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Kang, Ling, Shangwen Jiang, Xiaoyong Hu, and Changwen Li. "Evaluation of Return Period and Risk in Bivariate Non-Stationary Flood Frequency Analysis." Water 11, no. 1 (2019): 79. http://dx.doi.org/10.3390/w11010079.
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The concept of a traditional return period has long been questioned in non-stationary studies, and the risk of failure was recommended to evaluate the design events in flood modeling. However, few studies have been done in terms of multivariate cases. To investigate the impact of non-stationarity on the streamflow series, the Yichang station in the Yangtze River was taken as a case study. A time varying copula model was constructed for bivariate modeling of flood peak and 7-day flood volume, and the non-stationary return period and risk of failure were applied to compare the results between stationary and non-stationary models. The results demonstrated that the streamflow series at the Yichang station showed significant non-stationary properties. The flood peak and volume series presented decreasing trends in their location parameters and the dependence structure between them also weakened over time. The conclusions of the bivariate non-stationary return period and risk of failure were different depending on the design flood event. In the event that both flood peak and volume are exceeding, the flood risk is smaller with the non-stationary model, which is a joint effect of the time varying marginal distribution and copula function. While in the event that either flood peak or volume exceed, the effect of non-stationary properties is almost negligible. As for the design values, the non-stationary model is characterized by a higher flood peak and lower flood volume. These conclusions may be helpful in long-term decision making in the Yangtze River basin under non-stationary conditions.
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Latif, Shahid, and Firuza Mustafa. "Bivariate Hydrologic Risk Assessment of Flood Episodes using the Notation of Failure Probability." Civil Engineering Journal 6, no. 10 (2020): 2002–23. http://dx.doi.org/10.28991/cej-2020-03091599.
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Floods are becoming the most severe and challenging hydrologic issue at the Kelantan River basin in Malaysia. Flood episodes are usually thoroughly characterized by flood peak discharge flow, volume and duration series. This study incorporated the copula-based methodology in deriving the joint distribution analysis of the annual flood characteristics and the failure probability for assessing the bivariate hydrologic risk. Both the Archimedean and Gaussian copula family were introduced and tested as possible candidate functions. The copula dependence parameters are estimated using the method-of-moment estimation procedure. The Gaussian copula was recognized as the best-fitted distribution for capturing the dependence structure of the flood peak-volume and peak-duration pairs based on goodness-of-fit test statistics and was further employed to derive the joint return periods. The bivariate hydrologic risks of flood peak flow and volume pair, and flood peak flow and duration pair in different return periods (i.e., 5, 10, 20, 50 and 100 years) were estimated and revealed that the risk statistics incrementally increase in the service lifetime and, at the same instant, incrementally decrease in return periods. In addition, we found that ignoring the mutual dependency can underestimate the failure probabilities where the univariate events produced a lower failure probability than the bivariate events. Similarly, the variations in bivariate hydrologic risk with the changes of flood peak in the different synthetic flood volume and duration series (i.e., 5, 10, 20, 50 and 100 years return periods) under different service lifetimes are demonstrated. Investigation revealed that the value of bivariate hydrologic risk statistics incrementally increases over the project lifetime (i.e., 30, 50, and 100 years) service time, and at the same time, it incrementally decreases in the return period of flood volume and duration. Overall, this study could provide a basis for making an appropriate flood defence plan and long-lasting infrastructure designs. Doi: 10.28991/cej-2020-03091599 Full Text: PDF
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Tosunoğlu, Fatih, Gianfausto Salvadori, and Muhammet Yilmaz. "Multivariate Assessment of Low-Flow Hazards via Copulas: The Case Study of the Çoruh Basin (Turkey)." Water 12, no. 10 (2020): 2848. http://dx.doi.org/10.3390/w12102848.
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Bivariate modeling and hazard assessment of low flows are performed exploiting copulas. 7-day low flows observed, respectively, in the upper, middle and lower parts of the Çoruh basin (Turkey) are examined, considering three pairs of certified stations located in different sub-basins. A thorough statistical analysis indicates that the GEV distribution can be used to model the marginal behavior of the low-flow. The joint distributions at each part are modeled via a dozen of copula families. As a result, the Husler–Reiss copula adequately fits the joint low flows in the upper part, while the t-Student copula turns out to best fit the other parts. In order to assess the low-flow hazard, these copulas are then used to compute joint return periods and failure probabilities under a critical bivariate “AND” hazard scenario. The results indicate that the middle and lower parts of the Çoruh basin are likely to experience the largest drought hazards. As a novelty, the statistical tools used allow to objectively quantify drought threatening in a thorough multivariate perspective, which involves distributional analysis, frequency analysis (return periods) and hazard analysis (failure probabilities).
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Gu, Lei, Jie Chen, Jiabo Yin, et al. "Projected increases in magnitude and socioeconomic exposure of global droughts in 1.5 and 2 °C warmer climates." Hydrology and Earth System Sciences 24, no. 1 (2020): 451–72. http://dx.doi.org/10.5194/hess-24-451-2020.
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Abstract. The Paris Agreement sets a long-term temperature goal to hold global warming to well below 2.0 ∘C and strives to limit it to 1.5 ∘C above preindustrial levels. Droughts with either intense severity or a long persistence could both lead to substantial impacts such as infrastructure failure and ecosystem vulnerability, and they are projected to occur more frequently and trigger intensified socioeconomic consequences with global warming. However, existing assessments targeting global droughts under 1.5 and 2.0 ∘C warming levels usually neglect the multifaceted nature of droughts and might underestimate potential risks. This study, within a bivariate framework, quantifies the change in global drought conditions and corresponding socioeconomic exposures for additional 1.5 and 2.0 ∘C warming trajectories. The drought characteristics are identified using the Standardized Precipitation Evapotranspiration Index (SPEI) combined with the run theory, with the climate scenarios projected by 13 Coupled Model Inter-comparison Project Phase 5 (CMIP5) global climate models (GCMs) under three representative concentration pathways (RCP 2.6, RCP4.5 and RCP8.5). The copula functions and the most likely realization are incorporated to model the joint distribution of drought severity and duration, and changes in the bivariate return period with global warming are evaluated. Finally, the drought exposures of populations and regional gross domestic product (GDP) under different shared socioeconomic pathways (SSPs) are investigated globally. The results show that within the bivariate framework, the historical 50-year droughts may double across 58 % of global landmasses in a 1.5 ∘C warmer world, while when the warming climbs up to 2.0 ∘C, an additional 9 % of world landmasses would be exposed to such catastrophic drought deteriorations. More than 75 (73) countries' populations (GDP) will be completely affected by increasing drought risks under the 1.5 ∘C warming, while an extra 0.5 ∘C warming will further lead to an additional 17 countries suffering from a nearly unbearable situation. Our results demonstrate that limiting global warming to 1.5 ∘C, compared with 2 ∘C warming, can perceptibly mitigate the drought impacts over major regions of the world.
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Latif, Shahid, and Slobodan P. Simonovic. "Parametric Vine Copula Framework in the Trivariate Probability Analysis of Compound Flooding Events." Water 14, no. 14 (2022): 2214. http://dx.doi.org/10.3390/w14142214.
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The interaction between oceanographic, meteorological, and hydrological factors can result in an extreme flooding scenario in the low-lying coastal area, called compound flooding (CF) events. For instance, rainfall and storm surge (or high river discharge) can be driven by the same meteorological forcing mechanisms, tropical or extra-tropical cyclones, resulting in a CF phenomenon. The trivariate distributional framework can significantly explain compound events’ statistical behaviour reducing the associated high-impact flood risk. Resolving heterogenous dependency of the multidimensional CF events by incorporating traditional 3D symmetric or fully nested Archimedean copula is quite complex. The main challenge is to preserve all lower-level dependencies. An approach based on decomposing the full multivariate density into simple local building blocks via conditional independence called vine or pair-copulas is a much more comprehensive way of approximating the trivariate flood dependence structure. In this study, a parametric vine copula of a drawable (D-vine) structure is introduced in the trivariate modelling of flooding events with 46 years of observations of the west coast of Canada. This trivariate framework searches dependency by combining the joint impact of annual maximum 24-h rainfall and the highest storm surge and river discharge observed within the time ±1 day of the highest rainfall event. The D-vine structures are constructed in three alternative ways by permutation of the conditioning variables. The most appropriate D-vine structure is selected using the fitness test statistics and estimating trivariate joint and conditional joint return periods. The investigation confirms that the D-vine copula can effectively define the compound phenomenon’s dependency. The failure probability (FP) method is also adopted in assessing the trivariate hydrologic risk. It is observed that hydrologic events defined in the trivariate case produce higher FP than in the bivariate (or univariate) case. It is also concluded that hydrologic risk increases (i) with an increase in the service design life of the hydraulic facilities and (ii) with a decrease in return periods.
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Shiau, J. T. "Return period of bivariate distributed extreme hydrological events." Stochastic Environmental Research and Risk Assessment (SERRA) 17, no. 1-2 (2003): 42–57. http://dx.doi.org/10.1007/s00477-003-0125-9.
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Li, Qian, Liutong Chen, Zhengtao Yan, and Yingjun Xu. "Exploration of Copula Models Use in Risk Assessment for Freezing and Snow Events: A Case Study in Southern China." Sustainability 14, no. 5 (2022): 2568. http://dx.doi.org/10.3390/su14052568.
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Due to cold waves, low and extremely low temperatures occur every winter. Sudden cooling can cause freezing and snow disasters, which seriously affect transportation, power, safety, and other activities, resulting in serious economic losses. Based on precipitation and average temperature data from 258 national meteorological stations over the past 70 years, this study established a historical freezing and snow event data set, extracting the accumulated precipitation intensity (API) and accumulated temperature intensity (ATI). We selected the optimal distribution function and joint distribution function for each station and calculated the univariate and bivariate joint return periods. The return period accuracy plays an important role in risk assessment results. By comparing the calculations with the real return period for historical extreme events, we found that the bivariate joint return period based on a copula model was more accurate than the univariate return period. This is important for the prediction and risk assessment of freezing and snow disasters. Additionally, a risk map based on the joint return period showed that Jiangsu and Anhui, as well as some individual stations in the central provinces, were high-risk areas; however, the risk level was lower in Chongqing and the southern provinces.
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Stamatatou, Nikoletta, Lampros Vasiliades, and Athanasios Loukas. "Bivariate Flood Frequency Analysis Using Copulas." Proceedings 2, no. 11 (2018): 635. http://dx.doi.org/10.3390/proceedings2110635.
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Flood frequency estimation for the design of hydraulic structures is usually performed as a univariate analysis of flood event magnitudes. However, recent studies show that for accurate return period estimation of the flood events, the dependence and the correlation pattern among flood attribute characteristics, such as peak discharge, volume and duration should be taken into account in a multivariate framework. The primary goal of this study is to compare univariate and joint bivariate return periods of floods that all rely on different probability concepts in Yermasoyia watershed, Cyprus. Pairs of peak discharge with corresponding flood volumes are estimated and compared using annual maximum series (AMS) and peaks over threshold (POT) approaches. The Lyne-Hollick recursive digital filter is applied to separate baseflow from quick flow and to subsequently estimate flood volumes from the quick flow timeseries. Marginal distributions of flood peaks and volumes are examined and used for the estimation of typical design periods. The dependence between peak discharges and volumes is then assessed by an exploratory data analysis using K-plots and Chi-plots, and the consistency of their relationship is quantified by Kendall’s correlation coefficient. Copulas from Archimedean, Elliptical and Extreme Value families are fitted using a pseudo-likelihood estimation method, verified using both graphical approaches and a goodness-of-fit test based on the Cramér-von Mises statistic and evaluated according to the corrected Akaike Information Criterion. The selected copula functions and the corresponding joint return periods are calculated and the results are compared with the marginal univariate estimations of each variable. Results indicate the importance of the bivariate analysis in the estimation of design return period of the hydraulic structures.
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Vandenberghe, S., M. J. van den Berg, B. Gräler, et al. "Joint return periods in hydrology: a critical and practical review focusing on synthetic design hydrograph estimation." Hydrology and Earth System Sciences Discussions 9, no. 5 (2012): 6781–828. http://dx.doi.org/10.5194/hessd-9-6781-2012.
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Abstract. Most of the hydrological and hydraulic studies refer to the notion of a return period to quantify design variables. When dealing with multiple design variables, the well-known univariate statistical analysis is no longer satisfactory and several issues challenge the practitioner. How should one incorporate the dependence between variables? How should the joint return period be defined and applied? In this study, an overview of the state-of-the-art for defining joint return periods is given. The construction of multivariate distribution functions is done through the use of copulas, given their practicality in multivariate frequency analysis and their ability to model numerous types of dependence structures in a flexible way. A case study focusing on the selection of design hydrograph characteristics is presented and the design values of a three-dimensional phenomenon composed of peak discharge, volume and duration are derived. Joint return period methods based on regression analysis, bivariate conditional distributions, bivariate joint distributions, and Kendal distribution functions are investigated and compared highlighting theoretical and practical issues of multivariate frequency analysis. Also an ensemble-based method is introduced. For a given design return period, the method chosen clearly affects the calculated design event. Eventually, light is shed on the practical implications of a chosen method.
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Requena, A. I., L. Mediero, and L. Garrote. "A bivariate return period based on copulas for hydrologic dam design: accounting for reservoir routing in risk estimation." Hydrology and Earth System Sciences 17, no. 8 (2013): 3023–38. http://dx.doi.org/10.5194/hess-17-3023-2013.
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Abstract. A multivariate analysis on flood variables is needed to design some hydraulic structures like dams, as the complexity of the routing process in a reservoir requires a representation of the full hydrograph. In this work, a bivariate copula model was used to obtain the bivariate joint distribution of flood peak and volume, in order to know the probability of occurrence of a given inflow hydrograph. However, the risk of dam overtopping is given by the maximum water elevation reached during the routing process, which depends on the hydrograph variables, the reservoir volume and the spillway crest length. Consequently, an additional bivariate return period, the so-called routed return period, was defined in terms of risk of dam overtopping based on this maximum water elevation obtained after routing the inflow hydrographs. The theoretical return periods, which give the probability of occurrence of a hydrograph prior to accounting for the reservoir routing, were compared with the routed return period, as in both cases hydrographs with the same probability will draw a curve in the peak-volume space. The procedure was applied to the case study of the Santillana reservoir in Spain. Different reservoir volumes and spillway lengths were considered to investigate the influence of the dam and reservoir characteristics on the results. The methodology improves the estimation of the Design Flood Hydrograph and can be applied to assess the risk of dam overtopping.
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Volpi, Elena. "On return period and probability of failure in hydrology." Wiley Interdisciplinary Reviews: Water 6, no. 3 (2019): e1340. http://dx.doi.org/10.1002/wat2.1340.
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Volpi, E., and A. Fiori. "Hydraulic structures subject to bivariate hydrological loads: Return period, design, and risk assessment." Water Resources Research 50, no. 2 (2014): 885–97. http://dx.doi.org/10.1002/2013wr014214.
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Mesbahzadeh, Tayyebeh, Maryam Mirakbari, Mohsen Mohseni Saravi, Farshad Soleimani Sardoo, and Nir Y. Krakauer. "Joint Modeling of Severe Dust Storm Events in Arid and Hyper Arid Regions Based on Copula Theory: A Case Study in the Yazd Province, Iran." Climate 8, no. 5 (2020): 64. http://dx.doi.org/10.3390/cli8050064.
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Natural disasters such as dust storms are random phenomena created by complicated mechanisms involving many parameters. In this study, we used copula theory for bivariate modeling of dust storms. Copula theory is a suitable method for multivariate modeling of natural disasters. We identified 40 severe dust storms, as defined by the World Meteorological Organization, during 1982–2017 in Yazd province, central Iran. We used parameters at two spatial vertical levels (near-surface and upper atmosphere) that included surface maximum wind speed, and geopotential height and vertical velocity at 500, 850, and 1000 hPa. We compared two bivariate models based on the pairs of maximum wind speed–geopotential height and maximum wind speed–vertical velocity. We determined the bivariate return period using Student t and Gaussian copulas, which were considered as the most suitable functions for these variables. The results obtained for maximum wind speed–geopotential height indicated that the maximum return period was consistent with the observed frequency of severe dust storms. The bivariate modeling of dust storms based on maximum wind speed and geopotential height better described the conditions of severe dust storms than modeling based on maximum wind speed and vertical velocity. The finding of this study can be useful to improve risk management and mitigate the impacts of severe dust storms.
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Requena, A. I., L. Mediero, and L. Garrote. "Bivariate return period based on copulas for hydrologic dam design: comparison of theoretical and empirical approach." Hydrology and Earth System Sciences Discussions 10, no. 1 (2013): 557–96. http://dx.doi.org/10.5194/hessd-10-557-2013.
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Abstract. Hydrologic frequency analyses are usually focused on flood peaks. Multivariate analyses on flood variables have not been so exhaustively studied despite the fact that they are required to represent the full hydrograph, which is essential for designing some structures like dams. In this work, a bivariate copula model was used to obtain the bivariate joint distribution of flood peak and volume. An empirical bivariate return period was defined in terms of acceptable risk to the dam through the maximum water elevation reached during the routing process, in order to perform a risk assessment of dam overtopping. A Monte Carlo procedure was developed to compare the probability of occurrence of a flood with the return period linked to the risk of dam overtopping. The procedure is applied to the case study of the Santillana reservoir in Spain. A set of synthetic peak-volume pairs was generated by the fitted copula and synthetic hydrographs were routed through the reservoir. Different reservoir volumes and spillway lengths were considered. Hydrographs with the same risk were represented by a curve in the peak-volume space. These curves were compared to those linked to the probability of occurrence of a flood event, in order to improve the estimation of the Design Flood Hydrograph.
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da Rocha Júnior, Rodrigo Lins, Fabrício Daniel dos Santos Silva, Rafaela Lisboa Costa, Heliofábio Barros Gomes, David Duarte Cavalcante Pinto, and Dirceu Luis Herdies. "Bivariate Assessment of Drought Return Periods and Frequency in Brazilian Northeast Using Joint Distribution by Copula Method." Geosciences 10, no. 4 (2020): 135. http://dx.doi.org/10.3390/geosciences10040135.
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The Northeast region of Brazil (NRB) is the most populous semiarid area in the world and is extremely susceptible to droughts. The severity and duration of these droughts depend on several factors, and they do not necessarily follow the same behavior. The aim of this work is to evaluate the frequency of droughts in the NRB and calculate the return period of each drought event using the copula technique, which integrates the duration and severity of the drought in the NRB in a joint bivariate distribution. Monthly precipitation data from 96 meteorological stations spatially distributed in the NRB, ranging from 1961 to 2017, are used. The copula technique is applied to the Standardized Precipitation Index (SPI) on the three-month time scale, testing three families of Archimedean copula functions (Gumbel–Hougaard, Clayton and Frank) to reveal which model is best suited for the data. Averagely, the most frequent droughts observed in the NRB are concentrated in the northern sector of the region, with an observed duration varying from three and a half to five and a half months. However, the eastern NRB experiences the most severe droughts, lasting for 14 to 24 months. The probability distributions that perform better in modeling the series of severity and duration of droughts are exponential, normal and lognormal. The observed severity and duration values show that, for average values, the return period across the region is approximately 24 months. Still in this regard, the southernmost tip of the NRB stands out for having a return period of over 35 months. Regarding maximum observed values of severity and duration, the NRB eastern strip has the longest return period (>60 months), mainly in the southeastern portion where a return period above 90 months was observed. The northern NRB shows the shortest return period (~45 months), indicating that it is the NRB sector with the highest frequency of intense droughts. These results provide useful information for drought risk management in the NRB.
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Gabriel, Rosemary Kiama, and Yurui Fan. "Multivariate Hydrologic Risk Analysis for River Thames." Water 14, no. 3 (2022): 384. http://dx.doi.org/10.3390/w14030384.
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This study analyzed the multivariate flood risk for the river Thames at Kingston based on historical flood data from the National River Flow Archive (NRFA) website. The bivariate risk analysis framework was prepared from the joint return periods of the peak flow (m3/s) and 3-day annual maximum flow (m3/s) flood pair. A total of 137 samples of flood pairs from 1883 to 2019 were adopted for risk analysis. The multivariate return periods were characterized depending on the quantification of the bivariate flood frequency analysis of the pair through copulas methods. The unknown parameter of each copula was estimated using the method-of-moment (MOM) estimator based on Kendall’s tau inversion, in which the Clayton copula performed best to model the dependence of the two flood variables. Then, the bivariate hydrologic risk was characterized based on the joint return period in AND, established from the Clayton copula method. The results reveal that the flood pair would keep a constant hydrologic risk value for some time then moderately decrease as the 3-day AMAX flow increases from 700 m3/s. This hydrologic risk indicator was analyzed under four service time scenarios and three peak flows whose return periods were positioned at 50, 100, and 150 years. The outcomes from the bivariate risk analysis of the flood pairs can be used as decision support during the design of flood defenses and hydraulic facilities.
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Yanmaz, A. Melih, and M. Engin Gunindi. "Assessment of overtopping reliability and benefits of a flood detention dam." Canadian Journal of Civil Engineering 35, no. 10 (2008): 1177–82. http://dx.doi.org/10.1139/l08-052.
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There is a growing tendency to assess safety levels of existing dams and to design new dams using probabilistic approaches according to project characteristics and site-specific conditions. This study is a probabilistic assessment of the overtopping reliability of a dam, which will be designed for flood detention purpose, and will compute the benefits that can be gained as a result of the implementation of this dam. In a case study, a bivariate flood frequency analysis was carried out using a five-parameter bivariate gamma distribution. A family of joint return period curves relating the runoff peak discharges to the runoff volumes at the dam site was derived. A number of hydrographs were also obtained under a joint return period of 100 years to observe the variation of overtopping tendency. The maximum reservoir elevation and overtopping reliability were determined by performing a probabilistic reservoir routing based on Monte Carlo simulations.
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De Luca, Davide Luciano, and Daniela Biondi. "Bivariate Return Period for Design Hyetograph and Relationship with T-Year Design Flood Peak." Water 9, no. 9 (2017): 673. http://dx.doi.org/10.3390/w9090673.
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Sahoo, Bibhuti Bhusan, Ramakar Jha, Anshuman Singh, and Deepak Kumar. "Bivariate low flow return period analysis in the Mahanadi River basin, India using copula." International Journal of River Basin Management 18, no. 1 (2019): 107–16. http://dx.doi.org/10.1080/15715124.2019.1576698.
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Chamorro, Alejandro, Tobias Houska, Shailesh Singh, and Lutz Breuer. "Projection of Droughts as Multivariate Phenomenon in the Rhine River." Water 12, no. 8 (2020): 2288. http://dx.doi.org/10.3390/w12082288.
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Drought is a complex phenomenon whose characterization is best achieved from a multivariate perspective. It is well known that it can generate adverse consequences in society. In this regard, drought duration, severity, and their interrelationship play a critical role. In a climate change scenario, drought characterization and the assessment of the changes in its pattern are essential for a proper quantification of water availability and managing strategies. The purpose of this study is to characterize hydrological droughts in the Rhine River in a multivariate perspective for the historical period and estimate the expected multivariate drought patterns for the next decades. Further, a comparison of bivariate drought patterns between historical and future projections is performed for different return periods. This will, first, indicate if changes can be expected and, second, what the magnitudes of these possible changes could be. Finally, the underlying uncertainty due to climate projections is estimated. Four Representative Concentration Pathways (RCP) are used along with five General Circulation Models (GCM). The HBV hydrological model is used to simulate discharge in both periods. Characterization of droughts is accomplished by the Standardized Runoff Index and the interdependence between drought severity and duration is modelled by a two-dimensional copula. Projections from different climate models show important differences in the estimation of the number of drought events for different return periods. This study reveals that duration and severity present a clear interrelationship, suggesting strongly the appropriateness of a bivariate model. Further, projections show that the bivariate interdependencies between drought duration and severity show clearly differences depending on GCMs and RCPs. Apart from the influence of GCMs and RCMs, it is found that return periods also play an important role in these relationships and uncertainties. Finally, important changes in the bivariate drought patterns between the historical period and future projections are estimated constituting important information for water management purposes.
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Goodarzi, Ehsan, Majid Mirzaei, and Mina Ziaei. "Evaluation of dam overtopping risk based on univariate and bivariate flood frequency analyses." Canadian Journal of Civil Engineering 39, no. 4 (2012): 374–87. http://dx.doi.org/10.1139/l2012-012.
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There is a growing tendency to assess safety of dams by mathematical and statistical methods in hydrosystem engineering. This research presents the application of risk and uncertainty analysis to dam overtopping based on univariate and bivariate flood frequency analyses by applying Gumbel logistic distribution. The bivariate frequency analyses produced six inflow hydrographs with a joint return period of 100 years. Afterward, the overtopping risk of the Doroudzan Dam was evaluated for all six inflow hydrographs by considering quantile of flood peak discharge, initial depth of water in the reservoir, and discharge coefficient of spillway as uncertain variables and using two uncertainty analysis methods; Monte Carlo simulation and Latin hypercube sampling. Finally, the results of both univariate and bivariate frequency analyses were compared to show the significance of bivariate analysis on dam overtopping.
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Bouabdelli, Senna, Mohamed Meddi, Ayoub Zeroual, and Ramdane Alkama. "Hydrological drought risk recurrence under climate change in the karst area of Northwestern Algeria." Journal of Water and Climate Change 11, S1 (2020): 164–88. http://dx.doi.org/10.2166/wcc.2020.207.
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Abstract This study aims to estimate hydrological drought risk using probabilistic analysis of bivariate drought characteristics to assess both past and future drought severity and duration in three basins located in the widest karst massif of northern Algeria. The procedures entail: (1) identification of extent of meteorological drought that could trigger corresponding hydrological drought through their characteristics; (2) assessment of future risk of extreme drought according to two emission scenarios of the representative concentration pathway (RCP 4.5 and 8.5); and (3) estimation of drought return periods using bivariate frequency analysis and investigation of their future change rates under climate change. Hydrological droughts were computed by using the bias-corrected future climate projections from nine global climate models downscaled using the Rossby Centre Regional Climate model (RCA4), and GR2M hydrological model. The analysis revealed a connection between meteorological and hydrological drought occurrences and the response time depended on the memory effect of the considered basin. We also found strong consensus between past drought event return periods, determined by bivariate frequency analysis, and those determined by climate models under RCP8.5 scenario. Finally, in regards to drought return periods (10, 50 and 100 years), the risk of extreme drought recurrence in the future has been projected to be larger than the reference period.
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Kim, Yoo, Chung, and Kim. "Hydrologic Risk Assessment of Future Extreme Drought in South Korea Using Bivariate Frequency Analysis." Water 11, no. 10 (2019): 2052. http://dx.doi.org/10.3390/w11102052.
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Recently, climate change has increased the frequency of extreme weather events. In South Korea, extreme droughts are frequent and cause serious damage. To identify the risk of extreme drought, we need to calculate the hydrologic risk using probabilistic analysis methods. In particular, future hydrologic risk of extreme drought should be compared to that of the control period. Therefore, this study quantitatively assessed the future hydrologic risk of extreme drought in South Korea according to climate change scenarios based on the representative concentration pathway (RCP) 8.5. A threshold level method was applied to observation-based rainfall data and climate change scenario-based future rainfall data to identify drought events and extract drought characteristics. A bivariate frequency analysis was then performed to estimate the return period considering both duration and severity. The estimated return periods were used to calculate and compare hydrologic risks between the control period and the future. Results indicate that the average duration of drought events for the future was similar with that for the control period, however, the average severity increased in most future scenarios. In addition, there was decreased risk of maximum drought events in the Yeongsan River basin in the future, while there was increased risk in the Nakdong River basin. The median of risk of extreme drought in the future was calculated to be larger than that of the maximum drought in the control period.
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Li, Ning, Xueqin Liu, Wei Xie, Jidong Wu, and Peng Zhang. "The Return Period Analysis of Natural Disasters with Statistical Modeling of Bivariate Joint Probability Distribution." Risk Analysis 33, no. 1 (2012): 134–45. http://dx.doi.org/10.1111/j.1539-6924.2012.01838.x.
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Requena, Ana I., Ilaria Prosdocimi, Thomas R. Kjeldsen, and Luis Mediero. "A bivariate trend analysis to investigate the effect of increasing urbanisation on flood characteristics." Hydrology Research 48, no. 3 (2016): 802–21. http://dx.doi.org/10.2166/nh.2016.105.
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Flood frequency analyses are usually based on the assumption of stationarity, which might be unrealistic if changes in climate, land uses or urbanisation impact the study catchment. Moreover, most non-stationarity studies only focus on peak flows, ignoring other flood characteristics. In this study, the potential effect of increasing urbanisation on the bivariate relationship of peak flows and volumes is investigated in a case study in the northwest of England, consisting of an increasingly urbanised catchment and a nearby hydrologically and climatologically similar unchanged rural (control) catchment. The study is performed via Kendall's tau and copulas. Temporal trends are studied visually and by formal tests, considering variables individually and jointly. Bivariate joint return period curves associated with consecutive time periods are compared to understand the joint implications of such bivariate trends. Although no significant bivariate trends were detected, hydrologically relevant trends were found in the urbanised catchment.
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Bačová Mitková, Veronika, and Dana Halmová. "Joint modeling of flood peak discharges, volume and duration: a case study of the Danube River in Bratislava." Journal of Hydrology and Hydromechanics 62, no. 3 (2014): 186–96. http://dx.doi.org/10.2478/johh-2014-0026.
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Abstract The study is focused on the analysis and statistical evaluation of the joint probability of the occurrence of hydrological variables such as peak discharge (Q), volume (V) and duration (t). In our case study, we focus on the bivariate statistical analysis of these hydrological variables of the Danube River in Bratislava gauging station, during the period of 1876-2013. The study presents the methodology of the bivariate statistical analysis, choice of appropriate marginal distributions and appropriate copula functions in representing the joint distribution. Finally, the joint return periods and conditional return periods for some hydrological pairs (Q-V, V-t, Q-t) were calculated. The approach using copulas can reproduce a wide range of correlation (nonlinear) frequently observed in hydrology. Results of this study provide comprehensive information about flood where a devastating effect may be increased in the case where its three basic components (or at least two of them) Q, V and t have the same significance.
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Gräler, B., M. J. van den Berg, S. Vandenberghe, et al. "Multivariate return periods in hydrology: a critical and practical review focusing on synthetic design hydrograph estimation." Hydrology and Earth System Sciences 17, no. 4 (2013): 1281–96. http://dx.doi.org/10.5194/hess-17-1281-2013.
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Abstract. Most of the hydrological and hydraulic studies refer to the notion of a return period to quantify design variables. When dealing with multiple design variables, the well-known univariate statistical analysis is no longer satisfactory, and several issues challenge the practitioner. How should one incorporate the dependence between variables? How should a multivariate return period be defined and applied in order to yield a proper design event? In this study an overview of the state of the art for estimating multivariate design events is given and the different approaches are compared. The construction of multivariate distribution functions is done through the use of copulas, given their practicality in multivariate frequency analyses and their ability to model numerous types of dependence structures in a flexible way. A synthetic case study is used to generate a large data set of simulated discharges that is used for illustrating the effect of different modelling choices on the design events. Based on different uni- and multivariate approaches, the design hydrograph characteristics of a 3-D phenomenon composed of annual maximum peak discharge, its volume, and duration are derived. These approaches are based on regression analysis, bivariate conditional distributions, bivariate joint distributions and Kendall distribution functions, highlighting theoretical and practical issues of multivariate frequency analysis. Also an ensemble-based approach is presented. For a given design return period, the approach chosen clearly affects the calculated design event, and much attention should be given to the choice of the approach used as this depends on the real-world problem at hand.
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Brunner, Manuela I., Katharina Liechti, and Massimiliano Zappa. "Extremeness of recent drought events in Switzerland: dependence on variable and return period choice." Natural Hazards and Earth System Sciences 19, no. 10 (2019): 2311–23. http://dx.doi.org/10.5194/nhess-19-2311-2019.
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Abstract. The 2018 drought event had severe ecological, economic, and social impacts. How extreme was it in Switzerland? We addressed this question by looking at different types of drought, including meteorological, hydrological, agricultural, and groundwater drought, and at the two characteristics deficit and deficit duration. The analysis consisted of three main steps: (1) event identification using a threshold-level approach, (2) drought frequency analysis, and (3) comparison of the 2018 event to the severe 2003 and 2015 events. In Step 2 the variables precipitation, discharge, soil moisture, and low-flow storage were first considered separately in a univariate frequency analysis; pairs of variables were then investigated jointly in a bivariate frequency analysis using a copula model for expressing the dependence between the two variables under consideration. Our results show that the 2018 event was especially severe in north-eastern Switzerland in terms of soil moisture, with return periods locally exceeding 100 years. Slightly longer return periods were estimated when discharge and soil moisture deficits were considered together. The return period estimates depended on the region, variable, and return period considered. A single answer to the question of how extreme the 2018 drought event was in Switzerland is therefore not possible – rather, it depends on the processes one is interested in.
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Naz, Saba, Muhammad Ahsanuddin, Syed Inayatullah, Tanveer Ahmed Siddiqi, and Muhammad Imtiaz. "Copula-Based Bivariate Flood Risk Assessment on Tarbela Dam, Pakistan." Hydrology 6, no. 3 (2019): 79. http://dx.doi.org/10.3390/hydrology6030079.
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Flooding from the Indus river and its tributaries has regularly influenced the region of Pakistan. Therefore, in order to limit the misfortune brought about by these inevitable happenings, it requires taking measures to estimate the occurrence and effects of these events. The current study uses flood frequency analysis for the forecast of floods along the Indus river of Pakistan (Tarbela). The peak and volume are the characteristics of a flood that commonly depend on one another. For progressively proficient hazard investigation, a bivariate copula method is used to measure the peak and volume. A univariate analysis of flood data fails to capture the multivariate nature of these data. Copula is the most common technique used for a multivariate analysis of flood data. In this paper, four Archimedean copulas have been tried using the available information, and in light of graphical and measurable tests, the Gumbel Hougaard copula was found to be most appropriate for the data used in this paper. The primary (TAND, TOR), conditional and Kendall return periods have been also determined. The copula method was found to be a powerful method for the distribution of marginal variables. It also gives the Kendall return period for the multivariate analysis the consequences of flooding.
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Neary, Vincent S., Seongho Ahn, Bibiana E. Seng, et al. "Characterization of Extreme Wave Conditions for Wave Energy Converter Design and Project Risk Assessment." Journal of Marine Science and Engineering 8, no. 4 (2020): 289. http://dx.doi.org/10.3390/jmse8040289.
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Best practices and international standards for determining n-year return period extreme wave (sea states) conditions allow wave energy converter designers and project developers the option to apply simple univariate or more complex bivariate extreme value analysis methods. The present study compares extreme sea state estimates derived from univariate and bivariate methods and investigates the performance of spectral wave models for predicting extreme sea states at buoy locations within several regional wave climates along the US East and West Coasts. Two common third-generation spectral wave models are evaluated, a WAVEWATCH III® model with a grid resolution of 4 arc-minutes (6–7 km), and a Simulating WAves Nearshore model, with a coastal resolution of 200–300 m. Both models are used to generate multi-year hindcasts, from which extreme sea state statistics used for wave conditions characterization can be derived and compared to those based on in-situ observations at National Data Buoy Center stations. Comparison of results using different univariate and bivariate methods from the same data source indicates reasonable agreement on average. Discrepancies are predominantly random. Large discrepancies are common and increase with return period. There is a systematic underbias for extreme significant wave heights derived from model hindcasts compared to those derived from buoy measurements. This underbias is dependent on model spatial resolution. However, simple linear corrections can effectively compensate for this bias. A similar approach is not possible for correcting model-derived environmental contours, but other methods, e.g., machine learning, should be explored.
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Goodarzi, E., M. Mirzaei, L. T. Shui, and M. Ziaei. "Evaluation dam overtopping risk based on univariate and bivariate flood frequency analysis." Hydrology and Earth System Sciences Discussions 8, no. 6 (2011): 9757–96. http://dx.doi.org/10.5194/hessd-8-9757-2011.
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Abstract. There is a growing tendency to assess the safety levels of existing dams based on risk and uncertainty analysis using mathematical and statistical methods. This research presents the application of risk and uncertainty analysis to dam overtopping based on univariate and bivariate flood frequency analyses by applying Gumbel logistic distribution for the Doroudzan earth-fill dam in south of Iran. The bivariate frequency analysis resulted in six inflow hydrographs with a joint return period of 100-yr. The overtopping risks were computed for all of those hydrographs considering quantile of flood peak discharge (in particular 100-yr), initial depth of water in the reservoir, and discharge coefficient of spillway as uncertain variables. The maximum height of the water, as most important factor in the overtopping analysis, was evaluated using reservoir routing and the Monte Carlo and Latin hypercube techniques were applied for uncertainty analysis. Finally, the achieved results using both univariate and bivariate frequency analysis have been compared to show the significance of bivariate analyses on dam overtopping.
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Chang, Kook-Hyun, and Byung-Jo Yoon. "Forecasting the Currency Spot with the Trading Volume and the Trading Volume Volatility of Currency Futures in Won/Dollar FX Market." Journal of Derivatives and Quantitative Studies 18, no. 3 (2010): 1–23. http://dx.doi.org/10.1108/jdqs-03-2010-b0001.
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This paper tries to empirically investigate whether the information contained in trading volume, volume volatility of Won/Dollar currency futures may be statistically useful in forecasting currency spot return. This paper uses both the jump-diffusion GARCH model and the bivariate GARCH type BEKK model to estimate the trading volume volatility of currency futures and the volatility of currency spot, sampled daily during 1/4/2000~12/30/2009 period. According to the findings of this study, previous information contained in both trading volume and the volume volatility of Won/Dollar currency futures might be useful in explaining the future return of the currency spot.
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Li, Tianyuan, Shenglian Guo, Zhangjun Liu, Lihua Xiong, and Jiabo Yin. "Bivariate design flood quantile selection using copulas." Hydrology Research 48, no. 4 (2016): 997–1013. http://dx.doi.org/10.2166/nh.2016.049.
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Flood event consists of peak discharge and flood volume that are mutually correlated and can be described by a copula function. For a given bivariate joint distribution, a choice of design return period will lead to infinite combinations of peak discharge and flood volume. A boundary identification method is developed to define the feasible ranges of flood peak and volume suitable for combination, and two combination methods, i.e., equivalent frequency combination (EFC) method and conditional expectation combination method for estimating unique bivariate flood quantiles are also proposed. Monte Carlo simulation method is used to evaluate the performance of these combination methods. The Geheyan reservoir in China was selected as case study. It is shown that the joint design values estimated by the two proposed combination methods are both within the feasible range, which means that the methods could be selected for designing unique flood quantiles. The proposed bivariate combination methods are also compared with univariate method, and the reservoir water level estimated by EFC method is higher than the other methods, which means the EFC method is safer for reservoir design. The developed approach provides an applicable way for the identification of feasible range and flood quantile estimation.
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Orcel, Olivier, Philippe Sergent, and François Ropert. "Trivariate copula to design coastal structures." Natural Hazards and Earth System Sciences 21, no. 1 (2021): 239–60. http://dx.doi.org/10.5194/nhess-21-239-2021.
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Abstract. Some coastal structures must be redesigned in the future due to rising sea levels caused by climate change. The design of structures subjected to the actions of waves requires an accurate estimate of the long return period of such parameters as wave height, wave period, storm surge and more specifically their joint exceedance probabilities. The simplified Defra method that is currently used in particular for European coastal structures makes it possible to directly connect the joint exceedance probabilities to the product of the univariate probabilities by means of a single factor. These schematic correlations do not, however, represent all the complexity of the reality because of the use of this single factor. That may lead to damaging errors in coastal structure design. The aim of this paper is therefore to remedy the lack of robustness of these current approaches. To this end, we use copula theory with a copula function that aggregates joint distribution functions to their univariate margins. We select a bivariate copula that is adapted to our application by the likelihood method. In order to integrate extreme events, we also resort to the notion of tail dependence. The optimal copula parameter is estimated through the analysis of the tail dependence coefficient, the likelihood method and the mean error. The most robust copulas for our practical case with applications in Saint-Malo and Le Havre (in northern France) are the Clayton copula and the survival Gumbel copula. The originality of this paper is the creation of a new and robust trivariate copula with an analysis of the sensitivity to the method of construction and to the choice of the copula. Firstly, we select the best fitting of the bivariate copula with its parameter for the two most correlated univariate margins. Secondly, we build a trivariate function. For this purpose, we aggregate the bivariate function with the remaining univariate margin with its parameter. We show that this trivariate function satisfies the mathematical properties of the copula. We finally represent joint trivariate exceedance probabilities for a return period of 10, 100 and 1000 years. We finally conclude that the choice of the bivariate copula is more important for the accuracy of the trivariate copula than its own construction.
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Skenderi, Nagip, and Adem Dreshaj. "Influence of Macroeconomic Factors in Failure of Return of Bank Loans in Kosovo." Mediterranean Journal of Social Sciences 9, no. 5 (2018): 97–106. http://dx.doi.org/10.2478/mjss-2018-0141.
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Abstract The risk from non-payment of loans is a challenge for all the banks. Payment of the loans is a crucial issue for efficient functioning of the banking system. Loaning is one of the main uncertainties in the banking business, for loan payment can be rarely guaranteed completely. Often, a question occurs: what are the factors that influence in failure of the return of bank loan? What are the politics that must be followed to stimulate the return of bank loans? Through this research we aim to highlight the reasons of debtors in failing of loan return by studying the link of macroeconomic factors with NPL (non-performing loans). This is a first research in Kosovo that analyses the link of the macroeconomic factors influence (GDP, interest norms, unemployment, inflation, maturity period and grace period) these referred in the research as “independent variables” in failure of bank loan return that in the study bellow are referred as “dependent variable NPL for the Kosovo bank sector. This study argues as what is needed for the Kosovo banking system and presents the ideas of sustainable development of banking system in correspondence with non-performing loans, acknowledgment of the factors that hinder the return of the bank loans and reorientation of the loaning politics.
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Stamatatou, Nikoletta, Lampros Vasiliades, and Athanasios Loukas. "The Effect of Sample Size on Bivariate Rainfall Frequency Analysis of Extreme Precipitation." Proceedings 7, no. 1 (2018): 19. http://dx.doi.org/10.3390/ecws-3-05815.
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The objective of this study is to compare univariate and joint bivariate return periods of extreme precipitation that all rely on different probability concepts in selected meteorological stations in Cyprus. Pairs of maximum rainfall depths with corresponding durations are estimated and compared using annual maximum series (AMS) for the complete period of the analysis and 30-year subsets for selected data periods. Marginal distributions of extreme precipitation are examined and used for the estimation of typical design periods. The dependence between extreme rainfall and duration is then assessed by an exploratory data analysis using K-plots and Chi-plots and the consistency of their relationship is quantified by Kendall’s correlation coefficient. Copulas from Archimedean, Elliptical, and Extreme Value families are fitted using a pseudo-likelihood estimation method, evaluated according to the corrected Akaike Information Criterion and verified using both graphical approaches and a goodness-of-fit test based on the Cramér-von Mises statistic. The selected copula functions and the corresponding conditional and joint return periods are calculated and the results are compared with the marginal univariate estimations of each variable. Results highlight the effect of sample size on univariate and bivariate rainfall frequency analysis for hydraulic engineering design practices.
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Subramaniam, Srividya, Gagan Sharma, and Srishti Sehgal. "Profitability of Style based Investment Strategies: Evidence from India." Asian Journal of Finance & Accounting 9, no. 2 (2017): 1. http://dx.doi.org/10.5296/ajfa.v9i2.11456.
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In this paper, we aim to identify profitable investment styles on the Indian stock market by using various combinations of important stock pricing anomalies consisting of. size, value, volume, profitability, earnings surprises, short term and long term prior returns. Using NSE200 stocks, three different investment styles viz. univariate, independent bivariate and conditional bivariate are constructed for the period July 2005-June 2016.Results show that on an absolute return basis, bivariate strategies do not seem to outperform univariate strategies. The unifactor CAPM is able to absorb 42% of the returns owing to the explanatory power of beta. After adjusting for risk using the three factor Fama and French (1993) model, 42% of the alphas are explained. However, additional risk factors from the Carhart (1997) model and Fama and French (2015) model do not provide any incremental explanatory power over the three factor model, recommending the use of the latter as a baseline to evaluate investment strategies in India. The highest supernormal returns of 1.1% per month are obtained from combining attributes and employing the conditional bivariate investment strategy viz.E2L1 (earnings momentum-Liquidity), M2S1 (price momentum-size), E2M3 (earnings momentum-price momentum). The findings are pertinent to portfolio managers, financial regulators and other stakeholders.
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Vandenberghe, S., N. E. C. Verhoest, E. Buyse, and B. De Baets. "A stochastic design rainfall generator based on copulas and mass curves." Hydrology and Earth System Sciences Discussions 7, no. 3 (2010): 3613–48. http://dx.doi.org/10.5194/hessd-7-3613-2010.
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Abstract. The use of design storms can be very useful in many hydrological and hydraulic practices. In this study, the concept of a copula-based secondary return period in combination with the concept of mass curves is used to generate design storms. The analysis is based on storms selected from the 105 year rainfall time series with a 10 min resolution, measured at Uccle, Belgium. In first instance, bivariate copulas and secondary return periods are explained, together with a focus on which couple of storm variables is of highest interest for the analysis and a discussion of how the results might be affected by the goodness-of-fit of the copula. Subsequently, the fitted copula is used to sample storms with a predefined secondary return period for which characteristic variables such as storm duration and total storm depth can be derived. In order to construct design storms with a realistic storm structure, mass curves of 1st, 2nd, 3rd and 4th quartile storms are developed. An analysis shows that the assumption of independence between the secondary return period and the internal storm structure could be made. Based on the mass curves, a technique is developed to randomly generate an intrastorm structure. The coupling of both techniques eventually results in a methodology for stochastic design storm generation. Finally, its practical usefulness for design studies is illustrated based on the generation of design storm ensembles and rainfall-runoff modelling.
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Vandenberghe, S., N. E. C. Verhoest, E. Buyse, and B. De Baets. "A stochastic design rainfall generator based on copulas and mass curves." Hydrology and Earth System Sciences 14, no. 12 (2010): 2429–42. http://dx.doi.org/10.5194/hess-14-2429-2010.
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Abstract. The use of design storms can be very useful in many hydrological and hydraulic practices. In this study, the concept of a copula-based secondary return period in combination with the concept of mass curves is used to generate point-scale design storms. The analysis is based on storms selected from the 105 year rainfall time series with a 10 min resolution, measured at Uccle, Belgium. In first instance, bivariate copulas and secondary return periods are explained, together with a focus on which couple of storm variables is of highest interest for the analysis and a discussion of how the results might be affected by the goodness-of-fit of the copula. Subsequently, the fitted copula is used to sample storms with a predefined secondary return period for which characteristic variables such as storm duration and total storm depth can be derived. In order to construct design storms with a realistic storm structure, mass curves of 1st, 2nd, 3rd and 4th quartile storms are developed. An analysis shows that the assumption of independence between the secondary return period and the internal storm structure could be made. Based on the mass curves, a technique is developed to randomly generate an intrastorm structure. The coupling of both techniques eventually results in a methodology for stochastic design storm generation. Finally, its practical usefulness for design studies is illustrated based on the generation of a set of statistically identical design storm and rainfall-runoff modelling.
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Kho, Jenniefer Y., Michael P. Gaspar, Patrick M. Kane, Sidney M. Jacoby, and Eon K. Shin. "Prognostic Variables for Patient Return-to-Work Interval Following Carpal Tunnel Release in a Workers’ Compensation Population." HAND 12, no. 3 (2016): 246–51. http://dx.doi.org/10.1177/1558944716661991.
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Background: We hypothesize that depressive and anxiety disorders, chronic pain conditions, and work-related factors are significant determinants of the time interval for return to work (RTW) in the workers’ compensation (WC) population following carpal tunnel release (CTR) surgery. Methods: We retrospectively reviewed records of all WC patients who underwent open CTR surgery over a 5-year period by 1 of 3 fellowship-trained hand surgeons. One hundred fifty-two wrists in 108 patients (64 unilateral, 44 bilateral) met the inclusion criteria. Demographic, medical, and surgical data were obtained from patient records. Bivariate and multivariate analyses were performed to assess predictors of RTW. Results: Eighty-nine percent of all patients returned to work full-duty. Average RTW duration in all wrists was 12.5 ± 11.3 weeks. Predictors of delayed RTW in bivariate and multivariate analyses were depression with or without anxiety, chronic pain disorders including fibromyalgia, preoperative opioid use, and modified preoperative work status. Job type, motor nerve conduction velocity, and bilateral surgery were not predictive of delayed RTW interval. Conclusions: WC patients with depression, anxiety, or fibromyalgia and other chronic pain disorders were significantly more likely to have delayed RTW following CTR than were WC patients without these conditions. In addition, those who use opioid medications preoperatively and those with preoperative work restrictions were also found to have a significantly delayed RTW after CTR. Knowledge of these risk factors may help care providers and employers identify those WC patients who are most likely to have a protracted postoperative recovery period.
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Pabaghi, Zeynab, Ommolbanin Bazrafshan, Hossein Zamani, Marzieh Shekari, and Vijay P. Singh. "Bivariate Analysis of Extreme Precipitation Using Copula Functions in Arid and Semi-Arid Regions." Atmosphere 14, no. 2 (2023): 275. http://dx.doi.org/10.3390/atmos14020275.
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This study analyzed extreme precipitation events, using daily rainfall data for 1966–2015. A Mann–Kendall trend test was used to evaluate trends in extreme precipitation, copula functions were applied to compute the joint return periods of extreme events, and univariate and bivariate distributions were used to determine risk. The results showed that the decrease in consecutive wet days (CWD) was significant in the west and the northwest of Iran, while the consecutive dry days (CDD) index was increasing therein. The precipitation on more than the 90th percentile (P90) very wet days and annual number of days with precipitation less than the 90th percentile threshold (D90) indices followed similar patterns, with no significant trend in most parts of Iran, but at several stations in the north, west, and northwest, their decline was extreme. Furthermore, the increase of D10 (annual number of days with precipitation less than the 90th percentile threshold) and P10 (total precipitation of D10 of a year) was extreme in the wet regions of Iran, including the north, west, and northwest areas, and also part of the center. More than 50 percent of Iran experienced a low risk level, with a return period of extreme events (CWD, CDD) of more than 27.5 years, and the joint return periods of (D10, D90), (P10, P90), and (D10, P10) pairs were less than 100 years in most regions of Iran. Due to the increasing number of dry days in the north, west, and northwest of Iran, the drought risk increased. Based on the changes in extreme precipitation indices in recent years, the findings of this study will be useful for copula-based frequency analysis under a changing environment at regional and global scales.
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Najib, Mohamad Khoirun, Sri Nurdiati, and Faiqul Fikri. "Rarity of Joint Probability Between Interest and Inflation Rates in the 1998 Economic Crisis in Indonesia and Their Comparison Over Three Time Periods." Jurnal Matematika MANTIK 8, no. 1 (2022): 10–17. http://dx.doi.org/10.15642/mantik.2022.8.1.10-17.
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After more than twenty years, there has been no economic crisis as severe as 1998 based on inflation and interest rates. It is interesting to compare the conditions before and after the 1998 crisis and the economic conditions in the last decade in Indonesia. Therefore, this study aims to analyze the relationship between inflation and interest rates using a copula-based joint distribution. The joint return period of the 1998 economic crisis is estimated from this joint distribution. The results showed that the Gumbel copula is the most suitable bivariate copula to construct a joint distribution between inflation and interest rates in 1990-2019, with an upper tail dependency of 0.6224. Moreover, the joint return period between inflation and interest rates more severe than 1998 is 389 years with a 95% confidence interval of [47, ∞] years. This result is uncertain because many factors affect inflation and interest rates. The inflation rate decreased after the 1998 crisis. Meanwhile, in the last decade, the inflation and interest rates were much lower than in the two previous periods.
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Yoo, Chulsang, Minkyu Park, Hyeon Jun Kim, and Changhyun Jun. "Comparison of annual maximum rainfall events of modern rain gauge data (1961–2010) and Chukwooki data (1777–1910) in Seoul, Korea." Journal of Water and Climate Change 9, no. 1 (2017): 58–73. http://dx.doi.org/10.2166/wcc.2017.110.
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Abstract In this study, the annual maximum rainfall event series were constructed and compared for both the modern flip-bucket type rainfall data, collected since 1961 (the modern data), and the old Chukwooki rainfall data, collected from 1777 to 1910 (the Chukwooki data). First, independent rainfall events were derived, by applying the same rainfall threshold of 2 mm and data collection time interval of 2 hours, to both the Chukwooki and the modern data. Annual maximum rainfall event series were then constructed, by applying Freund's bivariate exponential distribution annually. Finally, bivariate frequency analysis was done for the annual maximum rainfall event series constructed, by applying the bivariate logistic model to evaluate and quantify their characteristics. The results are in summary: (1) characteristics of the Chukwooki rainfall events and modern rainfall events are very similar to each other; (2) the annual maximum rainfall events of modern data are slightly larger than those of the Chukwooki data. The total rainfall depth per rainfall event for any given return period is thus estimated to be a little higher for the modern data than that of the Chukwooki data. However, based on the findings in this study, it could not be concluded that the rainfall characteristics have significantly changed during the last 200 years.
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ABID, FATHI, and NADER NAIFAR. "THE IMPACT OF STOCK RETURNS VOLATILITY ON CREDIT DEFAULT SWAP RATES: A COPULA STUDY." International Journal of Theoretical and Applied Finance 08, no. 08 (2005): 1135–55. http://dx.doi.org/10.1142/s0219024905003372.
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The aim of this paper is to study the impact of stock returns volatility of reference entities on credit default swap rates using a new dataset from the Japanese market. The majority of empirical research suggests the inadequacy of multinormal distribution and then the failure of methods based on correlation for measuring the structure of dependency. Using a copula approach, we can model the different relationships that can exist in different ranges of behavior. We study the bivariate distributions of credit default swap rates and the measure of stock return volatility estimated with GARCH (1,1) and focus on one parameter Archimedean copula. Starting from the empirical rank correlation statistics (Kendall's tau and Spearman's rho), we estimate the parameter values of each copula function presented in our study. Then, we choose the appropriate Archimedean copula that better fit to our data. We emphasize the finding that pairs with higher rating present a weaker dependence coefficient and then, the impact of stock return volatility on credit default swap rates is higher for the lowest rating class.
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Balistrocchi, M., and B. Bacchi. "Derivation of flood frequency curves through a bivariate rainfall distribution based on copula functions: application to an urban catchment in northern Italy's climate." Hydrology Research 48, no. 3 (2017): 749–62. http://dx.doi.org/10.2166/nh.2017.109.
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The utilization of continuous approaches, namely analytical-probabilistic methods, has often been advocated for hydraulic device sizing, in order to overcome some deficiencies of the design event method. In the analytical distribution derivation, however, strong simplifying hypotheses are usually adopted. Rainfall depth and duration independency is the most unrealistic, even if it usually leads to satisfactory agreements between derived and benchmarking distributions. The reason can lie in drawbacks related to conventional assessment techniques of multivariate rainfall distributions. Copula functions recently provided a significant improvement in statistical inference capabilities and greatly simplified the distribution assessment. Nonetheless, the generalization of the return period concept, well defined in the univariate case, to multivariate cases has not found a blanket solution yet. Effective estimate methods can, however, be developed for the design and performance assessment of specific hydraulic devices. With regard to urban catchment applications, a criterion to derive flood frequency curves from a rainfall volume and duration distribution is herein proposed. Further, a method to estimate the return period of bivariate rainfall events based on a device-targeted approach is developed. Hydrologic simulations are conducted to support model reliability through a test case, featuring a northern Italian rainfall regime.
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Sarno, Lucio, Daniel L. Thornton, and Giorgio Valente. "The Empirical Failure of the Expectations Hypothesis of the Term Structure of Bond Yields." Journal of Financial and Quantitative Analysis 42, no. 1 (2007): 81–100. http://dx.doi.org/10.1017/s0022109000002192.
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AbstractThis paper tests the expectations hypothesis (EH) using U.S. monthly data for bond yields spanning the 1952–2003 sample period and ranging in maturity from one month to 10 years. We apply the Lagrange multiplier test developed by Bekaert and Hodrick (2001) and extend it to increase the test power by introducing economic variables as conditioning information and by using more than two bond yields in the model and testing the EH jointly on more than one pair of yields. While the conventional bivariate procedure provides mixed results, the more powerful testing procedures suggest rejection of the EH throughout the maturity spectrum examined.
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Hung, Ngo Thai. "Return and volatility spillover across equity markets between China and Southeast Asian countries." Journal of Economics, Finance and Administrative Science 24, no. 47 (2019): 66–81. http://dx.doi.org/10.1108/jefas-10-2018-0106.
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Purpose This paper aims to study the daily returns and volatility spillover effects in common stock prices between China and four countries in Southeast Asia (Vietnam, Thailand, Singapore and Malaysia). Design/methodology/approach The analysis uses a vector autoregression with a bivariate GARCH-BEKK model to capture return linkage and volatility transmission spanning the period including the pre- and post-2008 Global Financial Crisis. Findings The main empirical result is that the volatility of the Chinese market has had a significant impact on the other markets in the data sample. For the stock return, linkage between China and other markets seems to be remarkable during and after the Global Financial Crisis. Notably, the findings also indicate that the stock markets are more substantially integrated into the crisis. Practical implications The results have considerable implications for portfolio managers and institutional investors in the evaluation of investment and asset allocation decisions. The market participants should pay more attention to assess the worth of across linkages among the markets and their volatility transmissions. Additionally, international portfolio managers and hedgers may be better able to understand how the volatility linkage between stock markets interrelated overtime; this situation might provide them benefit in forecasting the behavior of this market by capturing the other market information. Originality/value This paper would complement the emerging body of existing literature by examining how China stock market impacts on their neighboring countries including Vietnam, Thailand, Singapore and Malaysia. Furthermore, this is the first investigation capturing return linkage and volatility spill over between China market and the four Southeast Asian markets by using bivariate VAR-GARCH-BEKK model. The authors believe that the results of this research’s empirical analysis would amplify the systematic understanding of spillover activities between China stock market and other stock markets.
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Zeng, Ning. "Monetary Stability and Stock Returns: A Bivariate Generalized Autoregressive Conditional Heteroscedasticity Modelling Study." Business and Economic Research 5, no. 2 (2015): 1. http://dx.doi.org/10.5296/ber.v5i2.7623.
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<p class="ber"><span lang="EN-GB">This paper employs a constant conditional correlation bivariate EGARCH-in-mean model to investigate interactions among the rate of inflation, stock returns and their respective volatilities. This approach is capable of accommodating all the possible causalities among the four variables simultaneously, and therefore could deliver contemporary evidence of the nexus between monetary stability and stock market. The postwar dataset of the US inflation and stock returns is divided into pre- and post- Volcker period and the estimation results show some significant changes of inflation-stock return relation, as well as indirect links between two volatilities. The core findings in this study suggest that promoting monetary stability contributes to more mutual interactions among the four variables, in particular, common stock is a more effective hedge against inflation, and the level of inflation rate is central to explaining the relation between the two volatilities.</span></p>
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Sasongko, Leopoldus Ricky, and Bambang Susanto. "The Mean Value Theorem for Integrals Method for Estimating Two-Dimensional Renewal Functions." JTAM | Jurnal Teori dan Aplikasi Matematika 4, no. 1 (2020): 49. http://dx.doi.org/10.31764/jtam.v4i1.1831.
Full textAbstract:
An important aspect in the provision of a two-dimensional warranty is the expected number of failures of a component during the two-dimensional warranty period. The purpose of this paper is to present a new method to obtain the expected number of failures of a nonrepairable component from the two-dimensional renewal functions as the solution of two-dimensional renewal integral equations through the Mean Value Theorem for Integrals (MeVTI) method. The two-dimensional renewal integral equation involves Lu-Bhattacharyya’s bivariate Weibull model as a two-dimensional failure model. It turns out that the estimation of the expected number of failures using the MeVTI method is close to that of the other method, Riemann-Stieljies method. The bivariate data behaviour of the failures of an automobile component is also studied in this paper.
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Naghibi, Farzaneh, and Gordon A. Fenton. "Calibration of resistance factors for geotechnical seismic design." Canadian Geotechnical Journal 56, no. 8 (2019): 1134–41. http://dx.doi.org/10.1139/cgj-2018-0433.
Full textAbstract:
The next edition of the Canadian Highway Bridge Design Code will contain a table of geotechnical resistance factors to be used for seismic design. This paper will estimate the geotechnical resistance factors for shallow foundations required to achieve various target maximum acceptable failure probabilities, which in turn may depend on the assumed design earthquake return period. The investigation will include consideration of design lifetime, uncertainty in the magnitude of the maximum lifetime earthquake event, and the uncertainty in ground properties. The results suggest resistance factors that are lower than commonly used at the moment in Canada and that the failure probability is not greatly dependent on the return period of the design earthquake. The paper will present recommendations on geotechnical resistance factors for seismic design that can be used to guide and calibrate future editions of civil design codes in Canada.