R.Garçon, F.Garavaglia, J.Gailhard, E.Paquet, F.Gottardi EDF-DTG

Transcription

1 Homogeneous samples and reliability of probabilistic models : using an atmospheric circulation patterns sampling for a better estimation of extreme rainfall probability R.Garçon, F.Garavaglia, J.Gailhard, NICDS workshop : Statistical Methods for Geographic and Spatial Data in the management of Natural Resources Montréal, 3-5 mars 2010 E.Paquet, F.Gottardi EDF-DTG

2 Towards the extreme rainfall quest Our main concern : estimating extreme rainfall probability Example : 10 3 to 10 4 year return time daily rainfall estimation Application : design and assessment of dam safety level 2

3 Extremes : is it only a mathematical problem? A mathematical background : extreme value theory Blocks maxima : GEV family law Peaks Over Threshold : GPD family law Some options Sampling method : Blocks length or threshold selection Parameter estimation method : Maximum Likelihood, Moments, Weighted Moments, L-Moments, etc 3

4 Statistical homogeneity? The sample s statistical homogeneity is favored by the sampling method (BM, POT) which focuses on distribution tails Homogeneity could also be improved by seasonal or monthly sub-sampling Is it enough? Finding sources of heterogeneity 4

5 Atmospheric circulation influences rainfall regime like seasons Which leads to homogeneous sub-samples based on atmospheric circulations 5

6 Some words about meteorology Spatial variations of pressure field drive atmospheric circulation : Atmospheric pressure field And wind 6

7 Toward a Weather Pattern classification 1000hPa and 700hPa geopotential fields at 0H and 24H describe synoptic situations of rainfall in south of France The Teweless-Wobus score is used to compare these four fields : 2 days are similar if TW scores are close to 0 7

8 8 Weather Pattern types 8 clusters are build around 8 pre-selected typical pressure fields : Date Cluster Each day of the period is associated to the nearest center : 8

9 Weather patterns : Pressure and rainfalls (1) WP 1 : Atlantic Wave (7%) WP 2 : Steady Oceanic (24%) WP 3 : Southwest Circulation (8%) WP 4 : South Circulation (18%) 9

10 Weather patterns : Pressure and rainfalls (2) WP 5 : Northeast Circulation (7%) WP 6 : East Return (6%) WP 7 : Central Depression (3%) WP 8 : Anticyclonic (27%) 10

11 An efficient WP classification allows to emphasize contrasted rainfall patterns between different atmospheric circulations (1) WP2 mean rainfall field over France WP4 mean rainfall field over France 11

12 An efficient WP classification allows to emphasize contrasted rainfall patterns between different atmospheric circulations (2) P 2 > 7.P 4 P 4 > 10.P 2 Ratio between WP2 and WP4 mean rainfall field 12

13 An efficient WP classification allows to emphasize contrasted rainfall risks between different atmospheric circulations WP 2 WP 4 Fall daily rainfall at Issarlès (Ardèche, 07) For each WP : A good fit by an exponential distribution 13

14 Compound of daily rainfall seasonal risk Fall daily rainfall at Issarlès (Ardèche, 07) 14

15 Compound of daily rainfall seasonal risk Fall daily rainfall at Issarlès (Ardèche, 07) 15

16 Compound of daily rainfall seasonal risk Fall daily rainfall at Issarlès (Ardèche, 07) 16

17 Compound of daily rainfall seasonal risk Fall daily rainfall at Issarlès (Ardèche, 07) 17

18 Compound of daily rainfall seasonal risk Fall daily rainfall at Issarlès (Ardèche, 07) 18

19 Compound of daily rainfall seasonal risk Fall daily rainfall at Issarlès (Ardèche, 07) 19

20 Compound of daily rainfall seasonal risk Fall daily rainfall at Issarlès (Ardèche, 07) 20

21 Compound of daily rainfall seasonal risk Fall daily rainfall at Issarlès (Ardèche, 07) 21

22 Compound of daily rainfall seasonal risk Fall daily rainfall at Issarlès (Ardèche, 07) MEWP (Multi-Exponential Weather Pattern) compound distribution, as used in the SCHADEX method 22

23 Compound of daily rainfall seasonal risk Fall daily rainfall at Pontarlier The mix of the 8 WP sub-samples induces a strong bend 23

24 Atmospheric circulation influences could be very variable in space (1) Site 1 Circulation type B Site 1 24

25 Atmospheric circulation influences could be very variable in space (2) Decreased B-Rainfall Site 2 Circulation type B Site 1 Site 2 25 For a given station, rainfall risks between different WP can vary quickly in space and influence strongly the shape of the compound distribution

26 Atmospheric circulation influences could be very variable in space (3) Increased B-Rainfall Site 3 Circulation type B Site 1 Site 3 This bend comes from the sub-sample risk heterogeneity. No conclusion can be drawn for asymptotic behaviour! 26

27 Asymptotic behaviour analysis (1) M = Mean(P;P>S) Mean Residual Life = M - S 200 P (mm/24h) S U=-Log(-Log(F)) 27

28 Asymptotic behaviour analysis (1) St Etienne en Devoluy ( ) Daily rainfall - All weather patterns and all seasons M - S S ξ > 0! 28

29 Asymptotic behaviour analysis (2) St Etienne en Devoluy ( ) Daily rainfall - All weather patterns and fall season M - S S ξ > 0! 29

30 Asymptotic behaviour analysis(3) St Etienne en Devoluy ( ) Daily rainfall - Weather pattern 4 and fall season M - S Working on an homogeneous sub-sample improves mean residual life s stability ξ = 0! S 30

31 Now, it s decision time! Should we : Fit exponential distributions to homogeneous sub-samples? or Fit GPD distribution to a heterogeneous sample? Let s assess predictive capabilities of these different approaches on real-world cases 31

32 Assessment of different statistical distributions and sampling methods on fall daily rainfalls Gumbel distribution on annual (fall) block maxima Exponential distribution on POT GEV distribution on annual (fall) block maxima GP distribution on POT Exponential Distribution on Weather Patterns samples (MEWP) Calibration by Maximum Likelihood POT sampling : 2 events/year 32

33 Daily rainfall dataset : 515 raingauges

34 Comparison of P T=1000 yr - MEWP and others GEV GPD Gumbel Exp 34

35 Robustness Sensitivity to the highest value with MEWP Sensitivity to the highest value with GPD 35

36 Accuracy Test : definition of FF test Accuracy is the ability to assign the correct probability to high observed values FF test is based on the split-sample procedure applied on a regional dataset of M stations: Calibration (Validation) Validation (Calibration) Global Period The probability of non-exceedance of max observed on validation period is computed with the PDF fitted on calibration period FF j = 1to M = Pr( X X j Validation = max( x j i,..., x j N ) ) = j j [ G ( X )] N Calibration Validation 2M values of FF probabilities are available If FF is a reasonable model for considered population, it should lie close to the unit diagonal in a probability plot (Coles, 2003) 36

37 Accuracy Test : results of FF test Comparison of FF distribution for GEV, Gumbel and MEWP probabilistic models Perfect model 37

38 Conclusions Sample heterogeneity due to atmospheric circulation may be strong The bended asymptotic behaviour is not necessary justified Exponential distribution is good model when working on sub-samples based on atmospheric circulations Estimated extreme rainfall risks seem to be reliable (France, daily precipitation) The MEWP distribution is the basis of the SCHADEX method used in an industrial context at EDF, for extreme flood estimation 38

39 References Coles, S.; Pericchi, L. R. & Sisson, S.A fully probabilistic approach to extreme rainfall modeling Journal of Hydrology, 2003, 273, 35-5 Garavaglia, F., Gailhard, J., Paquet, E., Lang, M., Garçon, R., and Bernardara, P.: Introducing a rainfall compound distribution model based on weather patterns sub-sampling, Hydrol. Earth Syst. Sci. Discuss., 7, , Gottardi, F., Paquet, E., Obled, C., Gailhard, J., Statistical estimation of precipitation over french mountain ranges. International Conference on Alpine Meteorology, 4-8 June Chambéry, France. Gottardi, F. Estimation statistique et réanalyse des précipitations en montagne. PhD Thesis. Polytechnic Institute of Grenoble., Paquet, E.; Gailhard, J. & Garçon, R. Evolution de la méthode du gradex: approche par type de temps et modélisation hydrologique. La Houille Blanche, 2006, 5, Teweless, J. & Wobus, H. Verification of prognosis charts. Bull. Am. Meteorol. Soc., 1954, 35,