NON STATIONARY RETURN LEVELS FOR RAINFALL IN SPAIN (IP)

Transcription

1 NON STATIONARY RETURN LEVELS FOR RAINFALL IN SPAIN (IP) F.J. Acero, S. Parey, T.T.H. Hoang, D. Dacunha-Castelle University of Extremadura, EDF/R&D, University of Paris/Orsay October 2014

2 OUTLINE 1. OBSERVATION TIME SERIES 2. FUTURE RETURN LEVEL ESTIMATIONS 3. COMPARISON FOR OBSERVATION PERIOD 4. FUTURE 20-YEAR RETURN LEVELS 5. CONCLUSIONS AND PERSPECTIVES

3 OBSERVATIONS Long and homogeneous daily rainfall timeseries covering the Iberian Peninsula No missing data, no change in measurement device or location 76 selected time-series 70 from Spanish National Weather Agency (AEMET) 5 from ECA&D database the Real Observatorio de la Armada in San Fernando, Spain (longest precipitation record in Spain with no change in location)

4 TRENDS ARE OBSERVED Example: WINTER MEAN VARIANCE NUMBER RAINY DAYS + (signif) - (signif) + (signif) - (signif) + (signif) - (signif) AUTUMN 17 (4) 59 (23) 33 (2) 43 (5) 68 (26) 8 (1) WINTER 11 (2) 65 (36) 19 (2) 57 (12) 38 (11) 38 (5) SPRING 22 (2) 54 (31) 34 (3) 42 (8) 51 (16) 25 (2)

5 Simulated as: with Future RL estimations Statistical Extreme Value Theory, POT All days / rainy days RL: I u = Nu/n =Nu/nr*nr/n Varying threshold and trend in Pareto (s) (Roth et al. 2012): extrapolation, average u and s last year Rainy days: role of mean, variance and number of rainy days evolutions (20-year averages around 2020); possible use of climate model results M. Roth, T.A. Buishand, G. Jongbloed, A.M.G. Klein Tank and J.H. van Zanten: A regional peaks over threshold model in a nonstationary climate; Water Resources Research, vol 48, W11533, 2012

6 MEAN AND VARIANCE / EXTREMES Y t X t m s t t X t is the observed rainfall in rainy days timeseries; m t the trend in mean and s t the trend in standard deviation The hypothesis: the extremes of Y t are stationary How to test this hypothesis? 1) define a distance between 2 time functions 1 D( f, g) ( ( ) ( ))² f t g t dt T 1/ 2 2) compute a statistical table for D using a stationary GPD + Poisson 500 samples of the stationary GPD+Poisson law (x Y, s Y, I v ) Estimate parameters: 1) constant 2) time varying Compute D

7 HYPOTHESIS TESTING RESULTS In autumn,72 (95%) observatories OK for s and I, 4 only I In winter, 70 (92%) observatories OK for s and I, 6 only I In spring, 69 (91%) observatories OK for s and I, 5 only I and the last one only s

8 VALIDATION: OBSERVATION PERIOD All days, threshold 98 th percentile Rainy days, threshold 95 th percentile Through mean, variance and number of rainy days evolutions All days and rainy days only: good agreement Rainy days only: Method 1: Direct Method 2: Through mean, variance and nb rainy days evolutions Y>v X>sv+m X>w For u>w x u = x w s u = s v s +x(u-w) I ru =(1+x/ (s v s)*(u-w)) -1/x *I v I u = I ru *nr/n Globally, method2 RLs fall inside CI of method 1 Green: included (open >, filled <) Blue: not included (open >, filled <)

9 COMPARISON Stationary Return level Parameters estimated from observed extremes as constants New approach: use of the mean, variance and mean number of rainy days But, there are trends Example : winter, station tol Method 1: 32.1 [28.9;35.4] Method 2: mo, so, nbo whole period: 28.7 [26,0;31.4] mo, so, nbo first half: 29.7 [26.9;32.5]

10 Future Return Levels Globally, extrapolation of mean, variance and number of rainy days give RLs included in the CI of RL1 (Roth et al., 2012) Exceptions: Trends in mean and variance but no trends in Pareto Trends in Pareto and not in mean and variance: generally, trend very sensitive to slight threshold changes Very special cases, both methods not adapted

11 Illustration Winter, station par Present 20-year RL: 51.3 [42.0;60.6] Future 20-year RL: Roth et al.: threshold, constant s 49.9 [29.6;70.2] method 2 : mean and variance 26.1 [9.0;30.9]

12 RL changes Green: non significant (open, filled ) Red: significant (open, filled )

13 Conclusion and perspectives Comparison of different approaches to compute future rainfall return levels with POT RL computed from all days or rainy days only coherent Important role of mean and variance evolution for rainy days Use of mean and variance information give comparable results (difficulty of comparison when non stationary) Future return levels Generally both approaches give comparable results Use of mean and variance allows taking changes into account even if significant changes in parameters not identified cases for which both approaches fail RL evolution depend on season: generally, but some in fall and spring Comparison with same EMS approaches 2014 UC1 06/10/14 with GEV

14 THANKS