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Comparison of annual maximum and peaks-over-threshold methods with automated threshold selection in flood frequency analysis: a case study for Australia

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Abstract

Flood frequency analysis (FFA) involves fitting of a probability distribution to observed flood data. Two main models, annual maximum (AM) and peaks over threshold (POT), are generally adopted in FFA. The POT model is underemployed due to its complexity and uncertainty associated with threshold selection and meeting independence criteria in selecting POT data series. This study evaluates the POT and AM models using data from 188 gauged stations in southeast Australia. The POT model adopted in this study applies different average numbers of events per year fitted with generalized Pareto (GP) distribution with an automated threshold detection method. For the AM model, the GP distribution is also adopted, and flood quantiles estimated by the two models are compared. It has been found that there are notable differences in design flood estimates between the AM and POT models. The study uses catchment characteristics data to understand the differences in quantile estimates between the AM and POT models. The percentage differences between the AM and POT models can be explained by mean annual rainfall (MAR) and mean annual evapotranspiration (MAE) (ARIs of 1.01–5 years), MAR (10-year ARI), stream density (SDEN) (for 20- and 50-year ARIs) and SDEN, main stream slope (S1085) and MAE (for 100-year ARI). Stations showing smaller % differences have relatively higher MAR and smaller MAE (indicating wetter condition); conversely, stations showing higher % differences have smaller MAR and higher MAE (drier condition).

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Data availability

The analysis is carried out using R (R Core Team 2021) and POT package (Ribatet and Dutang 2019). The primary streamflow data series used in this study can be obtained from Australian Government agencies by paying a prescribed fee.

References

  • Bačová-Mitková V, Onderka M (2010) Analysis of extreme hydrological events on the sanube using the peak over threshold method. J Hydrol Hydromech 58(2):88–101

    Article  Google Scholar 

  • Ball JE, Babister MK, Nathan R, Weinmann PE, Weeks W, Retallick M et al (2016) Australian rainfall and runoff—A guide to flood estimation. Commonwealth of Australia, Canberra

    Google Scholar 

  • Bernardara P, Mazas F, Weiss J, Andreewsky M, Kergadallan X, Benoît M, Hamm L (2012) On the two step threshold selection for over-threshold modelling. Coast Eng Proc 1(33):1–6

    Google Scholar 

  • Bezak N, Brilly M, Šraj M (2014) Comparison between the peaks-over-threshold method and the annual maximum method for flood frequency analysis. Hydrol Sci J 59(5):959–977

    Article  Google Scholar 

  • Bhunya PK, Singh RD, Berndtsson R, Panda SN (2012) Flood analysis using generalized logistic models in partial duration series. J Hydrol 420–421:59–71

    Article  Google Scholar 

  • Bhuyan MK, Jena J, Bhunya PK (2016) At-site flood analysis using exponential and generalized logistic models in partial duration series (PDS). Int J Eng Technol 8(1):501–514

    Google Scholar 

  • Bobée B, Cavadias G, Ashkar F, Bernier J, Rasmussen PF (1993) Towards a systematic approach to comparing distributions used in flood frequency analysis. J Hydrol 142(1–4):121–136

    Article  Google Scholar 

  • Coles S (2001) An introduction to statistical modelling of extreme values. Springer, London

    Book  Google Scholar 

  • Curceac S, Atkinson PM, Milne A, Wu L, Harris P (2020) An evaluation of automated GPD threshold selection methods for hydrological extremes across different scales. J Hydrol 585:124845

    Article  Google Scholar 

  • Dowdy AJ, Mills GA, Timbal B, Griffiths M, Wang Y (2013) Understanding rainfall projections in relation to extratropical cyclones in eastern Australia. Aust Met Oceanogr J 63:355–364

    Article  Google Scholar 

  • Durocher M, Burn DH, Ashkar F (2019) Comparison of estimation methods for a nonstationary index-flood model in flood frequency analysis using peaks over threshold. Water Resour Res 55(11):9398–9416

    Article  Google Scholar 

  • Durocher M, Mostofi Zadeh S, Burn DH, Ashkar F (2018) Comparison of automatic procedures for selecting flood peaks over threshold based on goodness-of-fit tests. Hydrol Process 32(18):2874–2887

    Article  Google Scholar 

  • Gottschalk L, Krasovskaia I (2002) L-moment estimation using annual maximum (AM) and peak over threshold (POT) series in regional analysis of flood frequencies. Nor Geogr Tidsskr 56(2):179–187

    Article  Google Scholar 

  • Haddad, K, Rahman, A (2015), 'Estimation of large to extreme floods using a regionalization model', in Landscape Dynamics, Soils and Hydrological Processes in Varied Climates, pp 279–92

  • Haddad, K, Rahman, A, Kuczera, G, Weinmann, E (2012) 'A new regionalisation model for large flood estimation in Australia: Consideration of inter-site dependence in modelling', pp 969–76, Scopus

  • Haddad, K, Rahman, A, Weeks, W, Kuczera, G, Weinmann, PE (2011) 'Towards a new regional flood frequency analysis method for Western Australia', pp 3788–95, Scopus

  • Haddad, K, Zaman, M, Rahman, A, Shrestha, S (2010) 'Regional flood modelling: Use of Monte Carlo cross-validation for the best model selection', pp 2831–40, Scopus

  • Herath, S, Prasad Basnayake, A, Coremans, D (2015) 'Comparison of flood frequency analysis by annual maximum and peak over threshold approaches for Fitzroy River, Western Australia', pp 682–90, Scopus

  • Hosking JRM, Wallis JR (1987) Parameter and quantile estimation for the generalized pareto distribution. Technometrics 29(3):339–349

    Article  Google Scholar 

  • Ishak EH, Rahman A, Westra S, Sharma A, Kuczera G (2013) Evaluating the non-stationarity of australian annual maximum flood. J Hydrol 494:134–145

    Article  Google Scholar 

  • Karim F, Hasan M, Marvanek S (2017) Evaluating annual maximum and partial duration series for estimating frequency of small magnitude floods. Water (Switzerland) 9(7):481

    Google Scholar 

  • Khan S, Hussain I, Rahman A (2021) Identification of homogeneous rainfall regions in New South Wales, Australia. Tellus A Dyn Meteorol Oceanography 73(1):1–11

    Google Scholar 

  • Lang M, Ouarda TBMJ, Bobée B (1999) Towards operational guidelines for over-threshold modeling. J Hydrol 225(3):103–117

    Article  Google Scholar 

  • Langbein, WB (1949) 'Annual floods and the partial-duration flood series', Eos, Transactions American Geophysical Union, 30(6), 879–81, viewed 2020/06/12

  • Madsen H, Rasmussen PF, Rosbjerg D (1997) Comparison of annual maximum series and partial duration series methods for modeling extreme hydrologic events 1. At-site modeling. Water Resour Res 33(4):747–757

    Article  Google Scholar 

  • Mostofi Zadeh S, Durocher M, Burn DH, Ashkar F (2019) Pooled flood frequency analysis: a comparison based on peaks-over-threshold and annual maximum series. Hydrol Sci J 64(2):121–136

    Article  Google Scholar 

  • Önöz B, Bayazit M (2001) Effect of the occurrence process of the peaks over threshold on the flood estimates. J Hydrol 244(1–2):86–96

    Article  Google Scholar 

  • Pan, X, Rahman, A (2018) 'Comparison of annual maximum and peaks-over-threshold methods in flood frequency analysis', pp 614–25, Scopus

  • Pickands J (1975) Statistical inference using extreme order statistics. Ann Statist 3(1):119–131

    Google Scholar 

  • R Core Team (2021) R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. URL https://www.R-project.org/

  • Ribatet, M, Dutang, C (2019) POT: generalized pareto distribution and peaks over threshold. R package version 1.1–7

  • Robson, A, Reed, D (1999) Statistical Procedures for Flood Frequency Estimation, Flood Estimation Handbook, Centre for Ecology & Hydrology, Wallingford, UK

  • Thompson P, Cai Y, Reeve D, Stander J (2009) Automated threshold selection methods for extreme wave analysis. Coast Eng 56(10):1013–1021

    Article  Google Scholar 

  • USWRC (1976) Guidelines for determining flood flow frequency, US Department of the Interior, Geological Survey, Office of Water Data Coordination

Download references

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Authors and Affiliations

  1. School of Engineering, Design and Built Environment, Western Sydney University, Building XB, Kingswood, Sydney, NSW, 2751, Australia

    Xiao Pan & Ataur Rahman

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  1. Xiao Pan
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  2. Ataur Rahman
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Contributions

XP developed the models, wrote computer programs, carried out analysis and drafted the manuscript, and AR checked the results and updated the manuscript by editing/rewriting.

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Correspondence to Ataur Rahman.

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The authors declare that there is no conflicts of interest and the research did not involve any human participants and/or animals.

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Pan, X., Rahman, A. Comparison of annual maximum and peaks-over-threshold methods with automated threshold selection in flood frequency analysis: a case study for Australia. Nat Hazards 111, 1219–1244 (2022). https://doi.org/10.1007/s11069-021-05092-y

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