Lower Return Periods Research Articles

Increase in insurance losses caused by North Atlantic hurricanes in a warmer climate

North Atlantic hurricanes are a major driver of property losses in the United States and a critical peril for the reinsurance industry globally. We leverage insurance loss data and stochastic modeling to investigate the impacts of projected changes in hurricane climatology on the insurance industry, for +2 °C and +4 °C warming scenarios. We find that, relative to the historical baseline 1950-2022, expected changes in wind speed and rainfall may increase hurricane losses by 5% −15% (+2 °C) and 10% − 30% (+4 °C), with greater impacts at lower return periods than in the tail. The historical 100-year loss event may therefore be exceeded on average every 80 years (+2 °C) and 70 years (+4 °C). The expected changes in average annual loss are projected to be 10% (+2 °C) and 15% (+4 °C), with the largest relative increase attributable to precipitation-induced losses. Under the extreme SSP5-8.5 scenario, the expected loss inflation due to climate change is thus on the order of 0.5% per annum.

Multi-round decentralized dataset distillation with federated learning for Low Earth Orbit satellite communication

Satellite communication and Low Earth Orbit (LEO) satellites are important components of the 6G network, widely used for Earth observation tasks due to their low cost and short return period, making them a key technology for 6G network connectivity. Due to limitations in satellite system technology and downlink bandwidth, it is not feasible to download all high-resolution image information to ground stations. Even in existing federated learning (FL) methods, sharing well-trained parts of the model can still bottleneck with increasing model size. To address these challenges, we propose a new federated learning framework (FL-M3D) for LEO satellite communication that employs multi-round decentralized dataset distillation techniques. It allows satellites to independently extract local datasets and transmit them to ground stations instead of exchanging model parameters. Communication costs depend only on the size of the synthesized dataset and do not increase with larger models. However, the heterogeneity of satellite datasets can lead to sample ambiguity and decreased model convergence speed. Therefore, we propose distilling the datasets to mitigate the negative effects of data heterogeneity. Through experiments using real-world image datasets, FL-M3D reduces communication volume in simulated satellite networks by approximately 49.84% and achieves improved model performance.

Effectiveness of regional risk mitigation policies in equitably improving connectivity to essential service during hurricane-induced floods

This study aimed to evaluate the effectiveness of regional disaster mitigation policies in providing equitable access to essential services during hurricane-induced floods in Southeast Louisiana. Studies have been conducted on access to essential service facilities during and after disasters. However, there is limited research on whether current regional disaster mitigation plans ensure equitable access to emergency facilities. To this end, a methodology was developed to assess the effect of the 2017 Louisiana Coastal Master Plan developed by the Coastal Protection and Restoration Agency (CPRA) on equity in connectivity to essential service facilities (hospitals and fire stations) in a case study region in southeastern Louisiana. First, a graph-based model was used to represent the road network and determine the connectivity of five demographic groups during hurricane-induced flood scenarios. Herein, a hurricane-induced flood scenario with a low return period (50 years) was chosen for future years up to 2065, considering sea level rise and subsidence. Roads with flood depths exceeding 30 cm were considered impassable and were removed from the network. Connectivity was then determined using breadth-first search. Monte Carlo simulations were performed to propagate uncertainties in flood depths. It was found that minority groups were at a higher risk of losing access to emergency services during the selected hazard scenario. Native American and Asian populations were found to be at the highest risk of disconnection, followed by the Hispanic and African-American populations. Overall, the coastal master plan did not affect the equity (or lack thereof) in connectivity to essential service facilities.

Comparative Study of Low Flow Frequency Analysis Using Bivariate Copula Model at Soyanggang Dam and Chungju Dam

A univariate analysis that relies solely on precipitation data in low flow frequency analysis is a technique to express meteorological drought, so it is limited to analyzing the characteristics of hydrological drought related to available water resources. In addition, if the data for the model calibration are insufficient, the uncertainty of a single variable limits the construction of a reliable model. To improve this problem, a frequency analysis was performed by constructing a bivariate copula model as a multivariate model with a high correlation between variables targeting reservoir inflows. The methodology utilizes the theory of runs to identify low flow events, establishing a threshold based on the mandatory regional water supply plan, and determining the low flow duration and cumulative water deficit. The Gumbel copula function, effective in capturing correlations between hydrological variables, was applied to derive a joint bivariate probability distribution, facilitating the calculation of combined low flow event return periods. This study compared low flow frequencies at Soyanggang dam (’74–’22) and Chungju dam (’86–‘22), which are in the same Han River basin but have different capacities and water demands, using a bivariate copula model. The top four extreme low flow events for the two adjacent dam basins did not occur in the same year and, in the years of the extreme low flow events at one of the two dam basins, there was an insignificant magnitude at the remaining dam basin. This result is noteworthy because it shows that the possibility of extreme low flow events appearing simultaneously in both watersheds is not as high as expected. The operational efficiency can be improved by setting the coordinated operation rules of the two reservoirs using the copula dependency structure.

Operation Risk Simulation and Interaction Impact of Stormwater and Sewage Systems Based on Storm Water Management Model

With the increasing urbanization rate, higher demand is placed on drainage systems, necessitating analysis of their risk profiles. While many studies focus on the individual hydraulic modeling of stormwater and wastewater systems when considering operational risks, they often overlook the exacerbating effects of combined stormwater and wastewater flows on each other’s risks. In this study, we constructed a model of the combined stormwater and wastewater drainage system in Lijiao, Guangdong Province. We analyzed the operational risks of both stormwater and sewage networks in different scenarios, focusing on full-load pipes, overload pipes, node overflows, and minimum flow velocities. Furthermore, we compared the exacerbating effects of sewage and stormwater on each other’s network operational risks. Simulation results indicated that, for sewage networks with combined sewer sections, the lengths of full-load pipes and overload pipes increased by an average of 27.4% and 16.3%, respectively, during rainy weather scenarios compared to dry weather. After considering the inflow of sewage into combined sewer sections, the average length of full-load pipes increased by 3.8 km, overload pipe length increased by 1.1 km, and overflow volume increased by 2.26 × 104 m3. As the return period of rainfall events increases, these inter-system impacts gradually diminish. Therefore, when modeling drainage systems and assessing operational risks, particularly during low return period rainfall events, the inclusion of both stormwater and sewage in combined sewer networks should be comprehensively considered.

A new nonparametric copula framework for the joint analysis of river water temperature and low flow characteristics for aquatic habitat risk assessment

This study proposed a nonparametric copula hazard framework in the joint risk of river water temperature (RWT) and low flow (LF) events for aquatic ecosystems, specifically ectotherm fish. This nonparametric copula density can adapt to any mutual dependence structure, providing greater flexibility. This can reduce the risk of misspecification if the underlying assumption is violated compared to conventional parametric or semiparametric copula settings. The analysis uses nonparametric copulas densities like Beta kernel copula estimator (BKCE), Bernstein copula estimator (BCE), and Transformation kernel estimator (TKE), conjoined with Gaussian Kernel density estimations (GKDEs) and parametric marginals for joint annual maximum RWT (AMRWT) and LF. The study compares different models for analyzing five Swiss river basins: parametric copulas with best-fitted GKDE and parametric margins, versus nonparametric copula. Six bandwidth selectors are estimated to fit GKDE. BKCE with GKDE margins outperformed most stations, while TKE and BCE density with GKDE margins work best for only one station. However, at one station, BKCE with best-fitted parametric margins is outperformed. All stations except Station 2473 are characterized by temperature and low flows that may be conducive to stress of a number of aquatic species, causing high AMRWT (exceeding 19 °C) and minimum LF or specific discharge, SD) quantiles at low AND-joint return periods (RP). AND (i.e. low flow AND high temperature) hazard events are less likely to occur together than OR hazard events, while univariate RPs happen more often than OR-joint RPs. In addition, the joint RP of AMRWT, given LF at different percentiles, significantly affected AMRWT for various LF conditions. Higher AMRWT with low flow conditions results in lower joint RP (except station 2473), and this stress level would be reduced when conditioned with high LF events at the same AMRWT. Station 2473 has high LF even at low percentiles, and with low AMRWT makes it very less stressful than other station under different LF conditions. Summer river flow maintenance can improve aquatic environments with high RWT. Analyzing joint statistics is crucial to understanding mutual risk in freshwater ecosystems.

Stress from attention: The relationship between climate change attention and crude oil markets

Investors' focus on specific topics could translate into actual trading behavior, subsequently influencing market prices. Within the crude oil market, the issue of climate change risk arising from carbon emissions has garnered considerable attention recently, as investors' search behavior regarding this topic may impact crude oil prices. Based on the search information provided by Google, this paper employs quantile and quantile-on-quantile regression (QQR) methods to examine the relationship between investors' attention to climate change risk and crude oil futures price returns. The results reveal the following: (1) Simultaneous opposite correlations are observed, with a significantly positive relationship between attention and returns during high returns and a significantly negative relationship during periods of low returns. The correlation between the two exhibits considerable variation across different market performances. (2) A significant negative correlation exists mainly between attention to physical and opportunity risk and returns, while positive correlations exist mainly between attention to regulatory risk and returns. (3) Higher levels of climate change attention intensify these effects, as evidenced by an increase in the absolute value of the regression coefficients. The findings of this study can serve as a reference for investment institutions and policymakers in constructing investment portfolios and managing the impact of climate risk.

Impact of Land Use and Land Cover Change on Hydrological Processes in Urban Watersheds: Analysis and Forecasting for Flood Risk Management

Land use and land cover (LULC) change is one of the primary contributors to hydrological change in urban watersheds and can potentially influence stream flow and flood volume. Understanding the impacts of LULC change on urban hydrological processes is critical to effective urban water management and minimizing flood risks. In this context, this study aims to determine the impacts of LULC change on hydrological response in a fast transitioning watershed for the predicted years of 2050 and 2080. This research employs the hybrid land use classification technique, Cellular Automata–Markov (CA–Markov) model to predict land use changes, utilizing land use data from 2001, 2013, and 2021. Additionally, it incorporates a calibrated, event-specific hydrologic model known as the Personal Computer Storm Water Management Model (PCSWMM) to assess alterations in hydrological responses for storm events of various magnitudes. The findings indicate a transition of the watershed into an urbanized landscape, replacing the previous dominance of agriculture and forested areas. The initial urban area, constituting 11.6% of the total area in 2021, expands to cover 34.1% and 44.2% of the total area by 2050 and 2080, respectively. Due to the LULC changes, there are increases in peak discharge of 5% and 6.8% and in runoff volume of 8% and 13.3% for the years 2050 and 2080 for a 100-year return period storm event. Yet, the extent of these changes intensifies notably during storm events with lower return periods. This heightened impact is directly attributed to the swift urbanization of the watershed. These results underscore the pressing necessity to regulate LULC change to preserve the hydrological equilibrium.

Effect of unreinforced masonry infills on seismic performance of reinforced concrete frame‐shear wall buildings

SummaryReinforced concrete (RC) shear wall buildings with unreinforced masonry (URM) infilled moment frames are common in India and neighboring countries. This study assesses the influence of the URM infills on their seismic performance. Fully infilled, open first‐storied, and bare frame versions of a 25‐story shear wall building are considered. Multiple stripe analysis is conducted at five return periods to estimate their performance. Fragility functions for the collapse prevention limit state, which is based on seven engineering demand parameter exceedance thresholds, are generated and compared. The presence of infills (full or partial) is observed to have an overall positive effect on the performance of the RC frame‐shear wall buildings. The performance of the open first‐story building was comparable to that of the fully infilled building. The ratio of story shear carried by the moment frames and shear walls is studied at all return periods to understand the variation in frame shear wall interaction with increased damage for each building. In the case of buildings with infills, the frames carry a higher proportion of story shear at lower return periods. For all three buildings, the fraction of story shear carried by moment frames increases along the height of the building.

Hydrological reduction and control effect evaluation of sponge city construction based on one-way coupling model of SWMM-FVCOM: A case in university campus

The exacerbation of global warming, the frequent incidence of extreme weather events, and the rapid urbanization have collectively contributed to the heightened prevalence of flooding in urban areas. As a result of this challenge, sponge city (SPC) has been adopted in China as an efficient means of preventing and controlling urban floods. To evaluate the hydrological reduction and control effect of sponge city construction (SPCC) within a university campus, a one-way coupled model integrating one-dimensional sewer hydrodynamic model (SWMM) and two-dimensional surface flow model (FVCOM), namely SWMM-FVCOM model, was established. The Nash-Sutcliffe efficiency (NSE) of the SWMM were greater than 0.75 under there rainfalls with different intensity, indicating the good reliability and stability of this model could be used in the subsequent simulation. An analysis of drainage capacity and the risk of urban flooding was conducted using this model before and after the implementation of SPCC, considering six rainfall scenarios. Implementing SPCC demonstrated an effective performance in mitigating surface runoff, regulating inspection well overflow, and reducing overflow volume in the study region. However, the efficacy of runoff control diminished proportionally with the escalation of rainfall return period. Simultaneously, the implementation of low impact development (LID) measures can significantly decrease the extent and magnitude of surface inundations. The reduction rate of SPCC on the area of waterlogging ranged from 55.84% to 72.50%. But the control rate decreased with increasing rainfall return periods, demonstrating that adopting SPCC can effectively mitigate the severity of urban flooding resulting from low rainfall return period events (Tr < 20 years). This study can provide scientific foundation for environment managers to evaluate the impact of urban flooding prevention and control on runoff pollution mitigation when adopting the implementation of SPCC.

Assessing the impact of climate change on fluvial flood losses in urban areas: a case study of Pamplona (Spain)

ABSTRACT Climate change is expected to increase the frequency and magnitude of flooding. Furthermore, in recent years, there has been an increase in city extent and population densities. This study considers the metropolitan area of Pamplona (Spain) as a case study. The delta changes in precipitation quantiles in the Arga River catchment, obtained from 12 climate models, have been transformed into peak flow delta changes using the Real-time Interactive Basin Simulator (RIBS) model. Also, three percentiles of flood quantile delta changes are selected. Water depths and flood extents expected in future flood events have been obtained using the two-dimensional Iber hydrodynamic model. The Safer_DAMAGE algorithm has been used to assess flood losses in urban areas at the building scale. The results show that flood losses are expected to be smaller for low return periods and greater for high return periods.

Investigating the Reliability of Stationary Design Rainfall in a Mediterranean Region under a Changing Climate

Extreme rainfall events have been more frequent in recent decades, potentially as a climate change effect. This has been leading to a higher risk of the failure of existing hydraulic infrastructures, and to a higher awareness regarding the unreliability of design rainfall calculated with reference to historical data recorded in the last century. With this in mind, the present study questions the stationary assumption of the rainfall Depth–Duration–Frequency curves commonly used in Sicily, the biggest island of the Mediterranean Sea. Quantiles derived from the most up-to-date regional method, regarding Sicily, based on observations in the period 1928–2010, have been compared with those extracted from a high-resolution dataset related to the period 2002–2022, provided by the SIAS agency. The results showed a remarkable underestimation of the rainfall quantiles calculated with the regional approach, especially at the shortest durations and low return periods. This means that new hydraulic works should be designed with reference to longer return periods than in the recent past, and those that currently exist may experience a higher risk of failure. Future investigation of this aspect is crucial for enhancing the effectiveness of water management and detecting hydrological risks under a changing climate.

Uncertainty estimation of regionalised depth–duration–frequency curves in Germany

Abstract. The estimation of rainfall depth–duration–frequency (DDF) curves is necessary for the design of several water systems and protection works. These curves are typically estimated from observed locations, but due to different sources of uncertainties, the risk may be underestimated. Therefore, it becomes crucial to quantify the uncertainty ranges of such curves. For this purpose, the propagation of different uncertainty sources in the regionalisation of the DDF curves for Germany is investigated. Annual extremes are extracted at each location for different durations (from 5 min up to 7 d), and local extreme value analysis is performed according to Koutsoyiannis et al. (1998). Following this analysis, five parameters are obtained for each station, from which four are interpolated using external drift kriging, while one is kept constant over the whole region. Finally, quantiles are derived for each location, duration and given return period. Through a non-parametric bootstrap and geostatistical spatial simulations, the uncertainty is estimated in terms of precision (width of 95 % confidence interval) and accuracy (expected error) for three different components of the regionalisation: (i) local estimation of parameters, (ii) variogram estimation and (iii) spatial estimation of parameters. First, two methods were tested for their suitability in generating multiple equiprobable spatial simulations: sequential Gaussian simulations (SGSs) and simulated annealing (SA) simulations. Between the two, SGS proved to be more accurate and was chosen for the uncertainty estimation from spatial simulations. Next, 100 realisations were run at each component of the regionalisation procedure to investigate their impact on the final regionalisation of parameters and DDF curves, and later combined simulations were performed to propagate the uncertainty from the main components to the final DDF curves. It was found that spatial estimation is the major uncertainty component in the chosen regionalisation procedure, followed by the local estimation of rainfall extremes. In particular, the variogram uncertainty had very little effect on the overall estimation of DDF curves. We conclude that the best way to estimate the total uncertainty consisted of a combination between local resampling and spatial simulations, which resulted in more precise estimation at long observation locations and a decline in precision at unobserved locations according to the distance and density of the observations in the vicinity. Through this combination, the total uncertainty was simulated by 10 000 runs in Germany, and it indicated that, depending on the location and duration level, tolerance ranges from ± 10 %–30 % for low-return periods (lower than 10 years) and from ± 15 %–60 % for high-return periods (higher than 10 years) should be expected, with the very short durations (5 min) being more uncertain than long durations.

Multi-timescale dynamics of extreme river flood and storm surge interactions in relation with large-scale atmospheric circulation: Case of the Seine estuary

The present work investigates the multi-timescale dynamics of extreme fluvial-surge interactions (EFS) in a river-tide environment, in the case of the Seine estuary. This environment is considered an excellent natural laboratory to analyze river-surge interaction because of its time-varying flow and the available water-level records provided by tide gauges along the estuary. A spectral approach has been used to investigate the multi-timescale changes in EFS, governed by fluvial and marine contributions, in relation to the historical events of flood-storm concomitance and the large-scale atmospheric circulation. The spectral components of EFS, calculated at five stations along the estuary, highlighted a series of variability modes varying from the inter-month (∼3–6 months) to the inter-annual (∼2-, ∼3-5- and ∼6-8-years) scales and exhibiting, respectively, 55% and 20% of the total variability. The contribution of marine and fluvial effects in the EFS varies along the estuary and according to the timescale from seasons, when the interaction is governed by tidal deformation, to years. The connection of the historical flood-storm events with the EFS signal changes in their spectral signature according to their severity as well as the energetic physical drivers acting in each event: events with high return period are manifested at larger scales while events with low return period are limited to small scales.Finally, the examination of the physical relationships between the EFS and the global climate mechanisms has demonstrated the key role of the Sea Level Pressure (SLP) and the North Atlantic Oscillation (NAO) acting, respectively, in anti-phase at ∼1-2-yr and in phase at scales larger than 3-yr. The signature of the climate drivers operates differently according to the timescale; they are identified within the ∼80% of the inter-annual EFS. This signature is more significative since the 2000s when the increase in the NAO generates a rise in EFS variability. ∼20% of EFS would be related to the non-linear effects of the timescale interactions and other local mechanisms operating at such scales.This finding highlights the non-stationarity of the multi-timescale dynamics of marine storms and fluvial floods, and the relevance of the climate connection use for assessing the compound multi-hazard events at large-scales.

Offloading operation bivariate extreme response statistics for FPSO vessel

The Floating Production Storage and Offloading unit (FPSO) is an offshore unit producing and storing crude oil prior to tanker transport. An important design concern is an accurate prediction of risky dynamic hawser tensions during FPSO offloading operations. Bivariate extreme hawser tension contours are important for selecting proper design values. This paper employed the AQWA hydrodynamic software to analyze vessel hydrodynamic wave loads dynamic response, acting on FPSO vessels under realistic sea state conditions. This paper presents an efficient method for estimating FPSO bivariate response statistics based on numerical simulations validated by various experiments. The bivariate Average Conditional Exceedance Rate (ACER2D) method offers an accurate bivariate extreme value probability distribution and return period contours estimation, utilizing available data efficiently. The two-dimensional probability contours, corresponding to low probability return periods, are easily obtained by the ACER2D method. The performance of the presented method has shown that the ACER2D method provides an efficient and accurate prediction of extreme return period contours. The suggested approach may be used for FPSO vessel design, minimizing potential FPSO hawser damage. Bivariate contours yield bivariate design points, as opposed to a pair of uncoupled univariate design points with the same return period as currently adopted in the industry.

Construction and application of sponge city resilience evaluation system: a case study in Xi’an, China

Urban vulnerability is evident when highly complex flood risks overlap with diverse cities, and it is important to enhance the resilience of cities to flood shocks. In this study, a sponge city resilience assessment system is established considering engineering, environmental and social indicators, and the grey relational analysis method (GRA) is used to quantify sponge city resilience. At the same time, a multi-objective optimization model is established based on the three dimensions of water ecological environment, drainage safety, and waterlogging safety. The optimal configuration of grey-green infrastructure is weighed by combining the ideal point method, aiming to ensure that cities effectively reduce flood risk through the optimal configuration scheme. Taking the Xiaozhai area in Xi'an as the study area, the evaluation results show that the grey relational degree (GRD) of the resilience indexes of the original scheme is between 0.390 and 0.661 under the seven different return periods, while the optimization scheme ranges from 0.648 to 0.765, with the best sponge city resilience at a return period of 2a. Compared with the original scheme, the optimized sponge city resilience level increases from level II to nearly level I in the low return period and from level IV to level II in the high return period, indicating that city's ability to cope with waterlogging and pollution is enhanced significantly. Besides, the main factor affecting the sponge city resilience is the runoff control rate, followed by pollutant load reduction rate, which can provide a methodological framework for the assessment and improvement of sponge city resilience.

Regionalisation of rainfall depth–duration–frequency curves with different data types in Germany

Abstract. Rainfall depth–duration–frequency (DDF) curves are required for the design of several water systems and protection works. For the reliable estimation of such curves, long and dense observation networks are necessary, which in practice is seldom the case. Usually observations with different accuracy, temporal resolution and density are present. In this study, we investigate the integration of different observation datasets under different methods for the local and regional estimation of DDF curves in Germany. For this purpose, two competitive DDF procedures for local estimation (Koutsoyiannis et al., 1998; Fischer and Schumann, 2018) and two for regional estimation (kriging theory vs. index based) are implemented and compared. Available station data from the German Weather Service (DWD) for Germany are employed, which includes 5000 daily stations with more than 10 years available, 1261 high-resolution (1 min) recordings with an observation period between 10 and 20 years, and finally 133 high-resolution (1 min) recordings with 60–70 years of observations. The performance of the selected approaches is evaluated by cross-validation, where the local DDFs from the long sub-hourly time series are considered the true reference. The results reveal that the best approach for the estimation of the DDF curves in Germany is by first deriving the local extreme value statistics based on Koutsoyiannis et al.'s (1998) framework and later using the kriging regionalisation of long sub-hourly time series with the short sub-hourly time series acting as an external drift. The integration of the daily stations proved to be useful only for DDF values of a low return period (T[a] &lt; 10 years) but does not introduce any improvement for higher return periods (T[a] ≥ 10 years).

Discontinuance of Lower Neuadd reservoir

Lower Neuadd reservoir was created by an embankment dam constructed in 1884 in what has since become the Brecon Beacons National Park. The dam and spillway have exhibited a long history of concerns surrounding their integrity. The deteriorating spillway channel, faulty scour valve and the leakage through the core with associated settlement of the embankment dam reached a point where remediation was not reasonably practical. The chosen solution was discontinuance by excavating a notch through the embankment dam. Obtaining permission to alter listed structures within a national park required detailed environmental assessments and negotiation with the authorities. Construction was complicated by a mountainous catchment that created significant flows at low-return periods that could fill the empty reservoir basin in hours and overtop the works.

A Low-Return-Period Rainfall Intensity Formula for Estimating the Design Return Period of the Combined Interceptor Sewers

The design rainfall intensity and its return period of the combined interceptor sewer is an important factor affecting combined sewer overflow (CSO) occurrence. However, we often use the interceptor ratio (or interceptor multiple, n0) to design the interceptor sewer, and its equivalent design return period is often ignored. In this study, a low return period rainfall formula modeling method was proposed to estimate this return period. First, a new rainfall event separation approach was especially developed, and the minimum interevent time (MIET) was set to time of concentration of the tributary area corresponding to the most downstream interceptor well. Second, a new rainfall intensity sampling algorithm, annual multi—event—maxima (AMEM) sampling algorithm, was put forward. For this sampling algorithm, several maxima of rainfall intensity should be sampled annually, and only one maximum is sampled for each rainfall event. In addition, the empirical frequency values of the above sampled rainfall intensities can be obtained according to the mathematical expectation formula (Weibull formula). After comparison, the lognormal distribution was selected for the theoretical probability density function. Finally, parameters of the low return period rainfall intensity formula were estimated using three-parameter Horner formula and MCMC (Markov Chain Monte Carlo) algorithm. A case study was conducted to demonstrate the proposed method based on the recorded rainfall data from a meteorological station in southwestern China and a combined sewer system. Results revealed that: (1) A MIET determination method was proposed according to independence of CSO events. (2) An annual multi-event-maxima (AMEM) sampling was proposed for collecting samples of the low return period rainfall intensity. (3) For the case study, the best-fit distribution for low return period rainfall intensity was lognormal distribution. (4) Resulted low return period rainfall intensity formula was provided.

Integrating Long and Short‐Term Time Dependencies in Simulation‐Based Seismic Hazard Assessments

AbstractConventional probabilistic seismic hazard analysis (PSHA) only considers mainshock events and uses a time‐independent earthquake rupture forecast to describe the occurrence of mainshocks. This approach neglects the long‐term time‐dependency of mainshocks on specific fault segments, the interaction of adjacent faults, and the spatial and temporal clustering of aftershocks. This study integrates a recently proposed advanced fault‐based PSHA framework with an aftershock simulator based on the Epidemic‐Type Aftershock Sequence (ETAS) model, to overcome the aforementioned limitations. Central Italy is used as a case study to illustrate the proposed framework. The case‐study hazard curves show that including state‐of‐the‐art advances in fault‐based PSHA may increase the ground‐motion amplitudes for low return periods, and decrease the ground‐motion amplitudes for high return periods, relative to a conventional PSHA approach. The magnitude of ground‐motion estimate increases due to aftershock inclusion is dependent on the selected site and return period. Sensitivity analyses of the results demonstrate that: (a) close to modeled faults, high‐return‐period hazard estimates are more affected by fault‐related inputs than the aftershock inclusion; (b) close to modeled faults, the influence of aftershock inclusion is higher for low return periods than high ones; (c) away from modeled faults, aftershocks inclusion greatly affects the variance of the hazard results; and (d) fault interaction has a limited effect on the variance of the hazard estimates compared to other analysis inputs. This study could help with the future implementation of complex fault modeling approaches and aftershock hazard in seismic risk models.