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Статті в журналах з теми "Bivariate frequency analysis"

Автор: Grafiati
Опубліковано: 10 березня 2023

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1

Stamatatou, Nikoletta, Lampros Vasiliades, and Athanasios Loukas. "Bivariate Flood Frequency Analysis Using Copulas." Proceedings 2, no. 11 (August 3, 2018): 635. http://dx.doi.org/10.3390/proceedings2110635.

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Анотація:
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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2

Flamant, Julien, Nicolas Le Bihan, and Pierre Chainais. "Time–frequency analysis of bivariate signals." Applied and Computational Harmonic Analysis 46, no. 2 (March 2019): 351–83. http://dx.doi.org/10.1016/j.acha.2017.05.007.

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3

Mirakbari, M., A. Ganji, and S. R. Fallah. "Regional Bivariate Frequency Analysis of Meteorological Droughts." Journal of Hydrologic Engineering 15, no. 12 (December 2010): 985–1000. http://dx.doi.org/10.1061/(asce)he.1943-5584.0000271.

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4

Ziller, M., K. Frick, W. M. Herrmann, S. Kubicki, I. Spieweg, and G. Winterer. "Bivariate Global Frequency Analysis versus Chaos Theory." Neuropsychobiology 32, no. 1 (1995): 45–51. http://dx.doi.org/10.1159/000119211.

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5

Shiau, Jenq-Tzong, Hsin-Yi Wang, and Chang-Tai Tsai. "BIVARIATE FREQUENCY ANALYSIS OF FLOODS USING COPULAS1." Journal of the American Water Resources Association 42, no. 6 (December 2006): 1549–64. http://dx.doi.org/10.1111/j.1752-1688.2006.tb06020.x.

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6

Joo, Kyung-Won, Ju-Young Shin, and Jun-Haeng Heo. "Bivariate Frequency Analysis of Rainfall using Copula Model." Journal of Korea Water Resources Association 45, no. 8 (August 31, 2012): 827–37. http://dx.doi.org/10.3741/jkwra.2012.45.8.827.

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7

Razmkhah, Homa, Alireza Fararouie, and Amin Rostami Ravari. "Multivariate Flood Frequency Analysis Using Bivariate Copula Functions." Water Resources Management 36, no. 2 (January 2022): 729–43. http://dx.doi.org/10.1007/s11269-021-03055-3.

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8

Dong, N. Dang, V. Agilan, and K. V. Jayakumar. "Bivariate Flood Frequency Analysis of Nonstationary Flood Characteristics." Journal of Hydrologic Engineering 24, no. 4 (April 2019): 04019007. http://dx.doi.org/10.1061/(asce)he.1943-5584.0001770.

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9

Volpi, E., and A. Fiori. "Design event selection in bivariate hydrological frequency analysis." Hydrological Sciences Journal 57, no. 8 (October 10, 2012): 1506–15. http://dx.doi.org/10.1080/02626667.2012.726357.

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10

Zhang, L., and V. P. Singh. "Bivariate Flood Frequency Analysis Using the Copula Method." Journal of Hydrologic Engineering 11, no. 2 (March 2006): 150–64. http://dx.doi.org/10.1061/(asce)1084-0699(2006)11:2(150).

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11

Poulin, Annie, David Huard, Anne-Catherine Favre, and Stéphane Pugin. "Importance of Tail Dependence in Bivariate Frequency Analysis." Journal of Hydrologic Engineering 12, no. 4 (July 2007): 394–403. http://dx.doi.org/10.1061/(asce)1084-0699(2007)12:4(394).

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12

Yue, Sheng. "Applying Bivariate Normal Distribution to Flood Frequency Analysis." Water International 24, no. 3 (September 1999): 248–54. http://dx.doi.org/10.1080/02508069908692168.

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13

Mirabbasi, Rasoul, Ahmad Fakheri-Fard, and Yagob Dinpashoh. "Bivariate drought frequency analysis using the copula method." Theoretical and Applied Climatology 108, no. 1-2 (September 27, 2011): 191–206. http://dx.doi.org/10.1007/s00704-011-0524-7.

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14

Yoo, Jiyoung, Hyun-Han Kwon, Tae-Woong Kim, and Jae-Hyun Ahn. "Drought frequency analysis using cluster analysis and bivariate probability distribution." Journal of Hydrology 420-421 (February 2012): 102–11. http://dx.doi.org/10.1016/j.jhydrol.2011.11.046.

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15

Lee, Chang Hwan, Tae-Woong Kim, Gunhui Chung, Minha Choi, and Chulsang Yoo. "Application of bivariate frequency analysis to the derivation of rainfall–frequency curves." Stochastic Environmental Research and Risk Assessment 24, no. 3 (July 8, 2009): 389–97. http://dx.doi.org/10.1007/s00477-009-0328-9.

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16

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 (November 8, 2011): 9757–96. http://dx.doi.org/10.5194/hessd-8-9757-2011.

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Анотація:
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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17

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 (April 2012): 374–87. http://dx.doi.org/10.1139/l2012-012.

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Анотація:
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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18

Yue, Sheng. "A Bivariate Extreme Value Distribution Applied to Flood Frequency Analysis." Hydrology Research 32, no. 1 (February 1, 2001): 49–64. http://dx.doi.org/10.2166/nh.2001.0004.

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Анотація:
This article presents a procedure for use of the Gumbel logistic model to represent the joint distribution of two correlated extreme events. Parameters of the distribution are estimated using the method of moments. On the basis of marginal distributions, the joint distribution, the conditional distributions, and the associated return periods can be deduced. The applicability of the model is demonstrated by using multiple episodic flood events of the Harricana River basin in the province of Quebec, Canada. It is concluded that the model is useful for describing joint probabilistic behavior of multivariate flood events.
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19

Li, Tianyuan, Shenglian Guo, Lu Chen, and Jiali Guo. "Bivariate Flood Frequency Analysis with Historical Information Based on Copula." Journal of Hydrologic Engineering 18, no. 8 (August 2013): 1018–30. http://dx.doi.org/10.1061/(asce)he.1943-5584.0000684.

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20

Amirataee, Babak, Majid Montaseri, and Hossein Rezaie. "An advanced data collection procedure in bivariate drought frequency analysis." Hydrological Processes 34, no. 21 (August 3, 2020): 4067–82. http://dx.doi.org/10.1002/hyp.13866.

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21

Park, Cheol-Soon, Chul-Sang Yoo, and Chang-Hyun Jun. "Bivariate Rainfall Frequency Analysis and Rainfall-runoff Analysis for Independent Rainfall Events." Journal of Korea Water Resources Association 45, no. 7 (July 31, 2012): 713–27. http://dx.doi.org/10.3741/jkwra.2012.45.7.713.

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22

Farsadnia, F., B. Ghahreman, R. Modarres, and A. Moghaddam Nia. "Hydrologic Drought Frequency Analysis in Karkhe Basin Based on Bivariate Statistical Analysis." Journal of Water and Soil Science 22, no. 3 (November 1, 2018): 339–55. http://dx.doi.org/10.29252/jstnar.22.3.339.

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23

Kar, Anil Kumar, Pradip Kumar Das, and Raj Beer Padhee. "Bivariate flood frequency analysis a case study of Hirakud reservoir inflow." International Journal of Hydrology Science and Technology 1, no. 1 (2021): 1. http://dx.doi.org/10.1504/ijhst.2021.10039223.

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24

Cheolsoo Park, D. Looney, P. Kidmose, M. Ungstrup, and D. P. Mandic. "Time-Frequency Analysis of EEG Asymmetry Using Bivariate Empirical Mode Decomposition." IEEE Transactions on Neural Systems and Rehabilitation Engineering 19, no. 4 (August 2011): 366–73. http://dx.doi.org/10.1109/tnsre.2011.2116805.

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25

Lunsford, P. J., G. W. Rhyne, and M. B. Steer. "Frequency-domain bivariate generalized power series analysis of nonlinear analog circuits." IEEE Transactions on Microwave Theory and Techniques 38, no. 6 (June 1990): 815–18. http://dx.doi.org/10.1109/22.130986.

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26

Li, Min, Ting Zhang, and Ping Feng. "Bivariate frequency analysis of seasonal runoff series under future climate change." Hydrological Sciences Journal 65, no. 14 (September 29, 2020): 2439–52. http://dx.doi.org/10.1080/02626667.2020.1817927.

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27

Yue, Sheng, and Peter Rasmussen. "Bivariate frequency analysis: discussion of some useful concepts in hydrological application." Hydrological Processes 16, no. 14 (2002): 2881–98. http://dx.doi.org/10.1002/hyp.1185.

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28

Yue, Sheng. "A bivariate gamma distribution for use in multivariate flood frequency analysis." Hydrological Processes 15, no. 6 (2001): 1033–45. http://dx.doi.org/10.1002/hyp.259.

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29

Padhee, Raj Beer, Anil Kumar Kar, and Pradip Kumar Das. "Bivariate flood frequency analysis - a case study of Hirakud reservoir inflow." International Journal of Hydrology Science and Technology 14, no. 4 (2022): 390. http://dx.doi.org/10.1504/ijhst.2022.126433.

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30

Tsakiris, G., N. Kordalis, and V. Tsakiris. "Flood Double Frequency Analysis: 2D-Archimedean Copulas vs Bivariate Probability Distributions." Environmental Processes 2, no. 4 (September 9, 2015): 705–16. http://dx.doi.org/10.1007/s40710-015-0078-2.

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31

Hidalgo, J. "Spectral Analysis for Bivariate Time Series with Long Memory." Econometric Theory 12, no. 5 (December 1996): 773–92. http://dx.doi.org/10.1017/s0266466600007155.

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Анотація:
This paper provides limit theorems for spectral density matrix estimators and functionals of it for a bivariate covariance stationary process whose spectral density matrix has singularities not only at the origin but possibly at some other frequencies and, thus, applies to time series exhibiting long memory. In particular, we show that the consistency and asymptotic normality of the spectral density matrix estimator at a frequency, say λ, which hold for weakly dependent time series, continue to hold for long memory processes when λ lies outside any arbitrary neighborhood of the singularities. Specifically, we show that for the standard properties of spectral density matrix estimators to hold, only local smoothness of the spectral density matrix is required in a neighborhood of the frequency in which we are interested. Therefore, we are able to relax, among other conditions, the absolute summability of the autocovariance function and of the fourth-order cumulants or summability conditions on mixing coefficients, assumed in much of the literature, which imply that the spectral density matrix is globally smooth and bounded.
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32

Zhou, Ting, Zhiyong Liu, Juliang Jin, and Hongxiang Hu. "Assessing the Impacts of Univariate and Bivariate Flood Frequency Approaches to Flood Risk Accounting for Reservoir Operation." Water 11, no. 3 (March 6, 2019): 475. http://dx.doi.org/10.3390/w11030475.

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Анотація:
Flood frequency analysis plays a fundamental role in dam planning, reservoir operation, and risk assessment. However, conventional univariate flood frequency analysis carried out by flood peak inflow or volume does not account for the dependence between flood properties. In this paper, we proposed an integrated approach to estimate reservoir risk by combining the copula-based bivariate flood frequency (peak and volume) and reservoir routing. Through investigating the chain reaction of “flood frequency—reservoir operation-flood risk”, this paper demonstrated how to simulate flood hydrographs using different frequency definitions (copula “Or” and “And” scenario), and how these definitions affect flood risks. The approach was applied to the Meishan reservoir in central China. A set of flood hydrographs with 0.01 frequency under copula “Or” and “And” definitions were constructed, respectively. Upstream and downstream flood risks incorporating reservoir operation were calculated for each scenario. Comparisons between flood risks from univariate and bivariate flood frequency analysis showed that bivariate flood frequency analysis produced less diversity in the results, and thus the results are more reliable in risk assessment. More importantly, the peak-volume combinations in a bivariate approach can be adjusted according to certain prediction accuracy, providing a flexible estimation of real-time flood risk under different prediction accuracies and safety requirements.
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33

Campos-Aranda, Daniel Francisco. "Aplicación de la distribución GVE bivariada en el Análisis de Frecuencias Conjunto de Crecientes." Tecnología y ciencias del agua 13, no. 6 (November 1, 2022): 534–602. http://dx.doi.org/10.24850/j-tyca-13-06-11.

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Анотація:
Las crecientes que ocurren en nuestro país cada año generan daños y ponen en peligro a los embalses, cuyo dimensionamiento hidrológico está basado en el hidrograma de la creciente de diseño. La estimación más simple de tal hidrograma se basa en el análisis de frecuencias conjunto del gasto pico y volumen anuales. En este estudio se ajustó la distribución general de valores extremos bivariada (GVEb), al registro de 55 crecientes anuales en la estación hidrométrica La Cuña, sobre el Río Verde de la Región Hidrológica No. 12-3, México. Este proceso abarca nueve etapas: (1) selección y prueba de los registros anuales; (2) verificación de su aleatoriedad; (3) estimación de las probabilidades empíricas conjuntas; (4) ajuste de la función GVEb a través del método de máxima verosimilitud; (5) validación de la función GVEb; (6) ratificación de las marginales GVE; (7) verificación de las restricciones de probabilidad; (8) estimación de eventos de diseño univariados híbridos, y (9) estimación de eventos de diseño conjuntos y selección del subgrupo crítico. En la etapa 1 se aplica un test simple de la GVE. La etapa 2 se realiza con base en el Test de Wald-Wolfowitz. En la etapa 4 se emplea el algoritmo Complex. Las etapas 5 y 6 utilizan el Test de Kolmogorov–Smirnov. En la etapa 9 se usan las gráficas del periodo de retorno conjunto de tipo AND. Por último, se formulan las conclusiones, las cuales destacan el enfoque de maximización adoptado y las ventajas de aplicar la GVEb.
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34

Chun, Si-Young, Yong-Tak Kim, and Hyun-Han Kwon. "Drought Frequency Analysis Using Hidden Markov Chain Model and Bivariate Copula Function." Journal of the Korean Water Resources Association 48, no. 12 (December 30, 2015): 969–79. http://dx.doi.org/10.3741/jkwra.2015.48.12.969.

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35

Pathak, Abhishek A., and B. M. Dodamani. "Connection between Meteorological and Groundwater Drought with Copula-Based Bivariate Frequency Analysis." Journal of Hydrologic Engineering 26, no. 7 (July 2021): 05021015. http://dx.doi.org/10.1061/(asce)he.1943-5584.0002089.

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36

Tang, Mingyu, and Grant B. Weller. "Bivariate tail risk analysis for high-frequency returns via extreme value theory." Model Assisted Statistics and Applications 12, no. 1 (March 8, 2017): 1–14. http://dx.doi.org/10.3233/mas-160379.

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37

Park, Minkyu, Chulsang Yoo, Hyeonjun Kim, and Changhyun Jun. "Bivariate Frequency Analysis of Annual Maximum Rainfall Event Series in Seoul, Korea." Journal of Hydrologic Engineering 19, no. 6 (June 2014): 1080–88. http://dx.doi.org/10.1061/(asce)he.1943-5584.0000891.

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38

Yu, Jisoo, Si-Jung Choi, Hyun-Han Kwon, and Tae-Woong Kim. "Assessment of regional drought risk under climate change using bivariate frequency analysis." Stochastic Environmental Research and Risk Assessment 32, no. 12 (July 6, 2018): 3439–53. http://dx.doi.org/10.1007/s00477-018-1582-5.

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39

Reddy, M. Janga, and Poulomi Ganguli. "Bivariate Flood Frequency Analysis of Upper Godavari River Flows Using Archimedean Copulas." Water Resources Management 26, no. 14 (September 11, 2012): 3995–4018. http://dx.doi.org/10.1007/s11269-012-0124-z.

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40

Santhosh, D., and V. V. Srinivas. "Bivariate frequency analysis of floods using a diffusion based kernel density estimator." Water Resources Research 49, no. 12 (December 2013): 8328–43. http://dx.doi.org/10.1002/2011wr010777.

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41

San Antolín, A., and R. A. Zalik. "Some Bivariate Smooth Compactly Supported Tight Framelets with Three Generators." Abstract and Applied Analysis 2013 (2013): 1–7. http://dx.doi.org/10.1155/2013/818907.

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Анотація:
For any dilation matrix with integer entries and , we construct a family of smooth compactly supported tight wavelet frames with three generators in . Our construction involves some compactly supported refinable functions, the oblique extension principle, and a slight generalization of a theorem of Lai and Stöckler. Estimates for the degrees of smoothness are given. With the exception of a polynomial whose coefficients must in general be computed by spectral factorization, the framelets are expressed in closed form in the frequency domain, in terms of elementary transcendental functions. By means of two examples we also show that for low degrees of smoothness the use of spectral factorization may be avoided.
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42

Won, Jeongeun, Jeonghyeon Choi, Okjeong Lee, Moo Jong Park, and Sangdan Kim. "Two Ways to Quantify Korean Drought Frequency: Partial Duration Series and Bivariate Exponential Distribution, and Application to Climate Change." Atmosphere 11, no. 5 (May 7, 2020): 476. http://dx.doi.org/10.3390/atmos11050476.

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Анотація:
Studies using drought index to examine return levels of drought can be classified into two approaches: univariate frequency analysis using annual series extracted from drought index time series and multivariate frequency analysis that simultaneously reflects various characteristics of drought. In the case of drought analysis, it is important to properly consider the duration, so, in this study, univariate frequency analysis is performed using the partial duration series. In addition, a bivariate frequency analysis is performed using a relatively simple bivariate exponential distribution to give a more realistic return level to major drought events in the past while reflecting the correlation between drought severities and durations. The drought severity–duration–frequency curves using each of the two frequency analyses are derived, and these curves are used to examine how the drought phenomenon currently in progress is evolving. From this, the advantages and disadvantages of the two approaches, as well as the points to be aware of in application, are discussed. Finally, using the two approaches to the proposed drought frequency analysis, the behavior of Korea’s future extreme droughts is investigated under the conditions of various future climate change scenarios.
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43

Huqqani, Ilyas A., Lea Tien Tay, and Junita Mohamad Saleh. "Analysis of landslide hazard mapping of penang island malaysia using bivariate statistical methods." Indonesian Journal of Electrical Engineering and Computer Science 16, no. 2 (November 1, 2019): 781. http://dx.doi.org/10.11591/ijeecs.v16.i2.pp781-786.

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Анотація:
Landslide is one of the disasters which cause property damages, infrastructure destruction, injury and death. This paper presents the analysis of landslide hazard mapping of Penang Island Malaysia using bivariate statistical methods. Bivariate statistical methods are simple approach which are capable to produce good results in short computational time. In this study, three bivariate statistical methods, i.e. Frequency Ratio (FR), Information Value (IV) and Modified Information Value (MIV) are used to generate the landslide hazard maps of Penang Island. These bivariate statistical methods are computed using MATLAB tool. Landslide hazard map is categorized into 4 levels of hazard. The accuracy of each method and effectiveness in predicating landslides are validated and determined by using Receiver of Characteristics curve. The accuracies of FR, IV and MIV methods are 79.58%, 79.14% and 79.37% respectively.
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44

Mohammadi, Tayeb, Soleiman Kheiri, and Morteza Sedehi. "Analysis of Blood Transfusion Data Using Bivariate Zero-Inflated Poisson Model: A Bayesian Approach." Computational and Mathematical Methods in Medicine 2016 (2016): 1–7. http://dx.doi.org/10.1155/2016/7878325.

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Анотація:
Recognizing the factors affecting the number of blood donation and blood deferral has a major impact on blood transfusion. There is a positive correlation between the variables “number of blood donation” and “number of blood deferral”: as the number of return for donation increases, so does the number of blood deferral. On the other hand, due to the fact that many donors never return to donate, there is an extra zero frequency for both of the above-mentioned variables. In this study, in order to apply the correlation and to explain the frequency of the excessive zero, the bivariate zero-inflated Poisson regression model was used for joint modeling of the number of blood donation and number of blood deferral. The data was analyzed using the Bayesian approach applying noninformative priors at the presence and absence of covariates. Estimating the parameters of the model, that is, correlation, zero-inflation parameter, and regression coefficients, was done through MCMC simulation. Eventually double-Poisson model, bivariate Poisson model, and bivariate zero-inflated Poisson model were fitted on the data and were compared using the deviance information criteria (DIC). The results showed that the bivariate zero-inflated Poisson regression model fitted the data better than the other models.
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45

Stamatatou, Nikoletta, Lampros Vasiliades, and Athanasios Loukas. "The Effect of Sample Size on Bivariate Rainfall Frequency Analysis of Extreme Precipitation." Proceedings 7, no. 1 (November 15, 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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46

Yu, Ji Soo, Ji Young Yoo, Joo-Heon Lee, and Tea-Woong Kim. "Estimation of drought risk through the bivariate drought frequency analysis using copula functions." Journal of Korea Water Resources Association 49, no. 3 (March 31, 2016): 217–25. http://dx.doi.org/10.3741/jkwra.2016.49.3.217.

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47

Tosunoglu, Fatih, and Ibrahim Can. "Application of copulas for regional bivariate frequency analysis of meteorological droughts in Turkey." Natural Hazards 82, no. 3 (February 26, 2016): 1457–77. http://dx.doi.org/10.1007/s11069-016-2253-9.

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48

Jun, Changhyun, Xiaosheng Qin, Thian Yew Gan, Yeou-Koung Tung, and Carlo De Michele. "Bivariate frequency analysis of rainfall intensity and duration for urban stormwater infrastructure design." Journal of Hydrology 553 (October 2017): 374–83. http://dx.doi.org/10.1016/j.jhydrol.2017.08.004.

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49

Yu, Ji Soo, Ji Yae Shin, Minsung Kwon, and Tea-Woong Kim. "Bivariate Drought Frequency Analysis to Evaluate Water Supply Capacity of Multi-Purpose Dams." Journal of The Korean Society of Civil Engineers 37, no. 1 (February 1, 2017): 231–38. http://dx.doi.org/10.12652/ksce.2017.37.1.0231.

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50

Yoo and Cho. "Effect of Multicollinearity on the Bivariate Frequency Analysis of Annual Maximum Rainfall Events." Water 11, no. 5 (April 29, 2019): 905. http://dx.doi.org/10.3390/w11050905.

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A rainfall event, simplified by a rectangular pulse, is defined by three components: the rainfall duration, the total rainfall depth, and mean rainfall intensity. However, as the mean rainfall intensity can be calculated by the total rainfall depth divided by the rainfall duration, any two components can fully define the rainfall event (i.e., one component must be redundant). The frequency analysis of a rainfall event also considers just two components selected rather arbitrarily out of these three components. However, this study argues that the two components should be selected properly or the result of frequency analysis can be significantly biased. This study fully discusses this selection problem with the annual maximum rainfall events from Seoul, Korea. In fact, this issue is closely related with the multicollinearity in the multivariate regression analysis, which indicates that as interdependency among variables grows the variance of the regression coefficient also increases to result in the low quality of resulting estimate. The findings of this study are summarized as follows: (1) The results of frequency analysis are totally different according to the selected two variables out of three. (2) Among three results, the result considering the total rainfall depth and the mean rainfall intensity is found to be the most reasonable. (3) This result is fully supported by the multicollinearity issue among the correlated variables. The rainfall duration should be excluded in the frequency analysis of a rainfall event as its variance inflation factor is very high.
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