A simple raster-based model for floodplain inundation and uncertainty assessment
Case study city Kulmbach
Wissenschaftliche Arbeit zur Erlangung des Grades M.Sc. an der Ingenieurfakultät Bau Geo Umwelt der Technischen Universität München.
Betreut von M.Sc. Punit Kumar Bhola und Dr. Jorge Leandro Lehrstuhl für Hydrologie und Flussgebietsmanagement
Eingereicht von Saskia Ederle Bischoffstraße 2 80937 München Eingereicht am München, den 28.04.2017
Abstract
In this study, simple 2D hydrodynamical flood models for the rivers in the area of the city of Kulmbach are developed. Kulmbach has experienced several floods over the years. Flood mitigation measures have been built in early years, so major damage can be prevented. But still, reoccurring flood events lead to flooding of infrastructures, such as traffic routes and land used by agriculture. To develop the models, HEC-RAS 2D and TELEMAC 2D are applied. As input data, a digital elevation model to extract the topography of the floodplain and rivers is used. In addition, boundary conditions are gained from recorded hydrographs and water levels. Both models used the HQ100, a flood event statistically happening once every 100 years, as discharge for the computation. To check validity of the results, the simulation results are mapped and compared to official flood risk maps. For the HEC-RAS model, additionally an uncertainty analysis is performed. The method used is called GLUE, which is based on the Monte Carlo Simulation (MCS). The results of the MCS are evaluated by comparing the simulated values with the observations using a likelihood measure. As calibration data, recorded values of the water levels at eight locations in Kulmbach of the January 2011 flood event are used. The results of both models showed satisfactory inundation areas in terms of water level and size of flooded area. The uncertainty assessment showed, that the HEC-RAS 2D model reacts sensitive to changes of roughness parameters (Manning’s n). A detailed calibration of further input parameters has been excluded and should be subject of further studies.
Kurzfassung
In dieser Arbeit werden 2D hydrodynamische Hochwassermodelle für die Flüsse im Bereich der Stadt Kulmbach entwickelt. Kulmbach hat im Laufe der Jahre mehrere Überschwemmungen erlebt, weshalb bereits in frühen Jahren Hochwasserminderungsmaßnahmen gebaut wurden, so dass große Schäden vermieden werden konnten. Dennoch führen wiederkehrende Hochwasserereignisse zu Überschwemmungen von Infrastrukturen, wie zum Beispiel Verkehrswegen und Flächen, die von der Landwirtschaft genutzt werden. Zur Entwicklung der Modelle werden HEC-RAS 2D und TELEMAC 2D angewendet. Als Eingangsinformation wird ein digitales Höhenmodell verwendet, um die Topographie der Überschwemmungsflächen und der Flüsse zu nutzen. Darüber hinaus werden die Randbedingungen aus aufgezeichneten Abflussganglinien und Wasserständen gewonnen. Beide Modelle nutzten das HQ100, ein Hochwasserereignis, das statisch einmal alle 100 Jahre stattfindet, als Abfluss für die Berechnung. Um die Aussagekraft der Ergebnisse zu überprüfen, werden die Simulationsergebnisse graphisch in einer Karte dargestellt und mit den offiziellen Hochwasserrisikokarten verglichen. Für das HEC-RAS-Modell wird zusätzlich eine Unsicherheitsanalyse durchgeführt. Die verwendete Methode heißt GLUE, und basiert auf der Monte Carlo Simulation (MCS). Die Ergebnisse der MCS werden durch Vergleich der simulierten Werte mit den Beobachtungen, mit einem Wahrscheinlichkeitsmaß bewertet. Als Kalibrierungsdaten werden aufgezeichnete Werte der Wasserstände an acht Standorten in Kulmbach des Hochwasserereignisses im Januar 2011, verwendet. Die Ergebnisse beider Modelle zeigten zufriedenstellende Ergebnisse der Überschwemmungsgebiete in Bezug auf den Wasserstand und die Größe der überschwemmten Fläche. Die Unsicherheitsbeurteilung zeigte, dass das HEC-RAS 2D Modell empfindlich auf Änderungen der Rauheitsparameter (Mannings n) reagiert. Eine detaillierte Kalibrierung weiterer Eingabeparameter wurde ausgeschlossen und sollte Gegenstand weiterer Studien sein.
Acknowledgement
I want to thank Professor Disse for giving me the opportunity to write my Master’s thesis on this interesting topic at his chair. Further, I want to thank all members of the Chair of Hydrology and River Basin Management for the pleasant working atmosphere. Finally, my special thanks go to Punit Kumar Bhola for supervising me during my Master’s thesis. Additionally, I want to thank the Wasserwirtschaftsamt Hof for the assistance in my search for complementary data, and especially Michael Stocker for sending me the data needed for calibration.
Danksagung
Ich möchte Professor Disse dafür danken, dass er mir die Gelegenheit gegeben hat, meine Masterarbeit über dieses interessante Thema an seinem Lehrstuhl zu schreiben. Weiterhin möchte ich mich bei allen Mitgliedern des Lehrstuhls für Hydrologie und Flussgebietsmanagement für die angenehme Arbeitsatmosphäre bedanken. Insbesondere geht mein Dank an Punit Kumar Bhola, der mich während meiner Masterarbeit betreut hat.
Darüber hinaus möchte ich dem Wasserwirtschaftsamt Hof, für die Unterstützung bei der Suche nach ergänzenden Daten, und vor allem Michael Stocker, für die Zusendung der für die Kalibrierung benötigten Daten, danken.
Content
Abstract I
Kurzfassung II
Acknowledgement III
Danksagung III
Content V
1 Introduction 1
1.1 Motivation ...... 1
1.2 Outline of the thesis ...... 2
2 Literature review 3
2.1 Modeling fundamentals ...... 3
2.2 Data ...... 3
2.3 Comparison of different raster based models ...... 4
2.3.1 Models based on full Shallow Water Equations ...... 4
2.3.2 Models based on 2D Diffusion Wave ...... 6
2.3.3 Selection of models ...... 7
3 Model approach 8
3.1 Hydrodynamic Modeling...... 8
3.1.1 Mass Conservation (Continuity) Equation ...... 9
3.1.2 Momentum Conservation Equation ...... 9
3.1.3 Bottom Friction ...... 9
3.2 Numerical Discretization ...... 10
3.2.1 Finite difference method ...... 10
3.2.2 Finite volume method ...... 11
3.2.3 Finite element method ...... 11
3.3 HEC-RAS ...... 12
3.3.1 Computational Mesh ...... 13
3.3.2 Limitations of HEC-RAS 2D ...... 13
3.4 TELEMAC 2D ...... 14
3.4.1 Special characteristics of TELEMAC 2D ...... 14
3.4.2 Limitations of TELEMAC 2D ...... 15
3.5 Additional software tools ...... 16
4 Description of Study Area 17
4.1 Kulmbach ...... 17
4.2 Flood events and flood protection measures ...... 18
4.3 Characteristics of the study area...... 19
5 Model Development 24
5.1 HEC-RAS Development ...... 24
5.1.1 Grid generation ...... 26
5.1.2 Boundary conditions ...... 28
5.1.3 Unsteady Flow simulation ...... 28
5.1.4 Post-processing ...... 28
5.2 TELEMAC 2D Development ...... 28
5.2.1 Blue Kenue ...... 30
5.2.2 Fudaa-Prepro ...... 32
5.2.3 Post-processing ...... 32
6 Uncertainty Assessment 33
6.1 Uncertainties in floodplain inundation modeling ...... 33
6.2 Generalized Likelihood Uncertainty Estimation (GLUE) ...... 34
6.3 Implementation ...... 35
6.3.1 Generation of roughness parameters ...... 35
6.3.2 Inflow data and observations...... 39
6.3.3 Execution of MCS ...... 41
6.3.4 GLUEWIN ...... 41
7 Results 43
7.1 Flood hazard maps ...... 43
7.2 Model Performances ...... 47
7.3 Uncertainty Analysis ...... 48
7.4 Limitations ...... 52
8 Conclusion and Outlook 55
8.1 Conclusion ...... 55
8.2 Outlook ...... 55
9 Literature 57
10 Appendix I 60
11 Appendix II 61
12 Appendix III 63
13 Appendix IV 68
14 Appendix V 71
15 Appendix VI 72
List of Figures 80
List of Tables 83
1 Introduction
1.1 Motivation
Bavaria has a long record of flood events with the first records dating back to the 11th century. A regular observation of water levels started in the 19th century (Bayerisches Landesamt für Umwelt). During the last 30 years, Germany suffered from a major flood event almost every year. Compared to the far more frequently occurring storm events, floods are only the second most common incidents due to weather. Reoccurring floods are still dangerous events, which have the power to destroy whole regions, weaken infrastructure and sometimes even claim fatalities. According to Munich RE, floods cause the largest economic losses (NatCatSERVICE, 2016). The most recent flood event took place in June 2016 when several regions in Germany suffered from severe damages due to heavy rain. Lower Bavaria was hit particularly hard, where a flood event in the district of Rottal-Inn claimed seven lives and left a damage of hundreds of millions of Euro (tagesschau.de, 2016).
This thesis focuses on Kulmbach, a small city in the north of Bavaria, Germany. The city invests more than 11.5 Mio Euro in the restructuring of already existing flood protection measures to mitigate impacts of future events (Wasserwirtschaftsamt Hof, 2016). Although, the effects in Kulmbach have been small compared to large floods that spread out through Europe, there were still severe impacts. Especially infrastructure got damaged during reoccurring flood events. Often bridges and riverside roads cannot be passed because of persistent inundation. Flood modelling is an important part of natural risk management. Hydrodynamic flow models are used to describe channel flow and floodplain routing, in order to evaluate risks of flood inundation. These models can vary from a very simple representation of the water surface to complex three-dimensional solutions of the Navier-Stokes equations. Depending on computational power and available calculation time, several different models provide satisfying results. Regarding the creation of flood inundation maps for real time forecast applications, fast and reliable models are necessary. Therefore, the idea of using a raster-based model is supported. However, these models have uncertainties from all variables involved, e.g., input data, model parameters and also the modelling approaches. The quantification of these uncertainties is achieved in a calibration process. During calibration, the difference between observed data and the model output is minimized and afterwards checked in validation.
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The Chair of Hydrology and River Basin Management of the Technische Universität München, currently works on the project “FloodEvac”, which is a bilateral research collaboration between Germany and India. The sub project “Flood Modeling and Flooded Areas” focuses on the development of a management tool for flood prediction in catchments of medium sizes. This allows for a speed up of future flood warnings. One part of the project is the creation of a flood model for the city Kulmbach and the surrounding region (Universität der Bundeswehr München).
The objective of this master thesis is the development of a raster-based model for floodplain inundation for the city Kulmbach, which is then followed by an uncertainty assessment. Since there are large numbers of hydraulic flood models available, the best fitting model needs to be found by analyzing several types. In this thesis two models were developed and subsequently the inundation area is compared. Afterwards the models were calibrated and post-processed. Finally, an uncertainty analysis was performed.
1.2 Outline of the thesis
Chapter 2 describes the literature review. It includes a description of the basic principles used within the study, e.g., the basic theory of hydrodynamical flood models and all input data needed for the setup of these models. The chapter ends with a comprehensive review of several 2D models to choose the perfect model. Chapter 3 gives a detailed explanation of the model approach. The important hydrodynamical equations are discussed and numerical solving schemes are introduced. Additionally, special features of both HEC-RAS and TELEMAC models are presented. Chapter 4 provides an overview of the study area in Kulmbach and hydrological information about the rivers and characteristics of land use are given. Additionally, background knowledge about historical flood events is outlined. Chapter 5 describes the development of the HEC-RAS 2D and TELEMAC 2D models. The relevant features of the used simulation software and additional software tools are introduced. Chapter 6 deals with the uncertainty analysis. Possible uncertainties in flood inundation modelling are described. Furthermore, the chosen method to determine uncertainties in the model is introduced and the implementation for the HEC-RAS model is presented. The results from the simulations and the uncertainty analysis are presented and discussed in Chapter 7. Finally, in Chapter 8 conclusions and final considerations are presented. 2 Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here.
2 Literature review
2.1 Modeling fundamentals
Scientific models are used to represent natural processes in a simplified form. The simplification and underlying assumptions depend on the problem definition as well as on the spatial resolution. Therefore, a large number of varied models for floodplain inundation is available. Hence, the selection of a suitable model is based on several questions. The hydrodynamical modeling can be differentiated between one-dimensional and two- dimensional models. In 1D modeling the mean flow velocity is calculated only in flow direction. In case of floodplain modeling this means that the floodplain flow is a part of the calculation but is assumed to be parallel to the main channel. 2D models are based on the depth averaged shallow water equations. This approach neglects the flow velocities in vertical direction and is suitable for study areas that have small vertical expansion compared to the horizontal expansion. Therefore, 2D modeling is the preferred choice for urban areas (Néelz, Pender, Great Britain - Environment Agency, & Great Britain - Department for Environment Food Rural Affairs, 2009). In this study the two-dimensional modeling approach is used. A more precise explanation of the theory is provided in Chapter 3.
2.2 Data
All 2D hydrodynamic models for flood inundation need similar input data. The floodplain topography is provided by a Digital Elevation Model (DEM). The DEM represents the surface of a terrain and is obtained using remote sensing techniques. From this DEM, the river network can be extracted, which includes other important elements, such as cross sections and river banks, that provide the channel width and bed elevations. Also, the course of the river and junctions to all sub-reaches are gained from the DEM. The data is used, to generate the calculation grid. The channel and floodplain friction is defined by the roughness coefficients, also called Manning’s n. These coefficients are usually estimated, depending on the vegetation and soil properties of the study area. For unsteady flow simulations, boundary conditions are needed for all inflow and outflow boundaries. For this, usually flow hydrographs or water levels from measurement records and estimations of the energy line gradient are used.
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2.3 Comparison of different raster based models
At the beginning, a suitable model needs to be chosen. Therefore, a wide literature research was carried out to compare eleven available 2D models. In addition to several benchmarking reports from the Environment Agency, which are sponsored by the British Department for Environment, Food and Rural Affairs, (e.g “Desktop review of 2D hydraulic modelling packages” (Néelz et al., 2009), “Benchmarking the latest generation of 2D hydraulic modelling packages” (Néelz & Pender, 2013)), a large variety of scientific articles (the most applicable are “A simple raster-based model for flood inundation simulation” (Bates & De Roo, 2000) and “Evaluation of 1D and 2D numerical models for predicting river flood inundation” (Horritt & Bates, 2002)) have been used to find appropriate models. The research is complemented by information from the user manuals of each model and the model’s websites. In the following subchapters, the evaluated models are briefly introduced and the results of the literature research are presented. An overview table of all models (Table 6), explained in the next subchapters, is added in the Appendix.
2.3.1 Models based on full Shallow Water Equations The Shallow Water Equations (SWE) are simplifications of the Navier-Stokes equation. Based on the assumption, that vertical momentum is small, compared to the horizontal momentum, the equation can be integrated over the depth. This assumption is met for long and shallow waves, which is the case for most rivers. This results in a two-dimensional set of equations (Chow, 1959). A more detailed explanation of this topic is given in Chapter 3.1. iRIC Nays 2DH iRIC Nays 2DH is a freeware model developed by the Foundation of Hokkaido River Disaster Prevention Research Center. The software can use parallel computing by OpenMP. A graphical user interface (GUI) is available which also provides the possibility to animate results. The model solves the full SWE (Shimizu & Takebayashi, 2014), (iRIC Project, 2010).
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TUFLOW
TUFLOW is a commercial software developed by BMT WBM. There are two different modules available: TUFLOW (Classic) uses an implicit solution, so no parallelization is possible. The GPU Module uses the parallel computing ability of GPUs. The model can be used with SMS or GIS software and solves the full SWE. A Wiki and several tutorial models are provided by the developer (BMT WBM, 2016), (BMT WBM, 2015).
MIKE 21 FM
MIKE 21 FM is a commercial model developed by MIKE Powered by DHI. The model engines run on multiple cores and are available in two parallelized versions: Open MP and MPI. A GUI is integrated and the model solves the shallow water equations averaged in depth. The discretization method is the finite volume method with an unstructured mesh. An Online Help system provides support (MIKE Powerred by DHI, 2015), (MIKE Powerred by DHI).
TELEMAC 2D
The TELEMAC-MASCARET hydro-informatics project was launched in 1987 by the National Hydraulics and Environment Laboratory of the Research and Development Directorate of the French Electricity Board (EDF-R&D). Since 2009 TELEMAC- MASCARET is a freeware platform managed by a consortium of users and developers. TELEMAC-MASCARET provides several solvers in the field of free-surface flow. In this study, the hydrodynamical component for the modelling of two-dimensional flows, called TELEMAC 2D, is used. The model can be used with several GUIs (Fudaa-Prepro and Blue Kenue; both freeware). It solves the shallow water equations averaged in depth. An advantage is the existence of an Online-Wiki and a Forum (Lang, Desombre, Ata, Goeury, & Hervouet, 2014).
InfoWorks 2D
InfoWorks 2D is a commercial software developed by Innovyze, which runs on multiple cores. A GUI is integrated, that allows the creation of triangular 2D meshes and fully animated flood maps. The model solves the full SWE (Innovyze, 2011).
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JFLOW
JFlow is a commercial model developed by JBA Consulting. Since 2010 JFlow SWE which uses the full SWE is available. The code executes on multiple GPU devices and a GIS user interface was released recently (JBA, 2014).
FloodArea HPC
FloodArea HPC is commercial software developed by geomer GmbH. The model is completely integrated in ArcGIS, which makes modelling and postprocessing easy and fast. The calculation is based on a hydrodynamic approach using the Manning-Strickler formula to calculate the discharge volume (geomer GmbH, 2016a), (geomer GmbH, 2016b).
HYDRO_AS-2D
HYDRO_AS-2D is a commercial model developed by Dr.-Ing. M. Nujic. The software is based on the shallow water equations averaged in depth. The discretization method is the finite volume method with an unstructured mesh consisting of triangular and rectangular elements (Nujić, 2014).
2.3.2 Models based on 2D Diffusion Wave 2D Diffusion Wave is a further simplification of the SWE: It is based on the assumption, that inertial terms can be neglected since gravitational terms and the bottom friction are dominant in some shallow flows. Therefore, the equations can be reduced to an even easier form (Chow, 1959). A more detailed explanation is given in Chapter 3.3 .
LISFLOOD-FP
LISFLOOD-FP is a freeware model developed as a joint effort by the University of Bristol and the EU Joint Research Centre. If available, it uses multiple CPU cores for multi- processing. The model doesn’t provide any GUI, which makes using a command line interface necessary. The model solves an approximation to the 2D diffusion wave using a normalized flow in x- and y-directions. It is one of the most popular models, has been tested by various researchers and has also been evaluated in urban areas. Therefore, lots of literature can be found. However, LISFLOOD-FP is limited to grids of 10^6 elements, which limits its applicability for certain cases (Bates, Trigg, Neal, & Dabrowa, 2013), (Bates). 6 Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here.
HEC-RAS
HEC-RAS is a freeware model developed by the Hydrologic Engineering Center of the U.S. Army Corps of Engineers. The 2D module was developed to support parallel processing. HEC-RAS 2D computations can use as many CPU cores as available. It includes an easy-to-use GUI, and has the options to run the 2D Diffusion Wave equations, or the full SWE. 2D Diffusion Wave equation is faster and more stable. Additionally, lots of literature is available for HEC-RAS (US Army Corps of Engineers, 2016b).
P-DWave
P-DWave is a numerical model that solves the 2D Diffusion Wave approximation of the shallow water equations. It makes use of multi-processors. The discretization method is an explicit first order finite volume scheme as detailed in Leandro et. all (Leandro, Chen, & Schumann, 2014).
2.3.3 Selection of models The appropriate models for the Kulmbach environment, were chosen based on the usability (e.g. parallel processing, integrated GUI), and the reliability, that they can be used as a proven tool. Because of the diverse literature and previous tests, HEC-RAS and TELEMAC 2D seem to be the best choice out of the freeware models. Both models are open source software and have graphical user interfaces available for pre- and post- processing which simplify the usage. The models offer two different approaches, which allow for an interesting comparison. HEC-RAS uses the 2D Diffusion Wave Approximation, whereas TELEMAC 2D solves the full Shallow Water Equations. The functionality of both models and mathematical theory are explained in the following Chapters 3 and 5. Error! Reference source not found. in the Appendix, highlights the chosen models.
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3 Model approach
This chapter describes the theoretical background of flood modelling. The most important hydrodynamical equations, including the mass conservation equation and the momentum conservation equation, are introduced. The numerical solution methods for the differential equations are summarized. Finally, the theoretical background and special features of both hydrodynamical models, used in this study, are presented in detail.
3.1 Hydrodynamic Modeling
The first mathematical description of unsteady flow in open channels was developed by Barre de Saint Venant in 1871 (Litrico & Fromion, 2009). The so-called Saint Venant equations are derived from the Navier-Stokes equations integrated in depth. The equations consist of the continuity or mass conservation equation and the momentum conservation equation. The principle of the continuity equation is that mass is always conserved in fluid systems. That means, that the inflow at a control volume equals the outflow, if there are no additional inflows or outflows. The principle of the conservation of momentum states that the net rate of momentum that enters a control volume plus the sum of all external forces are equal to the rate of accumulation of momentum. The external forces are the forces resulting from pressure, gravity and friction. The velocity of open channel flow is derived from the Manning’s equation on the basis of the Darcy-Weisbach equation for hydraulic head losses due to wall friction (Chow, 1959). In the following, the most important theories necessary for the understanding and interpretation of the hydraulic modeling are introduced.
Figure 1: Water surface elevation (US Army Corps of Engineers, 2016a)
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In the following equations, the water surface elevation H is given by the bottom surface elevation z and the water depth h (see Equation 1 (US Army Corps of Engineers, 2016a)). Figure 1 shows this relation schematically.
H(x, y, t) = z(x, y) + h(x, y, t) 1
3.1.1 Mass Conservation (Continuity) Equation The law of mass conservation is defined as:
휕퐻 휕(ℎ푢) 휕(ℎ푣) + + + 푞 = 0 2 휕푡 휕푥 휕푦 where t is the time, u and v are the components of the velocity in x- and y-direction, and q is a term describing sources or sinks of the flux.
The Continuity equation can be transformed into its vector form:
휕퐻 + ∇ ∙ ℎ푉 + 푞 = 0 3 휕푡 where V=(u,v) is the velocity vector (US Army Corps of Engineers, 2016a).
3.1.2 Momentum Conservation Equation The law of momentum conservation is defined as:
휕푉 + 푉 ∙ ∇푉 = −푔∇퐻 + 푣 ∇2푉 − 푐 푉 + 푓푘×푉 4 휕푡 푡 푓 where g is the gravitational acceleration, vt is the horizontal eddy viscosity coefficient, cf is the bottom friction coefficient, f is the Coriolis parameter and k is the unit vector in the vertical direction (US Army Corps of Engineers, 2016a).
Each term describes a physical equivalent. From left to right, the terms describe unsteady acceleration, convective acceleration, barotropic pressure, eddy diffusion, bottom friction, and Coriolis force.
3.1.3 Bottom Friction To describe the bottom friction, the Chézy equation is used. The Chézy coefficient is approximated by the Gauckler-Manning-Strickler equation or short, Manning’s equation.
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The Manning’s equation is an empirical formula for estimating the channel flow velocity. Using the Chézy equation and Manning’s equation the bottom friction can be calculated by:
푛2푔|푉| 푐 = 5 푓 푅4⁄3 where n is the empirically derived roughness coefficient, called Manning’s n, and R is the hydraulic radius (US Army Corps of Engineers, 2016a).
3.2 Numerical Discretization
Numerical analysis uses approximations of mathematical equations to solve complex processes, such as differential equations, which cannot be solved analytically. A discretization of the study area is needed to transfer the continuous area into discrete counterparts, that can then be solved numerically. The finer this discretization is, the more exact the solution will be. However, the computational effort increases simultaneously. There are several numerical discretization methods available. The most known techniques are the Finite Difference Method, the Finite Volume Method and the Finite Element Method. Those methods are often-used standards for computational fluid mechanics (Martin, 2011).
Independently from the discretization, there are two different solution methods:
• Explicit methods use the current state of the system to calculate the next step. The equation is therefore simpler but needs smaller time steps.
• Implicit methods use a system of equations, that consists of both, the current state and the next step, that needs to be solved. For this method, the time steps can be larger, but the solution of the equation systems is more complex (Martin, 2011).
3.2.1 Finite difference method The numerical solution of the finite difference method approximates derivatives on the mesh nodes with different quotients, that means, they are basically considered as the difference of two quantities. The differential equation is approximated by a system of difference equations. Given two adjacent cells with water surface elevations H1 and H2, the derivative in the direction of n’ is approximated by 10 Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here.
휕퐻 퐻 − 퐻 ≈ 2 1 6 휕푛′ 훥푛′ with 훥푛′ being the distance between the cell centers (US Army Corps of Engineers, 2016a). The finite difference method is very effective for structured grids, whereas unstructured grids highly raise the complexity of the method.
3.2.2 Finite volume method The numerical solution of the finite volume method requires the definition of so-called control volumes. These control volumes are defined around each mesh node, with the center of gravity being the node itself. The solution is obtained by calculating the numerical flow at each border of the control volume (US Army Corps of Engineers, 2016a). In Figure 2 the blue nodes and lines represent the computational mesh. The grey control volumes are defined by the red dashed lines and crosses. The arrow nk’ represents the numerical flow. The finite volume method is in general more complex than the finite difference method, but it benefits from the usability with arbitrary meshes.
Figure 2: Exemplary control volumes for the computational mesh (US Army Corps of Engineers, 2016a)
3.2.3 Finite element method The finite element method (FEM) approximates the solution of partial differential equations by dividing a large problem in small parts, which are called finite elements. The area is divided into a specific number of non-overlapping elements with finite sizes, so the actual size stays relevant. Inside of these elements the so-called trial functions, which are usually polynomials, are defined. Together with boundary and initial conditions, the trial functions are inserted into the differential equation to be solved. The resulting system of equations Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. 11
can then be solved numerically (Prof. Dr.-Ing. habil. Duddeck, 2012). Compared to the FVM, the complexity of the FEM is comparable. However, the FEM has the advantage to be more adaptable to every type of geometry.
3.3 HEC-RAS
The HEC-RAS Hydraulic Reference Manual gives a very detailed overview of all equations, underlying theory and complete solution algorithms. The main features of HEC- RAS are described in this study to help with understanding
HEC-RAS uses an implicit finite difference solution algorithm to discretize time derivatives and hybrid approximations, combining finite differences and finite volumes, to discretize spatial derivatives. The implicit method allows for larger computational time steps compared to an explicit method. HEC-RAS solves either the 2D Saint Venant equations or the 2D Diffusion Wave equations, which can be chosen by the user. Since the 2D Diffusion Wave equations allow for a faster calculation and have greater stability properties due to the less complex numerical schemes, this study uses the 2D Diffusion Wave equations.
For the calculation of 2D Diffusive Wave Approximation it is assumed, that the barotropic pressure term and the bottom friction term are dominant. Therefore, the terms for unsteady acceleration, convective acceleration, eddy diffusion and the Coriolis Effect of the momentum equation can be neglected. Simplifying Equation 4 results in this easier form of the momentum equation:
푛2|푉|푉
4⁄3 = −∇퐻 7 (푅(퐻))
Additionally, the system of equations used for the Diffusion Wave Approximation can be simplified to a one equation form. By substituting the simplified momentum equation (Equation 6) in the mass conservation equation (Equation 3), the classical differential form of the Diffusion Wave Approximation of the Shallow Water equations can be written as
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휕퐻 − 푉 ∙ 훽∇퐻 + 푞 = 0 8 휕푡
5⁄3 (푅(퐻)) where: 훽 = . 푛|∇퐻|1⁄2
3.3.1 Computational Mesh Topographic data can be generated in very high resolution via modern remote sensing techniques such as LIDAR survey. However, numerical models can only provide fast and accurate results up to a certain amount of computational cells. Therefore, the high resolution data can only be used as a relatively coarse mesh where lot of data is neglected. To solve this problem HEC-RAS uses the sub-grid bathymetry approach. The computational grid cells include additional information about the underlying topography to the geometric and hydraulic property tables. Details concerning hydraulic radius, volume and cross sectional area are pre-computed from the fine bathymetry. Therefore, computational cells do not necessarily have a flat bottom, and cell faces do not have to be a straight line with a single slope. This allows the model, to have a quite coarse computational grid compared to the fine terrain data (see Figure 3).
Figure 3: 1m DEM and computational grid
The outer boundary of the mesh is defined by a polygon. Inside of this polygon the computational mesh is assembled with a mixture of cell shapes and sizes that can be triangles, rectangles or even elements with up to eight edges (US Army Corps of Engineers, 2016a).
3.3.2 Limitations of HEC-RAS 2D Currently, no bridge modeling capabilities are implemented to the two-dimensional modeling of HEC-RAS. Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. 13
Boundary conditions can only be placed at the boundary of the 2D flow area. Therefore, it’s complicated and time intensive to implement flows starting in the middle of the mesh. This limitation can be circumvented by adding slots to the mesh.
Figure 4: Definition of internal inflow boundary conditions in HEC-RAS 2D
3.4 TELEMAC 2D
3.4.1 Special characteristics of TELEMAC 2D TELEMAC 2D solves the full Saint-Venant shallow water equations averaged in depth for an unstructured, triangular mesh. Equations 9 - 11 show the mass conservation and momentum conservation that TELEMAC 2D solves simultaneously. A complete documentation of equations and theory is available in the Principle Manual (Lang et al., 2014).
Mass conservation equation:
휕ℎ + 푉 ∙ ∇(ℎ) + ℎ푑𝑖푣(푢⃗ ) = 푞 9 휕푡
Momentum conservation along x:
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휕푢 휕퐻 1 + 푢⃗ ∇⃗⃗ (푢) = −푔 + 푆 + 푑𝑖푣(ℎ푣 ∇⃗⃗ 푢) 10 휕푡 휕푥 푥 ℎ 푡
Momentum conservation along y:
휕푣 휕퐻 1 + 푢⃗ ∇⃗⃗ (푣) = −푔 + 푆 + 푑𝑖푣(ℎ푣 ∇⃗⃗ 푣) 11 휕푡 휕푦 푦 ℎ 푡
For these equations the following applies:
푣푡 is the momentum diffusion coefficient, 푆푥 and 푆푦 are source or sink terms in dynamic equations, which stand for the bottom friction, the Coriolis force, influences of wind, and atmospheric pressure (Lang et al., 2014), (TELEMAC-MASCARET, 2001).
The variables h, and the horizontal components of the depth-averaged velocity u and v are solved in two steps using the method of fractional steps. The first step calculates the advection terms, which treats the transport of the physical variables h, u, and v. This is solved with the characteristics method. In the second step, all remaining terms are considered. This includes propagation, diffusion, and the source terms, such as bottom friction or wind stress. Here the finite element method is used to solve the differential equations with a discretization of time (TELEMAC-MASCARET, 2001).
The mesh consists of triangular elements, but can also work with quadrilateral elements. Additionally, TELEMAC has also functions of tracer conservation.
3.4.2 Limitations of TELEMAC 2D Boundary conditions can only be placed on borders of the mesh. To solve this problem, TELEMAC allows the existence of single holes in the mesh (compare Figure 5:).
Another problem that may occur during the mesh preparation is, that TELEMAC can only handle coordinates with up to 7 digits. If the Gauß-Krüger coordinate system is used, the coordinates are most likely to have more than 7 digits. This issue can be addressed by changing the coordinate origin and thus, shifting the hole mesh closer to zero, so that the coordinate value decreases. If additional geographic information is used during the post- processing, the shift needs to be reversed to match the original coordinates.
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Figure 5: Definition of internal inflow boundary conditions in TELEMAC 2D
3.5 Additional software tools
For the preparation of maps and geographic information (e.g. the DEM, and postprocessing of the simulation results) the geographic information system ArcGIS is used, which is developed by Esri. For this study, especially the application ArcMap is beneficial for converting data into desired formats (Esri, 2017).
Since TELEMAC doesn’t have a GUI implemented, it is convenient to use additional software for the model development. In this study, Blue Kenue and Fudaa-Prepro are used for the generation of the mesh and the preparation of the model file. Both tools are explained in more detail in chapter 5.2.
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4 Description of Study Area
In the following, a detailed overview of the study area is given. The description includes the geographic location, and an introduction to the climatic, topographic and hydrologic characteristics of the region. Highlighting several past flood events and flood protection measures demonstrate the necessity of flood modelling.
4.1 Kulmbach
Kulmbach is a city in the middle of the Bavarian district Upper Franconia. It is located about 20 km north of Bayreuth and covers an area of 92.77 km². The population size is a total of about 26,500 in 2016 with a population density of 285/km² (Stadt Kulmbach, 2016).
On the western part of the city the river Main results from its two headstreams, the White Main (Weißer Main) and the Red Main (Roter Main). The Red Main, with a length of 71.8 km, originates about 10 km south of Bayreuth in the area of the Franconian Switzerland. The White Main originates in the Fichtelgebirge and has a length of 45.3 km. Although the White Main is much shorter, it has a higher discharge compared to the Red Main (Regierung von Unterfranken, 2013). On the eastern part of Kulmbach the White Main is joined by the Schorgast. In Table 1 the four main rivers are analyzed, with regard to length, differences in height, size of the catchment area and discharge data, such as the 100-year return period (HQ100) and the average discharge MQ.
White Main Red Main Schorgast Main
Max. Elevation [m] 887 581 534 298
Min. Elevation [m] 298 298 308 82
Height difference 589 283 226 216 [m] Length [km] 53 76 19.8 472.4
Catchment [km²] 637 519 248 27,292
HQ100 [m³/s] 123 200 106 357 MQ [m³/s] 4.09 4.59 3.66 14.5 Table 1: Main rivers in study area (Regierung von Unterfranken, 2013)
Inside of the city center the White Main is joined by the Kohlenbach and the Kinzelsbach from the left. Both waters are piped through the city center of Kulmbach. Coming from North, the Dobrach with a length of 10 km also joines the White Main from the right. These three rivers are relatively small, and therefore not added to the analysis in Table 1. Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. 17
However, especially Kohlenbach and Kinzelsbach still contribute to floodings of the White Main in the city area and need to be considered in inundation models of Kulmbach.
The geology is characterized by a scarpland consisting of Bunter sandstone, Muschelkalk (Middle Trias), Keuper as wells as Black, Brown, and White Jurassic (Regierung von Unterfranken). This alternating arrangement of aquifers and aquicludes shape the discharge characteristics of the area.
The land use of the catchment area of the Main is dominated by forest and agricultural use. About 60 % of the subarea Upper Main is covered with forest. About 34 % is used agriculturally for farming.
4.2 Flood events and flood protection measures
In the 1930s a flood channel was built north of the city center. To continue the operation of the water mills the streams haven’t been changed completely. Two weir systems controlled the stream, so that only a maximum of 6 m³/s could flow through the original path of the White Main, which passes through the city center of Kulmbach. The rest flows through the flood channel. In the 1980s the weir systems were rebuilt so that the passability of the weir system for fish and other aquatic life has been improved.
In 2009 it was decided to renew the flood protection measures. The stability and the height of the dikes weren’t considered sufficient anymore, and also the straight path of the flood channel needed improvements (Wasserwirtschaftsamt Hof, 2016). In September 2016, the construction work on the river bed were completed (Bayerischer Runkfunk, 2016). In 2014 it was decided to renovate the original path of the White Main as well. From today’s perspective, the channel isn’t sufficient anymore to drain floods. In March 2017, the construction works started (Wasserwirtschaftsamt Hof, 2016).
Consequences of a recent flood event in January 2011 can be seen in Figure 6 and Figure 7. It was one of the biggest floods in the past few years and affected the whole area of Upper Frankonia. Streets and large amounts of agricultural land were flooded, which made them unusable.
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Analyzing the largest recorded flood events, it is significant, that most of them took place in recent years. This illustrates that there is an urgent need of the renewal and maintenance of the existing flood measures.
Figure 6: Photograph of Theodor-Heuss-Allee in Kulmbach during the flood event of January 2011 (Source: Wasserwirtschaftsamt Hof)
Figure 7: Photograph of flooded agricultural land during the flood event of January 2011 (Source: Wasserwirtschaftsamt Hof)
4.3 Characteristics of the study area
The area used in this study only covers a small part of the whole Bavarian Main catchment area. The extend of the study area and the position of all rivers can be seen in Figure 8. The outlined area includes a large part of the city and stretches east and west of the city Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. 19
to cover the possible inundation areas. The study area has a total size of 11.49 km². The complete length of the river network is 102.98 km. The lengths of the river sections used for this study can be collected from Table 2.
River Name Length [km] Branch Main 3.2 Schorgast 3.3 Roter Main 4.9 Upper Main 9.1
Table 2: Lengths of the river sections
Figure 8: Location and outline of study area in red. Rivers are plotted in blue. The dashed arrows represent smaller tributaries. The flood channel is displayed striped. The inset shows the approximate location of Kulmbach in Germany.
To illustrate size proportions in Figure 9 , two cross sections of the White Main are plotted. Graph (a) displays a cross section of the flood channel. Here the measures built for flood protection are clearly apparent. On both sides of the channel the dikes and space for additional water retention are visible. These measures enlarge the extent of the river to a width of 45 m and a depth of 4 m. Graph (b) shows the cross section, right after the White Main is joined by the Schorgast.
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Outside of the city, the White Main has a natural course. The river has a width of about 20 m and a depth of approximately 3 m.
Figure 9: Cross sections at two positions of the White Main and the flood channel
In Figure 10 a topographic map based on the elevations of the DEM of the study area is shown. The inclination extends from the highest point in the East to the lowest point at the outflow boundary of the Main in the West.
Figure 10: Topographical map of study area including cross-section A - A
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The study area has an elongated, very narrow shape. From East to West, the area extends across more than 10 km. From North to South, the area is only 2 km wide. With a maximum elevation of 315 m and a minimum of 290 m, the inclination of the study area, with a value of 2.1 ‰, is very flat. Compare Figure 11 to see the consistent inclination of the study area from East to West. The exact location of the cross section A – A can be seen in Figure 10.
320 315 310 305 300
Elevation[m] 295 290 285 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 Length [m]
Figure 11: East-West Cross Section A - A
The land use of the study area varies significantly with the majority being agricultural and urban areas. 62 % of the area are used for agriculture and grassland. The urban area covers 26 %, including industrial use, residential area, and infrastructure like roads and railway tracks. Water bodies take up 7 % space and forest forms only a very small part of about 5%. See Figure 12 for a land use map of the Kulmbach area.
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Figure 12: Land cover of the study area Kulmbach
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5 Model Development
This chapter describes the development of both models by explaining the main features of each modelling software. The most important step for the model set up is the grid generation. Both models have different pre-processing tools to develop the grid. Location and type of the boundary conditions are defined in a second step. Finally, the model results are post-processed.
5.1 HEC-RAS Development
All tools necessary for pre-processing, running the simulation and post-processing are implemented in HEC-RAS. In this study HEC-RAS version 5.0.3 is used and a typical view of the GUI is shown in Figure 14.
A HEC-RAS 2D model consists of three parts (US Army Corps of Engineers, 2016b):
- The geometry data (.g##), which stores all information of the terrain, the computational grid and additional break lines. From this, HEC-RAS additionally calculates the geometry hdf file (.g##.hdf), which stores the information in HDF5 format, - The unsteady flow file (.u##) stores hydrographs and initial conditions. If a hot start is desired, here also the path of the hot start file (.p##.rst) is specified, - The Plan file (.p##) defines each simulation. It contains a list of all input files and all simulation options.
Another important tool is the so-called RAS Mapper. It can be used to import the terrain data, the land cover data and visualizes the results. HEC-RAS stores information about layers, projections and basic settings for the RAS Mapper in the .rasmapper file. Most of the output is stored in the plan hdf file (.p##.hdf). Besides, e.g., water levels and velocities, all the geometry input is saved in the HDF5 format.
Each simulation saves the computational messages from the computation window in a log file (.comp_msgs.txt), so that they can be checked for debugging. Additionally a detailed computational level output file (.hyd##) can be generated. Both files can be helpful for troubleshooting or finding stability problems.
A flowchart showing the most important files can be seen in Figure 13.
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Unsteady Hot start file Flow file .p##.rst .u01
Plan hdf file .p01.hdf
Plan file Project file .p01 .prj
Computational level output .hyd01
Geometry Geometry hdf file file .g01 .g01.hdf
Figure 13: Flowchart of HEC-RAS 2D
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Figure 14: Screenshot of the software HEC-RAS including the Geometric Editor and the finished computation mesh
5.1.1 Grid generation The base of the grid generation in HEC-RAS is the terrain data which is imported to the RAS Mapper. The RAS Mapper can import terrain data, in the floating point grid format (*.flt), GeoTIFF (*.tif), or in several other formats. Terrain data of the study area was available in the vector-based triangular irregular networks (TIN) format. Therefore, it needed to be converted into the GeoTIFF format. ArcMap was used for this conversion. The new TIN data set could keep all relevant details about elevation and hydraulic properties.
The grid itself has been created in the Geometry data editor. The outlines of the computational grid are defined by a polygon that defines a 2D Flow Area. In this area, the HEC-RAS two-dimensional flow computation is performed. To optimize the mesh, break lines along the river channels are added to ensure that the flow stays in the channel until 26 Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here.
it is high enough to overtop the banks. Break lines force the mesh to align along these lines.
Because of the Sub-grid bathymetry approach explained in chapter 3, the grid size can be chosen relatively coarse. Some tests were performed with a grid size of 10 m, with the main advantage of a faster calculation time. But due to better accuracy in the resulting flood maps a grid size of 5 m has been chosen for the final calculations.
After importing land cover data to the RAS Mapper, the Manning’s n values can be edited before adding them to the mesh.
The boundary condition lines need to be added, before the grid generation can be finished. These lines define the location of each upstream and downstream boundary condition.
Figure 15: Close-up view of HEC-RAS mesh including the boundary condition line
The finished mesh contains 424775 cells with an average cell size of 24.82 m². The minimum cell size is 6.79 m² and the maximum cell size is 59.77 m². In Figure 15 a close- up view of the finished mesh can be seen. Most of the mesh consists of even squares. At the borders of the mesh, and due to the refinement of the mesh close to the river banks the size and shape of the cells varies, which is clearly visible along the bank lines. The distribution of cells along the break lines of the bank lines can be further refined. On the right edge of the mesh, the boundary condition line for the definition of the Red Main inflow is represented graphically by a black line with red dots. Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. 27
5.1.2 Boundary conditions For this simulation, upstream boundary conditions are defined with a flow hydrograph combined with the Energy Slope. Since the hydrograph at the downstream end of the study area was unknown, the normal depth was used as downstream boundary condition. Manning’s equation calculates the water level at the last grid cell from an entered value for the energy slope. Since the energy slope is often unknown, it can be approximated by the value for the channel slope in the area of the downstream boundary.
As inflow hydrograph, the 100 years return flow (HQ100) was used. To avoid instabilities during the calculation a base flow of approximately 10 % of the HQ100 was used as a hot- start before the calculation.
5.1.3 Unsteady Flow simulation To start an unsteady flow simulation several parameters need to be defined upfront, e.g., the simulation time and computation settings such as the computation interval in a so- called unsteady flow plan.
5.1.4 Post-processing Simulation results in .hdf format are automatically added to the RAS Mapper. All output parameters (e.g., depth, velocity, and water surface elevation) can be mapped in individual layers. Depending on the output interval chosen in the unsteady flow plan, the changes over time are displayed as well. Single time steps, or the maximum value can be exported as raster data. This data can be used to create additional flood maps in ArcGIS.
5.2 TELEMAC 2D Development
Several graphic user interfaces are available for the pre- and post-processing. Blue Kenue and Fudaa-Prepro are used in this case and explained in the following subchapters 5.2.1 and 5.2.2.
The TELEMAC 2D model needs several input files. The most important files are the following:
- The Steering file (.cas) is the main part of the TELEMAC simulation. It defines all simulation parameters and the names of further input data, - The Geometry file (.slf) contains all information concerning the calculation mesh, - The Boundary condition file (.cli) defines location and types of boundary conditions,
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- One text file each that defines all flow hydrographs (.liq) and all stage-discharge curves (.txt)
The output is saved in a result file (.slf), which enables the post-processing in, e.g., Blue Kenue. All different output information is saved to a new layer, which can be visualized for detailed analysis.
A flowchart with the most important files is shown in Figure 16.
Boundary conditions file .cli
Stage discharge curve .txt Steering Output file .cas .slf Inflow hydrograph .liq
Geometry file .slf
Figure 16: Flowchart of TELEMAC 2D
The main component, that is necessary to execute the model, is the so called steering file (‘cas’ file), which is a text file, that is edited by the user to assign key variables and activate various features. The steering file indicates the names of the grid file, the boundary condition file, the TELEMAC version number and the number of parallel processors. In addition, most of the steering file contains information about the simulation parameters. These are for example, the computation time-step, the number of iterations, the choice of output variables to be saved to the results file, the turbulence scheme, and the choice and settings for the numerical solvers. The steering can be created manually or with the help of tools like Fudaa-Prepro (Cerema, 2005) (see chapter 5.2.2). An example for the steering file used in this study can be found in the Appendix.
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The simulation can be started in a command window. First the directory needs to be changed to the folder, where all the input files and the steering files are stored. Next the simulation is started by entering “telemac2d.py steeringfile.cas”. In this study TELEMAC v7p1 is used.
5.2.1 Blue Kenue Blue Kenue is a software tool, developed by the Canadian Hydraulics Centre of the National Research Council Canada. It is used for data preparation, analysis, and visualization for hydraulic models. Blue Kenue supports several data types as input, including common GIS data formats and allows the import of various mesh types. In addition to the possibility of importing already existing computational meshes, Blue Kenue also generates rectangular and triangular meshes (Canadian Hydraulics Centre, 2016). Data can be visualized in 2D and 3D view. This is useful for editing the mesh and helps to identify possible outliers of the data. As input the software uses points, lines, and even other grids as sub-meshes. The generated mesh has a uniform grid size that can be chosen by the user. By integrating sub-meshes, the resulting computational mesh can consist of different grid sizes, so that individual areas can be represented more detailed. This can be used, by generating individual sub-meshes for the river bed, that should have finer grid sizes compared to the floodplains. It also offers the opportunity to include “hard points” and “break lines” that are incorporated to the mesh as fixed component, in order to further refine the mesh. A typical view of the interface of Blue Kenue, which was used in Version 3.3.4, is given in Figure 17.
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Figure 17: Graphical interface of Blue Kenue
The finished mesh, used for the simulation in TELEMAC 2D contains 54,808 nodes and 107,491 triangular elements. The element size varies from a minimum of 0.63 m² up to 232.16 m². Figure 18 shows a close-up view for a fraction of the finished mesh. To emphasize height differences, the z-scale is plotted with a magnification factor of 2.
Figure 18: Close-up of mesh generated in Blue Kenue in 3D view
Besides the computational mesh, and the preparation of a boundary conditions file, which contains the location and the type of the boundary condition, Blue Kenue can also be used for post-processing of the results.
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5.2.2 Fudaa-Prepro Fudaa-Prepro is an interface that helps editing the steering file, and modifying the input parameters. It is developed by the “Direction technique Eau, mer et fleuves” of Cerema (France). Cerema works closely with the French Ministry for Sustainable Development and Transport and the Ministry of Urban Planning. All relevant files that include the grid and the boundary conditions file generated in Blue Kenue can be imported. Additionally, parameters can be entered and the steering file is created automatically. Fudaa-Prepro can also be used to analyze results and has the possibility to export files to GIS format (Cerema, 2005). This tool was used to assemble the main structure of the steering file, while further editing was done manually. In this study Fudaa-Prepro Version 1.2.0 is used.
5.2.3 Post-processing The results of the TELEMAC 2D calculation can easily be imported to Blue Kenue. Here the several layers can be added to 2D or 3D views to analyze water levels and velocities. Additionally, the temporal development can be animated. To create inundation maps, GeoTIFF files can be imported to Blue Kenue and added to the view as background maps. These results can be viewed in ArcGIS by exporting iso-lines for desired depths (e.g. as shapefiles) or converting the data to ASCII files.
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6 Uncertainty Assessment
In this chapter uncertainties in flood inundation models are described. These comprise mostly input data, used for the model generation. Additionally, the so called Generalized Likelihood Uncertainty Estimation (GLUE), used for the uncertainty assessment, is explained. GLUE is based on Monte Carlo simulations using different parameter values as input. The objective of GLUE is to find a set of parameters that provide realistic results for the computation.
6.1 Uncertainties in floodplain inundation modeling
The accuracy of flood inundation models is determined by the uncertainty that correlates with all data and input parameters. Many modeling processes contribute to those error sources. Starting with simplifications to physical processes that are assumed, to keep the computational effort low, also the numerical solution is based on approximations. However, input data contributes the largest source of uncertainty. The uncertainties of topographic data are depending on the accuracy of the used DEM. With increasing accuracy and resolution of topographic data, the uncertainties get lower. Though, due to the parametrization process used for the calculation of the models, the computation mesh is lowered in resolution, which increases uncertainties again. Hydrological data is used for boundary and initial conditions. They give major information about the physics. Data for these values can come from rainfall-runoff modelling or, in this case, from hydrometric measurements of the catchment area. Gauges installed at the upstream and downstream ends of the study area record flow and water level data. Accuracy of water level measurements are typically at an error of about 1 cm. Whereas the variance of measured discharge is ± 5 % (Keith Beven, 2014). Roughness parametrization is a very important parameter of hydraulic models. They represent land use types, which, themselves, are indicate conditions for flow velocity and run-off behavior. The roughness coefficient should also be distinguished between the river bed and floodplains. And of course, scenarios like dam breaches are also possibilities that contribute to the long list of uncertainties. Many studies focused on the uncertainty analysis of floodplain modeling, with the aim to eliminate those potential sources of errors. However, there is no chance to eliminate all uncertainties. But by performing calibration and uncertainty analysis, the influence of uncertainties can be taken to a minimum.
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Several studies dealt with the effects of roughness coefficients during the calibration process. Here a special focus lies on “Uncertainty Quantification in Flood Inundation Modelling- Applying the GLUE Methodology” by Bhola, P. K. (Bhola, Prof. Dr. Disse, Kammereck, & Haas, 2016) and “Spatially distributed observations in constraining inundation modelling uncertainties” by Werner, M. (Werner, Blazkova, & Petr, 2005)). Both studies showed, that the roughness coefficients contribute to the highest source of uncertainties.
6.2 Generalized Likelihood Uncertainty Estimation (GLUE)
Calibration is required to identify parameters, so that the model is able to reproduce observed events. This typically considers roughness coefficients for floodplain and water bodies (Keith Beven, 2014). Calibration does not rely on physical theories, but only compares the outcome of the model with real observations. Therefore, the parameters, identified by the calibration of the model, may not necessarily have physical interpretation. A principle that often occurs within open systems is called equifinality: The concept is based on the fact, that a given end state can be achieved by many different approaches. Numerical models have a very large number of degrees of freedom. Therefore, there are a lot of different possible combinations of input parameters that can lead to equally good results. The possibility of equifinality has led to the development of several sensibility analysis methods. The method used in this study is called the Generalized Likelihood Uncertainty Estimation (GLUE), which has been introduced by Beven and Binley in 1992 (K. Beven & Binley, 1992). It is a popular method to describe uncertainties in flood inundation calculation and mapping (Pappenberger, Beven, Horritt, & Blazkova, 2005). The procedure of GLUE is based on Monte Carlo Simulations. The procedure of the Monte Carlo Simulation consists of three simple steps. A number of n samples are generated randomly from the distribution of input variables X, where n equals the number of iterations.
Then the function g(xi) is evaluated n times for each sample value xi, which generates n output values. To conclude the method, the output is analyzed statistically (Prof. Dr. Straub, 2013). GLUE uses the results of these simulations to determine both the uncertainty in model predictions (Uncertainty Analysis) and the input variables, that contribute to this uncertainty (Global Sensitivity Analysis) (Ratto & Saltelli, 2001).
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In case of the flood inundation modeling, this is implemented by performing a large number of model runs, each with a different set of parameters. The exact number of required model runs can’t be determined exactly beforehand, but it needs to be large enough to cover all possibilities. The parameters are chosen randomly from specified distributions, which is explained in more detail in the next chapter. At certain points the calculated water levels are extracted as output and used for further analysis. In GLUE, outputs from the model runs are weighted by a likelihood measure using the Bayes equation, to describe how good the result matches observed data. The sensitivity analysis identifies sets with almost zero likelihood and classifies them as non-behavioral, which results in a rejection of those sets. The likelihood of the parameter set xi, given the observation as result is written as
푛표푏푠 2 (푦̂(풙 ) − 푦(푗)) 퐿(풙 |풚) = 푒푥푝 (− ∑ 풊 ) 12 풊 푠푡푑(풚̂ − 푦(푗)) 푗=1 where 풙풊 is the ith element of the sample of the model input factors, 풚 =
(1) (푗) (푛표푏푠) (푦 , … , 푦 , … , 푦 ) is the vector of observations of the scalar variable y, 푛표푏푠 is the (푗) number of observations, 푦̂(풙풊) is the i-th model run and 푠푡푑(풚̂ − 푦 ) is the weighting factor in the sum of square errors, equal to the standard deviation of the model errors with respect to the j-th observation (Ratto & Saltelli, 2001). In general, the higher the likelihood measure indicates, the better is a fit between the model output and the observed data. Then, a threshold for the likelihood measure classifies the model outputs as behavioral, which means the results are accepted, or nonbehavioral.
6.3 Implementation
To implement the GLUE process, the following steps need to be performed. The first two steps of the Monte Carlo Simulation are performed separately. Parameter sets are created randomly and for each set a HEC-RAS calculation is started automatically in a loop. For the last step of the Monte Carlo Simulation, the analysis of the results, a software called GLUEWIN is used. This tool uses the parameters and the output of the MCS to compare it with observational data. It also creates plots to make the analysis of different parameters easy.
6.3.1 Generation of roughness parameters As explained in Chapter 6.1, in this study the most uncertain parameter is the roughness parameter. In principle, the roughness parameter can be distinguished between the Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. 35
roughness of the river bed and of the floodplains. To differentiate further, floodplains are also split into five sub-categories. The predominant land cover type in the study area is grassland, which includes agricultural use. Also, urban areas cover a large part. This is divided into houses, streets and areas of mixed use. The large range of roughness values require this separation. However, since houses shouldn’t be flooded, the roughness value remains at 푛 = 1. The last land cover category is forest. For each category, a likelihood distribution is defined. Types and parameters of the distributions are based on values of the roughness parameters, that are commonly used. Based on the real roughness coefficients in the area and commonly used values for each land use type, a range of values is defined. Since Manning’s n can only be determined empirically, it’s challenging to find perfect values. Many studies address the problem of determining roughness parameters close to reality. Out of this large comprehensive offer of studies, a few were taken to find out suitable values. To identify sensible ranges, especially “Open-Channel Hydraulics” by Chow 1959 (Chow, 1959) and several reports of the USGS (Zhang et al., 2012), (Arcement Jr., Schneider, & USGS) were used, since they provide a complete summary of possible roughness values. The ranges, composed from those studies, can be found in Table 3.
As likelihood distribution, a continuous uniform distribution is used. Uniform distributions are naturally found in the allocation of human populations and plants. Furthermore, agricultural practices create uniform distributions in areas where naturally different land uses and thus, distributions exist. Therefore, the Uniform distribution is suitable for the representation of the roughness coefficients for flood plains. For the continuous uniform distribution, each value is equally likely. The distribution is defined for the interval [a, b], where a is the minimum and b is the maximum. Hence, the selected ranges for each land use type can be used as parameters for the uniform distributions.
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Land type Range
Channel and water 0.015 - 0.15 Agricultural 0.025 - 0.11 Forest 0.11 - 0.2 Streets 0.012 - 0.02 Urban areas of mixed use 0.04 - 0.08
Table 3: Uniform distributions of roughness parameters
From the ranges given in Table 3, a total of 1000 parameter sets were generated. In Figure 19 the frequency distributions of the random values for each land use type is displayed in form of histograms. Each range of values is divided into ten intervals of equal size. Due to the uniform distribution, the frequency in each interval is approximately equal.
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Figure 19: Histograms of generated random values for Manning’s n
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6.3.2 Inflow data and observations As calibration data, a flood event of January 2011 in Kulmbach is used. Intense rainfall and snow melting in the Fichtelgebirge caused floods in several rivers of Upper Frankonia. Within five days two peak discharges were recorded. The first one occurred on the 9th January, the second one was measured five days later and caused even higher water levels and discharges. Especially agricultural land and partly also traffic routes were flooded, but no serious damage was done. In Kulmbach the dam was likely to collapse due to the huge masses of water. But because of measures from the water management, the weir could be opened which led to a great improvement of the situation (Wasserwirtschaftsamt Hof, 2017). The Wasserwirtschaftsamt Hof carried out data collection during the flooding and recorded water levels at eight locations in the city. The locations can be seen in Figure 20 and related values of the recorded water levels are shown in Table 4.
Figure 20: Locations of calibration data
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Point number Water level [m]
1 304.06 2 303.35 3 302.02 4 301.99 5 297.12 6 301.35 7 300.06 8 300.04
Table 4: Water levels used for calibration
Corresponding discharge values for the event were gathered from the Gewässerkundlicher Dienst Bayern. Starting on 5th January plots for the three main gages are shown in Figure 21. On 14th January 2011, the maximum of the flood wave occurred for all three gages. The gage Unterzettlitz of the Red Main had a maximum discharge of 252 m³/s. Kauerndorf, which lies at the Schorgast achieved a maximum of 92.5 m³/s and at the gage Ködnitz of the White Main a maximum of 75.3 m³/s was recorded.
300
250
200
150
100 Discharge Discharge [m²/s]
50
0 1/5/2011 0:00 1/8/2011 0:00 1/11/2011 0:00 1/14/2011 0:00 1/17/2011 0:00 1/20/2011 0:00
Ködnitz Kauerndorf Unterzettlitz
Figure 21: Discharge for the January 2011 event
To keep the simulation time low, not the whole flood event was simulated. Flow hydrographs with a duration of 25 hours have been created. According to the recorded discharge data from the Gewässerkundlicher Dienst Bayern, the maximum values for each river are used to compute values of a normal distribution (see Figure 22).
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Inflow hydrograph 250.000
200.000
150.000 Unterzettlitz 100.000 Ködnitz
Discharge Discharge [m³/s] Kauerndorf
50.000
0.000 0 4 8 12 16 20 24 Time [h]
Figure 22: Inflow hydrographs used for uncertainty analysis
6.3.3 Execution of MCS To run 1000 simulations of HEC-RAS in a loop, the input files need to be updated with new values outside of the software. The roughness parameters are stored in the geometry file and can be changed in the text-file easily. For each parameter set an individual geometry file is generated which can be moved to the HEC-RAS project folder for each simulation.
The simulations are automatized using a loop with Microsoft Visual Basic for Applications in Excel. For each run, the geometry file in the HEC-RAS plan is updated to change the input parameters. Afterwards the HEC-RAS plan is executed. To extract the relevant water levels and velocities from the output files, a MATLAB function is implemented to the loop. This function imports the “.hdf” output-file and extracts all relevant water level data and velocities to an ASCII format. The whole code to perform the simulations and generate the geometry files from a template is added to the appendix.
6.3.4 GLUEWIN GLUEWIN is a tool developed by the Joint Research Centre (JRC) which works as the science and knowledge service of the European Commission. It is used for analyzing the output of Monte Carlo runs and compares it to empirical observations of the model output. GLUEWIN makes use of a combination of GLUE and Global Sensitivity Analysis techniques.
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The software allows to define specific likelihood weight for model runs and uses those, for the uncertainty estimation of model predictions. Furthermore, the analysis can be performed with the use of observational data. Several posterior distributions are compiled such as marginal cumulative distributions to perform a sensitivity analysis, or the possibility to analyze the covariance structure. GLUEWIN also provides visual analysis of the results with the help of scatter plots and cumulative distributions.
To start the analysis of GLUEWIN several input files need to be generated. These include
- a matrix for the input parameters of each MCS run, - a matrix for the model outputs for each MCS run, - a matrix with observation values.
Each file contains of a list of basic parameters, e.g., the number of MCS runs, the parameter names, and number of parameters. This is followed by the corresponding data. GLUEWIN automatically calculates likelihood measures based on mean square errors and absolute errors.
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7 Results
7.1 Flood hazard maps
To verify the modelling results, flood hazard maps were created and compared to the official flood hazard maps of the Hochwasserrisikomanagement-Plan of the Bavarian governments. The maps are based on a discharge that occurs statistically once in 100 years, is the so-called the HQ100. Flood hazard maps show flooded areas and the depths of water levels. They form an important basis to assess risks in the case of a flood event. The maps are prepared, so that hazards are recognized fast and easy. They also serve as evaluation basis for newly planned flood mitigation measures.
Based on hydrographs for the HQ100 event, unsteady-flow simulations were performed. In Figure 23 all discharge data used for the calculation and the locations of the boundary conditions can be seen.
Figure 23: Boundary conditions of flood hazard map run
To reduce the calculation time, a hot start file was created. The hot start file stores the results from a previous run. In this run the initial conditions are set, and a constant discharge is used to create a water surface elevation to use as true starting depth.
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In Figure 24 the results of the HEC-RAS calculation are shown. The top figure shows the inundated area calculated with HEC-RAS. To make the comparison with the official flood risk maps easy, the scale and the colours of the water levels were adjusted. In general, size and form of the inundated area matches very well. Also, the depths appear to be similar to the original data. Since there is no exact data available, both assessments can only be estimated from visual interpretation. The size of inundated area calculated by HEC-RAS is about 5.6 km². However, a more detailed view brings out differences. Especially in the area between the flood channel and the original path of the White Main, the HEC-RAS model computes almost no flooding. The flood risk maps display quite large inundation area on both sides of the White Main. Here the HEC-RAS model clearly underestimates the flooding.
In Figure 25 the results of the TELEMAC 2D calculation are shown. Here likewise, the top figure shows the inundated area of the TELEMAC 2D simulation. It is plotted in the same colour scheme as the HEC-RAS results, to make it comparable. Overall, the shape of the inundation area calculated by TELEMAC 2D also is quite similar to the original map. The size of inundated area calculated by TELEMAC 2D is about 6.0 km². Compared to the size of HEC-RAS, the area is a lot larger. These differences can be seen in Figure 24 and Figure 25 as well. On the right edge of the plotted map, the TELEMAC model overestimates the inundation area right of the White Main a lot. This error could be fixed by a further improvement of the computational mesh in this area. Additionally, TELEMAC has the same underestimation of the area between the flood channel and White Main in the city center as the HEC-RAS model.
Additionally, further tests with changed inflow conditions were made. The simulation of an event with increased inflow for Kinzelsbach and Kohlenbach was tested to optimize the inundation area between the original course of the White Main and the flood channel. However, the flooded area only changed negligible. Boundary conditions and a flood hazard map of this test can be found in the Appendix.
Results of the 10 m grid of the HEC-RAS model can be found in the Appendix as well. This shows, that larger grid sizes lead to more imprecise results.
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Figure 24: HEC-RAS Result for HQ100 and official flood hazard map (Regierung von Unterfranken, Regierung von Oberfranken, Regierung von Mittelfranken, & Regierung der Oberpfalz)
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Figure 25: TELEMAC 2D Result for HQ100 and official flood hazard map (Regierung von Unterfranken et al.)
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7.2 Model Performances
Due to a very simple handling the model setup in HEC-RAS is easy. All functions that are necessary are implemented to the software, therefore no additional programs are needed. The implementation of the TELEMAC model is more demanding. Despite the fact, that additional software for the creation of the mesh is needed, also the preparation of input data, such as boundary conditions and input parameters is more complex. Nevertheless, both models result in satisfactory outcomes. The mapping of flood inundation is close to the original inundation area.
It is assumed, that a further refinement of the meshes in both models, will result in even better outputs for small scale. But a smaller computational mesh, results in increased simulation time, simultaneously, which will increase computational effort greatly for large scale models.
For this study area, the HEC-RAS 2D model, needs a time step of 20 seconds to work best. To create the desired flood hazard maps, a total simulation time of about 24 hours is necessary, which equals about 86,000 time steps. The TELEMAC 2D has an optimal time step of 1 second. A total of 35,000 time steps, which equals about 9.7 hours were sufficient to create the flood hazard maps. The duration of the simulation time for both models is similar.
To perform the 1,000 HEC-RAS simulations for the uncertainty analysis, the MCS was executed in parallel on several computers. Thus, the correlation between the computational complexity and different computer setups (processors, number of cores and clock frequencies) can be analyzed. In general, a higher number of cores results in faster calculation as the simulation allows for parallelization. However, a quadruplication of the number of cores doesn’t lead necessarily to a quadruplication of computation speed. This effect is related to a scalability of less then 100 %. Therefore, the calculation time is also highly affected by the clock frequency. Additionally, as a lot of data is read and written during a simulation run, the speed of the data storage is an important factor. The use of fast solid state drives (SSD) is beneficial and accelerates the calculation. These observations correspond to experiences made by other users of HEC-RAS (Goodell & Brunner, 2016). The TELEMAC 2D model wasn’t tested as thoroughly, therefore no exact statements about the simulation time and correlation to the computer hardware can be made.
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7.3 Uncertainty Analysis
The analysis of results of the uncertainty analysis was performed in GLUEWIN.
For all observation points, the sensitivity of the five different roughness parameters is similar. The water level shows almost no sensitivity to forest, streets, and urban area. Whereas the water level reacts strongly to changes in roughness of waterbody and agricultural area. This is probably due to the fact, that waterbodies and agricultural areas are the predominant type of land use. The inundated areas predominantly affect agricultural land. Furthermore, almost all observation points are located in the river or at the river banks. Therefore, impacts due to streets and urban areas are small.
In Figure 26, scatter plots of the results for observation point 1, depending on the roughness parameters, are shown. The blue dots are the simulation results and the line of red dots marks the observation data. The parameters Forest, Street and Urban Area show no correlation. Waterbody and Agriculture are related to the water level. Generally speaking, the lower the Manning’s n, the lower the water level. Further scatter plots for all other seven observation points can be found in the Appendix.
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Figure 26: Scatter Plots of Manning’s n and water level at location 1
Figure 27 shows the uncertainty analysis of the output at location 1 given the likelihood measure of location 1. The density plot illustrates the likelihood by using the discrete model outcomes, and plots them in a normalized histogram, which consists of 20 bars. The height of each bar, shows the proportion of results, that fall into this interval. The vertical red line shows the mean, and the vertical green line marks the observed value. The cumulative density plot, corresponds to the integral of the density plot. The red x marks indicate the 5 % and 95 % quantiles. The blue line shows the mean value and the green line corresponds to the observation.
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Figure 27: Uncertainty plots of Likelihood Function Graphs from GLUEWIN at location 1
Table 5 shows a statistical analysis of the MCS results. For each observation point the result range gives minimum and maximum value of computed results. The median gives the value, for which 50 % of the results are situated above and below this number each. By comparing the 5 % quantile, 95 % quantile and the variance, statements about the scattering of the result values can be made. The smaller the variance, the smaller is the
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spreading around the median. Observation point 6 has the lowest spreading, whereas point 1 and 2 show quite large spreadings. The result range spreads over more than 2 m.
Observatio Result range Median 5 % quantile 95 % quantile Variance n point
1 302.87 – 305.04 304.03 303.22 304.89 0.28 2 302.36 – 304.23 303.34 302.47 304.13 0.28 3 300.96 – 302.96 302.19 301.38 302.85 0.23 4 301.68 – 302.86 302.17 301.68 302.76 0.13 5 296.11 - 297.98 297.41 296.93 297.87 0.10 6 300.95 – 301.81 301.47 301.03 301.76 0.05 7 298.63 – 300.53 300.01 299.01 300.42 0.17 8 298.56 – 300.51 299.98 298.98 300.41 0.17
Table 5: Statistical Analysis of GLUE
In Figure 25 uncertainties for all 8 observation points are plotted. Each column plots the mean value of model results, which is represented by the blue bar, and additionally displays the 5 % and 95 % quantiles. The observation value is added as an orange point. Here, the statistical analysis is plotted descriptively. The smaller the range between 95 % quantile and 5 % quantile, the less variation is in the simulation results. At the locations of observation point 5 and 6, the changes of roughness parameters show the least sensitivity to the results. Whereas point 1, 2 and 3 show quite large variation in water level.
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Figure 28: Uncertainties of water level
In Figure 29 a comparison of the 5 % quantile, mean, and 95 % quantile run is shown. The inundated area of the mean run is quite comparable to the results of the HEC-RAS run, tested with the HQ100 (compare Figure 24). The 5 % quantile underestimates the inundated area clearly. Whereas the 95 % quantile overestimates the water levels.
7.4 Limitations
To conclude the outcomes of this study it is also important to address the major limitations. Most of the problems result from assumptions that were made to simplify the calculations.
A reduction of the grid size of both models can strongly improve the accuracy of the results. However, this is associated with a higher computational effort, and thus longer computation time.
Additionally, no structures have been implemented to the models. Most bridges are represented by the DTM sufficiently, but an optimization of the mesh is beneficial to accurate results.
A calibration of roughness parameters of the TELEMAC 2D model also could improve results and make the models more comparable.
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Figure 29: Comparison of results for different parameter sets that correspond to 5 % quantile, mean and 95 % quantile
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8 Conclusion and Outlook
8.1 Conclusion
The main goal of this master thesis was to create a simple flood inundation model for the city of Kulmbach. Two different models were set up for the study area using the same input data. They differ mainly in the model structure. HEC-RAS 2D solves the 2D Diffusion Wave equation. The computation mesh consists of elements with up to eight edges, but consists mainly of squares. Due to the subgrid bathymetry approach, the grid size can be much coarser. Whereas TELEMAC 2D solves the full shallow water equations. The computational mesh is solely built out of triangles that map the topography. A comparison with official flood hazard maps from the Regierung von Unterfranken, Regierung von Oberfranken, Regierung von Mittelfranken and Regierung der Oberpfalz shows, that both models provide good results, that resemble the real conditions.
For the HEC-RAS model the method GLUE was performed to determine uncertainties. Changes in the roughness parameters were analyzed to find the best fitting parameter set and to see dependences between Manning’s n and the resulting water level.
During generation of the models the main issues were finding the perfect grid size and computational time step. They are strongly related and affect the calculation time enormously. To get accurate results as quickly as possible, the size of elements, and consequently the time step interval, have to be balanced.
8.2 Outlook
During uncertainty analysis, in this study only model parameters were changed. Further studies should concentrate on calibrating input data such as inflow hydrographs as they are also highly uncertain parameters. The discharges used as boundary conditions have a large effect on the resulting height of the water level. Also, further structures, such as bridges and weirs, should be included in the models. These structures affect hydrodynamical flow, which could change the course and velocity of the water. Since the evaluation of the model runs corresponding to 5 % quantile, mean, and 95 % quantile showed, that changes in the roughness parameter affect also the size of the inundation area between the original course of the White Main and the flood channel, further calibration of Manning’s n, may improve the model results to a better fit to the original flood hazard maps.
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To improve the calibration process and speed up simulation time, high performance computing is beneficial. Further studies could concentrate on using the LRZ Compute Cloud, which is provided by the Leibniz Supercomputing Centre (LRZ).
Regarding real time forecasting, after further calibration, the models can be used to perform fast simulation of impending events at any time. The results from this simulation can then be used to figure out areas at risk, for the construction of additional mitigation measures and if necessary, warn the general public against forthcoming floods.
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9 Literature
Arcement Jr., G. J., Schneider, V. R., & USGS. Guide for Selecting Manning's Roughness Coefficients for Natural Channels and Flood Plains. Retrieved from Bates, P. D. LISFLOOD-FP. Retrieved from http://www.bristol.ac.uk/geography/research/hydrology/models/lisflood/ Bates, P. D., & De Roo, A. P. J. (2000). A simple raster-based model for flood inundation simulation. Journal of Hydrology, 236(236), 54-77. Bates, P. D., Trigg, M., Neal, J., & Dabrowa, A. (2013). LISFLOOD-FP, User manual. Bristol: School of Geographical Sciences, University of Bristol. Bayerischer Runkfunk. (2016). Neue Flutmulde für den Weißen Main. Retrieved from http://www.br.de/nachrichten/oberfranken/inhalt/hochwasserschutz-kulmbach- renaturierung-100.html Bayerisches Landesamt für Umwelt. Historische Hochwasserereignisse. Retrieved from http://www.lfu.bayern.de/wasser/hw_ereignisse/historisch/index.htm Beven, K. (2014). Applied uncertainty analysis for flood risk management. London: Imperial College Press. Beven, K., & Binley, A. (1992). The Future Of Distributed Models - Model Calibration And Uncertainty Prediction. Hydrological Processes, 6, 279 - 298. Bhola, P. K., Prof. Dr. Disse, M., Kammereck, B., & Haas, S. (2016). Uncertainty Quantification in Flood Inundation Modelling- Applying the GLUE Methodology. BMT WBM. (2015). TUFLOW Flood and Coastal Simulation Software. Retrieved from http://www.tuflow.com/ BMT WBM. (2016). TUFLOW User Manual: BMT WBM. Canadian Hydraulics Centre. (2016). Blue Kenue™: Software tool for hydraulic modellers. Retrieved from http://www.nrc- cnrc.gc.ca/eng/solutions/advisory/blue_kenue_index.html Cerema. (2005). Graphic User Interface for Telemac. Chow, V. T. (1959). Open-Channel Hydraulics. United States of America: McGraw-Hill Book Company, Inc. Esri. (2017). ArcGIS. Retrieved from https://www.arcgis.com/features/index.html geomer GmbH. (2016a). FloodArea for ArcGIS® - hydrodynamic modelling. Retrieved from http://www.geomer.de/en/software/floodarea/index.html geomer GmbH. (2016b). FloodAreaHPC - Desktop, User Manual. Heidelberg.
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Goodell, C., & Brunner, G. (2016). Optimizing Your Computer for Fast HEC-RAS Modeling. Retrieved from http://hecrasmodel.blogspot.de/2016/08/optimizing-your-computer- for-fast-hec.html Horritt, M. S., & Bates, P. D. (2002). Evaluation of 1D and 2D numerical models for predicting river flood inundation. Journal of Hydrology, 268, 87-99. Innovyze. (2011). InfoWorks 2D, Applying the 2D module to Collection Systems, Technical Review. iRIC Project. (2010). Nays2DH. Retrieved from http://i-ric.org/en/software/17 JBA. (2014). JFlow Award-winning 2D hyraulic model. Retrieved from http://www.jflow.co.uk/ Lang, P., Desombre, J., Ata, R., Goeury, C., & Hervouet, J. M. (2014). Telemac-2D Software, User Manual: EDF-R&D. Leandro, J., Chen, A. S., & Schumann, A. (2014). A 2D parallel diffusive wave model for floodplain inundation with variable time step (P-DWave). Journal of Hydrology, 517. Litrico, X., & Fromion, V. (2009). Modeling and Control of Hydrosystems: Springer London. Martin, H. (2011). Numerische Strömungssimulation in der Hydrodynamik: Springer-Verlag Berlin Heidelberg. MIKE Powerred by DHI. MIKE 21. Retrieved from https://www.mikepoweredbydhi.com/products/mike-21 MIKE Powerred by DHI. (2015). MIKE 21 & MIKE 3 Flow Model FM, Hydrodynamic Module, Short Description. NatCatSERVICE. (2016). Schadenereignisse in Deutschland 1980 – 2015 [Press release] Néelz, S., & Pender, G. (2013). Benchmarking the latest generation of 2D hydraulic modelling packages. Retrieved from Néelz, S., Pender, G., Great Britain - Environment Agency, & Great Britain - Department for Environment Food Rural Affairs. (2009). Desktop Review of 2D Hydraulic Modelling Packages: Environment Agency. Nujić, M. (2014). Benutzerhandbuch. HYDRO_AS-2D. 2D-Strömungsmodell für die wasserwirtschaftliche Praxis. Aachen: Hydrotec Ingenieurgesellschaft für Wasser und Umwelt mbH. Pappenberger, F., Beven, K., Horritt, M., & Blazkova, S. (2005). Uncertainty in the calibration of effective roughness parameters in HEC-RAS using inundation and downstream level observations. Journal of Hydrology, 302(1-4), 46-69. doi:10.1016/j.jhydrol.2004.06.036 Prof. Dr.-Ing. habil. Duddeck, F. (2012). Finite-Element-Methoden für das Umweltingenieurwesen. Prof. Dr. Straub, D. (2013). Lecture Notes in Engineering Risk Analysis. München.
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Ratto, M., & Saltelli, A. (2001). Model assessment in integrated procedures for environmental impact evaluation: software prototypes: Joint Research Centre of European Commission, Institute for the Protection and Security of the Citizen, Ispra. Regierung von Unterfranken. Einzugsgebiet bayerischer Main - Geologie. Retrieved from http://www.hopla-main.de/index.php/einzugsgebiet-bayerischer-main/geologie Regierung von Unterfranken. (2013). Hochwasserrisikomanagement-Plan: Einzugsgebiet bayerischer Main. Retrieved from http://www.hopla-main.de/ Regierung von Unterfranken, Regierung von Oberfranken, Regierung von Mittelfranken, & Regierung der Oberpfalz. Hochwasserrisikomanagement-Plan, Kartendienst. Retrieved from http://www.hwrmp-main.de/viewer.htm Shimizu, Y., & Takebayashi, H. (2014). Nays2DH Solver Manual: iRIC Project. Stadt Kulmbach. (2016). Stadtdaten von Kulmbach. Retrieved from http://www.kulmbach.de/xist4c/web/Kulmbach-Rathaus-Geschichte- Stadtdaten_id_274_.htm tagesschau.de. (2016). Schwere Schäden durch Hochwasser. Retrieved from https://www.tagesschau.de/inland/unwetter-481.html TELEMAC-MASCARET. (2001). TELEMAC-2D Version 3.0, Principle Note. Universität der Bundeswehr München. FloodEvac. Retrieved from http://www.floodevac.org/ US Army Corps of Engineers. (2016a). HEC-RAS Hydraulic Reference Manual (Version 5.0 ed.). Davis, CA: Hydrologic Engineering Center. US Army Corps of Engineers. (2016b). HEC-RAS User's Manual (Version 5.0 ed.). Davis, CA: Hydrologic Enigneering Center. Wasserwirtschaftsamt Hof. (2016). Hochwasserschutz Kulmbach. Retrieved from http://www.wwa- ho.bayern.de/hochwasser/hochwasserschutzprojekte/kulmbach/index.htm Wasserwirtschaftsamt Hof. (2017). Januar-Hochwasser 2011. Retrieved from http://www.wwa- ho.bayern.de/hochwasser/hochwasserereignisse/januar2011/index.htm Werner, M., Blazkova, S., & Petr, J. (2005). Spatially distributed observations in constraining inundation modelling uncertainties. Hydrological Processes, 19(16), 3081-3096. doi:10.1002/hyp.5833 Zhang, K., Liu, H., Li, Y., Xu, H., Shen, J., Rhome, J., & Smith III, T. J. (2012). The role of mangroves in attenuating storm surges. Retrieved from https://sofia.usgs.gov/publications/papers/mang_storm_surges/cest.html
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10 Appendix I
Table 6: 2D hydrodynamical model comparison
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11 Appendix II
TELEMAC steering file:
/------/ TELEMAC2D Version v6p2 Feb 23, 2017 / nom inconnu /------
/------/ BOUNDARY CONDITIONS /------
STAGE-DISCHARGE CURVES =0;0;0;0;1;0
/------/ EQUATIONS /------
LAW OF BOTTOM FRICTION =4
FRICTION COEFFICIENT =0.06
TURBULENCE MODEL =3
/------/ EQUATIONS, BOUNDARY CONDITIONS /------
OPTION FOR LIQUID BOUNDARIES =1;1;1;1;1;1
PRESCRIBED ELEVATIONS =0;0;0;0;0;0
PRESCRIBED FLOWRATES =0;0;0;0;0;0
VELOCITY PROFILES =1;1;1;1;1;1
/------/ EQUATIONS, INITIAL CONDITIONS /------INITIAL CONDITIONS ='CONSTANT DEPTH'
INITIAL DEPTH =0.01
/------/ INPUT-OUTPUT, FILES /------
STEERING FILE ='kulmbach_unsteadyrun.cas'
GEOMETRY FILE ='kulmbach_geometry.slf'
STAGE-DISCHARGE CURVES FILE ='rating_curve/rating_curve_kulmbach.txt'
RESULTS FILE ='results/kulmbach_unsteady_results.slf'
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LIQUID BOUNDARIES FILE ='inflow_hydrograph/hydrograph_kulmbach.liq'
BOUNDARY CONDITIONS FILE ='kulmbach_BC.cli'
/------/ INPUT-OUTPUT, GRAPHICS AND LISTING /------
VARIABLES FOR GRAPHIC PRINTOUTS =U,V,B,H,S
LISTING PRINTOUT PERIOD =100
GRAPHIC PRINTOUT PERIOD =100
/------/ NUMERICAL PARAMETERS /------
FREE SURFACE GRADIENT COMPATIBILITY =0.9
TIME STEP =1
TREATMENT OF THE LINEAR SYSTEM =2
NUMBER OF TIME STEPS =35000
/------/ NUMERICAL PARAMETERS, SOLVER /------
SOLVER =1
SOLVER ACCURACY =1.E-6
/------/ NUMERICAL PARAMETERS, VELOCITY-CELERITY-HIGHT /------
IMPLICITATION FOR VELOCITY =1
IMPLICITATION FOR DEPTH =1
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12 Appendix III
Source code for generation, automation and processing
• The VBA function generate1000GeometryFiles() generates 1000 HEC-RAS geometry files with different roughness parameters. Therefore, a template geometry file with placeholders for material values (Manning’s) and timestamps was created. The function loadMaterialData(run As Integer) loads the values which were copied to a table in the excel file. These values are used to replace the placeholder in the template and saved to a new geometry file.
Sub generate1000GeometryFiles() Dim file As Integer Dim filePath As String Dim fileContent As String Dim newFileContent As String Dim i As Integer
'Open template file with placeholders for material values and timestamp path = "C:\Users\Sassi\Desktop\geometryFiles\template.g05" file = FreeFile Open path For Input As file fileContent = Input(LOF(file), file) Close file
'replace placeholder for material values and create 1000 geometry files For i = 1 To 1000 newFileContent = Replace(fileContent, "###MATERIAL_VALUES###", loadMaterialData(i))
path = "C:\Users\Sassi\Desktop\geometryFiles\projekt_" & i & ".g05" file = FreeFile Open path For Output As file Print #file, newFileContent Close file Next i End Sub
Function loadMaterialData(run As Integer) As String Dim i As Integer Dim line As String Dim manningValue As Double Dim output As String
'load random values from Excel sheet and adjust formatting ( "Material name, Manning's") For i = 2 To 49 manningValue = Sheets("randData").Cells(run, Sheets("Main").Cells(i, 2)) line = Sheets("Main").Cells(i, 1).value & "," & Str(manningValue) & vbCrLf output = output + line Next i loadMaterialData = output End Function Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. 63
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• The VBA function main() automates the simulation with HEC-RAS and data export in MATLAB. This allows to do a large number of HEC-RAS simulations on multiple computer without the need to manually control this workflow. Therefore, this function scans a folder for available HEC-RAS geometry files and automatically starts the HEC-RAS simulations and following MATLAB data export. This process is divided into multiple steps which are repeated until all geometry files are processed: o First, the VBA function loadGeometryFile(fileName As String) loads the HEC-RAS geometry file and updates the timestamp placeholder. Using this timestamp HEC-RAS detects the changes in the geometry file. o Next, the VBA function RunRAS() loads the HEC-RAS project file and starts the simulation. o Finally, the VBA function runMatlab(fileName As String) executes the MATLAB function createtxt(name) which loads the generated HEC-RAS .hdf files and exports the water level and water velocity at specific cell and cell faces. These values are exported to text files for further processing and evaluation.
Public Const path As String = "C:\Users\Sassi\Desktop\hec-ras_ederle\"
Function main() Dim i As String Dim objFSO As Object Dim objFolder As Object Dim objFile As Object
Set objFSO = CreateObject("Scripting.FileSystemObject") 'Define name of folder with template geometry files Set objFolder = objFSO.GetFolder(path & "geometryFiles")
Debug.Print ("------BEGINN ------") 'Loop to perform calculations for every file in the folder i = 0 For Each objFile In objFolder.Files i = i + 1 Debug.Print ("RUN " & i & ":") Application.DisplayAlerts = False
loadGeometryFile (objFile.name) Debug.Print ("----GEOMETRY FILE " & objFile.name & " LOADED")
Call RunRAS DoEvents Debug.Print ("----HECRAS CALC")
Call runMatlab(objFile.name) DoEvents Debug.Print ("----MATLAB SCRIPT")
Application.DisplayAlerts = True Debug.Print ("----RUN FINISHED") Next objFile Debug.Print ("------ALL FINISHED ------") Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. 65
End Function
Function loadGeometryFile(fileName As String) Dim file As Integer Dim filePath As String Dim fileContent As String
'Open geometry file with placeholder for timestamp filePath = path & "geometryFiles\" & fileName file = FreeFile Open filePath For Input As file fileContent = Input(LOF(file), file) Close file
'Update placeholder for timestamp with current time fileContent = Replace(fileContent, "###TIMESTAMP###", Format(Now(), "MMM/dd/yyyy hh:mm:ss"))
'Save the geometry file to the HEC-RAS project directory filePath = path & "projekt.g05" file = FreeFile Open filePath For Output As file Print #file, fileContent Close file End Function
Function RunRAS() Dim HRC As New HECRASController Dim strRASProject As String Dim lngMessages As Long Dim strMessages() As String Dim blnDidItCompute As Boolean
strRASProject = path & "projekt.prj" HRC.Project_Open strRASProject blnDidItCompute = HRC.Compute_CurrentPlan(lngMessages, strMessages(), True) HRC.QuitRas
End Function
Function runMatlab(fileName As String) Dim MatLab As Object Set MatLab = CreateObject("Matlab.Application") Result = MatLab.Execute("cd " & path) Result = MatLab.Execute("createtxt('" & fileName & "')") End Function
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function createtxt(name) % Read output file .hdf and import tables for water surface elevation and velocities data_waterlevel = hdf5read('projekt.p03.hdf','/Results/Unsteady/Output/Output Blocks/Base Output/Unsteady Time Series/2D Flow Areas/area1/Water Surface'); data_velocity = hdf5read('projekt.p03.hdf','/Results/Unsteady/Output/Output Blocks/Base Output/Unsteady Time Series/2D Flow Areas/area1/Face Velocity'); % Defines cells and cell faces for all 8 observation locations find_cell = [183201, 131494, 419045, 154432, 22487, 32353, 47230, 84894]; find_face = [403584, 403629, 403627, 403628, 289396, 294033, 292554, 292555, 309087, 312705, 307771, 309011, 309088, 343324, 343353, 343351, 343354, 343352, 52148, 52741, 52716, 52715, 73116, 73123, 73124, 73120, 108943, 107201, 107192, 107194, 186379, 188426, 188427, 188425];
% Write water level to textfile f = fopen(strcat('output_waterlevel_',name,'.txt'), 'w'); fprintf(f,'%f %f %f %f %f %f %f %f\r\n',data_waterlevel(find_cell,:)); fclose(f);
% Write velocities to textfile g = fopen(strcat('output_velocity_',name,'.txt'), 'w'); fprintf(f,'%f %f %f %f %f %f %f %f %f %f %f %f %f %f %f %f %f %f %f %f %f %f %f %f %f %f %f %f %f %f %f %f %f %f\r\n',data_velocity(find_face,:)); fclose(f); end
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13 Appendix IV
Figure 30: Large scale view of HEC-RAS results
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Figure 31: Large scale view of TELEMAC results
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Figure 32: Results of HEC-RAS with 10 m grid size
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14 Appendix V
Figure 33: Boundary conditions for test run
Figure 34: Results of test run with changed boundary conditions
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15 Appendix VI
Figure 35: Uncertainty plots of Likelihood Function Graphs from GLUEWIN at location 5
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Figure 36: Scatter Plots of Manning’s n and water level at location 2
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Figure 37: Scatter Plots of Manning’s n and water level at location 3
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Figure 38: Scatter Plots of Manning’s n and water level at location 4
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Figure 39: Scatter Plots of Manning’s n and water level at location 5
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Figure 40: Scatter Plots of Manning’s n and water level at location 6
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Figure 41: Scatter Plots of Manning’s n and water level at location 7
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Figure 42: Scatter Plots of Manning’s n and water level at location 8
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List of Figures
Figure 1: Water surface elevation (US Army Corps of Engineers, 2016a) ...... 8
Figure 2: Exemplary control volumes for the computational mesh (US Army Corps of Engineers, 2016a) ...... 11
Figure 3: 1m DEM and computational grid ...... 13
Figure 4: Definition of internal inflow boundary conditions in HEC-RAS 2D ...... 14
Figure 5: Definition of internal inflow boundary conditions in TELEMAC 2D ...... 16
Figure 6: Photograph of Theodor-Heuss-Allee in Kulmbach during the flood event of January 2011 (Source: Wasserwirtschaftsamt Hof) ...... 19
Figure 7: Photograph of flooded agricultural land during the flood event of January 2011 (Source: Wasserwirtschaftsamt Hof) ...... 19
Figure 8: Location and outline of study area in red. Rivers are plotted in blue. The dashed arrows represent smaller tributaries. The flood channel is displayed striped. The inset shows the approximate location of Kulmbach in Germany...... 20
Figure 9: Cross sections at two positions of the White Main and the flood channel ...... 21
Figure 10: Topographical map of study area including cross-section A - A ...... 21
Figure 11: East-West Cross Section A - A ...... 22
Figure 12: Land cover of the study area Kulmbach ...... 23
Figure 13: Flowchart of HEC-RAS 2D ...... 25
Figure 14: Screenshot of the software HEC-RAS including the Geometric Editor and the finished computation mesh ...... 26
Figure 15: Close-up view of HEC-RAS mesh including the boundary condition line ...... 27
Figure 16: Flowchart of TELEMAC 2D ...... 29
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Figure 17: Graphical interface of Blue Kenue ...... 31
Figure 18: Close-up of mesh generated in Blue Kenue in 3D view ...... 31
Figure 19: Histograms of generated random values for Manning’s n ...... 38
Figure 20: Locations of calibration data ...... 39
Figure 21: Discharge for the January 2011 event ...... 40
Figure 22: Inflow hydrographs used for uncertainty analysis ...... 41
Figure 23: Boundary conditions of flood hazard map run ...... 43
Figure 24: HEC-RAS Result for HQ100 and official flood hazard map (Regierung von Unterfranken, Regierung von Oberfranken, Regierung von Mittelfranken, & Regierung der Oberpfalz) ...... 45
Figure 25: TELEMAC 2D Result for HQ100 and official flood hazard map (Regierung von Unterfranken et al.) ...... 46
Figure 26: Scatter Plots of Manning’s n and water level at location 1 ...... 49
Figure 27: Uncertainty plots of Likelihood Function Graphs from GLUEWIN at location 1 ...... 50
Figure 28: Uncertainties of water level ...... 52
Figure 29: Comparison of results for different parameter sets that correspond to 5 % quantile, mean and 95 % quantile ...... 54
Figure 30: Large scale view of HEC-RAS results ...... 68
Figure 31: Large scale view of TELEMAC results ...... 69
Figure 32: Results of HEC-RAS with 10 m grid size ...... 70
Figure 33: Boundary conditions for test run ...... 71
Figure 34: Results of test run with changed boundary conditions ...... 71
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Figure 35: Uncertainty plots of Likelihood Function Graphs from GLUEWIN at location 5 ...... 72
Figure 36: Scatter Plots of Manning’s n and water level at location 2 ...... 73
Figure 37: Scatter Plots of Manning’s n and water level at location 3 ...... 74
Figure 38: Scatter Plots of Manning’s n and water level at location 4 ...... 75
Figure 39: Scatter Plots of Manning’s n and water level at location 5 ...... 76
Figure 40: Scatter Plots of Manning’s n and water level at location 6 ...... 77
Figure 41: Scatter Plots of Manning’s n and water level at location 7 ...... 78
Figure 42: Scatter Plots of Manning’s n and water level at location 8 ...... 79
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List of Tables
Table 1: Main rivers in study area (Regierung von Unterfranken, 2013) ...... 17
Table 2: Lengths of the river sections ...... 20
Table 3: Uniform distributions of roughness parameters ...... 37
Table 4: Water levels used for calibration ...... 40
Table 5: Statistical Analysis of GLUE ...... 51
Table 6: 2D hydrodynamical model comparison ...... 60
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Erklärung
Ich versichere hiermit, dass ich die von mir eingereichte Abschlussarbeit selbstständig verfasst und keine anderen als die angegebenen Quellen und Hilfsmittel benutzt habe.
München, 28.04.2017, Unterschrift