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

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Presentation transcript:

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

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

Used data STATIONDATATYPEFROMTO TiszabecsH TivadarH TivadarQ VásárosnaményH VásárosnaményQ ZáhonyH ZáhonyQ PolgárH PolgárQ SzolnokH SzolnokQ SzegedH SzegedQ

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

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

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.

Average exceed curve Szeged(H)

Szeged(Q)

Polgár(H) y = x Küszöbérték (cm) Átlagos meghaladás (cm)

Average exceed curve Polgár(Q) y = x Küszöbérték (m 3 /s) Átlagos meghaladás (m 3 /s)

Shape parameter

Záhony(H)

Záhony(H)

Záhony(Q)

Záhony(Q)

Polgár(H)

Polgár(Q)

Results, Vásárosnamény DatatypeThreshold Scale parameter Shape parameter Return level in 100 years Confidence interval (95%) H300 cm cm[893, 944] H400 cm cm[893, 948] H500 cm cm[892, 946] H600 cm cm[889, 956] Q800 m 3 /s m 3 /s[3426, 4307] Q1100 m 3 /s m 3 /s[3427, 4395] Q1300 m 3 /s m 3 /s[3434, 4258] Q1500 m 3 /s m 3 /s[3441, 4253]

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]

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