Frequency Analysis for Non stationary Flood Series

Transcription

1 Frequency Analysis for Non saionary Flood Series Prepared By: Narendra Kumar Goel, Sunil Poudel and R.B. Jigajinni Indian Insiue of Technology, Roorkee Presened By: Sunil Poudel

2 INTRODUCTION Wha is saionariy and non saionariy? Facors causing non saionariy? Sandard approaches o flood frequency analysis is assumpion of saionariy. Esimae for a design flood quanile is sill required for a river ha demonsraes nonsaionariy.

3 STUDY AREA AND DATA AVAILABILITY ZONE 3 MAP Bordered by red Line

4 CONTD... Table 1: Summary of annual flood daa used Sub-Zone River Basin Number of Sies Cachmen Area (km 2 ) 3 (a) Mahi and Sabarmai (b) Lower Narmada and Tapi (c) Upper Narmada and Tapi (d) Mahanadi (e) Upper Godavari (f) Lower Godavari (g) Indravai 0 3 (h) Krishna and Penner (i) Kaveri 0

5 CONTD... Table 2: Summary of rainfall daa used in he sudy Sae Number of rain gauge saions Andhra Pradesh 24 Bihar 6 Gujara 25 Karnaaka 27 Kerala 10 Maharashra 46 Orissa 15 Tamilnadu 31 Wes Bengal 21

6 INVESTIGATION OF NON STATIONARITY Non saionariy due o shor erm dependence and long erm dependence have been examined. Shor erm dependence was examined using: (i) Median crossing es (Fisz, 1963); (ii) Turning poin es (Kendall and Suar, 1976); (iii) Rank difference es (Meacham, 1968); (iv) Kendall s rank correlaion es (Kendall, 1970); (v) Run es (Guman e al.,1971); (vi) Linear regression es ( Koegoda, 1980); (vii) Wald Wolfowiz es (Wald and Wolfowiz, 1943);

7 CONTD.. (viii) Runs above and below he median es (Shiau and Condie, 1980); (ix) Rank Von Neumann raio es (Madansky, 1988); (x) Von Neumann raio es (Madansky, 1988); and (xi) Auo correlaion es (Yevjevich, 1971) Long erm dependence was examined using: Hurs Coefficien (K) has been examined including boosrapping approach.

8 ANALYSIS OF ANNUAL FLOOD SERIES AND ANNUAL DAILY MAXIMUM RAINFALL SERIES Variable AFS ADMRS r o o 0.65 Hurs s K o o Shor-erm dependence 9.21% series 9.76% series Long-erm dependence 17.10% series 11.22% series The probabiliies are fairly high and here is no reason o disregard long erm dependence. If a series shows shor-erm independence, one should sill invesigae for long-erm dependence.

9 IMPACT OF NON STATIONARITY ON FREQUENCY ESTIMATES The impac of dependencies in exreme flow and rainfall esimaes were examined using synheic sequences. Daa sequences were generaed using a mixed noise model (Booy and Lye, 1989). X w a (a) (a) (b) (b) (c) (c) a X 1 w b bx 1 w c cx 1 (d) (d) X w d d 1 where, w a,w b,w c and w d are weighs, and a, b, c and d are serial correlaion coefficiens, (a), (b), (c), (d) are independen processes, having zero mean and variances (1- a2 ), (1- b2 ), (1- c2 ), (1- d2 ) respecively.

10 CONTD Parameers of mixed-noise model i.e. w a,w b,w c,w d, a, b, c and d are compued as per procedure given by (Booy and Lye, 1989). In his sudy, wo ypes of daa ses are generaed samples of 100 years lengh having r 1 and K of original series samples of 100 years lengh having r 1 =0.0 and K=0.5 This modelling approach is designed o reproduce, on average, he lag one serial correlaion coefficien and he Hurs coefficien, K. Quaniles for 50 years, 100 years, 200 years reurn period are compued using General Exreme Value disribuion and probabiliy weighed momens (PWM) mehod. The expeced values of flood quaniles for reurn periods of 50, 100 and 200 years i.e. E (Q 50 ), E (Q 100 ), E (Q 200 ) are compued for generaed series.

11 CONTD In annual flood series, average Hurs s K for series, having long-erm dependence is For annual daily maximum rainfall series average Hurs s K is Daases wih long erm dependence 50 years reurn period Underesimaion on 100 years reurn period 200 years reurn period Annual flood series 44.28% 54.20% 64.26% Annual daily maximum rainfall series 30.88% 42.28% 54.83%

12 CONTD I is quie eviden ha on he independence assumpion, when he series is in fac non-saionary leads o underesimaion of quaniles. This underesimaion increases wih he increase in reurn period. This has also been found o be direcly relaed wih he Hurs coefficien. The under esimaion due o independence assumpion were obained as per he procedure explained in he previous secion. For a reurn period of 100 years he underesimaion has been found o be linearly varying wih Hurs coefficien (K) as follows: Y= X ; r=0.69 Where, Y is % underesimaion in 100 years reurn period quanile, X is Hurs s coefficien (K) and r is coefficien of correlaion.

13 CONCLUSIONS Before esimaion of flood quaniles, he daa series are invesigaed no for shor erm and long-erm dependence. The long-erm dependence should be aken ino accoun as i may significanly increase he risk associaed wih fuure peak flows. Daa sequences are generaed using mixed noise model. The inen wih mixed noise model is o preserve in he generaed daa sequences boh shor-erm and long-erm dependence observed in he original series. Long-erm dependence, if presen in a daa series, increases degree of uncerainy associaed wih exreme flow quaniles.

14 THANK YOU For Your Kind Aenion!!