Similarity of empirical copulas of flood peak-volume relationships: a regional case study of North-West Austria

Abstract This paper analyses the bivariate relationship between flood peaks and corresponding flood event volumes modelled by empirical copulas in a regional context in the North-West of Austria. Flood data of a total of 69 catchments in the region are analysed for the period 1976–2007. In order to increase the sample size and the homogeneity of the samples for the statistical analysis, 24872 hydrologically independent flood events were isolated and assigned to one of three flood process types: synoptic floods, flash floods or snowmelt floods in contrary to the more traditional engineering approach of selecting annual maxima of flood peaks and corresponding flood volumes. The first major part of the paper examines whether the empirical peak-volume copulas of different flood process types are statistically distinguishable, separately for each catchment. The results indicate that the empirical copulas of flash floods tend to be different from those of the synoptic and snowmelt floods in the target region. The second part examines how similar are the empirical flood peak-volume copulas between catchments for a given flood type. For the majority of catchment pairs, the empirical copulas of all flood types are indeed statistically similar. The flash floods show the largest degree of spatial heterogeneity. It is concluded that there is merit in treating flood types separately and in pooling events of the same type in a region when analysing and estimating flood peak-volume dependence copulas; however, the sample size of the analysed events is a limiting factor in spite of the introduced event selection procedure.

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Process-based selection of copula types for flood peak-volume relationships in Northwest Austria: a case study

Contributions to Geophysics and Geodesy ◽

10.1515/congeo-2016-0015 ◽

2016 ◽

Vol 46 (4) ◽

pp. 245-268 ◽

Cited By ~ 1

Author(s):

Silvia Kohnová ◽

Ladislav Gaál ◽

Tomáš Bacigál ◽

Ján Szolgay ◽

Kamila Hlavčová ◽

...

Keyword(s):

Sample Size ◽

Goodness Of Fit ◽

Real Life ◽

Flash Floods ◽

Flood Events ◽

Copula Models ◽

Flood Peak ◽

Flood Peaks ◽

Selection Of

Abstract The case study aims at selecting optimal bivariate copula models of the relationships between flood peaks and flood volumes from a regional perspective with a particular focus on flood generation processes. Besides the traditional approach that deals with the annual maxima of flood events, the current analysis also includes all independent flood events. The target region is located in the northwest of Austria; it consists of 69 small and mid-sized catchments. On the basis of the hourly runoff data from the period 1976- 2007, independent flood events were identified and assigned to one of the following three types of flood categories: synoptic floods, flash floods and snowmelt floods. Flood events in the given catchment are considered independent when they originate from different synoptic situations. Nine commonly-used copula types were fitted to the flood peak - flood volume pairs at each site. In this step, two databases were used: i) a process-based selection of all the independent flood events (three data samples at each catchment) and ii) the annual maxima of the flood peaks and the respective flood volumes regardless of the flood processes (one data sample per catchment). The goodness-of-fit of the nine copula types was examined on a regional basis throughout all the catchments. It was concluded that (1) the copula models for the flood processes are discernible locally; (2) the Clayton copula provides an unacceptable performance for all three processes as well as in the case of the annual maxima; (3) the rejection of the other copula types depends on the flood type and the sample size; (4) there are differences in the copulas with the best fits: for synoptic and flash floods, the best performance is associated with the extreme value copulas; for snowmelt floods, the Frank copula fits the best; while in the case of the annual maxima, no firm conclusion could be made due to the number of copulas with similarly acceptable overall performances. The general conclusion from this case study is that treating flood processes separately is beneficial; however, the usually available sample size in such real life studies is not sufficient to give generally valid recommendations for engineering design tasks.

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A regional comparative analysis of empirical and theoretical flood peak-volume relationships

Journal of Hydrology and Hydromechanics ◽

10.1515/johh-2016-0042 ◽

2016 ◽

Vol 64 (4) ◽

pp. 367-381 ◽

Cited By ~ 16

Author(s):

Ján Szolgay ◽

Ladislav Gaál ◽

Tomáš Bacigál ◽

Silvia Kohnová ◽

Kamila Hlavčová ◽

...

Keyword(s):

Sample Size ◽

Goodness Of Fit ◽

Flash Floods ◽

Regional Differentiation ◽

Sufficient Information ◽

Multivariate Statistical ◽

Data Set ◽

North West ◽

Flood Peak ◽

Flood Peaks

Abstract This paper analyses the bivariate relationship between flood peaks and corresponding flood event volumes modelled by empirical and theoretical copulas in a regional context, with a focus on flood generation processes in general, the regional differentiation of these and the effect of the sample size on reliable discrimination among models. A total of 72 catchments in North-West of Austria are analysed for the period 1976–2007. From the hourly runoff data set, 25 697 flood events were isolated and assigned to one of three flood process types: synoptic floods (including long- and short-rain floods), flash floods or snowmelt floods (both rain-on-snow and snowmelt floods). The first step of the analysis examines whether the empirical peak-volume copulas of different flood process types are regionally statistically distinguishable, separately for each catchment and the role of the sample size on the strength of the statements. The results indicate that the empirical copulas of flash floods tend to be different from those of the synoptic and snowmelt floods. The second step examines how similar are the empirical flood peak-volume copulas between catchments for a given flood type across the region. Empirical copulas of synoptic floods are the least similar between the catchments, however with the decrease of the sample size the difference between the performances of the process types becomes small. The third step examines the goodness-of-fit of different commonly used copula types to the data samples that represent the annual maxima of flood peaks and the respective volumes both regardless of flood generating processes (the traditional engineering approach) and also considering the three process-based classes. Extreme value copulas (Galambos, Gumbel and Hüsler-Reiss) show the best performance both for synoptic and flash floods, while the Frank copula shows the best performance for snowmelt floods. It is concluded that there is merit in treating flood types separately when analysing and estimating flood peak-volume dependence copulas; however, even the enlarged dataset gained by the process-based analysis in this study does not give sufficient information for a reliable model choice for multivariate statistical analysis of flood peaks and volumes.

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Personalized Social Services Provided to Children Living with Disabilities: A Case Study in the North-West Region of Romania

10.15405/epsbs.2016.09.59 ◽

2016 ◽

Author(s):

Maria Hanyecz-Debelka ◽

Ildiko Szanto

Keyword(s):

Social Services ◽

North West ◽

The North ◽

West Region

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Variations of overt and covert language practices of educators in the North West Province: Case study of the use of Setswana and Sesotho at primary and secondary schools

South African Journal of African Languages ◽

10.1080/02572117.2016.1186891 ◽

2016 ◽

Vol 36 (1) ◽

pp. 15-24 ◽

Cited By ~ 3

Author(s):

Michael M Kretzer

Keyword(s):

Secondary Schools ◽

Language Practices ◽

North West ◽

The North ◽

North West Province

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Kerbside collection: A case study from the north-west of England

Resources Conservation and Recycling ◽

10.1016/j.resconrec.2007.02.006 ◽

2007 ◽

Vol 52 (2) ◽

pp. 381-394 ◽

Cited By ~ 24

Author(s):

C.D.H. Wilson ◽

I.D. Williams

Keyword(s):

North West ◽

The North

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The use of high-resolution stratigraphy and derived lithoclasts to document structural inversion; a case study from the Paleogene, Isle of Wight, U.K.

Journal of the Geological Society ◽

10.1144/jgs2020-156 ◽

2021 ◽

pp. jgs2020-156

Author(s):

Andy Gale

Keyword(s):

The West ◽

North West ◽

Geologic Time ◽

Northern Limb ◽

The North ◽

Basement Faults ◽

Structural Inversion ◽

Geologic Time Scale ◽

Radiometric Ages

The effects of structural inversion, generated by the Pyrenean Orogeny on the southerly bounding faults of the Hampshire Basin (Needles and Sandown Faults) on Eocene sedimentation in the adjacent regions were studied in outcrops by sedimentary logging, dip records and the identification of lithoclasts reworked from the crests of anticlines generated during inversion. The duration and precise age of hiatuses associated with inversion was identified using bio- and magnetostratigraphy, in comparison with the Geologic Time Scale 2020. The succession on the northern limb of the Sandown Anticline (Whitecliff Bay) includes five hiatuses of varying durations which together formed a progressive unconformity developed during the Lutetian to Priabonian interval (35-47Ma). Syn-inversion deposits thicken southwards towards the southern margin of the Hampshire Basin and are erosionally truncated by unconformities. The effects of each pulse of inversion are recorded by successively shallower dips and the age and nature of clasts reworked from the crest of the Sandown Anticline. Most individual hiatuses are interpreted as minor unconformities developed subsequent to inversion, rather than eustatically-generated sequence boundaries:transgressive surfaces. In contrast, the succession north of the Needles Fault (Alum Bay) does not contain hiatuses of magnitude or internal unconformities. In the north-west of the island, subsidiary anticlinal and synclinal structures developed in response to Eocene inversion events by the reactivation of minor basement faults. The new dates of the Eocene inversion events correspond closely with radiometric ages derived from fracture vein-fill calcites in Dorset, to the west (36-48Ma).

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