Skip to main content
Erschienen in: Water Resources Management 2/2015

01.01.2015

Downstream-Directed Performance Assessment of Reservoirs in Multi-Tributary Catchments by Application of Multivariate Statistics

verfasst von: Markus Schulte, Andreas Schumann

Erschienen in: Water Resources Management | Ausgabe 2/2015

Einloggen

Aktivieren Sie unsere intelligente Suche um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

In the past the flood design was dominated by safety oriented concepts. A design flood was chosen with the basic assumption that it defines the limit up to which a flood can be controlled completely by technical measures. Often peak values with very small probabilities are used. Thus the risk of an event beyond the design flood seems to be very small and even negligible. Caused by the increasing risk awareness, changes of the design philosophy became necessary. The remaining danger of failure, which may result from the hydrological risk of an extreme event, but also from operational and technical risks, requires more complex assessments. For this purpose a differentiated view on hydrological risk becomes essential. In this paper the multiple aspects of risk oriented specifications of hydrological loads are discussed. In difference to other applications of multivariate statistics which are used to specify the hydrological characteristics of flood events by consideration of peak-volume relationships, we are interested in spatial interactions of discharge waves from different tributaries. Here it is not sufficient to estimate the most critical combinations by scenarios but to estimate their probabilities. It is shown how the probability of coincidences of critical hydrograph characteristics can be specified by multivariate statistics, based on copulas. We discuss the influence of upstream flood detention measures on the discharge downstream of a confluence. For that purpose the effect of a reservoir is evaluated statistically downstream of a multi-tributary catchment. This more complex approach for flood risk assessments is demonstrated with two practical examples.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Literatur
Zurück zum Zitat Aas K, Czado C, Frigessi A, Bakken H (2009) Pair-copula constructions of multiple dependence. Insur Math Econ 44:182–198CrossRef Aas K, Czado C, Frigessi A, Bakken H (2009) Pair-copula constructions of multiple dependence. Insur Math Econ 44:182–198CrossRef
Zurück zum Zitat Bergström S (1992) The HBV model—its structure and applications. SMHI, RH4, Norrkoping Bergström S (1992) The HBV model—its structure and applications. SMHI, RH4, Norrkoping
Zurück zum Zitat Burton A, Kilsby CG, Fowler HJ, Cowperwait P, O’Connel PE (2008) RainSim: a spatial-temporal stochastic rainfall modelling system. Environ Model Softw 23:1356–1369CrossRef Burton A, Kilsby CG, Fowler HJ, Cowperwait P, O’Connel PE (2008) RainSim: a spatial-temporal stochastic rainfall modelling system. Environ Model Softw 23:1356–1369CrossRef
Zurück zum Zitat Chen L, Singh V, Shenglian G, Hao Z, Li T (2012) Flood coincidence risk analysis using multivariate copula functions. J Hydrol Eng ASCE 17(6):742–755CrossRef Chen L, Singh V, Shenglian G, Hao Z, Li T (2012) Flood coincidence risk analysis using multivariate copula functions. J Hydrol Eng ASCE 17(6):742–755CrossRef
Zurück zum Zitat De Michele C, Salvadori G, Canossi M, Petaccia A, Rosso R (2005) Bivariate statistical approach to check adequacy of dam spillway. J Hydrol Eng ASCE 10(1):50–57CrossRef De Michele C, Salvadori G, Canossi M, Petaccia A, Rosso R (2005) Bivariate statistical approach to check adequacy of dam spillway. J Hydrol Eng ASCE 10(1):50–57CrossRef
Zurück zum Zitat Escalante-Sandoval C (1998) Multivariate extreme value distribution with mixed Gumbel marginals. JAWRA J Am Water Resour Assoc 34(2):321–333CrossRef Escalante-Sandoval C (1998) Multivariate extreme value distribution with mixed Gumbel marginals. JAWRA J Am Water Resour Assoc 34(2):321–333CrossRef
Zurück zum Zitat Favre A-C, El Adlouni S, Perreault L, Thiemonge N, Bobee B (2004) Multivariate hydrological frequency analysis using copulas. Water Resour Res 40(1):W01101CrossRef Favre A-C, El Adlouni S, Perreault L, Thiemonge N, Bobee B (2004) Multivariate hydrological frequency analysis using copulas. Water Resour Res 40(1):W01101CrossRef
Zurück zum Zitat Genest C, Rivest L-P (1993) Statistical inference procedures for bivariate Archimedean copulas. J Am Stat Assoc 88(423):1034–1043CrossRef Genest C, Rivest L-P (1993) Statistical inference procedures for bivariate Archimedean copulas. J Am Stat Assoc 88(423):1034–1043CrossRef
Zurück zum Zitat Genest C, Favre AC (2007) Everything you always wanted to know about copula modeling but were afraid to ask. J Hydrol Eng ASCE 12(4):347–368CrossRef Genest C, Favre AC (2007) Everything you always wanted to know about copula modeling but were afraid to ask. J Hydrol Eng ASCE 12(4):347–368CrossRef
Zurück zum Zitat Genest C, Favre AC, Béliveau J, Jacques C (2007) Metaelliptical copulas and their use in frequency analysis of multivariate hydrological data. Water Resour Res 43:W09401CrossRef Genest C, Favre AC, Béliveau J, Jacques C (2007) Metaelliptical copulas and their use in frequency analysis of multivariate hydrological data. Water Resour Res 43:W09401CrossRef
Zurück zum Zitat Ghizzoni T, Roth G, Rudari R (2012) Multisite flooding hazard assessment in the Upper Mississippi River. J Hydrol 412:101–113CrossRef Ghizzoni T, Roth G, Rudari R (2012) Multisite flooding hazard assessment in the Upper Mississippi River. J Hydrol 412:101–113CrossRef
Zurück zum Zitat Goel NK, Seth SM, Chandra S (1998) Multivariate modeling of flood flows. J Hydrol Eng ASCE 124(2):146–155CrossRef Goel NK, Seth SM, Chandra S (1998) Multivariate modeling of flood flows. J Hydrol Eng ASCE 124(2):146–155CrossRef
Zurück zum Zitat Hundecha Y, Pahlow M, Klein B, Schumann A (2008) Entwicklung und Testung eines stochastischen Niederschlagsgenerators zur Erstellung hydrologischer Belastungsszenarien. Forum für Hydrologie und Wasserbewirtschaftung, Heft, p 23 Hundecha Y, Pahlow M, Klein B, Schumann A (2008) Entwicklung und Testung eines stochastischen Niederschlagsgenerators zur Erstellung hydrologischer Belastungsszenarien. Forum für Hydrologie und Wasserbewirtschaftung, Heft, p 23
Zurück zum Zitat Joe H (1997) Multivariate models and dependence concepts. Chapman and Hall, New YorkCrossRef Joe H (1997) Multivariate models and dependence concepts. Chapman and Hall, New YorkCrossRef
Zurück zum Zitat Kao SC, Govindaraju RS (2008) Trivariate statistical analysis of extreme rainfall events via the Plackett family of copulas. Water Resour Res 44(2):1–19CrossRef Kao SC, Govindaraju RS (2008) Trivariate statistical analysis of extreme rainfall events via the Plackett family of copulas. Water Resour Res 44(2):1–19CrossRef
Zurück zum Zitat Klein B, Pahlow M, Hundecha Y, Schumann A (2010) Probability analysis of hydrological loads for the design of flood control systems using copulas. J Hydrol Eng ASCE 15(5):360–369CrossRef Klein B, Pahlow M, Hundecha Y, Schumann A (2010) Probability analysis of hydrological loads for the design of flood control systems using copulas. J Hydrol Eng ASCE 15(5):360–369CrossRef
Zurück zum Zitat Nelson RB (2006) An introduction to copulas, 2nd edn. Springer New York, New York Nelson RB (2006) An introduction to copulas, 2nd edn. Springer New York, New York
Zurück zum Zitat Salvadori G, De Michele C (2004) Frequency analysis via copulas: theoretical aspects and applications to hydrological events. Water Resour Res 40(12):W12511CrossRef Salvadori G, De Michele C (2004) Frequency analysis via copulas: theoretical aspects and applications to hydrological events. Water Resour Res 40(12):W12511CrossRef
Zurück zum Zitat Salvadori G, De Michele C, Kottegoda N, Rosso R (2007) Extremes in nature: an approach using copulas, vol 56, Water science and technology library. Springer, Dordrecht Salvadori G, De Michele C, Kottegoda N, Rosso R (2007) Extremes in nature: an approach using copulas, vol 56, Water science and technology library. Springer, Dordrecht
Zurück zum Zitat Salvadori G, De Michele C (2010) Multivariate multiparameter extreme value models and return periods: a copula approach. Water Resour Res 46(10):W10501CrossRef Salvadori G, De Michele C (2010) Multivariate multiparameter extreme value models and return periods: a copula approach. Water Resour Res 46(10):W10501CrossRef
Zurück zum Zitat Schulte M, Schumann A (2013) Flood risk mitigation by reservoirs—application of multivariate statistical methods for risk assessments downstream. Submitted: Proceedings of the Joint IAHS-IAPSO-IASPEI Assembly in Gothenburg, Sweden, 2013 IAHS red book Schulte M, Schumann A (2013) Flood risk mitigation by reservoirs—application of multivariate statistical methods for risk assessments downstream. Submitted: Proceedings of the Joint IAHS-IAPSO-IASPEI Assembly in Gothenburg, Sweden, 2013 IAHS red book
Zurück zum Zitat Schumann A (ed) (2008) Abschlussbericht des BMBF-Verbundforschungsvorhabens “Integrative Nutzung des technischen Hochwasserrückhalts in Poldern und Talsperren am Beispiel des Flussgebiets der Unstrut”, Schriftenreihe Hydrologie / Wasserwirtschaft. Ruhr-Universität Bochum, Bochum Schumann A (ed) (2008) Abschlussbericht des BMBF-Verbundforschungsvorhabens “Integrative Nutzung des technischen Hochwasserrückhalts in Poldern und Talsperren am Beispiel des Flussgebiets der Unstrut”, Schriftenreihe Hydrologie / Wasserwirtschaft. Ruhr-Universität Bochum, Bochum
Zurück zum Zitat Schumann A (ed) (2009) Verbundvorhaben “Entwicklung integrativer Lösungen für das operationelle Hochwassermanagement am Beispiel der Mulde”, Abschlussbericht, Schriftenreihe Hydrologie / Wasserwirtschaft. Ruhr-Universität Bochum, Bochum Schumann A (ed) (2009) Verbundvorhaben “Entwicklung integrativer Lösungen für das operationelle Hochwassermanagement am Beispiel der Mulde”, Abschlussbericht, Schriftenreihe Hydrologie / Wasserwirtschaft. Ruhr-Universität Bochum, Bochum
Zurück zum Zitat Serinaldi F, Grimaldi S (2007) Fully nested 3-copula: procedure and application on hydrological data. J Hydrol Eng ASCE 12(4):420–430CrossRef Serinaldi F, Grimaldi S (2007) Fully nested 3-copula: procedure and application on hydrological data. J Hydrol Eng ASCE 12(4):420–430CrossRef
Zurück zum Zitat Shiau JT, Wang HY, Tsai CT (2006) Bivariate frequency analysis of floods using copulas. JAWRA J Am Water Resour Assoc 42(6):1549–1564CrossRef Shiau JT, Wang HY, Tsai CT (2006) Bivariate frequency analysis of floods using copulas. JAWRA J Am Water Resour Assoc 42(6):1549–1564CrossRef
Zurück zum Zitat Sklar A (1959) Fonctions de reparttion à n dimensions et leura Marges. Publ Inst Stat Univ Paris 8:220–231 Sklar A (1959) Fonctions de reparttion à n dimensions et leura Marges. Publ Inst Stat Univ Paris 8:220–231
Zurück zum Zitat Wong G, Lambert M, Leonard M, Metcalfe A (2010) Drought analysis using trivariate copulas conditional on climatic states. J Hydrol Eng ASCE 15(2):129–141CrossRef Wong G, Lambert M, Leonard M, Metcalfe A (2010) Drought analysis using trivariate copulas conditional on climatic states. J Hydrol Eng ASCE 15(2):129–141CrossRef
Zurück zum Zitat Yue S (2001) A bivariate gamma distribution for use in multivariate flood frequency analysis. Hydrol Process 15(6):1033–1045CrossRef Yue S (2001) A bivariate gamma distribution for use in multivariate flood frequency analysis. Hydrol Process 15(6):1033–1045CrossRef
Zurück zum Zitat Yue S (2002) The bivariate lognormal distribution for describing joint statistical properties of a multivariate storm event. Environmetrics 13:811–819CrossRef Yue S (2002) The bivariate lognormal distribution for describing joint statistical properties of a multivariate storm event. Environmetrics 13:811–819CrossRef
Zurück zum Zitat Zhang L, Singh VP (2006) Bivariate flood frequency analysis using the copula method. J Hydrol Eng ASCE 11(2):150–164CrossRef Zhang L, Singh VP (2006) Bivariate flood frequency analysis using the copula method. J Hydrol Eng ASCE 11(2):150–164CrossRef
Zurück zum Zitat Zhang L, Singh VP (2007) Trivariate flood frequency analysis using the Gumbel–Hougaard copula. J Hydrol Eng ASCE 12(4):431–439CrossRef Zhang L, Singh VP (2007) Trivariate flood frequency analysis using the Gumbel–Hougaard copula. J Hydrol Eng ASCE 12(4):431–439CrossRef
Metadaten
Titel
Downstream-Directed Performance Assessment of Reservoirs in Multi-Tributary Catchments by Application of Multivariate Statistics
verfasst von
Markus Schulte
Andreas Schumann
Publikationsdatum
01.01.2015
Verlag
Springer Netherlands
Erschienen in
Water Resources Management / Ausgabe 2/2015
Print ISSN: 0920-4741
Elektronische ISSN: 1573-1650
DOI
https://doi.org/10.1007/s11269-014-0815-8

Weitere Artikel der Ausgabe 2/2015

Water Resources Management 2/2015 Zur Ausgabe