 5 storylines were identified with a cluster analysis: These are (a) long duration, low intensity precipitation events with high precipitation depths, (b) long duration precipitation events with high precipitation depths and episodes of high intensities, (c) shorter duration events with high or (d) low precipitation intensity, respectively, and (e) rain‐on‐snow events. The event groups have distinct hydrological characteristics that can largely be explained by the storylines' respective properties. The long duration, high intensity storyline leads to the most adverse hydrological response, namely, a combination of high peak magnitudes, high volumes, and long durations of threshold exceedance. The results show that flood generating processes in mesoscale catchments can be distinguished on the basis of daily meteorological and catchment state parameters and that these process types can explain the hydrological flood properties in a qualitative way. Hydrological simulations of daily resolution can thus be analysed with respect to flood generating processes.     

Applications of cumulative absolute velocity to urban earthquake early warning systems

An early warning system forewarns an urban area of the forthcoming strong shaking, normally with a few seconds to a few tens of seconds of early warning time before the arrival of the destructive S-wave part of the strong ground motion. For urban and industrial areas susceptible to earthquake damage, where the fault rupture system is complex and the fault-site distances are short, there is usually insufficient time to compute the hypocenter, focal parameters and the magnitude of an earthquake. Therefore, simpler and robust early warning algorithm is needed. The direct (engineering) early warning systems are based on algorithms of the exceedance of specified threshold time domain amplitude levels. The continuous stations’ data are processed to compute specific engineering parameters robustly and compared with specified threshold levels. The parameters can be chosen as band-pass filtered peak ground accelerations and/or the bracketed cumulative absolute velocity (BCAV). In this paper, an enhancement to bracket cumulative absolute velocity for the application of online urban early warning systems results in a new parameter called window based bracketed cumulative absolute velocity (BCAV-W). The BCAV-W allows computation of cumulative absolute velocity in a specified window size and to include the vertical component of the motion. The importance of choosing optimum window size for the cumulative absolute velocity BCAV-W is discussed and the correlations between BCAV-W and the macro-seismic intensity are studied for three combinations of horizontal and vertical components of the motion. Empirical relationship is developed to estimate BCAV-W as a function of magnitude, distance, fault mechanism, and site category based on 1,208 recorded ground motion data from 75 earthquakes in active plate-margins.     

考虑非结构构件损伤的钢筋混凝土框架建筑多维地震易损性分析

基于单一指标的传统地震易损性分析忽略了非结构构件损伤对建筑抗震性能的影响。首先基于多维性能极限状态理论建立了三维性能极限状态方程,并对几种特殊情况下的三维阈值曲面进行了讨论。进而以最大层间位移角作为整体结构与位移敏感型非结构构件的性能指标,以峰值楼面加速度作为加速度敏感型非结构构件的性能指标,对建筑的结构损伤和非结构损伤进行描述。考虑各性能指标之间的相关性和各性能指标所对应的极限状态阈值的不确定性,建立了建筑在地震作用下的三维性能极限状态的超越概率函数。最后,采用Open Sees有限元软件对一7层钢筋混凝土框架填充墙建筑进行增量动力分析,得到其各性能水平下的地震易损性曲线。分析结果表明,当忽略非结构构件损伤时,各性能极限状态的超越概率均降低,从而高估了建筑剩余功能水平,进而导致低估建筑的损失。在考虑各性能指标的极限状态阈值的不确定性时,对任一性能极限状态,不同变异系数取值下的易损性曲线会出现交点,在交点之前超越概率随着变异系数的增大而增大,交点之后则随着变异系数的增大而减小。在考虑性能指标间的相关性时,对任一性能极限状态,超越概率随着相关系数的减小而增大。另外,性能指标阈值的不确定性与性能指标间的相关性对地震易损性的影响随着性能水平的提高而逐渐降低,且对低性能水平下建筑地震易损性有明显影响。     

Statistical characterization of temporal structure of storms

The authors present a statistical procedure to estimate the probability distributions of storm characteristics. The approach uses recent advances in stochastic hydrological modeling. The temporal dynamics of rainfall are modeled via a reward alternating renewal process that describes wet and dry phases of storms. In particular, the wet phase is modeled as a rectangular pulse process with dependent random duration and intensity; the global dependence structure is described using multidimensional copulas. The marginal distributions are described by Generalized Pareto laws. The authors derive both the storm volume statistics and the rainfall volume distribution within a fixed temporal window preceding a storm. Based on these results, they calculate the antecedent moisture conditions. The paper includes a thorough discussion of the validity of the assumptions and approximations introduced, and an application to actual rainfall data. The models presented here have important implications for improved design procedures of water resources and hydrologic systems.     

Linking frequency of rainstorms,runoff generation and sediment transport across hyperarid talus-pediment slopes

Documenting hillslope response to hydroclimatic forcing is crucial to our understanding of landscape evolution. The evolution of talus-pediment sequences (talus flatirons) in arid areas was often linked to climatic cycles, although the physical processes that may account for such a link remain obscure. Our approach is to integrate field measurements, remote sensing of rainfall and modeling to link between storm frequency, runoff, erosion and sediment transport. We present a quantitative hydrometeorological analysis of rainstorms, their geomorphic impact and their potential role in the evolution of hyperarid talus-pediment slopes in the Negev desert, Israel. Rainstorm properties were defined based on intensity–duration–frequency curves and using a rainfall simulator, artificial rainstorms were executed in the field. Then, the obtained measured experimental results were up-scaled to the entire slope length using a fully distributed hydrological model. In addition, natural storms and their hydro-geomorphic impacts were monitored using X-band radar and time-lapse cameras. These integrated analyses constrain the rainfall threshold for local runoff generation at rain intensity of 14 to 22 mm h^-1 for a duration of five minutes and provide a high-resolution characterization of small-scale runoff-generating rain cells. The current frequency of such runoff-producing rainstorms is ~1–3 per year. However, extending this local value into the full extent of hillslope runoff indicates that it occurs only under rainstorms with ≥ 100-years return interval, or 1% annual exceedance probability. Sheetwash efficiency rises with downslope distance; beyond a threshold distance of ~100 m, runoff during rainstorms with such annual exceedance probability are capable of transporting surface clasts. The erosion efficiency of these discrete rare events highlights their potential importance in shaping the landscape of arid regions. Our results support the hypothesis that a shift in the properties and frequency of extreme events can trigger significant geomorphic transitions in areas that remained hyperarid during the entire Quaternary. © 2020 John Wiley & Sons, Ltd.     

Alternative closed‐form solutions for the mean rate of exceedance of structural limit states

Two new closed‐form expressions representing the mean rate of exceedance of a given limit state are presented herein. These proposals overcome limitations that were identified with the original formulation of the well‐known SAC/FEMA approach. The new expressions involve new parametric functions for the modeling of the seismic hazard data and for the demand evolution for increasing values of the earthquake intensity measure. Given the carefully selected parametric form of these functions, mathematical tractability is able to be maintained to establish two new closed‐form solutions representing the mean rate of exceedance of a given limit state. The function proposed for the hazard exhibits nonlinear behavior in log‐log space and is able to represent the actual hazard data over a wider range of earthquake intensity levels. The function proposed for the demand evolution addresses issues related to the inadequate performance of the SAC/FEMA approach when force‐based demand parameters such as the shear force are considered. To illustrate the applicability of the new closed‐form solutions, the probability of occurrence of several limit states is determined for a reinforced concrete structure. Copyright © 2013 John Wiley & Sons, Ltd.     

Information Gains for Stress Release Models

The information gain of a point process model quantifies its predictability, relative to a reference model such as the Poisson process. This is bounded above by the entropy gain, or difference between the point process entropy rates. This provides a bound on the utility of the model as a forecasting tool, separate from the usual “goodness of fit” assessment criteria. The stress release model is a point process with an underlying state variable increasing linearly with time, and decreased by events. Assuming the intensity to be an exponential function of this state, we derive an analytic expression for the entropy gain. This is illustrated, using various magnitude distributions, for earthquake data from north China, and extensions to a multivariate linked model outlined. The results measure the effectiveness of the stress release process as a predictive tool. Comparisons are made with a scale derived from the Gamma renewal process and using Molchan's ν-τ diagram.     

Exceedance probability distributions of steady conduit flow in karst aquifers

Discharge exceedance probabilities are calculated for a simple model karst aquifer composed of a few multilevel conduits with recharge from a single sinking stream with an exponential flow exceedance distribution. It is assumed that outflow instantaneously matches inflow, so that the conduit volume is constant but discharge is governed by the head in a volumeless shaft at the top end of the system. It is shown that small single conduit aquifers will frequently overflow at the surface during floods and the exceedance probability of flow through the aquifer and over the surface can be defined as a function of the inflow distribution and the form of the aquifer. Systems with multiple conduits will overflow less frequently, but each conduit will exhibit a flow distribution characteristic of its form and position in the vertical hierarchy. Comparison of these findings with actual flow data from a conduit aquifer shows that the approach is valid, although imprecise. The model is unlikely to be applied directly, as it requires unusually detailed data. However, it provides for the first time an indication of typical flow durations for surface overflows and individual conduits in a karst aquifer. Contrasts in flow duration will have a profound influence on solutional and sedimentary processes in the karst system.     

The use of geometric and gamma-related distributions for frequency analysis of water deficit

This paper presents an approach to perform statistical frequency analysis of water deficit duration and severity using respectively the geometric and exponential distributions. Monthly mean water discharges are compared to a given threshold and classified in two mutually exclusive ways. This leads to a two state random variable such that: a success represents the absence of a water deficit event (mean monthly discharge exceeds threshold), and a failure, a water deficit event (mean monthly discharge is below threshold). If we suppose that this random variable gives rise to a Markov process of order 1, then the duration of a water deficit event X (consecutive months in deficit) will have a geometric distribution. In turn, the summation of discharges in deficit will give the severity of a water deficit event which can be represented by a one-parameter exponential distribution. The threshold or base level is taken as a percentile of the observed mean discharges of a given month. This base level, which varies from month to month, can be viewed as the limit of an acceptable deficit (or energetic failure) associated to a given empirical probability of being in deficit. The second step of the approach is to estimate the value of the parameter for each distribution using the maximum likelihood method. Expressions for the estimator of a given percentile, , as well as its variance are deduced. Finally, the presented models are applied to observed data.     

Order statistics of functionals of strong ground motion for a class of renewal processes

In this paper, probability distribution functions are derived for the order statistics of various functionals of strong ground motion at a site. These functionals can be: Modified Mercalli Intensity (MMI), peak ground acceleration (PGA), Fourier spectral amplitudes of acceleration, response spectrum amplitudes (spectral displacement, pseudo-spectral velocity and pseudo-spectral acceleration), and amplitudes of the peaks (local maxima and local minima) in the time historyof the response of SDOF and MDOF structures at the site. Three parameters of the response of a structure are considered: displacement, shear force and bending moment at each level (storey) of the structure. The earthquake sources contributing to the risk of ground motion at the site are a number of point, area or volume sources, each with defined frequency of occurence-magnitude relationship. The magnitudes of the possible events at these sources are discretized, and the occurrence of events of different magnitudes are assumed to be statistically independent. For each magnitude, it is assumed that the eartquakes occur in a Poissonian sequence or in a renewal process which is a generalization of the Poissonian. For these assumptions, the probability distribution functions are presented for the number of earthquakes, n, during which a given level of site or structural response is exceeded during the exposure time, and for the return period of the exceedances. For example, for single-degree- of-freedom: (SDOF) or multi-degree-of-freedom structures, (MDOF) n can be the number of earthquakes during which the response of a storey will exceed a given level at least m times(m = 1, 2, 3,…) during the exposure time. These probability distribution functions can be used to extend the concept of uniform probability functionals to more than one exceedance. A more important application is to generalize the uniform probability functionals method of site response (uniform probability Fourier or response spectra) to uniform probability envelopes of displacement, shears and bending moments of a given structure. The uniform probability envelopes can be for exceedance at least once during at least one earthquake, or, in general, for exceedance at least m times per earthquake (m = 1, 2,…) during at least n earthquakes. In other words, during at least n earthquakes at least m peaks in the response can be higher than the specified level. Such uniform probability envelopes can be used (1) to define new design guidelines for building codes based on cost-benefit analysis; (2) to construct more refined probability distribution functions for the damage and total economic losses caused by earthquakes; and (3) to develop planning and decision strategies on strengthening and retrofitting existing buildings.     

On the annual maximum distribution in dependent partial duration series

As a basis for development of the annual maximum distribution the so-called partial duration series with Poissonian occurrence times and exponentially distributed peak exceedance values has been selected. The model is generalized by allowing for a Markov dependence between succeeding peak values. Correlation values from p=0 to p=1 can be accounted for by introducing the Marshall-Olkin bivariate exponential distribution, which is presented in detail. The developed distribution function for the annual maximum is throughly analysed and a variety of distribution forms depending on the value of the correlation coefficient and the intensity in the Poisson process is hereby recognized. To a certain extent this might be considered as parallel to the scattering of hydrological regions with different generating mechanisms for the annual maxima.     

Modelling Seismic Hazard in Earthquake Loss Models with Spatially Distributed Exposure

The prediction of possible future losses from earthquakes, which in many cases affect structures that are spatially distributed over a wide area, is of importance to national authorities, local governments, and the insurance and reinsurance industries. Generally, it is necessary to estimate the effects of many, or even all, potential earthquake scenarios that could impact upon these urban areas. In such cases, the purpose of the loss calculations is to estimate the annual frequency of exceedance (or the return period) of different levels of loss due to earthquakes: so-called loss exceedance curves. An attractive option for generating loss exceedance curves is to perform independent probabilistic seismic hazard assessment calculations at several locations simultaneously and to combine the losses at each site for each annual frequency of exceedance. An alternative method involves the use of multiple earthquake scenarios to generate ground motions at all sites of interest, defined through Monte–Carlo simulations based on the seismicity model. The latter procedure is conceptually sounder but considerably more time-consuming. Both procedures are applied to a case study loss model and the loss exceedance curves and average annual losses are compared to ascertain the influence of using a more theoretically robust, though computationally intensive, procedure to represent the seismic hazard in loss modelling.An erratum to this article can be found at     

Low and high flow analyses and wavelet application for characterization of the Blue Nile River system

The low and high flow characteristic of the Blue Nile River (BNR) basin is presented. The study discusses low and high flow, flow duration curve (FDC) and trend analysis of the BNR and its major tributaries. Different probability density functions were fitted to better describe the low and high flows of the BNR and major tributaries in the basin. Wavelet analysis was used in understanding the variance and frequency‐time localization and detection of dominant oscillations in rainfall and flow. FDCs were developed, and low flow (below 50% exceedance) and high flow (over 75% exceedance) of the curves were analysed and compared. The Gravity Recovery and Climate Experiment (GRACE) satellite‐based maps of monthly changes in gravity converted to water equivalents from 2003 to 2006 for February, May and September showed an increase in the moisture influx in the BNR basin for the month of September, and loss of moisture in February and May. It was also shown that 2004 and 2005 were drier with less moisture influx compared to 2003 and 2006. On the basis of the Kolmogorov‐Smirnov, Anderson‐Darling and Chi‐square tests, Gen. Pareto, Frechet 3P, Log‐normal, Log‐logistics, Fatigue Life and Phased Bi‐Weibull distributions best describe the low and high flows within the BNR basin. This will be beneficial in developing flow hydrographs for similar ungauged watersheds within the BNR basin. The below 50% and above 75% exceedance on the FDC for five major rivers in addition to the BNR showed different characteristics depending on size, land cover, topography and other factors. The low flow frequency analysis of the BNR at Bahir Dar showed 0·55 m³/s as the monthly low flow with recurrence interval of 10 years. The wavelet analysis of the rainfall (at Bahir Dar and basin‐wide) and flows at three selected stations shows inter‐ and intra‐annual variability of rainfall and flows at various scales. Copyright © 2009 John Wiley & Sons, Ltd.     

Simulation of risk-consistent earthquake motion

A method to combine probabilistic seismic hazard analysis and stochastic earthquake motion models is presented. A set of parameters characterizing stochastic earthquake motion models is determined on a consistent probabilistic basis. The method proposed herein consists of two steps. First, the ground motion intensity is determined in the context of the conventional hazard curve technique. Next, other ground motion parameters such as duration, predominant frequency and spectral shape parameters are determined as conditional means corresponding to the annual probability of exceedance for the ground motion intensity. Some example applications are presented.     

Joint distribution of multiplicative errors in radar and satellite QPEs and its use in estimating the conditional exceedance probability

This paper characterizes the joint distribution of multiplicative errors (ME) in radar (R) and satellite (S) quantitative precipitation estimates (QPEs). A semi-parametric framework is established on the basis of this joint distribution to describe the probability of rainfall exceeding a particular threshold given concurrent R and S-based estimates (referred to as conditional exceedance probability, or CEP). This framework entails integrating copula-based joint distributions of MEs over a range of rainfall amounts to yield the joint probability of exceedance, which forms the basis for estimating CEP. In demonstrating this approach, MEs were computed for R (Weather Surveillance Radar-1988 Doppler) and S (Self-calibrating Multivariate Precipitation Retrieval) for central Texas over 2000–2007 using gauge records as the reference. Analysis of the MEs in R and S reveals a substantial correlation between the two, and it also shows that the interdependence is complex as a considerable portion of S QPEs are negatively biased while their concurrent R values are bias-neutral. CEP values from the semi-parametric approach is found to be generally superior to those empirically derived based on rainfall estimates: it yields values for a wide range of rainfall thresholds and suffers much fewer discontinuities and artifacts that the empirical results exhibit. For the lower range of S and R thresholds where sample size is relatively large (i.e., <20 mm h⁻¹ for the summer), the two sets of CEPs bear close resemblance, with both showing a relatively weak, but nevertheless substantial dependence on the threshold value for S. These findings confirm the plausibility of the semi-parametric CEP values, and demonstrate the utility of S QPEs in improving the confidence in rainfall exceedance under this framework.     

Evaluation of risk concepts in partial duration series

Conventional design practice aims at obtaining optimal estimates of floods with specified exceedance probabilities. Such estimates are, however, known on the average to be exceeded more frequently than expected. Alternatively, methods focusing on the expected exceedance probability can be used. Two different methods are considered here; the first is based on the sample distribution of true exceedance probabilities. The second is a Bayesian analogue using the likelihood function and a noninformative prior to describe the variability of exceedance probabilities. Appropriate analytical solutions are presented in both cases using the partial duration series approach.     

Evaluation of risk concepts in partial duration series

Conventional design practice aims at obtaining optimal estimates of floods with specified exceedance probabilities. Such estimates are, however, known on the average to be exceeded more frequently than expected. Alternatively, methods focusing on the expected exceedance probability can be used. Two different methods are considered here; the first is based on the sample distribution of true exceedance probabilities. The second is a Bayesian analogue using the likelihood function and a noninformative prior to describe the variability of exceedance probabilities. Appropriate analytical solutions are presented in both cases using the partial duration series approach.     

Establishing a threshold for rainfall-induced landslides by a kinetic energy–duration relationship

Many investigators have attempted to define the threshold of landslide failure, that is, the level of the selected climatic variable above which a rainfall-induced landslide occurs. Intensity–duration (I–d) relationships are the most common type of empirical thresholds proposed in the literature for predicting landslide occurrence induced by rainfall. Recent studies propose the use of the kinetic power per unit volume of rainfall (J m⁻² mm⁻¹) to quantify the threshold of landslides induced by rainfall. In this paper, the relationship between rainfall duration and kinetic power corresponding to landslides triggered by rain was used to propose a new approach to define the threshold for predicting landslide occurrence. In particular, for the first time, a kinetic power per unit volume of rainfall–duration relationship is proposed for defining the minimum threshold needed for landslide failure. This new method can be applied using commonly used relationship for estimating the kinetic power per unit volume of rainfall and a new equation based on the measured raindrop size distribution. The applicability of this last method was tested using the data of rainfall intensity, duration and median volume diameter for 51 landslides in Taiwan. For the 51 landslides, the comparison between the measured pairs' kinetic power–duration and all selected relationships demonstrated that the equation based on the measured raindrop size distribution is the best method to define the landslide occurrence threshold, as it is both a process-oriented approach and is characterized by the best statistical performance. This last method has also the advantage to allow the forecasting of landslide hazard before the end of the rainfall event, since the rainfall kinetic power threshold value can be exceeded for a time interval less than the event duration.     

Ground‐motion intensity and damage map selection for probabilistic infrastructure network risk assessment using optimization

In many parts of the world, earthquakes threaten regional infrastructure systems. For modeling risk using stochastic earthquake catalogs, random variables include rupture location and the damage state of different components. Thus, there is an infinite set of possible damage maps that a risk modeler could evaluate in an event‐based probabilistic loss model. Even a finite but large number of damage maps may not be practical, because many network performance measures are computationally expensive. Here, we show a computationally efficient method for selecting a subset of damage maps, corresponding ground‐motion intensity maps, and associated occurrence rates that reasonably estimates the full distribution of the ground‐motion intensity and a target performance measure using optimization. The method chooses a subset of maps and associated annual rates of occurrence that minimizes the error in estimating the distribution of a network performance measure as well as the marginal distributions of ground‐motion intensity exceedance. The joint distribution of the ground‐motion intensity is implicitly included in the objective function of the optimization problem via the network performance measure. We then show how to tune the optimization parameters based on consistency checks related to the network performance measure and the ground‐motion hazard. We illustrate the proposed method with a case study of the San Francisco Bay Area road network to estimate the exceedance curve of the average percentage change in morning commute trip time. This work facilitates expanded and risk‐consistent studies of the impacts of infrastructure networks on regional seismic risk and resiliency. Copyright © 2014 John Wiley & Sons, Ltd.