PMP and Climate Variability and Change: A Review

[EN] A state-of-the-art review on the probable maximum precipitation (PMP) as it relates to climate variability and change is presented. The review consists of an examination of the current practice and the various developments published in the literature. The focus is on relevant research where the effect of climate dynamics on the PMP are discussed, as well as statistical methods developed for estimating very large extreme precipitation including the PMP. The review includes interpretation of extreme events arising from the climate system, their physical mechanisms, and statistical properties, together with the effect of the uncertainty of several factors determining them, such as atmospheric moisture, its transport into storms and wind, and their future changes. These issues are examined as well as the underlying historical and proxy data. In addition, the procedures and guidelines established by some countries, states, and organizations for estimating the PMP are summarized. In doing so, attention was paid to whether the current guidelines and research published literature take into consideration the effects of the variability and change of climatic processes and the underlying uncertainties.The authors would like to acknowledge the support of the Global Water Futures Program and the Natural Sciences and Engineering Research Council of Canada (NSERC Discovery Grant RGPIN-2019-06894). The fourth author acknowledges the support of the Spanish Ministry of Science and Innovation, Project TETISCHANGE (RTI2018-093717-B-100). The first author appreciates the continuous support from the Scott College of Engineering of Colorado State University.Salas, JD.; Anderson, ML.; Papalexiou, SM.; Francés, F. (2020). PMP and Climate Variability and Change: A Review. Journal of Hydrologic Engineering. 25(12):1-16. https://doi.org/10.1061/(ASCE)HE.1943-5584.00020031162512Abbs, D. J. (1999). A numerical modeling study to investigate the assumptions used in the calculation of probable maximum precipitation. Water Resources Research, 35(3), 785-796. doi:10.1029/1998wr900013Alexander, G. N. (1963). Using the probability of storm transposition for estimating the frequency of rare floods. Journal of Hydrology, 1(1), 46-57. doi:10.1016/0022-1694(63)90032-5Balkema, A. A., & de Haan, L. (1974). Residual Life Time at Great Age. The Annals of Probability, 2(5). doi:10.1214/aop/1176996548Beauchamp J. 2010. “Estimation d’une PMP et d’une CMP d’un bassin versant septentional en contexte de changements climatiques.” Ph.D. dissertation École de Technologie Supérieure Université du Québec.Ben Alaya, M. A., Zwiers, F., & Zhang, X. (2018). Probable Maximum Precipitation: Its Estimation and Uncertainty Quantification Using Bivariate Extreme Value Analysis. Journal of Hydrometeorology, 19(4), 679-694. doi:10.1175/jhm-d-17-0110.1Benson M. A. 1973. “Thoughts on the design of design floods. Floods and droughts.” In Proc. 2nd Int. Symp. in Hydrology 27–33. Fort Collins CO: Water Resources Publications.Botero, B. A., & Francés, F. (2010). Estimation of high return period flood quantiles using additional non-systematic information with upper bounded statistical models. Hydrology and Earth System Sciences, 14(12), 2617-2628. doi:10.5194/hess-14-2617-2010Canadian Dam Association. 2013. “Dam safety guidelines.” Accessed August 24 2020. https://www.cda.ca/EN/Publications_Pages/Dam_Safety_Publications.aspx.Casas, M. C., Rodríguez, R., Nieto, R., & Redaño, A. (2008). The Estimation of Probable Maximum Precipitation. Annals of the New York Academy of Sciences, 1146(1), 291-302. doi:10.1196/annals.1446.003Casas, M. C., Rodríguez, R., Prohom, M., Gázquez, A., & Redaño, A. (2010). Estimation of the probable maximum precipitation in Barcelona (Spain). International Journal of Climatology, 31(9), 1322-1327. doi:10.1002/joc.2149Casas-Castillo, M. C., Rodríguez-Solà, R., Navarro, X., Russo, B., Lastra, A., González, P., & Redaño, A. (2016). On the consideration of scaling properties of extreme rainfall in Madrid (Spain) for developing a generalized intensity-duration-frequency equation and assessing probable maximum precipitation estimates. Theoretical and Applied Climatology, 131(1-2), 573-580. doi:10.1007/s00704-016-1998-0Castellarin, A., Merz, R., & Blöschl, G. (2009). Probabilistic envelope curves for extreme rainfall events. Journal of Hydrology, 378(3-4), 263-271. doi:10.1016/j.jhydrol.2009.09.030Chavan, S. R., & Srinivas, V. V. (2016). Regionalization based envelope curves for PMP estimation by Hershfield method. International Journal of Climatology, 37(10), 3767-3779. doi:10.1002/joc.4951Chen, X., & Hossain, F. (2018). Understanding Model-Based Probable Maximum Precipitation Estimation as a Function of Location and Season from Atmospheric Reanalysis. Journal of Hydrometeorology, 19(2), 459-475. doi:10.1175/jhm-d-17-0170.1Chen, X., & Hossain, F. (2019). Understanding Future Safety of Dams in a Changing Climate. Bulletin of the American Meteorological Society, 100(8), 1395-1404. doi:10.1175/bams-d-17-0150.1Chow, V. T. (1951). A general formula for hydrologic frequency analysis. Transactions, American Geophysical Union, 32(2), 231. doi:10.1029/tr032i002p00231Coles, S. (2001). An Introduction to Statistical Modeling of Extreme Values. Springer Series in Statistics. doi:10.1007/978-1-4471-3675-0COOKE, P. (1979). Statistical inference for bounds of random variables. Biometrika, 66(2), 367-374. doi:10.1093/biomet/66.2.367Cooley, D. (2009). Extreme value analysis and the study of climate change. Climatic Change, 97(1-2), 77-83. doi:10.1007/s10584-009-9627-xDawdy, D. R., & Lettenmaier, D. P. (1987). Initiative for Risk‐Based Flood Design. Journal of Hydraulic Engineering, 113(8), 1041-1051. doi:10.1061/(asce)0733-9429(1987)113:8(1041)Desa M., M. N., & Rakhecha, P. R. (2007). Probable maximum precipitation for 24-h duration over an equatorial region: Part 2-Johor, Malaysia. Atmospheric Research, 84(1), 84-90. doi:10.1016/j.atmosres.2006.06.005Dettinger, M. (2011). Climate Change, Atmospheric Rivers, and Floods in California - A Multimodel Analysis of Storm Frequency and Magnitude Changes1. JAWRA Journal of the American Water Resources Association, 47(3), 514-523. doi:10.1111/j.1752-1688.2011.00546.xDiaz A. J. K. Ishida M. L. Kavvas and M. L. Anderson. 2017. “Maximum precipitation estimation for five watersheds in the southern Sierra Nevada.” In Proc. 2017 World Environmental and Water Resources Congress 331–339. Reston VA: ASCE. https://doi.org/10.1061/9780784480618.032.Douglas, E. M., & Barros, A. P. (2003). Probable Maximum Precipitation Estimation Using Multifractals: Application in the Eastern United States. Journal of Hydrometeorology, 4(6), 1012-1024. doi:10.1175/1525-7541(2003)0042.0.co;2El Adlouni, S., Ouarda, T. B. M. J., Zhang, X., Roy, R., & Bobée, B. (2007). Generalized maximum likelihood estimators for the nonstationary generalized extreme value model. Water Resources Research, 43(3). doi:10.1029/2005wr004545Elíasson, J. (1994). Statistical Estimates of PMP Values. Hydrology Research, 25(4), 301-312. doi:10.2166/nh.1994.0010Elíasson, J. (1997). A statistical model for extreme precipitation. Water Resources Research, 33(3), 449-455. doi:10.1029/96wr03531England, J. F., Jarrett, R. D., & Salas, J. D. (2003). Data-based comparisons of moments estimators using historical and paleoflood data. Journal of Hydrology, 278(1-4), 172-196. doi:10.1016/s0022-1694(03)00141-0Fernandes, W., Naghettini, M., & Loschi, R. (2010). A Bayesian approach for estimating extreme flood probabilities with upper-bounded distribution functions. Stochastic Environmental Research and Risk Assessment, 24(8), 1127-1143. doi:10.1007/s00477-010-0365-4Fisher, R. A., & Tippett, L. H. C. (1928). Limiting forms of the frequency distribution of the largest or smallest member of a sample. Mathematical Proceedings of the Cambridge Philosophical Society, 24(2), 180-190. doi:10.1017/s0305004100015681Fontaine, T. A., & Potter, K. W. (1989). Estimating Probabilities of Extreme Rainfalls. Journal of Hydraulic Engineering, 115(11), 1562-1575. doi:10.1061/(asce)0733-9429(1989)115:11(1562)Foufoula-Georgiou, E. (1989). A probabilistic storm transposition approach for estimating exceedance probabilities of extreme precipitation depths. Water Resources Research, 25(5), 799-815. doi:10.1029/wr025i005p00799Francés, F. (1998). Using the TCEV distribution function with systematic and non-systematic data in a regional flood frequency analysis. Stochastic Hydrology and Hydraulics, 12(4), 267-283. doi:10.1007/s004770050021Frances, F., Salas, J. D., & Boes, D. C. (1994). Flood frequency analysis with systematic and historical or paleoflood data based on the two-parameter general extreme value models. Water Resources Research, 30(6), 1653-1664. doi:10.1029/94wr00154Gao, M., Mo, D., & Wu, X. (2016). Nonstationary modeling of extreme precipitation in China. Atmospheric Research, 182, 1-9. doi:10.1016/j.atmosres.2016.07.014García-Marín, A. P., Morbidelli, R., Saltalippi, C., Cifrodelli, M., Estévez, J., & Flammini, A. (2019). On the choice of the optimal frequency analysis of annual extreme rainfall by multifractal approach. Journal of Hydrology, 575, 1267-1279. doi:10.1016/j.jhydrol.2019.06.013Gilroy, K. L., & McCuen, R. H. (2012). A nonstationary flood frequency analysis method to adjust for future climate change and urbanization. Journal of Hydrology, 414-415, 40-48. doi:10.1016/j.jhydrol.2011.10.009Groisman, P. Y., Knight, R. W., & Zolina, O. G. (2013). Recent Trends in Regional and Global Intense Precipitation Patterns. Climate Vulnerability, 25-55. doi:10.1016/b978-0-12-384703-4.00501-3Gumbel, E. J. (1958). Statistics of Extremes. doi:10.7312/gumb92958Hershfield, D. M. (1965). Method for Estimating Probable Maximum Rainfall. Journal - American Water Works Association, 57(8), 965-972. doi:10.1002/j.1551-8833.1965.tb01486.xHershfield D. M. 1977. “Some tools for hydrometeorologists.” In Proc. 2nd Conf. on Hydrometeorology. Boston: American Meteorological Society.Hosking, J. R. M., & Wallis, J. R. (1997). Regional Frequency Analysis. doi:10.1017/cbo9780511529443Hosking, J. R. M., Wallis, J. R., & Wood, E. F. (1985). Estimation of the Generalized Extreme-Value Distribution by the Method of Probability-Weighted Moments. Technometrics, 27(3), 251-261. doi:10.1080/00401706.1985.10488049Houghton, J. C. (1978). Birth of a parent: The Wakeby Distribution for modeling flood flows. Water Resources Research, 14(6), 1105-1109. doi:10.1029/wr014i006p01105Hubert, P., Tessier, Y., Lovejoy, S., Schertzer, D., Schmitt, F., Ladoy, P., … Desurosne, I. (1993). Multifractals and extreme rainfall events. Geophysical Research Letters, 20(10), 931-934. doi:10.1029/93gl01245Hundecha, Y., St-Hilaire, A., Ouarda, T. B. M. J., El Adlouni, S., & Gachon, P. (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(11), 2745-2759. doi:10.1175/2008jamc1665.1Ishida, K., Kavvas, M. L., Jang, S., Chen, Z. Q., Ohara, N., & Anderson, M. L. (2015). Physically Based Estimation of Maximum Precipitation over Three Watersheds in Northern California: Atmospheric Boundary Condition Shifting. Journal of Hydrologic Engineering, 20(4), 04014052. doi:10.1061/(asce)he.1943-5584.0001026Ishida, K., Kavvas, M. L., Jang, S., Chen, Z. Q., Ohara, N., & Anderson, M. L. (2015). Physically Based Estimation of Maximum Precipitation over Three Watersheds in Northern California: Relative Humidity Maximization Method. Journal of Hydrologic Engineering, 20(10), 04015014. doi:10.1061/(asce)he.1943-5584.0001175Ishida, K., Ohara, N., Kavvas, M. L., Chen, Z. Q., & Anderson, M. L. (2018). Impact of air temperature on physically-based maximum precipitation estimation through change in moisture holding capacity of air. Journal of Hydrology, 556, 1050-1063. doi:10.1016/j.jhydrol.2016.10.008Jakob D. R. Smalley J. Meighen B. Taylor and K. Xuereb. 2008. “Climate change and probable maximum precipitation.” In Proc. Water Down Under 109–120. Melbourne Australia: Engineers Australia Causal Productions.Katz, R. W. (2012). Statistical Methods for Nonstationary Extremes. Water Science and Technology Library, 15-37. doi:10.1007/978-94-007-4479-0_2Katz, R. W., Parlange, M. B., & Naveau, P. (2002). Statistics of extremes in hydrology. Advances in Water Resources, 25(8-12), 1287-1304. doi:10.1016/s0309-1708(02)00056-8Kharin, V. V., Zwiers, F. W., Zhang, X., & Hegerl, G. C. (2007). Changes in Temperature and Precipitation Extremes in the IPCC Ensemble of Global Coupled Model Simulations. Journal of Climate, 20(8), 1419-1444. doi:10.1175/jcli4066.1Kijko, A. (2004). Estimation of the Maximum Earthquake Magnitude, m max. Pure and Applied Geophysics, 161(8), 1655-1681. doi:10.1007/s00024-004-2531-4Kim, I.-W., Oh, J., Woo, S., & Kripalani, R. H. (2018). Evaluation of precipitation extremes over the Asian domain: observation and modelling studies. Climate Dynamics, 52(3-4), 1317-1342. doi:10.1007/s00382-018-4193-4Koutsoyiannis, D. (1999). A probabilistic view of hershfield’s method for estimating probable maximum precipitation. Water Resources Research, 35(4), 1313-1322. doi:10.1029/1999wr900002Kundzewicz, Z. W., & Stakhiv, E. Z. (2010). Are climate models «ready for prime time» in water resources management applications, or is more research needed? Hydrological Sciences Journal, 55(7), 1085-1089. doi:10.1080/02626667.2010.513211Kunkel, K. E., Karl, T. R., Easterling, D. R., Redmond, K., Young, J., Yin, X., & Hennon, P. (2013). Probable maximum precipitation and climate change. Geophysical Research Letters, 40(7), 1402-1408. doi:10.1002/grl.50334Lan, P., Lin, B., Zhang, Y., & Chen, H. (2017). Probable Maximum Precipitation Estimation Using the Revised Km-Value Method in Hong Kong. Journal of Hydrologic Engineering, 22(8), 05017008. doi:10.1061/(asce)he.1943-5584.0001517Langousis, A., Veneziano, D., Furcolo, P., & Lepore, C. (2009). Multifractal rainfall extremes: Theoretical analysis and practical estimation. Chaos, Solitons & Fractals, 39(3), 1182-1194. doi:10.1016/j.chaos.2007.06.004Leclerc, M., & Ouarda, T. B. M. J. (2007). Non-stationary regional flood frequency analysis at ungauged sites. Journal of Hydrology, 343(3-4), 254-265. doi:10.1016/j.jhydrol.2007.06.021Lee, J., Choi, J., Lee, O., Yoon, J., & Kim, S. (2017). Estimation of Probable Maximum Precipitation in Korea using a Regional Climate Model. Water, 9(4), 240. doi:10.3390/w9040240Lenderink, G., & Attema, J. (2015). A simple scaling approach to produce climate scenarios of local precipitation extremes for the Netherlands. Environmental Research Letters, 10(8), 085001. doi:10.1088/1748-9326/10/8/085001Lepore, C., Veneziano, D., & Molini, A. (2015). Temperature and CAPE dependence of rainfall extremes in the eastern United States. Geophysical Research Letters, 42(1), 74-83. doi:10.1002/2014gl062247López, J., & Francés, F. (2013). Non-stationary flood frequency analysis in continental Spanish rivers, using climate and reservoir indices as external covariates. Hydrology and Earth System Sciences, 17(8), 3189-3203. doi:10.5194/hess-17-3189-2013Loriaux, J. M., Lenderink, G., & Siebesma, A. P. (2016). Peak precipitation intensity in relation to atmospheric conditions and large-scale forcing at midlatitudes. Journal of Geophysical Research: Atmospheres, 121(10), 5471-5487. doi:10.1002/2015jd024274Machado, M. J., Botero, B. A., López, J., Francés, F., Díez-Herrero, A., & Benito, G. (2015). Flood frequency analysis of historical flood data under stationary and non-stationary modelling. Hydrology and Earth System Sciences, 19(6), 2561-2576. doi:10.5194/hess-19-2561-2015Markonis, Y., Papalexiou, S. M., Martinkova, M., & Hanel, M. (2019). Assessment of Water Cycle Intensification Over Land using a Multisource Global Gridded Precipitation DataSet. Journal of Geophysical Research: Atmospheres, 124(21), 11175-11187. doi:10.1029/2019jd030855Martins, E. S., & Stedinger, J. R. (2000). Generalized maximum-likelihood generalized extreme-value quantile estimators for hydrologic data. Water Resources Research, 36(3), 737-744. doi:10.1029/1999wr900330Mejia G. and F. Villegas. 1979. “Maximum precipitation deviations in Colombia.” In Proc. 3rd Conf. on Hydrometeorology 74–76. Boston: America Meteorological Society.Merz, R., & Blöschl, G. (2008). Flood frequency hydrology: 1. Temporal, spatial, and causal expansion of information. Water Resources Research, 44(8). doi:10.1029/2007wr006744Micovic, Z., Schaefer, M. G., & Taylor, G. H. (2015). Uncertainty analysis for Probable Maximum Precipitation estimates. Journal of Hydrology, 521, 360-373. doi:10.1016/j.jhydrol.2014.12.033Mínguez, R., Méndez, F. J., Izaguirre, C., Menéndez, M., & Losada, I. J. (2010). Pseudo-optimal parameter selection of non-stationary generalized extreme value models for environmental variables. Environmental Modelling & Software, 25(12), 1592-1607. doi:10.1016/j.envsoft.2010.05.008Nathan, R., Jordan, P., Scorah, M., Lang, S., Kuczera, G., Schaefer, M., & Weinmann, E. (2016). Estimating the exceedance probability of extreme rainfalls up to the probable maximum precipitation. Journal of Hydrology, 543, 706-720. doi:10.1016/j.jhydrol.2016.10.044Nathan R. J. and S. K. Merz. 2001. “Estimation of extreme hydrologic events in Australia: Current practice and research needs.” Paper 13 in Proc. Hydrologic research needs for dam safety 69–77. Washington DC: FEMA.Nobilis, F., Haiden, T., & Kerschbaum, M. (1991). Statistical considerations concerning Probable Maximum Precipitation (PMP) in the Alpine Country of Austria. Theoretical and Applied Climatology, 44(2), 89-94. doi:10.1007/bf00867996NWS (National Weather Service). 2015. “Regions covered by different NWS PMP documents (as of 2015) (map).” Accessed May 1 2020. https://www.nws.noaa.gov/oh/hdsc/studies/pmp.html.Ohara, N., Kavvas, M. L., Anderson, M. L., Chen, Z. Q., & Ishida, K. (2017). Characterization of Extreme Storm Events Using a Numerical Model–Based Precipitation Maximization Procedure in the Feather, Yuba, and American River Watersheds in California. Journal of Hydrometeorology, 18(5), 1413-1423. doi:10.1175/jhm-d-15-0232.1Ohara, N., Kavvas, M. L., Kure, S., Chen, Z. Q., Jang, S., & Tan, E. (2011). Physically Based Estimation of Maximum Precipitation over American River Watershed, California. Journal of Hydrologic Engineering, 16(4), 351-361. doi:10.1061/(asce)he.1943-5584.0000324Papalexiou, S. M. (2018). Unified theory for stochastic modelling of hydroclimatic processes: Preserving marginal distributions, correlation structures, and intermittency. Advances in Water Resources, 115, 234-252. doi:10.1016/j.advwatres.2018.02.013Papalexiou, S. M., AghaKouchak, A., & Foufoula‐Georgiou, E. (2018). A Diagnostic Framework for Understanding Climatology of Tails of Hourly Precipitation Extremes in the United States. Water Resources Research, 54(9), 6725-6738. doi:10.1029/2018wr022732Papalexiou, S. M., & Koutsoyiannis, D. (2006). A probabilistic approach to the concept of Probable Maximum Precipitation. Advances in Geosciences, 7, 51-54. doi:10.5194/adgeo-7-51-2006Papalexiou, S. M., & Koutsoyiannis, D. (2012). Entropy based derivation of probability distributions: A case study to daily rainfall. Advances in Water Resources, 45, 51-57. doi:10.1016/j.advwatres.2011.11.007Papalexiou, S. M., & Koutsoyiannis, D. (2013). Battle of extreme value distributions: A global survey on extreme daily rainfall. Water Resources Research, 49(1), 187-201. doi:10.1029/2012wr012557Papalexiou, S. M., & Koutsoyiannis, D. (2016). A global survey on the seasonal variation of the marginal distribution of daily precipitation. Advances in Water Resources, 94, 131-145. doi:10.1016/j.advwatres.2016.05.005Papalexiou, S. M., Koutsoyiannis, D., & Makropoulos, C. (2013). How extreme is extreme? An assessment of daily rainfall distribution tails. Hydrology and Earth System Sciences, 17(2), 851-862. doi:10.5194/hess-17-851-2013Papalexiou, S. M., Markonis, Y., Lombardo, F., AghaKouchak, A., & Foufoula‐Georgiou, E. (2018). Precise Temporal Disaggregation Preserving Marginals and Correlations (DiPMaC) for Stationary and Nonstationary Processes. Water Resources Research, 54(10), 7435-7458. doi:10.1029/2018wr022726III, J. P. (1975). Statistical Inference Using Extreme Order Statistics. The Annals of Statistics, 3(1). doi:10.1214/aos/1176343003Rakhecha, P. R., Deshpande, N. R., & Soman, M. K. (1992). Probable maximum precipitation for a 2-day duration over the Indian Peninsula. Theoretical and Applied Climatology, 45(4), 277-283. doi:10.1007/bf00865518Rakhecha, P. R., & Soman, M. K. (1994). Estimation of probable maximum precipitation for a 2-day duration: Part 2 ? north Indian region. Theoretical and Applied Climatology, 49(2), 77-84. doi:10.1007/bf00868192Rastogi, D., Kao, S., Ashfaq, M., Mei, R., Kabela, E. D., Gangrade, S., … Anantharaj, V. G. (2017). Effects of climate change on probable maximum precipitation: A sensitivity study over the Alabama‐Coosa‐Tallapoosa River Basin. Journal of Geophysical Research: Atmospheres, 122(9), 4808-4828. doi:10.1002/2016jd026001Reed D. W. and E. J. Stewart. 1989. “Focus on rainfall growth estimation.” In Proc. 2nd National Hydrology Symp. Sheffield UK: British Hydrological Society.Rezacova, D., Pesice, P., & Sokol, Z. (2005). An estimation of the probable maximum precipitation for river basins in the Czech Republic. Atmospheric Research, 77(1-4), 407-421. doi:10.1016/j.atmosres.2004.10.011Rouhani, H., & Leconte, R. (2016). A novel method to estimate the maximization ratio of the Probable Maximum Precipitation (PMP) using regional climate model output. Water Resources Research, 52(9), 7347-7365. doi:10.1002/2016wr018603Rouhan