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Peaks-over-threshold models Szabolcs Erdélyi research assistant VITUKI Plc.

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Presentation on theme: "Peaks-over-threshold models Szabolcs Erdélyi research assistant VITUKI Plc."— Presentation transcript:

1 Peaks-over-threshold models Szabolcs Erdélyi research assistant VITUKI Plc.

2 Abstract – Used data – POT model – Choosing thresholds – Results – Summary

3 Used data STATIONDATATYPEFROMTO TiszabecsH19242000 TivadarH19012000 TivadarQ19512000 VásárosnaményH19012000 VásárosnaményQ19012000 ZáhonyH19011999 ZáhonyQ19311999 PolgárH19012000 PolgárQ19312000 SzolnokH19011999 SzolnokQ19201999 SzegedH19012000 SzegedQ19212000

4 POT model X 1, X 2, … independence, identically distributed random variables uhigh enough threshold H(z)distribution function of GPD when y > 0, and

5 POT model – Choosing threshold – Selecting data over threshold from daily maximum values – Declustering – Time of declustering (It’s necessary because of independence): 30-60 days – Calculate model parameters with maximum likelihood function – Representing results: return levels and confidence intervals with profile likelihood

6 Choosing threshold Expected value of GPD, when threshold is u 0 : when  u 0 : Expected value is linear, the shape parameter is constant function in u.

7 Average exceed curve Szeged(H)

8 Szeged(Q)

9 Polgár(H) y = -0.247x + 219.4 0 50 100 150 200 250 300 0100200 300400 500600 700800 Küszöbérték (cm) Átlagos meghaladás (cm)

10 Average exceed curve Polgár(Q) y = -0.2677x + 1237.4 300 400 500 600 700 800 0500100015002000250030003500 Küszöbérték (m 3 /s) Átlagos meghaladás (m 3 /s)

11 Shape parameter

12

13 Záhony(H)

14 Záhony(H)

15 Záhony(Q)

16 Záhony(Q)

17 Polgár(H)

18 Polgár(Q)

19 Results, Vásárosnamény DatatypeThreshold Scale parameter Shape parameter Return level in 100 years Confidence interval (95%) H300 cm345.4-0.5422908 cm[893, 944] H400 cm289-0.5372908 cm[893, 948] H500 cm238.8-0.5474908 cm[892, 946] H600 cm174.3-0.5108908 cm[889, 956] Q800 m 3 /s836.4-0.19043735 m 3 /s[3426, 4307] Q1100 m 3 /s781-0.19363727 m 3 /s[3427, 4395] Q1300 m 3 /s797-0.23463682 m 3 /s[3434, 4258] Q1500 m 3 /s772-0.24933677 m 3 /s[3441, 4253]

20 Other results StationDatatypeThreshold Return level in 100 years Confidence interval (95%) TiszabecsH300 cm679 cm[616, 864] TivadarH500 cm912 cm[875, 994] TivadarQ800 m 3 /s3188 m 3 /s[2692, 4680] ZáhonyH450 cm744 cm[718, 810] ZáhonyQ1500 m 3 /s3683 m 3 /s[3351, 4627] PolgárH470 cm789 cm[759, 871] SzolnokH600 cm949 cm[921, 1031] SzegedH550 cm937 cm[908, 1014] SzegedQ1500 m 3 /s4150 m 3 /s[3746, 5522]

21 Summary – On the majotity of data series the fitting is appropriate, the results are resonable – The final result is slighty affected by the selection of thresholds – In the cause of the data of Polgár(Q) and Szolnok(Q) the model does not fit properly – The reason for that can be found in the incidental errors of the calculation of data

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