A Review of Copula-Based Approach for Water Resources Time Series

Aas, K., Czado, C., Frigessi, A., Bakken, H. J. I. M., & economics. (2009). Pair-copula constructions of multiple dependence. 44(2), 182-198.

Abdi, A., Hassanzadeh, Y., Talatahari, S., Fakheri-Fard, A., & Mirabbasi, R. (2017). Regional bivariate modeling of droughts using L-comoments and copulas. Stochastic Environmental Research and Risk Assessment, 31(5), 1199-1210.

Ahangi, G., Khalili, K., & Nazeri Tahroudi, M. (2022). Frequency analysis and joint simulation of qualitative variables of river flow using copula functions. Water Harvesting Research, 5(1), 131-143.

Ahmadi, F., Radmaneh, F., Sharifi, M. R., & Mirabbasi, R. (2018). Bivariate frequency analysis of low flow using copula functions (case study: Dez River Basin, Iran). Environmental Earth Sciences, 77, 1-16.

Ayantobo, O. O., Li, Y., & Song, S. (2019). Multivariate drought frequency analysis using four-variate symmetric and asymmetric Archimedean copula functions. Water resources management, 33(1), 103-127.

Balistrocchi, M., & Bacchi, B. (2017). 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(3), 749-762.

Bárdossy, A., & Pegram, G. (2014). Infilling missing precipitation records–A comparison of a new copula-based method with other techniques. Journal of Hydrology, 519, 1162-1170.

Bedford T, Cooke RM. 2001. Probability density decomposition for conditionally dependent random variables modeled by vines. Ann. Math. Artif. Intell. 32:245–68

Bedford T, Cooke RM. 2002. Vines: a new graphical model for dependent random variables. Ann. Stat. 30(4):1031–68

Belagoune, F., & Boutoutaou, D. (2013). Hydrological Study of Watersheds Arid and Semi-Arid South-Eastern Algeria (Chott Melghir, Chott El Hodna and Highlands Constantine). International Journal of Geosciences, 4(10), 1483.

Bezak, N., Mikoš, M., & Šraj, M. (2014). Trivariate frequency analyses of peak discharge, hydrograph volume and suspended sediment concentration data using copulas. Water resources management, 28(8), 2195-2212.

Bezak, N., Šraj, M., & Mikoš, M. (2016). Copula-based IDF curves and empirical rainfall thresholds for flash floods and rainfall-induced landslides. Journal of Hydrology, 541, 272-284.

Brechmann EC, Joe H. 2015. Truncation of vine copulas using fit indices. J. Multivar. Anal. 138:19–33

Brechmann, E. C., & Schepsmeier, U. (2013). Modeling dependence with C-and D-vine copulas: the R package CDVine. Journal of statistical software, 52, 1-27.

Chang, J., Li, Y., Wang, Y., & Yuan, M. (2016). Copula-based drought risk assessment combined with an integrated index in the Wei river basin, China. Journal of Hydrology, 540, 824-834.

Chebana, F., & Ouarda, T. B. (2009). Index flood–based multivariate regional frequency analysis. Water Resources Research, 45(10).

Chebana, F., & Ouarda, T. B. (2011). Multivariate quantiles in hydrological frequency analysis. Environmetrics, 22(1), 63-78.

Chen, L., & Guo, S. (2019). Copula-Based Flood Frequency Analysis. In Copulas and Its Application in Hydrology and Water Resources (pp. 39-71). Springer, Singapore.

Czado, C. (2019). Analyzing dependent data with vine copulas. Lecture Notes in Statistics, Springer, 222.

Czado, C., & Nagler, T. (2022). Vine copula based modeling. Annual Review of Statistics and Its Application, 9, 453-477.

De Michele, C., & Salvadori, G. (2003). A generalized Pareto intensity‐duration model of storm rainfall exploiting 2‐copulas. Journal of Geophysical Research: Atmospheres, 108(D2).

De Michele, C., Salvadori, G., Canossi, M., Petaccia, A., & Rosso, R. (2005). Bivariate statistical approach to check adequacy of dam spillway. Journal of Hydrologic Engineering, 10(1), 50-57.

De Michele, C., Salvadori, G., Passoni, G., & Vezzoli, R. (2007). A multivariate model of sea storms using copulas. Coastal Engineering, 54(10), 734-751.

Dodangeh, E., Shahedi, K., Pham, B. T., & Solaimani, K. (2020). Joint frequency analysis and uncertainty estimation of coupled rainfall–runoff series relying on historical and simulated data. Hydrological Sciences Journal, 65(3), 455-469.

Evin, G., & Favre, A. C. (2008). A new rainfall model based on the Neyman‐Scott process using cubic copulas. Water Resources Research, 44(3).

Fan, Y. R., Huang, G. H., Li, Y. P., Wang, X. Q., & Li, Z. (2016). Probabilistic prediction for monthly streamflow through coupling stepwise cluster analysis and quantile regression methods. Water resources management, 30(14), 5313-5331.

Fan, Y., Huang, K., Huang, G. H., & Li, Y. P. (2020). A factorial Bayesian copula framework for partitioning uncertainties in multivariate risk inference. Environmental Research, 109215.

Favre, A. C., El Adlouni, S., Perreault, L., Thiémonge, N., & Bobée, B. (2004). Multivariate hydrological frequency analysis using copulas. Water Resources Research, 40(1).

Genest, C., Favre, A. C., Béliveau, J., & Jacques, C. (2007). Metaelliptical copulas and their use in frequency analysis of multivariate hydrological data. Water Resources Research, 43(9).

Gräler, B., van den Berg, M., Vandenberghe, S., Petroselli, A., Grimaldi, S., De Baets, B., . . . Sciences, E. S. (2013). Multivariate return periods in hydrology: a critical and practical review focusing on synthetic design hydrograph estimation. 17(4), 1281-1296.

Grimaldi, S., & Serinaldi, F. (2006a). Asymmetric copula in multivariate flood frequency analysis. Advances in Water Resources, 29(8), 1155-1167.

Grimaldi, S., & Serinaldi, F. (2006b). Design hyetograph analysis with 3-copula function. Hydrological Sciences Journal, 51(2), 223-238.

Guo, E., Zhang, J., Si, H., Dong, Z., Cao, T., & Lan, W. (2017). Temporal and spatial characteristics of extreme precipitation events in the Midwest of Jilin Province based on multifractal detrended fluctuation analysis method and copula functions. Theoretical and Applied Climatology, 130(1-2), 597-607.

Gupta, V., Kumar Jain, M., & Singh, V. P. (2020). Multivariate modeling of projected drought frequency and hazard over India. Journal of Hydrologic Engineering, 25(4), 04020003.

Haberlandt, U., & Radtke, I. (2014). Hydrological model calibration for derived flood frequency analysis using stochastic rainfall and probability distributions of peak flows. Hydrology and Earth System Sciences 18 (2014), Nr. 1, 18(1), 353-365.

Hangshing, L., & Dabral, P. P. (2018). Multivariate frequency analysis of meteorological drought using copula. Water resources management, 32(5), 1741-1758.

Hao, C., Zhang, J., & Yao, F. (2017). Multivariate drought frequency estimation using copula method in Southwest China. Theoretical and Applied Climatology, 127(3-4), 977-991.

Hawkes, P. J., Gouldby, B. P., Tawn, J. A., & Owen, M. W. (2002). The joint probability of waves and water levels in coastal engineering design. Journal of hydraulic research, 40(3), 241-251.

Hui-Mean, F., Yusof, F., Yusop, Z., & Suhaila, J. (2019). Trivariate copula in drought analysis: a case study in peninsular Malaysia. Theoretical and Applied Climatology, 138(1-2), 657-671.

Indu, J., & Kumar, D. N. (2014). Copula-based modeling of TMI brightness temperature with rainfall type. IEEE Transactions on Geoscience and Remote Sensing, 52(8), 4832-4845.

Joe H. 1996. Families of m-variate distributions with given margins and m(m-1)/2 bivariate dependence parameters. In Distributions with Fixed Marginals and Related Topics, ed. L Rüschendorf, B Schweizer, MD Taylor, pp. 120–41. N.p.: Inst. Math. Stat.

Joe H. 2018. Parsimonious graphical dependence models constructed from vines. Can. J. Stat. 46(4):532–55 Brechmann EC, Czado C, Aas K. 2012. Truncated regular vines and their applications. Can. J. Stat. 40(1):68–85

Joe, H., & Kurowicka, D. (Eds.). (2011). Dependence modeling: vine copula handbook. World Scientific.

Kao, S.-C., & Govindaraju, R. S. (2010). A copula-based joint deficit index for droughts. Journal of Hydrology, 380(1-2), 121-134.

Keef, C., Svensson, C., & Tawn, J. A. (2009). Spatial dependence in extreme river flows and precipitation for Great Britain. Journal of Hydrology, 378(3-4), 240-252.

Khashei, A., Shahidi, A., Nazeri-Tahroudi, M., & Ramezani, Y. (2022). Bivariate simulation and joint analysis of reference evapotranspiration using copula functions. Iranian Journal of Irrigation & Drainage, 16(3), 639-656.

Kraus, D., & Czado, C. (2017). D-vine copula based quantile regression. Computational Statistics & Data Analysis, 110, 1-18.

Kuchment, L., & Demidov, V. (2013). On the application of copula theory for determination of probabilistic characteristics of springflood. Russian Meteorology and Hydrology, 38(4), 263-271.

Kuhn, G., Khan, S., Ganguly, A. R., & Branstetter, M. L. (2007). Geospatial–temporal dependence among weekly precipitation extremes with applications to observations and climate model simulations in South America. Advances in Water Resources, 30(12), 2401-2423.

Kurowicka D. 2011. Optimal truncation of vines. In Dependence Modeling: Vine Copula Handbook, ed. D Kurowicka, H Joe, pp. 233–47. Singapore: World Sci.

Kurowicka, D., & Cooke, R. M. (2007). Sampling algorithms for generating joint uniform distributions using the vine-copula method. Computational statistics & data analysis, 51(6), 2889-2906.

Kwon, H. H., & Lall, U. (2016). A copula‐based nonstationary frequency analysis for the 2012–2015 drought in California. Water Resources Research, 52(7), 5662-5675.

Latif, S., & Mustafa, F. (2020). Copula-based multivariate flood probability construction: a review. Arabian Journal of Geosciences, 13(3), 132.

Lazoglou, G., & Anagnostopoulou, C. (2019). Joint distribution of temperature and precipitation in the Mediterranean, using the Copula method. Theoretical and applied climatology, 135(3-4), 1399-1411.

Li, F., & Zheng, Q. (2016). Probabilistic modelling of flood events using the entropy copula. Advances in water resources, 97, 233-240.

Li, H., Wang, D., Singh, V. P., Wang, Y., Wu, J., Wu, J., ... & Zhang, J. (2019). Non-stationary frequency analysis of annual extreme rainfall volume and intensity using Archimedean copulas: A case study in eastern China. Journal of hydrology, 571, 114-131.

Ming, X., Xu, W., Li, Y., Du, J., Liu, B., & Shi, P. (2015). Quantitative multi-hazard risk assessment with vulnerability surface and hazard joint return period. Stochastic Environmental Research and Risk Assessment, 29(1), 35-44.

Mirabbasi, R., Anagnostou, E. N., Fakheri-Fard, A., Dinpashoh, Y., & Eslamian, S. (2013). Analysis of meteorological drought in northwest Iran using the Joint Deficit Index. Journal of Hydrology, 492, 35-48.

Mirabbasi, R., Fakheri-Fard, A., & Dinpashoh, Y. (2012). Bivariate drought frequency analysis using the copula method. Theoretical and Applied Climatology, 108(1-2), 191-206.

Moncoulon, D., Labat, D., Ardon, J., Onfroy, T., Leblois, E., Poulard, C., . . . Quantin, A. (2013). Analysis of the French insurance market exposure to floods: a stochastic model combining river overflow and surface runoff. Natural Hazards and Earth System Sciences Discussions, 1(4), 3217-3261.

Müller D, Czado C. 2018. Representing sparse Gaussian DAGs as sparse R-vines allowing for non-Gaussian dependence. J. Comput. Graph. Stat. 27(2):334–44

Müller D, Czado C. 2019a. Dependence modelling in ultra high dimensions with vine copulas and the graphical lasso. Comput. Stat. Data Anal. 137:211–32

Müller D, Czado C. 2019b. Selection of sparse vine copulas in high dimensions with the lasso. Stat. Comput. 29(2):269–87

Nagler T, Bumann C, Czado C. 2019. Model selection in sparse high-dimensional vine copula models with an application to portfolio risk. J. Multivar. Anal. 172:180–92

Nagler, T., Krüger, D., & Min, A. (2022). Stationary vine copula models for multivariate time series. Journal of Econometrics, 227(2), 305-324.

Nazeri Tahroudi, M., & Mirabbasi, R. (2023a). Development of decomposition-based model using Copula-GARCH approach to simulate instantaneous peak discharge. Applied Water Science, 13(9), 182.

Nazeri Tahroudi, M., & Mirabbasi, R. (2023b). Frequency decomposition associated with machine learning algorithms and copula modeling for river flow prediction. Stochastic Environmental Research and Risk Assessment, 1-22.

Nazeri Tahroudi, M., & Mirabbasi, R. A. S. O. U. L. (2023c). Frequency analysis and rainfall-runoff simulation based on the tree sequence of the Vine copula. Water and Irrigation Management, 13(1), 259-274.

Nazeri Tahroudi, M., Ahmadi, F., & Mirabbasi, R. (2023a). Performance comparison of IHACRES, random forest and copula-based models in rainfall-runoff simulation. Applied Water Science, 13(6), 134.

Nazeri Tahroudi, M., Mohammadi, M., & Khalili, K. (2022a). The application of the hybrid copula-GARCH approach in the simulation of extreme discharge values. Applied Water Science, 12(12), 274.

Nazeri Tahroudi, M., Ramezani, Y., De Michele, C., & Mirabbasi, R. (2022c). Application of Copula Functions for Bivariate Analysis of Rainfall and River Flow Deficiencies in the Siminehrood River Basin, Iran. Journal of Hydrologic Engineering, 27(11), 05022015.

Nazeri Tahroudi, M., Ramezani, Y., De Michele, C., & Mirabbasi, R. (2022b). Trivariate joint frequency analysis of water resources deficiency signatures using vine copulas. Applied Water Science, 12(4), 67.

Nazeri Tahroudi, M., Ramezani, Y., De Michele, C., & Mirabbasi, R. (2022d). Application of vine copulas to dependence analysis of water quality data. Journal of Applied Research in Water and Wastewater, 9(1), 76-82.

Nazeri Tahroudi, M., Ramezani, Y., De Michele, C., & Mirabbasi, R. (2023b). Application of copula‐based approach as a new data‐driven model for downscaling the mean daily temperature. International Journal of Climatology, 43(1), 240-254.

Nazeri Tahroudi, M., Ramezani, Y., De Michele, C., & Mirabbasi, R. (2020). A new method for joint frequency analysis of modified precipitation anomaly percentage and streamflow drought index based on the

Nazeri, T. M., & Mirabbasi, N. R. (2023). Investigating the effect of precipitation series decomposition on the simulation of electrical conductivity of river flow (case study: Eskandari sub-basin). Journal of Drought and Climate change Research, 1(1), 33-48. doi: 10.22077/jdcr.2023.5950.1005

Nelsen, R. B. (2006). An introduction to copulas, ser. Lecture Notes in Statistics. New York: Springer.

Nguyen-Huy, T., Deo, R. C., Mushtaq, S., & Khan, S. (2020). Probabilistic seasonal rainfall forecasts using semiparametric d-vine copula-based quantile regression. In Handbook of Probabilistic Models (pp. 203-227). Butterworth-Heinemann.

Ozga-Zielinski, B., Ciupak, M., Adamowski, J., Khalil, B., & Malard, J. (2016). Snow-melt flood frequency analysis by means of copula based 2D probability distributions for the Narew River in Poland. Journal of Hydrology: Regional Studies, 6, 26-51.

Pronoos Sedighi, M., Ramezani, Y., Nazeri Tahroudi, M., & Taghian, M. (2023). Joint frequency analysis of river flow rate and suspended sediment load using conditional density of copula functions. Acta Geophysica, 71(1), 489-501.

Qian, L., Wang, H., Dang, S., Wang, C., Jiao, Z., & Zhao, Y. (2018). Modelling bivariate extreme precipitation distribution for data‐scarce regions using Gumbel–Hougaard copula with maximum entropy estimation. Hydrological Processes, 32(2), 212-227.

Ramezani, Y., Nazeri Tahroudi, M., De Michele, C., & Mirabbasi, R. (2023a). Application of copula-based and ARCH-based models in storm prediction. Theoretical and Applied Climatology, 151(3-4), 1239-1255.

Ramezani, Y., Tahroudi, M. N., & Sedighi, M. P. (2023b). Application of vine copulas to estimate dew point temperature. Atmósfera, 37, 501-514.

Renard, B., & Lang, M. (2007). Use of a Gaussian copula for multivariate extreme value analysis: some case studies in hydrology. Advances in Water Resources, 30(4), 897-912.

Ridolfi, E., Montesarchio, V., Rianna, M., Sebastianelli, S., Russo, F., & Napolitano, F. (2013). Evaluation of rainfall thresholds through entropy: Influence of bivariate distribution selection. Irrigation and Drainage, 62(S2), 50-60.

Salarpour, M., Yusop, Z., Yusof, F., Shahid, S., & Jajarmizadeh, M. (2016). Flood Frequency Analysis Based on Gaussian Copula. In ISFRAM 2015 (pp. 151-165): Springer.

Salvadori, G., & De Michele, C. (2004). Analytical calculation of storm volume statistics involving Pareto‐like intensity‐duration marginals. Geophysical Research Letters, 31(4).

Salvadori, G., & De Michele, C. (2006). Statistical characterization of temporal structure of storms. Advances in Water Resources, 29(6), 827-842.

Salvadori, G., & De Michele, C. (2007). On the use of copulas in hydrology: theory and practice. Journal of Hydrologic Engineering, 12(4), 369-380.

Salvadori, G., & De Michele, C. (2010). Multivariate multiparameter extreme value models and return periods: A copula approach. Water resources research, 46(10).

Salvadori, G., & De Michele, C. (2015). Multivariate real-time assessment of droughts via copula-based multi-site hazard trajectories and fans. Journal of Hydrology, 526, 101-115.

Salvadori, G., De Michele, C., Kottegoda, N. T., & Rosso, R. (2007). Extremes in nature: an approach using copulas (Vol. 56). Springer Science & Business Media.

Salvadori, G., De, M. C., & Durante, F. (2011). Multivariate design via copulas. Hydrol. Earth Syst. Sci. Discuss, 8:5523–5558. doi:10.5194/hessd-8-5523-2011

Samaniego, L., Bárdossy, A., & Kumar, R. (2010). Streamflow prediction in ungauged catchments using copula‐based dissimilarity measures. Water Resources Research, 46(2).

Schepsmeier, U. (2019). A goodness-of-fit test for regular vine copula models. Econometric Reviews, 38(1), 25-46.

Seo, B.-C., Krajewski, W. F., & Mishra, K. V. (2015). Using the new dual-polarimetric capability of WSR-88D to eliminate anomalous propagation and wind turbine effects in radar-rainfall. Atmospheric Research, 153, 296-309.

Serinaldi, F. (2008). Analysis of inter-gauge dependence by Kendall’s τK, upper tail dependence coefficient, and 2-copulas with application to rainfall fields. Stochastic Environmental Research and Risk Assessment, 22(6), 671-688.

Serinaldi, F. (2009). Copula-based mixed models for bivariate rainfall data: an empirical study in regression perspective. Stochastic Environmental Research and Risk Assessment, 23(5), 677-693.

Serinaldi, F., Bonaccorso, B., Cancelliere, A., & Grimaldi, S. (2009). Probabilistic characterization of drought properties through copulas. Physics and Chemistry of the Earth, Parts A/B/C, 34(10-12), 596-605.

Shafaei, M., Fakheri-Fard, A., Dinpashoh, Y., Mirabbasi, R., & De Michele, C. (2017). Modeling flood event characteristics using D-vine structures. Theoretical and Applied Climatology, 130(3-4), 713-724.

Shiau, J. (2006). Fitting drought duration and severity with two-dimensional copulas. Water Resources Management, 20(5), 795-815.

Sklar, M. (1959). Fonctions de repartition an dimensions et leurs marges. Publ. inst. statist. univ. Paris, 8, 229-231.

Song, S., & Singh, V. P. (2010). Meta-elliptical copulas for drought frequency analysis of periodic hydrologic data. Stochastic Environmental Research and Risk Assessment, 24(3), 425-444.

Sraj, M., Bezak, N., & Brilly, M. (2015). Bivariate flood frequency analysis using the copula function: a case study of the Litija station on the Sava River. Hydrological Processes, 29(2), 225-238.

Sun, Y., Cuesta-Infante, A., & Veeramachaneni, K. (2019, July). Learning vine copula models for synthetic data generation. In Proceedings of the AAAI Conference on Artificial Intelligence (Vol. 33, No. 01, pp. 5049-5057).

Suroso, S., & Bárdossy, A. (2018). Investigation of asymmetric spatial dependence of precipitation using empirical bivariate copulas. Journal of Hydrology, 565, 685-697.

Tabatabaei, S. M., Dastourani, M., Eslamian, S., & Nazeri Tahroudi, M. (2022). Ranking and optimizing the rain-gauge networks using the entropy–copula approach (Case study of the Siminehrood Basin, Iran). Applied Water Science, 12(9), 214.

Tagasovska N, Ackerer D, Vatter T. 2019. Copulas as high-dimensional generative models: vine copula autoencoders. In Proceedings of the 33rd Conference on Neural Information Processing Systems (NeurIPS 2019), ed. H Wallach, H Larochelle, A Beygelzimer, F d'Alché-Buc, E Fox, R Garnett. Red Hook, NY: Curran

Tahroudi, M. N., Ramezani, Y., De Michele, C., & Mirabbasi, R. (2022). Application of Copula Functions for Bivariate Analysis of Rainfall and River Flow Deficiencies in the Siminehrood River Basin, Iran. JOURNAL OF HYDROLOGIC ENGINEERING, 27(11).

Tong, X., Wang, D., Singh, V., Wu, J., Chen, X., & Chen, Y. (2014). Impact of data length on the uncertainty of hydrological Copula modeling. Journal of Hydrologic Engineering, 20(4), 05014019.

Tsakiris, G., Kordalis, N., Tigkas, D., Tsakiris, V., & Vangelis, H. (2016). Analysing drought severity and areal extent by 2D Archimedean copulas. Water Resources Management, 30(15), 5723-5735.

Vahidi, M. J., Mirabbasi, R., Khashei-Siuki, A., Tahroudi, M. N., & Jafari, A. M. (2023). Modeling of daily suspended sediment load by trivariate probabilistic model (case study, Allah River Basin, Iran). Journal of Soils and Sediments, 1-12.

Wang, X., Gebremichael, M., & Yan, J. (2010). Weighted likelihood copula modeling of extreme rainfall events in Connecticut. Journal of Hydrology, 390(1-2), 108-115.

Wei, T., & Song, S. (2018). Copula-based composite likelihood approach for frequency analysis of short annual precipitation records. Hydrology Research, 49(5), 1498-1512.

Wei, T., & Song, S. (2019). Utilization of the Copula-Based Composite Likelihood Approach to Improve Design Precipitation Estimates Accuracy. Water Resources Management, 33(15), 5089-5106.

Xiao, M., Yu, Z., & Zhu, Y. (2019). Copula-based frequency analysis of drought with identified characteristics in space and time: a case study in Huai River basin, China. Theoretical and Applied Climatology, 137(3-4), 2865-2875.

Xiao, Y., Guo, S., Liu, P., Yan, B., & Chen, L. (2009). Design flood hydrograph based on multicharacteristic synthesis index method. Journal of Hydrologic Engineering, 14(12), 1359-1364.

Xu, K., Milliman, J. D., & Xu, H. (2010). Temporal trend of precipitation and runoff in major Chinese Rivers since 1951. Global and Planetary Change, 73(3-4), 219-232.

Xu, Y., Huang, G., & Fan, Y. (2017). Multivariate flood risk analysis for Wei River. Stochastic environmental research and risk assessment, 31(1), 225-242.

Yendra, R., Hartono, A. P. D., Muhaijir, N., & Irawan, D. (2016). Relation Model of Storm Wet Duration and Storm Intensity for Various Rainfall Aggregation Levels using Copula Method. Global Journal of Pure and Applied Mathematics, 12(6), 4749-4758.

Yin, J., Guo, S., He, S., Guo, J., Hong, X., & Liu, Z. (2018). A copula-based analysis of projected climate changes to bivariate flood quantiles. Journal of Hydrology, 566, 23-42.

Zhang, D.-D., Yan, D.-H., Lu, F., Wang, Y.-C., & Feng, J. (2015). Copula-based risk assessment of drought in Yunnan province, China. Natural Hazards, 75(3), 2199-2220.

Zhang, L., & Singh, V. P. (2007a). Bivariate rainfall frequency distributions using Archimedean copulas. Journal of Hydrology, 332(1-2), 93-109.

Zhang, L., & Singh, V. P. (2007b). Gumbel–Hougaard copula for trivariate rainfall frequency analysis. Journal of Hydrologic Engineering, 12(4), 409-419.

Zhang, Q., Li, J., Singh, V. P., & Xu, C. Y. (2013). Copula‐based spatio‐temporal patterns of precipitation extremes in China. International Journal of Climatology, 33(5), 1140-1152.

Zhu, S., Xu, Z., Luo, X., Wang, C., & Wu, J. (2020). Assessing coincidence probability for extreme precipitation events in the Jinsha River basin. Theoretical and Applied Climatology, 139(1-2), 825-835