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Design flood estimation under uncertainty
Uppsala University, Disciplinary Domain of Science and Technology, Earth Sciences, Department of Earth Sciences. Uppsala University.ORCID iD: 0000-0002-5880-607X
2019 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [sv]

Att bestämma dimensionerande flöden, d.v.s. sannolikheten för att vat-tenföringen i ett vattendrag överskrider ett givet värde, är ett allmänt hydrologiskt problem som exempelvis används för att utvärdera över-svämningsrisker i vattendrag samt för att dimensionera hydrauliska kon-struktioner. Vanliga tillvägagångsätt för att bestämma dimensionerande flöden är baserade på: (i) hydrologiska metoder (t.ex. avrinningsmodel-lering), eller (ii) statistiska metoder (t.ex. anpassning av en sannolikhets-fördelning till en tidsserie med årliga vattenföringstoppar). I denna av-handling så jämförs dessa två tillvägagångssätt då olika osäkerhetskällor för dimensionerande flöden tillgodoses; valet av tillvägagångsätt, osä-kerhet i modellens uppbyggnad, osäkerheter i vattenföringsmätningar, samt mätfrekvens av dimensionerande flöden, begrundades i denna avhandling. Sannolikhetsfördelningen av vattenföringen i ett hypotetisk vattendrag antogs vara känt sedan tidigare; en uppsättning av virtuella experiment (’numeriska experiment där modellen antas vara sann och beskriva den modellerade processen korrekt’) utvecklades och tillämpa-des för båda tillvägagångssätten som utvärderades utifrån hur väl de uppskattade den sedan tidigare kända sannolikhetsfördelningen av vat-tenföringen. Resultaten visar att användningen av enklare avrinnings-modeller för att bestämma dimensionerande flöden har en lägre osäker-het än då statistiska metoder används, även för längre återkomstperi-oder. Båda tillvägagångsätten bör dock användas som komplement till varandra för att bestämma dimensionerande flöden, givet osäkerheten i båda.

Abstract [sv]

Att bestämma dimensionerande flöden, d.v.s. sannolikheten för att vat-tenföringen i ett vattendrag överskrider ett givet värde, är ett allmänt hydrologiskt problem som exempelvis används för att utvärdera över-svämningsrisker i vattendrag samt för att dimensionera hydrauliska kon-struktioner. Vanliga tillvägagångsätt för att bestämma dimensionerande flöden är baserade på: (i) hydrologiska metoder (t.ex. avrinningsmodel-lering), eller (ii) statistiska metoder (t.ex. anpassning av en sannolikhets-fördelning till en tidsserie med årliga vattenföringstoppar). I denna av-handling så jämförs dessa två tillvägagångssätt då olika osäkerhetskällor för dimensionerande flöden tillgodoses; valet av tillvägagångsätt, osä-kerhet i modellens uppbyggnad, osäkerheter i vattenföringsmätningar, samt mätfrekvens av dimensionerande flöden, begrundades i denna avhandling. Sannolikhetsfördelningen av vattenföringen i ett hypotetisk vattendrag antogs vara känt sedan tidigare; en uppsättning av virtuella experiment (’numeriska experiment där modellen antas vara sann och beskriva den modellerade processen korrekt’) utvecklades och tillämpa-des för båda tillvägagångssätten som utvärderades utifrån hur väl de uppskattade den sedan tidigare kända sannolikhetsfördelningen av vat-tenföringen. Resultaten visar att användningen av enklare avrinnings-modeller för att bestämma dimensionerande flöden har en lägre osäker-het än då statistiska metoder används, även för längre återkomstperi-oder. Båda tillvägagångsätten bör dock användas som komplement till varandra för att bestämma dimensionerande flöden, givet osäkerheten i båda.

Abstract [no]

A common task in hydrology is the estimation of the design flood, i.e. a value of river discharge corresponding to a given exceedance probability that is often expressed as a return period in years. Flood risk assessment, floodplain mapping and the design of hydraulic structures are a few examples of applications where estimates of design floods are required. Common approaches for estimating a design flood are based on: (i) hydrological methods such as continuous simulations with rainfall–runoff models, or (ii) statistical methods, such as the fitting of a probability distribution function to a record of annual maximum values. In this thesis, these alternative approaches are compared in view of the various sources of uncertainties affecting the estimation of the design flood. Since design floods are typically not known a priori, a series of virtual experiments was developed and implemented for both estimation methods, hence the magnitudes and frequencies of the design floods are known ab initio, and the quality of estimates (i.e., in terms of their accuracy and precision) were analysed. These virtual experiments are defined as ‘numerical experiments with a model considered as the truth and best understanding of the modelled processes’. This thesis looked at the influence of method of estimation, model structure uncertainty, errors in the flow data, and sampling on design flood estimation. The results show that design floods estimated by using a simple rainfall-runoff model have small uncertainties (i.e., variance of the errors) even for high return periods compared to statistical methods. Statistical methods performed better than the simple rainfall-runoff model in terms of median errors for high return periods, but their uncertainty (i.e. variance of the error) is larger. The thesis concludes that given the sources of uncertainty of statistical and hydrological methods, they both should be applied as complementary.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2019. , p. 47
Series
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 1832
Keywords [sv]
Dimensionerande flöden, osäkerheter, avrinningsmodellering, frekvens analys., Dimensionerande flöden, osäkerheter, avrinningsmodellering, frekvens analys.
Keywords [no]
Design flood, uncertainty, rainfall-runoff, frequency analysis.
National Category
Oceanography, Hydrology and Water Resources
Research subject
Hydrology
Identifiers
URN: urn:nbn:se:uu:diva-390362ISBN: 978-91-513-0706-0 (print)OAI: oai:DiVA.org:uu-390362DiVA, id: diva2:1341494
Public defence
2019-09-27, Hambergsalen Geocentrum, Villavägen 16, Uppsala, 10:00 (English)
Opponent
Supervisors
Available from: 2019-09-04 Created: 2019-08-08 Last updated: 2019-09-17
List of papers
1. Model averaging versus model selection: estimating design floods with uncertain river flow data
Open this publication in new window or tab >>Model averaging versus model selection: estimating design floods with uncertain river flow data
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2018 (English)In: Hydrological Sciences Journal, ISSN 0262-6667, E-ISSN 2150-3435, Vol. 63, no 13-14, p. 1913-1926Article in journal (Refereed) Published
Abstract [en]

This study compares model averaging and model selection methods to estimate design floods, while accounting for the observation error that is typically associated with annual maximum flow data. Model selection refers to methods where a single distribution function is chosen based on prior knowledge or by means of selection criteria. Model averaging refers to methods where the results of multiple distribution functions are combined. Numerical experiments were carried out by generating synthetic data using the Wakeby distribution function as the parent distribution. For this study, comparisons were made in terms of relative error and root mean square error (RMSE) referring to the 1-in-100 year flood. The experiments show that model averaging and model selection methods lead to similar results, especially when short samples are drawn from a highly asymmetric parent. Also, taking an arithmetic average of all design flood estimates gives estimated variances similar to those obtained with more complex weighted model averaging.

Keywords
model averaging, model selection, design flood, Akaike information criterion
National Category
Oceanography, Hydrology and Water Resources
Identifiers
urn:nbn:se:uu:diva-372899 (URN)10.1080/02626667.2018.1546389 (DOI)000453717400004 ()
Available from: 2019-01-14 Created: 2019-01-14 Last updated: 2019-08-09Bibliographically approved
2. Design Flood Estimation: Exploring the Potentials and Limitations of Two Alternative Approaches
Open this publication in new window or tab >>Design Flood Estimation: Exploring the Potentials and Limitations of Two Alternative Approaches
2019 (English)In: Water, E-ISSN 2073-4441, Vol. 11, no 4, article id 729Article in journal (Refereed) Published
Abstract [en]

The design of flood defence structures requires the estimation of flood water levels corresponding to a given probability of exceedance, or return period. In river flood management, this estimation is often done by statistically analysing the frequency of flood discharge peaks. This typically requires three main steps. First, direct measurements of annual maximum water levels at a river cross-section are converted into annual maximum flows by using a rating curve. Second, a probability distribution function is fitted to these annual maximum flows to derive the design peak flow corresponding to a given return period. Third, the design peak flow is used as input to a hydraulic model to derive the corresponding design flood level. Each of these three steps is associated with significant uncertainty that affects the accuracy of estimated design flood levels. Here, we propose a simulation framework to compare this common approach (based on the frequency analysis of annual maximum flows) with an alternative approach based on the frequency analysis of annual maximum water levels. The rationale behind this study is that high water levels are directly measured, and they often come along with less uncertainty than river flows. While this alternative approach is common for storm surge and coastal flooding, the potential of this approach in the context of river flooding has not been sufficiently explored. Our framework is based on the generation of synthetic data to perform a numerical experiment and compare the accuracy and precision of estimated design flood levels based on either annual maximum river flows (common approach) or annual maximum water levels (alternative approach).

Keywords
Design flood, Design flood levels
National Category
Water Engineering
Research subject
Hydrology
Identifiers
urn:nbn:se:uu:diva-390325 (URN)10.3390/w11040729 (DOI)000473105700099 ()
Projects
Hydraulic Engineering
Available from: 2019-08-08 Created: 2019-08-08 Last updated: 2019-09-09Bibliographically approved
3. A systematic comparison of statistical and hydrological methods for design flood estimation
Open this publication in new window or tab >>A systematic comparison of statistical and hydrological methods for design flood estimation
2019 (English)In: Hydrology Research, ISSN 1998-9563, E-ISSN 2224-7955Article in journal (Refereed) Submitted
Abstract [en]

We compare statistical and hydrological methods to estimate design floods by proposing a framework based on virtual reality. To illustrate the framework, we used probability model selection and model averaging as statistical methods, while continuous simulations made with a simple or a perfect rainfall-runoff model are used as hydrological methods. The results of our numerical exercise show that design floods estimated by using a simple rainfall-runoff model have small parameter uncertainty and limited errors, even for high return periods. Statistical methods perform better than the linear reservoir model in terms of median errors for high return periods, but their uncertainty (i.e. variance of the error) is larger. Moreover, selecting the best fitting probability distribution is associated with numerous outliers. On the contrary, using multiple probability distributions, regardless of their capability in fitting the data, leads to significantly less outliers, while keeping a similar accuracy. Thus, we find that, among the statistical methods, model averaging is a better option than model selection. Our results also show the relevance of the precautionary principle in design flood estimation, and thus help develop general recommendations for practitioners and experts involved in flood risk reduction.

National Category
Water Engineering
Research subject
Hydrology
Identifiers
urn:nbn:se:uu:diva-390357 (URN)
Available from: 2019-08-08 Created: 2019-08-08 Last updated: 2019-08-09
4. The effect of model averaging versus model selection in design flood estimates – a case study for the Tiber River, in Italy
Open this publication in new window or tab >>The effect of model averaging versus model selection in design flood estimates – a case study for the Tiber River, in Italy
(English)Manuscript (preprint) (Other academic)
Abstract [en]

This study aims at comparing model averaging to model selection techniques in design flood estimation. Model selection refers to the selection of  a single best distribution function by means of a suitable selection criterion, such as, Akaike Information Criterion (AIC). Model averaging refers to the modelling approach where the estimates from a number of probability models are combined together as a weighted average. We investigated two methods of model averaging. First, weighted model averaging (WMA) were differential weights are assigned to estimates based on different distribution functions with the distribution when the best fit having the highest weight. Second, equal weighting or model mean (MM) which is similar to taking the arithmetic mean of design flood estimates from all the distributions considered. MS and MA (which includes WMA and MM) were implemented using an exceptionally long time series of annual maximum flows recorded at the Tiber River in Rome, Italy.  For this study, comparisons we refer to the 1-in-100 year flood, i.e. the quantile of annual maximum flows corresponding to a 1% exceedance probability, widely used as a reference in flood risk management. The results suggest that MA performs better than MS. Specifically, MM performs better that WMA even though the latter can be judged as to be consistent with logical reasoning.

Keywords
Design flood
National Category
Water Engineering
Research subject
Hydrology
Identifiers
urn:nbn:se:uu:diva-390355 (URN)
Available from: 2019-08-08 Created: 2019-08-08 Last updated: 2019-08-09

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