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

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

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

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

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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

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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.

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Average exceed curve Szeged(H)

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Szeged(Q)

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

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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)

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Shape parameter

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Záhony(H)

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Záhony(H)

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Záhony(Q)

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Záhony(Q)

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Polgár(H)

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Polgár(Q)

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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]

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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]

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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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