Dynamic Flood Risk Conditional on Climate Variation: A New Direction for Managing Hydrologic Hazards in the 21 st Century? Upmanu Lall Dept. of Earth & Environmental Engineering & Intl. Research Institute For Climate Prediction Columbia University Co-authors: G. Pizarro, S. Arumugam and S. Jain

Climate Variability vs. Change Variability: Structured Inter-annual and Longer Variations that arise as a consequence of internal feedback processes in the climate system, with large spatial scales of organization – ENSO, PDO, …. Change: Secular changes due to anthropogenic causes – Global Warming and related effects Dynamic vs Static Flood Risk Seasonal Flood Forecasts /Warning – Insurance/ Preparedness Diagnosing Historical Record and Improving Regional Flood Frequency Estimates using Climate Information with non- overlapping periods of record

Outline Context through Sacramento Floods Nature of Nonstationarity: Washington Example Cane-Zebiak Model Inferences Prediction in the US West E[Annual Max Flood] for the upcoming year Reconstruction of Past floods Local Likelihood Method for Quantile Forecasts

Central Valley and the Delta have an extensive system of levees

19 th century : Personal Levees, Rebuild to higher than last biggest 20 th century : Dams, Levees, bypass, Heavily Federally Subsidized 21 st century : ??

American River at Fair Oaks - Ann. Max. Flood 100 yr flood estimated from 21 & 51 yr moving windows

100 Yr Quantile of 4 Rivers Index of annual flow from a Tree Ring Reconstruction (Meko et al., 1998) using a 51 year moving window and the Log Normal Distibution

Identifying Variability & co-variation with climate indices Moving Window Analyses Mean, Variance, T-year flood “Arrival Rate” – Non-homogeneous Poisson Process Correlations and Nonparametric Regression Spectrum (Frequency Domain) Multivariate Spectrum Composites of Climate Fields for High/Low Flood Years

Historical Record for the Blacksmith Fork river ( ) BFR Flood w/10yr smooth Spectrum Annual Max: Day of Water year Flood magnitude vs. timing Jain & Lall, 2000

Blacksmith Fork, Hyrum, UT Analyses of Flood Statistics using a 30 year Moving Window From Jain and Lall (2000) 100 yr flood (LN) Var(log(Q)) Mean(log(Q))

Flood mean given DJF NINO3 and PDO NINO3 PDO Flood Variance given DJF NINO3 and PDO NINO3 PDO Derived using weighted local regression with 30 neighbors Correlations: Log(Q) vs DJF NINO vs DJF PDO Jain & Lall, 2000

Similkameen River near Nighthawk, Washington, Correlations Jain & Lall, 2001

Floods as a Non-homogeneous Poisson Process: Prob. Of Exceedance of flood (t) = “rate of arrival” (t) = “rate of Poisson Process of exceedances” Kernel Estimate using a 30 year moving window Jain & Lall, 2001

Probability distribution of the number of anomalous exceedances of the flood series based on a quantile threshold. (a) 67%, (d) >90%. Quantiles are computed using a 30-year time window, and exceedances of each quantile are computed for the next 30 years on record.

Wavelet Analysis of 1000 year sample of annual maximum NINO3 from a 110,000 year integration of the Cane-Zebiak Model with stationary forcing ( Clement and Cane, 1999)

Probability distribution of the number of anomalous exceedances of the 90th percentile of the ZC model NINO3 series, for two successive n year periods using block or random sampling, where n is: (a) 50 years, (b) 200 years. - based on 1,000 years of control run data

Ann. Max. Flood Seasonality in the West Pizarro & Lall, 2002

Partial Correlations Pizarro & Lall, 2002 Flood with NINO3 | PDOFlood with PDO | NINO3

Predictors Considered (All Jan-Apr) First 2 PCs of the average SST and first 2 PCs of the Jan-Apr change of the Pacific SST over Lat (5S,60N) and Long(60E, 60W) NINO3 Average and Change PDO Average and Change

Projection Pursuit Regression Goal: Fit the multivariate model y = f(x) + e f(x) is approximated by univariate nonparameteric functions applied to linear combinations of x For a single response: S j (.) = Univariate Regression = Supersmoother Weighted unexplained variance reduction across all response variables used to choose # of basis functions Cross-validation (Randomly drop 10% of data 100 times) used to choose predictors From Friedman & Stuetzle, 1981

PPR Implementation Normalize Log(Flow) Data at each site in cluster Try several PPR models varying the number of basis functions (M …. 1), and Predictor Combinations. Choose m <=M basis functions as breakpoint of unexplained variance vs M for each predictor set Choose Predictor Combination using cross validated average error variance reduction across all sites in cluster From Cross-validation runs estimate: Unexplained variance per station Hindcasts/Forecasts for each station Approx. Confidence interval per station

Hindcast - Examples

Local Likelihood: Annual Conditional Flood Forecasts Arumugam and Lall, 2003 Conditional pdf with parameters  (X t ).

Summary Connections to key modes of low frequency climate variability provide a mechanism for new directions in managing flood risk with a season or longer lead time. Even with stationary underlying dynamics, finite sample statistics of a nonlinear dynamical system can be nonstationary. Thus, a dynamic risk framework may be more useful even in this case. A pathway for the reconstruction of missing values of prior history of annual floods is indicated. This provides a new direction for regional flood risk estimation Translating a dynamic risk framework into management options is feasible, but will require institutional reform.