Assessment of Nonstationarity and Uncertainty in Precipitation Extremes of a River Basin Under Climate Change

Abstract

In this study, an uncertainty analysis of extreme precipitation return levels was performed for the Chaliyar river basin, India, under representative concentration pathways (RCPs) 4.5 and 8.5. Weighted average projections of various climate models (for RCPs 4.5 and 8.5) using reliability ensemble averaging were used in the analysis for projecting the future extremes. To start with, the presence of nonstationarity in the observed annual maximum precipitation (AMP) series and the future ensemble averaged AMP projections were investigated. For this purpose, three generalized extreme value (GEV) models—one stationary model with constant parameters and two nonstationary models with trends in location and scale parameters—were applied to assess the goodness of fit using Akaike information criterion and likelihood ratio test. The best fit model was used in the uncertainty analysis, and the confidence bounds of extreme precipitation return levels were estimated. A nonparametric bootstrapping approach was followed in the uncertainty analysis. Results of the study suggest that a nonstationary GEV distribution with linear trend in location parameter and constant scale and shape parameters are the best fit distribution for the AMP series under the RCP scenarios, whereas the stationary GEV distribution fits the observed AMP series the best. The expected values and confidence bounds of return levels obtained from the uncertainty analysis reveal that precipitation extremes in the river basin would intensify under the projected climate change scenarios. Compared with the RCP4.5 scenario, the confidence intervals of return levels under the RCP8.5 scenario were wider, implying that uncertainty in the latter scenario is higher.

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Data Availability

The climate model projections used in this study are from Coordinated Regional Climate Downscaling Experiment (CORDEX). These can be accessed through the climate data portal of Centre for Climate Change Research (CCCR), Indian Institute of Tropical Meteorology (IITM), Pune, India (http://cccr.tropmet.res.in).

References

  1. 1.

    Pachauri, R. K, Allen, M. R, Barros, V. R., Broome, J., Cramer, W., Christ, R., & Dubash, N. K. (2014) Climate change 2014: synthesis report. Contribution of Working Groups I, II and III to the fifth assessment report of the Intergovernmental Panel on Climate Change (pp. 151). IPCC.

  2. 2.

    Trenberth, K. E. (1998). Atmospheric moisture residence times and cycling: Implications for rainfall rates and climate change. Climatic Change, 39(4), 667–694. https://doi.org/10.1023/A:1005319109110.

    Article  Google Scholar 

  3. 3.

    Muller, C. J., O’Gorman, P. A., & Back, L. E. (2011). Intensification of precipitation extremes with warming in a cloud-resolving model. Journal of Climate, 24(11), 2784–2800. https://doi.org/10.1175/2011JCLI3876.1.

    Article  Google Scholar 

  4. 4.

    Easterling, D. R., Meehl, G. A., Parmesan, C., Changnon, S. A., Karl, T. R., & Mearns, L. O. (2000). Climate extremes: observations, modeling, and impacts. Science, 289(5487), 2068–2074. https://doi.org/10.1126/science.289.5487.2068.

    CAS  Article  Google Scholar 

  5. 5.

    Frei, C., & Schär, C. (2001). Detection probability of trends in rare events: Theory and application to heavy precipitation in the Alpine region. Journal of Climate, 14(7), 1568–1584. https://doi.org/10.1175/1520-0442(2001)014%3c1568:DPOTIR%3e2.0.CO;2.

    Article  Google Scholar 

  6. 6.

    Goswami, B. N., Venugopal, V., Sengupta, D., Madhusoodanan, M. S., & Xavier, P. K. (2006). Increasing trend of extreme rain events over India in a warming environment. Science, 314(5804), 1442–1445. https://doi.org/10.1126/science.1132027.

    CAS  Article  Google Scholar 

  7. 7.

    Griffiths, G. M., Salinger, M. J., & Leleu, I. (2003). Trends in extreme daily rainfall across the South Pacific and relationship to the South Pacific convergence zone. International Journal of Climatology, 23(8), 847–869. https://doi.org/10.1002/joc.923.

    Article  Google Scholar 

  8. 8.

    Haylock, M., & Nicholls, N. (2000). Trends in extreme rainfall indices for an updated high quality data set for Australia, 1910–1998. International Journal of Climatology, 20(13), 1533–1615. https://doi.org/10.1002/1097-0088(20001115)20:13%3c1533::AID-JOC586%3e3.0.CO;2-J.

    Article  Google Scholar 

  9. 9.

    Salinger, M. J., & Griffiths, G. M. (2001). Trends in New Zealand daily temperature and rainfall extremes. International Journal of Climatology, 21(12), 1437–1452. https://doi.org/10.1002/joc.694.

    Article  Google Scholar 

  10. 10.

    Mishra, V., Aaadhar, S., Shah, H., Kumar, R., Pattanaik, D. R., & Tiwari, A. D. (2018). The Kerala flood of 2018: combined impact of extreme rainfall and reservoir storage. Hydrology and Earth System Sciences Discussions, 1–13, 2018. https://doi.org/10.5194/hess-2018-480.

    Article  Google Scholar 

  11. 11.

    Mukherjee, S., Aadhar, S., Stone, D., & Mishra, V. (2018). Increase in extreme precipitation events under anthropogenic warming in India. Weather and Climate Extremes, 20, 45–53. https://doi.org/10.1016/j.wace.2018.03.005.

    Article  Google Scholar 

  12. 12.

    Revadekar, J. V., Patwardhan, S. K., & Rupa Kumar, K. (2011). Characteristic features of precipitation extremes over India in the warming scenarios. Advances in Meteorology. https://doi.org/10.1155/2011/138425.

    Article  Google Scholar 

  13. 13.

    Riswana, K. P., & Sithara Beegam, C. R. (2019). Tale of tears: development and flood experience of Chaliyar grama panchayath, Malappuram. A Journal of Composition Theory.

  14. 14.

    Agana, N. A., Sefidmazgi, M. G., & Homaifar, A. (2015). Analysis of Nonstationary Extreme Events. MAICS, pp. 7–11.

  15. 15.

    Davison, A. C., & Smith, R. L. (1990). Models for exceedances over high thresholds. Journal of the Royal Statistical Society: Series B (Methodological)52(3), 393–425. www.jstor.org/stable/2345667.

  16. 16.

    Gumbel, E. J. (1941). The return period of flood flows. The Annals of Mathematical Statistics12(2), 163–190. www.jstor.org/stable/2235766.

  17. 17.

    Jenkinson, A. F. (1955). The frequency distribution of the annual maximum (or minimum) values of meteorological elements. Quarterly Journal of the Royal Meteorological Society, 81(348), 158–171. https://doi.org/10.1002/qj.49708134804.

    Article  Google Scholar 

  18. 18.

    Singh, V. (1998). Entropy-based parameter estimation in hydrology (Vol. 30). Springer Science & Business Media.

  19. 19.

    Katz, R. W., Parlange, M. B., & Naveau, P. (2002). Statistics of extremes in hydrology. Advances in Water Resources, 25(8), 1287–1304. https://doi.org/10.1016/S0309-1708(02)00056-8.

    Article  Google Scholar 

  20. 20.

    Bobée, B., & Rasmussen, P. F. (1995). Recent advances in flood frequency analysis. Reviews of Geophysics, 33(S2), 1111–1116. https://doi.org/10.1029/95RG00287.

    Article  Google Scholar 

  21. 21.

    Cunnane, C. (1989). Statistical distributions for flood frequency analysis. Operational Hydrology Report (WMO).

  22. 22.

    Volpi, E., Fiori, A., Grimaldi, S., Lombardo, F., & Koutsoyiannis, D. (2015). One hundred years of return period: Strengths and limitations. Water Resources Research, 51(10), 8570–8585. https://doi.org/10.1002/2015WR017820.

    Article  Google Scholar 

  23. 23.

    Leadbetter, M. R., Lindgren, G., & Rootzén, H. (2012). Extremes and related properties of random sequences and processes. Springer Science & Business Media. https://doi.org/10.1007/978-1-4612-5449-2.

    Article  Google Scholar 

  24. 24.

    Watson, G. S. (1954). Extreme values in samples from-dependent stationary stochastic processes. The Annals of Mathematical Statistics25(4), 798–800. www.jstor.org/stable/2236668.

  25. 25.

    Cheng, L., AghaKouchak, A., Gilleland, E., & Katz, R. W. (2014). Non-stationary extreme value analysis in a changing climate. Climatic Change, 127(2), 353–369. https://doi.org/10.1007/s10584-014-1254-5.

    Article  Google Scholar 

  26. 26.

    Milly, P. C., Betancourt, J., Falkenmark, M., Hirsch, R. M., Kundzewicz, Z. W., Lettenmaier, D. P., & Stouffer, R. J. (2008). Stationarity is dead: Whither water management? Science, 319(5863), 573–574. https://doi.org/10.1126/science.1151915.

    CAS  Article  Google Scholar 

  27. 27.

    Kundzewicz, Z. W., & Robson, A. J. (2004). Change detection in hydrological records-a review of the methodology/revue méthodologique de la détection de changements dans les chroniques hydrologiques. Hydrological Sciences Journal, 49(1), 7–19. https://doi.org/10.1623/hysj.49.1.7.53993.

    Article  Google Scholar 

  28. 28.

    Agilan, V., & Umamahesh, N. V. (2017). What are the best covariates for developing non-stationary rainfall intensity-duration-frequency relationship? Advances in Water Resources, 101, 11–22. https://doi.org/10.1016/j.advwatres.2016.12.016.

    Article  Google Scholar 

  29. 29.

    Prosdocimi, I., Kjeldsen, T. R., & Miller, J. D. (2015). Detection and attribution of urbanization effect on flood extremes using nonstationary flood-frequency models. Water Resources Research, 51(6), 4244–4262. https://doi.org/10.1002/2015WR017065.

    CAS  Article  Google Scholar 

  30. 30.

    Salas, J. D., & Obeysekera, J. (2013). Revisiting the concepts of return period and risk for nonstationary hydrologic extreme events. Journal of Hydrologic Engineering, 19(3), 554–568. https://doi.org/10.1061/(ASCE)HE.1943-5584.0000820.

    Article  Google Scholar 

  31. 31.

    Šraj, M., Viglione, A., Parajka, J., & Blöschl, G. (2016). The influence of non-stationarity in extreme hydrological events on flood frequency estimation. Journal of Hydrology and Hydromechanics, 64(4), 426–437. https://doi.org/10.1515/johh-2016-0032.

    Article  Google Scholar 

  32. 32.

    Strupczewski, W. G., Singh, V. P., & Feluch, W. (2001). Non-stationary approach to at-site flood frequency modelling I. Maximum likelihood estimation. Journal of Hydrology, 248(1), 123–142. https://doi.org/10.1016/S0022-1694(01)00397-3.

    Article  Google Scholar 

  33. 33.

    Mondal, A., & Mujumdar, P. P. (2016). Detection of change in flood return levels under global warming. Journal of Hydrologic Engineering, 21(8), 04016021. https://doi.org/10.1061/(ASCE)HE.1943-5584.0001326.

    Article  Google Scholar 

  34. 34.

    Vogel, R. M., Yaindl, C., & Walter, M. (2011). Nonstationarity: flood magnification and recurrence reduction factors in the United States 1. JAWRA Journal of the American Water Resources Association, 47(3), 464–474. https://doi.org/10.1111/j.1752-1688.2011.00541.x.

    Article  Google Scholar 

  35. 35.

    Bayazit, M. (2015). Nonstationarity of hydrological records and recent trends in trend analysis: a state-of-the-art review. Environmental Processes, 2(3), 527–542. https://doi.org/10.1007/s40710-015-0081-7.

    Article  Google Scholar 

  36. 36.

    Cooley, D. (2013). Return periods and return levels under climate change. Extremes in a Changing Climate (pp. 97–114). Dordrecht: Springer.

  37. 37.

    Tramblay, Y., Neppel, L., Carreau, J., & Sanchez-Gomez, E. (2012). Extreme value modelling of daily areal rainfall over Mediterranean catchments in a changing climate. Hydrological Processes, 26(25), 3934–3944. https://doi.org/10.1002/hyp.8417.

    Article  Google Scholar 

  38. 38.

    Yilmaz, A. G., Hossain, I., & Perera, B. J. C. (2014). Effect of climate change and variability on extreme rainfall intensity–frequency–duration relationships: a case study of Melbourne. Hydrology and Earth System Sciences, 18(10), 4065–4076. https://doi.org/10.5194/hess-18-4065-2014.

    Article  Google Scholar 

  39. 39.

    Khaliq, M. N., Ouarda, T. B. M. J., Ondo, J. C., Gachon, P., & Bobée, B. (2006). Frequency analysis of a sequence of dependent and/or non-stationary hydro- meteorological observations: A review. Journal of Hydrology, 329(3), 534–552. https://doi.org/10.1016/j.jhydrol.2006.03.004.

    Article  Google Scholar 

  40. 40.

    Agilan, V., & Umamahesh, N. V. (2018). Covariate and parameter uncertainty in non-stationary rainfall IDF curve. International Journal of Climatology, 38(1), 365–383. https://doi.org/10.1002/joc.5181.

    Article  Google Scholar 

  41. 41.

    Villarini, G., Smith, J. A., Serinaldi, F., Bales, J., Bates, P. D., & Krajewski, W. F. (2009). Flood frequency analysis for nonstationary annual peak records in an urban drainage basin. Advances in Water Resources, 32(8), 1255–1266. https://doi.org/10.1016/j.advwatres.2009.05.003.

    Article  Google Scholar 

  42. 42.

    Rigby, R. A., & Stasinopoulos, D. M. (2005). Generalized additive models for location, scale and shape. Journal of the Royal Statistical Society: Series C (Applied Statistics), 54(3), 507–554. https://doi.org/10.1111/j.1467-9876.2005.00510.x.

    Article  Google Scholar 

  43. 43.

    Cannon, A. J. (2010). A flexible nonlinear modelling framework for nonstationary generalized extreme value analysis in hydroclimatology. Hydrological Processes, 24(6), 673–685. https://doi.org/10.1002/hyp.7506.

    Article  Google Scholar 

  44. 44.

    Agilan, V., & Umamahesh, N. V. (2017). Non-stationary rainfall intensity-duration-frequency relationship: a comparison between annual maximum and partial duration series. Water Resources Management, 31(6), 1825–1841. https://doi.org/10.1007/s11269-017-1614-9.

    Article  Google Scholar 

  45. 45.

    Heo, J. H., & Salas, J. D. (1996). Estimation of quantiles and confidence intervals for the log-Gumbel distribution. Stochastic Hydrology and Hydraulics, 10(3), 187–207. https://doi.org/10.1007/BF01581463.

    Article  Google Scholar 

  46. 46.

    Michele, C. D., & Rosso, R. (2001). Uncertainty assessment of regionalized flood frequency estimates. Journal of Hydrologic Engineering, 6(6), 453–459. https://doi.org/10.1061/(ASCE)1084-0699(2001)6:6(453).

    Article  Google Scholar 

  47. 47.

    Obeysekera, J., & Salas, J. D. (2013). Quantifying the uncertainty of design floods under nonstationary conditions. Journal of Hydrologic Engineering, 19(7), 1438–1446. https://doi.org/10.1061/(ASCE)HE.1943-5584.0000931.

    Article  Google Scholar 

  48. 48.

    Obeysekera, J. T., & Salas, J. D. (2020). Hydrologic designs for extreme events under nonstationarity. Engineering Methods for Precipitation under a Changing Climate (pp. 63–82). https://doi.org/10.1061/9780784415528.ch04.

  49. 49.

    Serinaldi, F., & Kilsby, C. G. (2015). Stationarity is undead: Uncertainty dominates the distribution of extremes. Advances in Water Resources, 77, 17–36. https://doi.org/10.1016/j.advwatres.2014.12.013.

    Article  Google Scholar 

  50. 50.

    Das, J., & Umamahesh, N. V. (2018). Assessment of uncertainty in estimating future flood return levels under climate change. Natural Hazards, 93(1), 109–124. https://doi.org/10.1007/s11069-018-3291-2.

    Article  Google Scholar 

  51. 51.

    Raneesh, K. Y., & Thampi, S. G. (2013). A simple semi-distributed hydrologic model to estimate groundwater recharge in a humid tropical basin. Water Resources Management, 27(5), 1517–1532. https://doi.org/10.1007/s11269-012-0252-5.

    Article  Google Scholar 

  52. 52.

    Das, J., & Umamahesh, N. V. (2017). Uncertainty and nonstationarity in streamflow extremes under climate change scenarios over a river basin. Journal of Hydrologic Engineering, 22(10), 04017042. https://doi.org/10.1061/(ASCE)HE.1943-5584.0001571.

    Article  Google Scholar 

  53. 53.

    Bi, D., Dix, M., Marsland, S. J., O'Farrell, S., Rashid, H., Uotila, P., Hirst, A. C., Kowalczyk, E. A., Golebiewski, M., Sullivan, A., Yan, H., Hannah, N., Franklin, C. N., Sun, Z., Vohralik, P. F., Watterson, I. G., Zhou, X., Fiedler, R., Collier, M., Ma, Y., Noonan, J. A., Stevens, L., Uhe, P., Zhu, H., Griffies, S. M., Hill, R., Harris, C., & Puri, K. (2013). The ACCESS coupled model: description, control climate and evaluation. Australian Meteorological and Oceanographic Journal, 63(1), 41–64. https://doi.org/10.22499/2.6301.004.

  54. 54.

    Mcgregor, J. L., & Dix, M. R. (2001). The CSIRO conformal-cubic atmospheric GCM. IUTAM symposium on advances in mathematical modelling of atmosphere and ocean dynamics (pp. 197–202). Dordrecht: Springer. https://doi.org/10.1007/978-94-010-0792-4_25.

  55. 55.

    Gent, P. R., Danabasoglu, G., Donner, L. J., Holland, M. M., Hunke, E. C., Jayne, S. R., et al. (2011). The community climate system model version 4. Journal of Climate, 24(19), 4973–4991. https://doi.org/10.1175/2011JCLI4083.1.

    Article  Google Scholar 

  56. 56.

    Voldoire, A., Sanchez-Gomez, E., y Mélia, D. S., Decharme, B., Cassou, C., Sénési, S., Valcke, S., Beau, I., Alias, A., Chevallier, M. & Déqué, M. (2013). The CNRM-CM5.1 global climate model: description and basic evaluation. Climate Dynamics40(9–10), 2091–2121. https://doi.org/10.1007/s00382-011-1259-y.

  57. 57.

    Giorgetta, M. A., Jungclaus, J., Reick, C. H., Legutke, S., Bader, J., Böttinger, M., et al. (2013). Climate and carbon cycle changes from 1850 to 2100 in MPI-ESM simulations for the Coupled Model Intercomparison Project phase 5. Journal of Advances in Modeling Earth Systems, 5(3), 572–597. https://doi.org/10.1002/jame.20038.

    Article  Google Scholar 

  58. 58.

    Bentsen, M., Bethke, I., Debernard, J. B., Iversen, T., Kirkevåg, A., Seland, Ø., et al. (2013). The Norwegian earth system model, NorESM1-M—Part 1: Description and basic evaluation of the physical climate. Geoscientific Model Development, 6(3), 687–720. https://doi.org/10.5194/gmd-6-687-2013.

    Article  Google Scholar 

  59. 59.

    Arora, V. K., Scinocca, J. F., Boer, G. J., Christian, J. R., Denman, K. L., Flato, G. M., Kharin, V. V., Lee, W. G., & Merryfield, W. J. (2011). Carbon emission limits required to satisfy future representative concentration pathways of greenhouse gases. Geophysical Research Letters38(5). https://doi.org/10.1029/2010GL046270.

  60. 60.

    Giorgi, F., Coppola, E., Solmon, F., Mariotti, L., Sylla, M. B., Bi, X., et al. (2012). RegCM4: model description and preliminary tests over multiple CORDEX domains. Climate Research, 52, 7–29. https://doi.org/10.3354/cr01018.

    Article  Google Scholar 

  61. 61.

    Rotstayn, L. D., Jeffrey, S. J., Collier, M. A., Dravitzki, S. M., Hirst, A. C., Syktus, J. I., & Wong, K. K. (2012). Aerosol-and greenhouse gas-induced changes in summer rainfall and circulation in the Australasian region: a study using single-forcing climate simulations. Atmospheric Chemistry and Physics, 12(14), 6377. https://doi.org/10.5194/acp-12-6377-2012.

    CAS  Article  Google Scholar 

  62. 62.

    Dufresne, J. L., Foujols, M. A., Denvil, S., Caubel, A., Marti, O., Aumont, O., et al. (2013). Climate change projections using the IPSL-CM5 Earth System Model: from CMIP3 to CMIP5. Climate Dynamics, 40(9–10), 2123–2165. https://doi.org/10.1007/s00382-012-1636-1.

    Article  Google Scholar 

  63. 63.

    Jakob, D. (2013). Nonstationarity in extremes and engineering design. Extremes in a changing climate (pp. 363–417). Dordrecht: Springer.

  64. 64.

    Read, L. K., & Vogel, R. M. (2015). Reliability, return periods, and risk under nonstationarity. Water Resources Research, 51(8), 6381–6398. https://doi.org/10.1002/2015WR017089.

    Article  Google Scholar 

  65. 65.

    Brown, C., Templin, J., & Cohen, A. (2015). Comparing the two-and three-parameter logistic models via likelihood ratio tests: A commonly misunderstood problem. Applied Psychological Measurement, 39(5), 335–348. https://doi.org/10.1177/0146621614563326.

    Article  Google Scholar 

  66. 66.

    Mondal, A., & Mujumdar, P. P. (2017). Hydrologic extremes under climate change: Non-stationarity and uncertainty. Sustainable Water Resources Planning and Management Under Climate Change (pp. 39–60). Singapore: Springer.

  67. 67.

    Giorgi, F., & Mearns, L. O. (2003). Probability of regional climate change based on the Reliability Ensemble Averaging (REA) method. Geophysical Research Letters, 30(12). https://doi.org/10.1029/2003GL017130.

  68. 68.

    Xu, Y., Gao, X., & Giorgi, F. (2010). Upgrades to the reliability ensemble averaging method for producing probabilistic climate change projections. Climate Research, 41(1), 61–81. https://doi.org/10.3354/cr00835.

    Article  Google Scholar 

  69. 69.

    Riano, A. (2013). The Shift of Precipitation Maxima on the Annual Maximum Series using Regional Climate Model Precipitation Data. Arizona State University.

  70. 70.

    Dominguez, F., Cañon, J., & Valdes, J. (2010). IPCC-AR4 climate simulations for the Southwestern US: the importance of future ENSO projections. Climatic Change, 99(3–4), 499–514. https://doi.org/10.1007/s10584-009-9672-5.

    Article  Google Scholar 

  71. 71.

    Ehret, U., Zehe, E., Wulfmeyer, V., Warrach-Sagi, K., & Liebert, J. (2012). HESS Opinions "Should we apply bias correction to global and regional climate model data?". Hydrology & Earth System Sciences Discussions9(4). https://doi.org/10.5194/hess-16-3391-2012.

  72. 72.

    Switanek, M., Troch, P. A., Castro, C. L., Leuprecht, A., Chang, H. I., Mukherjee, R., & Demaria, E. M. (2017). Scaled distribution mapping: a bias correction method that preserves raw climate model projected changes. Hydrology and Earth System Sciences, 21(6), 2649–2666. https://doi.org/10.5194/hess-21-2649-2017.

    Article  Google Scholar 

  73. 73.

    Danandeh Mehr, A., & Kahya, E. (2016). Climate change impacts on catchment-scale extreme rainfall variability: case study of Rize Province Turkey. Journal of Hydrologic Engineering, 22(3), 05016037. https://doi.org/10.1061/(ASCE)HE.1943-5584.0001477.

    Article  Google Scholar 

  74. 74.

    Zhang, X., & Zwiers, F. W. (2013). Statistical indices for the diagnosing and detecting changes in extremes. Extremes in a Changing Climate (pp. 1–14). Dordrecht: Springer. https://doi.org/10.1007/978-94-007-4479-0_1.

  75. 75.

    Clarke, R. T. (2002). Fitting and testing the significance of linear trends in Gumbel-distributed data. Hydrology and Earth System Sciences Discussions, 6(1), 17–24. https://doi.org/10.5194/hess-6-17-2002.

    Article  Google Scholar 

  76. 76.

    Katz, R. W. (2013). Statistical methods for nonstationary extremes. Extremes in a changing climate (pp. 15–37). Dordrecht: Springer. https://doi.org/10.1007/978-94-007-4479-0_2.

  77. 77.

    Coles, S., Bawa, J., Trenner, L., & Dorazio, P. (2001). An introduction to statistical modeling of extreme values (Vol. 208). London: Springer.

    Google Scholar 

  78. 78.

    Westra, S., Alexander, L. V., & Zwiers, F. W. (2013). Global increasing trends in annual maximum daily precipitation. Journal of Climate, 26(11), 3904–3918. https://doi.org/10.1175/JCLI-D-12-00502.1.

    Article  Google Scholar 

  79. 79.

    Zwiers, F. W., Zhang, X., & Feng, Y. (2011). Anthropogenic influence on long return period daily temperature extremes at regional scales. Journal of Climate, 24(3), 881–892. https://doi.org/10.1175/2010JCLI3908.1.

    Article  Google Scholar 

  80. 80.

    Zhang, X., Zwiers, F. W., & Li, G. (2004). Monte Carlo experiments on the detection of trends in extreme values. Journal of Climate, 17(10), 1945–1952. https://doi.org/10.1175/1520-0442(2004)017%3c1945:MCEOTD%3e2.0.CO;2.

    Article  Google Scholar 

  81. 81.

    Sclove, S. L. (2011). A review of statistical model selection criteria: Application to prediction in regression, histograms, and finite mixture models. SSRN Electronic Journal. https://doi.org/10.2139/ssrn.1910768.

    Article  Google Scholar 

  82. 82.

    Kadane, J. B., & Lazar, N. A. (2004). Methods and criteria for model selection. Journal of the American statistical Association, 99(465), 279–290. https://doi.org/10.1198/016214504000000269.

    Article  Google Scholar 

  83. 83.

    Hastie, T., Tibshirani, R., & Friedman, J. (2009). Model assessment and selection. The elements of statistical learning (pp. 219–259). New York, NY: Springer. https://doi.org/10.1007/978-0-387-21606-5_7.

  84. 84.

    Akaikei, H. (1973). Information theory and an extension of maximum likelihood principle. In Proc. 2nd Int. Symp. on Information Theory, pp. 267–281.

  85. 85.

    Burnham, K. P., & Anderson, D. R. (2004). Multimodel inference: understanding AIC and BIC in model selection. Sociological Methods & Research, 33(2), 261–304. https://doi.org/10.1177/0049124104268644.

    Article  Google Scholar 

  86. 86.

    Lewis, F., Butler, A., & Gilbert, L. (2011). A unified approach to model selection using the likelihood ratio test. Methods in Ecology and Evolution, 2(2), 155–162. https://doi.org/10.1111/j.2041-210X.2010.00063.x.

    Article  Google Scholar 

  87. 87.

    Greene, W. H. (2003). Econometric Analysis. Pearson Education India.

  88. 88.

    Pol, D. (2004). Empirical problems of the hierarchical likelihood ratio test for model selection. Systematic Biology, 53(6), 949–962. https://doi.org/10.1080/10635150490888868.

    Article  Google Scholar 

  89. 89.

    Mondal, A., & Daniel, D. (2018). Return levels under nonstationarity: The need to update infrastructure design strategies. Journal of Hydrologic Engineering, 24(1), 04018060. https://doi.org/10.1061/(ASCE)HE.1943-5584.0001738.

    Article  Google Scholar 

  90. 90.

    Parey, S., Hoang, T. T. H., & Dacunha-Castelle, D. (2010). Different ways to compute temperature return levels in the climate change context. Environmetrics, 21(7–8), 698–718. https://doi.org/10.1002/env.1060.

    Article  Google Scholar 

  91. 91.

    Gao, M. (2018). Extreme value analysis and risk communication for a changing climate. Advances in Environmental Monitoring and Assessment. IntechOpen. https://doi.org/10.5772/intechopen.79301.

  92. 92.

    Efron, B. (1979). Bootstrap? Another look at Jackknife. Annals of Statistics, 7, 1–26.

    Article  Google Scholar 

  93. 93.

    Al Mamoon, A., & Rahman, A. (2014). Uncertainty in design rainfall estimation: A review. Journal of Hydrology and Environment Research, 2(1), 65–75.

    Google Scholar 

  94. 94.

    Kyselý, J. (2008). A cautionary note on the use of nonparametric bootstrap for estimating uncertainties in extreme-value models. Journal of Applied Meteorology and Climatology, 47(12), 3236–3332. https://doi.org/10.1175/2008JAMC1763.1.

    Article  Google Scholar 

  95. 95.

    Zucchini, W., & Adamson, P. T. (1989). Bootstrap confidence intervals for design storms from exceedance series. Hydrological Sciences Journal, 34(1), 41–48. https://doi.org/10.1080/02626668909491307.

    Article  Google Scholar 

  96. 96.

    Ning, L., Riddle, E. E., & Bradley, R. S. (2015). Projected changes in climate extremes over the northeastern United States. Journal of Climate, 28(8), 3289–3310. https://doi.org/10.1175/JCLI-D-14-00150.1.

    Article  Google Scholar 

  97. 97.

    Xu, K., Xu, B., Ju, J., Wu, C., Dai, H., & Hu, B. X. (2019). Projection and uncertainty of precipitation extremes in the CMIP5 multimodel ensembles over nine major basins in China. Atmospheric Research, 226, 122–137. https://doi.org/10.1016/j.atmosres.2019.04.018.

    Article  Google Scholar 

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The manuscript was prepared based on the discussion between Ms. Ansa Thasneem S, Dr. Chithra N R, and Dr. Santosh G Thampi. Ms. Ansa Thasneem S carried out all the numerical simulations included in the manuscript. The manuscript was prepared by Ms. Ansa Thasneem S, and this was reviewed and corrected by Dr. Santosh G Thampi and Dr. Chithra N R.

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Correspondence to S. Ansa Thasneem.

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Ansa Thasneem, S., Chithra, N.R. & Thampi, S.G. Assessment of Nonstationarity and Uncertainty in Precipitation Extremes of a River Basin Under Climate Change. Environ Model Assess (2021). https://doi.org/10.1007/s10666-021-09752-y

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Keywords

  • Climate change
  • Nonstationarity
  • Extreme precipitation
  • Uncertainty