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IUKWC Workshop Nov16: Developing Hydro-climatic Services for Water Security – Session 7 – Item 1 A_Mondal

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IUKWC Workshop Nov16: Developing Hydro-climatic Services for Water Security – Session 7. Arpita Mondal

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IUKWC Workshop Nov16: Developing Hydro-climatic Services for Water Security – Session 7 – Item 1 A_Mondal

  1. 1. Hydrologic Extremes under Climate Change: Non-stationarity and Uncertainty Arpita Mondal Assistant Professor, Department of Civil Engineering, & Interdisciplinary Program in Climate Studies, IIT Bombay. Acknowledgements Denzil Daniel P P Mujumdar marpita@civil.iitb.ac.in
  2. 2. The context of hydrologic extremes – floods and droughts Nov, 2016 IUKWC Workshop 2 California, 2014 guardianlv.com Mysore, KRS Dam, 2000 bangaloremirror.com Mumbai, 2005 viewspaper.net UK, 2000 theguardian.com Paris, 2016 Climatecentral.org
  3. 3. Approaches to define extremes Nov, 2016 IUKWC Workshop 3  Block Maxima  The maxima Mn of a sequence of random variables follow the Generalized Extreme Value (GEV) distribution  Threshold Exceedance (POT)  The excesses above a high threshold follow the Generalized Pareto (GP) distribution  Point Process Approach  The excesses above a threshold and their frequencies modeled simultaneously using a non- homogeneous Poisson process
  4. 4. The stationarity debate Nov, 2016 IUKWC Workshop 4
  5. 5. Design values under non-stationarity Nov, 2016 IUKWC Workshop 5
  6. 6. Using non-stationary POT approach to study variability of extreme rainfall over India Nov, 2016 IUKWC Workshop 6 Precipitation(mm) Mondal and Mujumdar, JoH, 2015
  7. 7. Nov, 2016 IUKWC Workshop 7 Intensity Duration Frequency Mondal and Mujumdar, JoH, 2015
  8. 8. Precipitation intensity-duration- frequency relationships Nov, 2016 IUKWC Workshop 8
  9. 9. Nov, 2016 IUKWC Workshop 9
  10. 10. Nov, 2016 IUKWC Workshop 10
  11. 11. • Find the level for which the expected waiting time for exceedance of this level is m years (Cooley, 2013; Salas and Obeysekara, 2013) • Equate with m and solve for r. Not straightforward! • This interpretation was first presented by Olsen et al. (1998) The expected number of events in m years is 1 (Cooley, 2013). This interpretation was first proposed by Parey et al. (2007) Equate with 1 and solve for r. Not used in hydrology so far. Fixes the design life as well as the probability of failure. Definition of return period under non-stationarity Nov, 2016 IUKWC Workshop 11 EWT ENE
  12. 12. • Basic info needed for design: i) design life period (say, 2011-2060); ii) the risk of a hazardous event • Thus, the design life level = 𝑇1 - 𝑇2 pM% extreme level • Estimate the CDF of the size of the largest daily rainfall in 2011-2060 as • The (1-pM)th quantile of this distribution is an estimate of the design life level for the risk pM. • This is just a special case of the risk-based design advocated by Serinaldi (2014)! • Uncertainties related to this design life level can be obtained by the Delta method. • Should we shift to risk-based designs now? The design life level (Rootzen and Katz, WRR, 2013) Nov, 2016 IUKWC Workshop 12
  13. 13. Nov, 2016 IUKWC Workshop 13 The minimax design level (Rootzen and Katz, WRR, 2013)
  14. 14. Are the non-stationary design levels really different from the traditional ones based on stationarity? Mondal and Mujumdar, AWR, 2015 0.00 5.00 10.00 15.00 20.00 25.00 30.00 0 10 20 30 40 50 60 Intensity Duration 5-yr return period Non-stationary Stationary Nov, 2016 IUKWC Workshop 14
  15. 15. Uncertainty in the estimation of design quantiles • Delta method (Oehlert, The Amer. Statistician.,1992) Var 𝑧 1−𝑝 ≈ 𝛻𝑧 1−𝑝 𝑇 𝑉 𝛻𝑧 1−𝑝 where 𝛻𝑧 1−𝑝 𝑇 = 𝜕𝑧 1−𝑝 𝜕𝜇 , 𝜕𝑧 1−𝑝 𝜕𝜎 , 𝜕𝑧 1−𝑝 𝜕𝜉 , evaluated at the estimated values of (µ, σ, ξ) • Confidence intervals can be computed for the quantiles assuming asymptotic normality of the MLE estimates • Can be extended to the implicit method in the non-stationary case • Performs as good as non-parametric methods Nov, 2016 IUKWC Workshop 15
  16. 16. Non stationary Vs Stationary IDF curves for precipitation at White Sands National Monument Station, New Mexico. Nov, 2016 IUKWC Workshop 16
  17. 17. Non stationary Vs Stationary IDF curves for precipitation at White Sands National Monument Station, New Mexico. Nov, 2016 IUKWC Workshop 17
  18. 18. Floods – Annual Maximum Daily Flows Nov, 2016 IUKWC Workshop 18
  19. 19. 100 yr return level of flow in Vamanapuram river basin at Ayilam stream gauge station (in cumecs) Estimate Variance Std.Dev CI_lower CI_upper Test statistic Stationary return level 687 5101.3 71.4 546.9 826.9 EWT based return level 1017 27435.8 165.6 691.9 1341.2 1.8 ENE based return level 972 26324.0 162.2 654.0 1290.0 1.6 2011-2111 5% design life level 1111 19697.4 140.3 835.9 1386.0 2.7 2011-2111 10% design life level 1046 18075.5 134.4 782.6 1309.7 2.4 2011-2111 2% minimax design life level 916 21242.2 145.7 630.0 1201.3 1.4 2011-2111 5% minimax design life level 832 20094.1 141.8 554.0 1109.6 0.9 2011-2111 0.1% minimax design life level 1186 26888.2 164.0 864.8 1507.6 2.8 Nov, 2016 IUKWC Workshop 19
  20. 20. Concluding Thoughts  Non-stationarity ⇒ deterministic relationship: can the future be deterministically known?  Hypothesis of non-stationarity not independent of data!  Complex models ⇒ less bias + more uncertainty: how to optimize this trade-off?  The non-stationary design levels are not significantly different from stationary design levels, when uncertainty in both is considered.  Stationary principles can still serve as benchmark (coincides with Serinaldi and Kilsby, AWR, 2015). Nov, 2016 IUKWC Workshop 20
  21. 21. Nov, 2016 IUKWC Workshop 21
  22. 22. Name of design level Advantages Disadvantages Effective return level / Minimax design level Communicates changing risk clearly. Simple to compute. Akin to changing flood plains every year, thus infeasible. A derived quantity representing average annual change – can mislead perception. Expected waiting time based return level Easy and sensible interpretation. More closely linked with life span calculation. Computationally challenging. Sensitive to how long the parameter-covariate relationship is projected. A derived quantity representing average annual chance – can mislead perception. Expected number of events based return level Easy interpretation. Easy computation, though iterative. Extrapolation of parameter-covariate relationship is only for the design life. Still involves extrapolation of the parameter-covariate relationship. A derived quantity representing average annual chance – can mislead perception. Design life level Does not necessitate the iid assumption. Represents collective risk across design life, and not average annual probability of exceedance. Conservative estimates. Leads to very high equivalent return period, therefore requires large dataset for estimation. Uncertainties are higher. Sensitive to how long the parameter-covariate relationship is projected. Nov, 2016 IUKWC Workshop 22

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