A nonstationary peaks-over-threshold approach for modelling daily precipitation with covariate-dependent thresholds

References

• Akaike, H. 1974. New look at statistical-model identification. IEEE Transaction on Automatic Control, AC 19 (6): 716–723.10.1109/TAC.1974.1100705
   Web of Science ®Google Scholar
• Balkema, A. A., and L. de Hann. 1974. Residual life time at great age. Annals of Probability 2 (5): 792–804.10.1214/aop/1176996548
   Web of Science ®Google Scholar
• Beguería, S., M. Angula-Martínez, S. Vincente-Serrano, J. I. López-Moreno, and A. El-Kenawy. 2011. Assessing trends in extreme precipitation events intensity and magnitude using non- stationary peaks-over-threshold analysis: A case study in northeast Spain from 1930 to 2006. International Journal of Climatology 31: 2102–2114.10.1002/joc.v31.14
   Web of Science ®Google Scholar
• British Columbia Ministry of Environment (BCME). 2007. Environmental trends in British Columbia: 2007, 352 pp.
   Google Scholar
• Burn, D. H. 2003. The use of resampling for estimating confidence intervals for single site and pooled frequency analysis. Hydrological Sciences Journal 48 (1): 25–38.10.1623/hysj.48.1.25.43485
   Web of Science ®Google Scholar
• Burn, D. H., R. Mansour, K. Zhang, and P. H. Whitfield. 2011. Trends in variability in extreme rainfall event in British Columbia. Canadian Water Resources Journal 36 (1): 67–82.10.4296/cwrj3601067
   Web of Science ®Google Scholar
• Burnham, K. P., and D. R. Anderson. 2002. Model selection and multimodel inference. New York, NY: Springer, 488 pp.
   Google Scholar
• Caires, S., V. R. Swail, and X. L. Wang. 2006. Projection and analysis of extreme wave climate. Journal of Climate 19: 5581–5605.10.1175/JCLI3918.1
   Web of Science ®Google Scholar
• Chang, S. E., M. Gregorian, K. Pathman, L. Yumagulova, and W. Tse. 2012. Urban growth and long-term changes in natural hazard risk. Environment and Planning A 44: 989–1008.10.1068/a43614
   Web of Science ®Google Scholar
• Coles, S. 1993. Regional modelling of extreme storms via max-stable processes. Journal of the Royal Statistical Society: Series B 55 (4): 797–816.
   Google Scholar
• Coles, S. 2001. An introduction to statistical modeling of extreme values. London, United Kingdom: Springer, 208 pp.10.1007/978-1-4471-3675-0
   Google Scholar
• Cunnane, C. 1979. A note on the Poisson assumption on partial duration series models. Water Resources Research 15 (2): 489–494.10.1029/WR015i002p00489
   Web of Science ®Google Scholar
• El Adlouni, S., T. B. M. J. Ouarda, X. Zhang, R. Roy, and B. Bobée. 2007. Generalized maximum likelihood estimators for the nonstationary generalized extreme value model. Water Resources Research 43: W03410. doi:10.1029/2005WR004545.
   Web of Science ®Google Scholar
• Gershunov, A., and T. P. Barnett. 1998. ENSO influence on intraseasonal extreme rainfall and temperature frequencies in the contiguous United States: Observations and model results. Journal of Climate 11: 1575–1586.10.1175/1520-0442(1998)011<1575:EIOIER>2.0.CO;2
   Web of Science ®Google Scholar
• Gilroy, K. L., and R. H. McCuen. 2012. A nonstationary flood frequency analysis method to adjust for future climate change and urbanization. Journal of Hydrology 414-415: 40–48.10.1016/j.jhydrol.2011.10.009
   Web of Science ®Google Scholar
• Hare, F. K., and M. K. Thomas. 1979. Climate Canada. 2nd ed. New York, NY: Wiley, 230 pp.
   Google Scholar
• Hartmann, D. L., A. M. G. Klein Tank, M. Rusticucci, L. V. Alexander, S. Brönnimann, Y. Charabi, F. J. Dentener, et al. 2013. Observations: Atmosphere and surface. In Climate change 2013: The physical science basis. Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change, eds. T. F. Stocker, D. Qin, G.–K. Platter, M. Tignor, S. K. Allen, J. Boschung, A. Nauels, et al. Cambridge, United Kingdom and New York, NY, USA: Cambridge University Press, 30 pp.
   Google Scholar
• Heffernan, J. E., and A. G. Stephenson. 2009. An introduction to statistical modeling of extreme values. R package ‘ismev’. http://cran.r-project.org/web/packages/ismev/ismev.pdf.
   Google Scholar
• Hundecha, Y., A. St-Hilaire, T. B. M. J. Ouarda, and S. El Adlouni. 2008. A nonstationary extreme value analysis for the assessment of changes in extreme annual wind speed over the Gulf of St. Lawrence, Canada. Journal of Applied Meteorology and Climatology 47: 2745–2759. doi:10.1175/2008JAMC1665.1.
   Web of Science ®Google Scholar
• Jonathan, P., K. Ewans, and D. Randell. 2013. Joint modelling of extreme ocean environments incorporating covariate effects. Coastal Engineering 79: 22–31.10.1016/j.coastaleng.2013.04.005
   Web of Science ®Google Scholar
• Jonathan, P., D. Randell, Y. Wu, and K. Ewans. 2013. Nonstationary conditional extremes of northern North Sea storm characteristics. Environmentrics 25: 172–188. doi:10.1002/env.2262.
   Web of Science ®Google Scholar
• Jonathan, P., D. Randell, Y. Wu, and K. Ewans. 2014. Return level estimation from non- stationary spatial data exhibiting multidimensional covariate effects. Ocean Engineering 88: 520–532.10.1016/j.oceaneng.2014.07.007
   Web of Science ®Google Scholar
• Katz, R. W. 2010. Statistics of extremes in climate change. Climatic Change 100: 71–76.10.1007/s10584-010-9834-5
   Web of Science ®Google Scholar
• Katz, R. W., M. B. Parlange, and P. Naveau. 2002. Statistics of extremes in hydrology. Advances in Water Resources 25: 1287–1304.10.1016/S0309-1708(02)00056-8
   Web of Science ®Google Scholar
• Kay, A. L., and D. A. Jones. 2012. Transient changes in flood frequency and timing in Britain under potential projections of climate change. International Journal of Climatology 32: 498–502.
   Web of Science ®Google Scholar
• Kendall, M. G. 1975. Rank correlation methods. London: Griffin, 202 pp.
   Google Scholar
• Khaliq, M. N., T. B. M. J. Ouarda, P. Gachon, L. Sushama, and A. St-Hilaire. 2009. Identification of hydrological trends in the presence of serial and cross correlations: A review of selected methods and their application to annual flow regimes of Canadian rivers. Journal of Hydrology 368: 117–130.10.1016/j.jhydrol.2009.01.035
   Web of Science ®Google Scholar
• Khaliq, M. N., T. B. M. J. Ouarda, J.-C. Ondo, P. Gachon, and B. Bobée. 2006. Frequency analysis of a sequence of dependent and/or non-sationary hydro-meteorological observations: A review. Journal of Hydrology 329: 534–552.10.1016/j.jhydrol.2006.03.004
   Web of Science ®Google Scholar
• Kharin, V. V., and F. W. Zwiers. 2005. Estimating extremes in transient climate change simulations. Journal of Climate 18: 1156–1173.10.1175/JCLI3320.1
   Web of Science ®Google Scholar
• Koenker, R. 2005. Quantile regression. New York, NY: Cambridge University Press, 352 pp.10.1017/CBO9780511754098
   Google Scholar
• Koenker, R., and B. G. Basset. 1978. Regression quantiles. Econometrica 46 (1): 33–50.10.2307/1913643
   Web of Science ®Google Scholar
• Kundzewicz, Z. W. and A. J. Robson. 2000. Detecting trend and other changes in hydrological data. World Climate Program-Data and Monitoring. World Meteorological Organization, Geneva (WMO/TD-No. 1013).
   Google Scholar
• Kyselý, J., and R. Beranová. 2009. Climate-change effects on extreme precipitation in central Europe: Uncertainties of scenarios based on regional climate models. Theoretical and Applied Climatology 95: 361–374.10.1007/s00704-008-0014-8
   Web of Science ®Google Scholar
• Kyselý, J., J. Picek, and R. Beronová. 2010. Estimating extremes in climate change simulations using the peaks-over-threshold method with a non-stationary threshold. Global and Planetary Change 72: 55–68.10.1016/j.gloplacha.2010.03.006
   Web of Science ®Google Scholar
• Lang, M., T. B. M. J. Ouarda, and B. Bobée. 1999. Towards operational guideline for over- threshold modeling. Journal of Hydrology 225: 103–117.10.1016/S0022-1694(99)00167-5
   Web of Science ®Google Scholar
• Li, J., and S. Tan. 2015. Nonstationary flood frequency analysis for annual flood peak series, adopting climate indices and check dam index as covariates. Water Resources Management 29: 5533–5550.10.1007/s11269-015-1133-5
   Web of Science ®Google Scholar
• Mailhot, A., S. Lachance-Cloutier, G. Talbot, and A.-C. Favre. 2013. Regional estimates of intense rainfall based on peaks-over-threshold (POT) approach. Journal of Hydrology 476: 188–199.10.1016/j.jhydrol.2012.10.036
   Web of Science ®Google Scholar
• Mann, H. B. 1945. Nonparametric tests against trend. Econometrica 13: 245–259.
   Web of Science ®Google Scholar
• Mantua, N. J., S. R. Hare, Y. Zhang, J. M. Wallace, and R. C. Francis. 1997. A Pacific interdecadal climate Oscillation with impact on salmon production. Bulletin of the American Meteorological Society 78: 1069–1079.10.1175/1520-0477(1997)078<1069:APICOW>2.0.CO;2
   Web of Science ®Google Scholar
• Milly, P. D. D., J. Betancourt, M. Falkenmark, R. Hirsch, W. Zbigniew, D. Kundzewicz, D. P. Lettenmaier, and R. J. Stouffer. 2008. Stationarity is dead: Whither water management? Science 319 (5863): 573–574.10.1126/science.1151915
   PubMed Web of Science ®Google Scholar
• Moore, R.D., D.L. Spittlehouse, P.H. Whitfield, and K. Stahl. 2010. Chapter 3: Weather and climate. In Compendium of forest hydrology and geomorphology in British Columbia, eds, R.G. Pike, T.E. Redding, R.D. Moore, R.D. Winkler, and K.D. Bladon, 47–84. BC Ministry of Forests and Range, Research Branch, Victoria, BC and FORREX Forest Research Extension Partnership, Kamloops, BC.
   Google Scholar
• Mote, P. W. 2003. Twentieth-century fluctuations and trends in temperature, precipitation, and mountain snowpack in the Georgia Basin – Puget Sound region. Canadian Water Resources Journal 28 (4): 567–585.10.4296/cwrj2804567
   Google Scholar
• Nadarajah, S. 2005. Extremes of daily rainfall in west central Florida. Climate Change 63: 325–342.10.1007/s10584-005-1812-y
   Google Scholar
• Nelder, J. A., and R. Mead. 1965. A simplex method for function minimization. Computer Journal 7: 308–313.10.1093/comjnl/7.4.308
   Web of Science ®Google Scholar
• Northrop, P. J., and P. Jonathan. 2011. Threshold modelling of spatially dependent non-stationary extremes with application to hurricane-induced wave heights. Environmetrics 22(7): 799–809. doi:10.1002/env.1106.
   Web of Science ®Google Scholar
• O’Brien, N. L., and D. H. Burn. 2014. A nonstationary index-flood technique for estimating extreme quantiles for annual maximum streamflow. Journal of Hydrology 519: 2040–2048.10.1016/j.jhydrol.2014.09.041
   Web of Science ®Google Scholar
• Önöz, B., and M.Bayazit. 2012. Block bootstrap for Mann-Kendall trend test of serially dependent data. Hydrological Processes 26: 3552–3560.
   Web of Science ®Google Scholar
• Ontario Ministry of the Environment (OME). 2008. Design guidelines for sewage works. ISBN 978-1-4249-8438-1. https://www.ontario.ca/document/design-guidelines-sewage-works.
   Google Scholar
• Osman, Y. Z., R. Fealy, and J. C. Sweeney. 2013. Downscaling extreme precipitation in Ireland using combined peaks-over-threshold generalized Pareto distribution model of varying parameters. Journal of Water and Climate Change 4 (4): 21–47. doi:10.2166/wcc.2013.071.
   Web of Science ®Google Scholar
• Ouarda, T. B. M. J., and S. El-Adlouni. 2011. Bayesian nonstationary frequency analysis of hydrological variables. Journal of the American Water Resources Association 47 (3): 496–505.10.1111/j.1752-1688.2011.00544.x
   Web of Science ®Google Scholar
• Pettitt, A. N. 1979. A non-parametric approach to the change-point problem. Journal of Applied Statistics 28: 126–135.10.2307/2346729
   Google Scholar
• Pickands, J. 1975. Statistical inference using extreme order statistics. Annals of Statistics 3 (1): 119–131.
   Web of Science ®Google Scholar
• R Core Team. 2016. R: A Language and Environment for Statistical Computing. Vienna, Austria: R Foundation for Statistical Computing. http://www.R-project.org/. ISBN 3-900051-07-0.
   Google Scholar
• Rajagopalan, B. 2010. Hydrologic frequency analysis in a changing climate. Workshop on Nonstationarity, Hydrologic Frequency Analysis, and Water Management, Jan 13-15, 107-114. Boulder, Colorado, U.S.A: Millennium Harvest House.
   Google Scholar
• Rayner, N. A., D. E. Parker, E. B. Horton, C. K. Folland, L. V. Alexander, D. P. Rowell, E. C. Kent, A. Kaplan. 2003. Global analyses of sea surface temperature, sea ice, and night marine air temperature since the late nineteenth century. Journal of Geophysical Research 108: 4407. doi. 10.1029/2002JD002670.
   Web of Science ®Google Scholar
• Renard, B., M. Lang, and P. Bois. 2006. Statistical analysis of extreme events in a non- stationary context via a Bayesian framework: Case study with peak-over-threshold data. Stochastic Environmental Research and Risk 21 (2): 97–112.10.1007/s00477-006-0047-4
   Web of Science ®Google Scholar
• Roth, M., T. A. Buishand, G. Jongbloed, A. M. G. Klein Tank, and J. H. van Zanten. 2012. A regional peaks-over-threshold model in a nonstationary climate. Water Resources Research 48: W11533. doi:10.1029/2012WR012214.
   Web of Science ®Google Scholar
• Roth, M., T. A. Buishand, G. Jongbloed, A. M. G. Klein Tank, and J. H. van Zanten. 2014. Projections of precipitation extremes based on a regional non-stationary peaks-over-threshold approach: A case study for the Netherlands and north-western Germany. Weather and Climate Extremes 4: 1–10.10.1016/j.wace.2014.01.001
   Google Scholar
• Roth, M., G. Jongbloed, and T. A. Buishand. 2016. Threshold selection for regional peaks- over-threshold data. Journal of Applied Statistics 43 (7): 1291–1309.10.1080/02664763.2015.1100589
   Web of Science ®Google Scholar
• Stephens, K. A., and P. Graham, D. Reid 2002. Stormwater planning: A guidebook for British Columbia. Province of British Columbia. http://www.env.gov.bc.ca/epd/epdpa/mpp/stormwater/guidebook/pdfs/stormwater.pdf.
   Google Scholar
• Stone, D. A., A. J. Weaver, and F. W. Zwiers. 2000. Trends in Canadian precipitation intensity. Atmosphere-Ocean 38 (2): 321–347.
   Web of Science ®Google Scholar
• Sugahara, S., R. Porfírio da Rocha, and R. Silveira. 2009. Non-stationary frequency analysis of extreme daily rainfall in Sao Paulo, Brazil. International Journal of Climatology 29: 1339–1349.10.1002/(ISSN)1097-0088
   Web of Science ®Google Scholar
• Sungwook, W., J. B. Valdés, S. Steinschneider, and T.-W. Kim. 2016. Non-stationary frequency analysis of extreme precipitation is South Korea using peaks-over-threshold and annual maxima. Stochastic Environmental Research and Risk Assessment 30: 583–606.
   Web of Science ®Google Scholar
• The International Disaster Database – Center for Research on the Epidemiology of Disasters – CRED (EM-DAT). 2016. http://www.emdat.be/.
   Google Scholar
• Tramblay, Y., L. Neppel, J. Carreau, and K. Najiib. 2013. Non-stationary frequency analysis of heavy rainfall events in southern France. Hydrological Sciences Journal 58 (2): 280–294.10.1080/02626667.2012.754988
   Web of Science ®Google Scholar
• Villarini, G., J. A. Smith, and F. Napolitano. 2010. Nonstationary modeling of a long record of rainfall an temperature over Rome. Advances in Water Resources 33: 1256–1267.10.1016/j.advwatres.2010.03.013
   Web of Science ®Google Scholar
• Villarini, G., J. A. Smith, A. A. Ntelekos, and U. Schwarz. 2011. Annual maximum and peaks- over-threshold analysis of daily rainfall accumulations for Austria. Journal of Geophysical Research 116: D05103. doi:10.1029/2010JD015038.
   Web of Science ®Google Scholar
• Vincent, L. A., and É. Mekis. 2006. Changes in daily and extreme temperature and precipitation indices for Canada over the twentieth century. Atmosphere-Ocean 44 (2): 177–193.10.3137/ao.440205
   Web of Science ®Google Scholar
• Vincent, L. A., and É. Mekis. 2009. Discontinuities in due to joining precipitation station observations in Canada. Journal of Applied Meteorology and Climatology 48: 156–166.10.1175/2008JAMC2031.1
   Web of Science ®Google Scholar
• Vinnikov, K. Y., and A. Robock. 2002. Trends in moments of climate indices. Geophysical Research Letters 29 (2): 743. doi:10.1029/2001GL014025.
   Web of Science ®Google Scholar
• von Storch, V. H. 1995. Misuses of statistical analysis in climate research. In Anlysis of climate variability: Applications of statistical techniques, ed. H. V. von Storch and A. Navarra, 11-26. Berlin: Springer-Verlag.10.1007/978-3-662-03167-4
   Google Scholar
• Walker, I., R. Sydneysmith, D. Allen, K. Bodtker, D. Bonin, B. Bonsal, S. Cohen, et al. 2008. Chapter 8: British Columbia. In From impacts to adaptation: Canada in a changing climate 2007, eds. D. S. Lemmen, F. J. Warren, J. Lacroix, and E. Bush, 329-386. Ottawa: Government of Canada.
   Google Scholar
• Whitfield, P. H., R. D. Moore, S. W. Flemming, and A. Zawadzki. 2010. Pacific decadal ocillation and the hydroclimatology of western Canada – review and prospects. Canadian Water Resources Journal. 35 (1): 1–28.10.4296/cwrj3501001
   Web of Science ®Google Scholar
• Yue, S., P. Pilon, and G. Cavadias. 2002. Power of the Mann-Kendall and Spearman’s rho tests for Detecting monotonic trends in hydrological series. Journal of Hydrology 259: 254–271.10.1016/S0022-1694(01)00594-7
   Web of Science ®Google Scholar
• Yue, S., P. Pilon, and B. Phinney. 2003. Canadian streamflow trend detection: Impacts of serial and cross-correlation. Hydrological Sciences Journal 48 (1): 51–63.10.1623/hysj.48.1.51.43478
   Web of Science ®Google Scholar
• Zhang, X., L. A. Vincent, W. D. Hogg, and A. Niitsoo. 2000. Temperature and precipitation trends in Canada during the 20th century. Atmosphere-Ocean 38 (3): 395–429.10.1080/07055900.2000.9649654
   Web of Science ®Google Scholar