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
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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.
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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).
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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:
𝜕𝐻
𝜕𝑡+
𝜕(ℎ𝑢)
𝜕𝑥+
𝜕(ℎ𝑣)
𝜕𝑦+ 𝑞 = 0 2
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:
𝜕𝐻
𝜕𝑡+ ∇ ∙ ℎ𝑉 + 𝑞 = 0 3
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:
𝜕𝑉
𝜕𝑡+ 𝑉 ∙ ∇𝑉 = −𝑔∇𝐻 + 𝑣𝑡∇
2𝑉 − 𝑐𝑓𝑉 + 𝑓𝑘×𝑉 4
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:
𝑐𝑓 =𝑛2𝑔|𝑉|
𝑅4 3⁄ 5
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
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𝜕𝐻
𝜕𝑛′≈
𝐻2 − 𝐻1
𝛥𝑛′ 6
with 𝛥𝑛′ 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
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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:
𝑛2|𝑉|𝑉
(𝑅(𝐻))4 3⁄
= −∇𝐻 7
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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𝜕𝐻
𝜕𝑡− 𝑉 ∙ 𝛽∇𝐻 + 𝑞 = 0 8
where: 𝛽 =(𝑅(𝐻))
5 3⁄
𝑛|∇𝐻|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.
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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:
𝜕ℎ
𝜕𝑡+ 𝑉 ∙ ∇(ℎ) + ℎ𝑑𝑖𝑣(�⃗� ) = 𝑞 9
Momentum conservation along x:
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𝜕𝑢
𝜕𝑡+ �⃗� ∇⃗⃗ (𝑢) = −𝑔
𝜕𝐻
𝜕𝑥+ 𝑆𝑥 +
1
ℎ𝑑𝑖𝑣(ℎ𝑣𝑡 ∇⃗⃗ 𝑢) 10
Momentum conservation along y:
𝜕𝑣
𝜕𝑡+ �⃗� ∇⃗⃗ (𝑣) = −𝑔
𝜕𝐻
𝜕𝑦+ 𝑆𝑦 +
1
ℎ𝑑𝑖𝑣(ℎ𝑣𝑡 ∇⃗⃗ 𝑣) 11
For these equations the following applies:
𝑣𝑡 is the momentum diffusion coefficient, 𝑆𝑥 and 𝑆𝑦 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 [m]
589 283 226 216
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.
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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
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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.
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.
285
290
295
300
305
310
315
320
0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000
Elev
atio
n [
m]
Length [m]
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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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Figure 13: Flowchart of HEC-RAS 2D
Project file.prj
UnsteadyFlow file
.u01
Hot start file.p##.rst
Plan file.p01
Plan hdf file .p01.hdf
Computationallevel output
.hyd01
Geometryhdf file
.g01.hdf
Geometryfile .g01
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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
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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.
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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.
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.
Steeringfile .cas
Boundary conditions
file .cli
Output .slf
Geometryfile .slf
Inflowhydrograph
.liq
Stage discharge curve .txt
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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
𝐿(𝒙𝒊|𝒚) = 𝑒𝑥𝑝(− ∑(�̂�(𝒙𝒊) − 𝑦(𝑗))
2
𝑠𝑡𝑑(�̂� − 𝑦(𝑗))
𝑛𝑜𝑏𝑠
𝑗=1
) 12
where 𝒙𝒊 is the ith element of the sample of the model input factors, 𝒚 =
(𝑦(1), … , 𝑦(𝑗), … , 𝑦(𝑛𝑜𝑏𝑠)) is the vector of observations of the scalar variable y, 𝑛𝑜𝑏𝑠 is the
number of observations, �̂�(𝒙𝒊) is the i-th model run and 𝑠𝑡𝑑(�̂� − 𝑦(𝑗)) 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
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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 𝑛 = 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.
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).
0
50
100
150
200
250
300
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
Dis
char
ge [
m²/
s]
Ködnitz Kauerndorf Unterzettlitz
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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.
0.000
50.000
100.000
150.000
200.000
250.000
0 4 8 12 16 20 24
Dis
char
ge [
m³/
s]
Time [h]
Inflow hydrograph
Unterzettlitz
Ködnitz
Kauerndorf
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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.
Observation point
Result range Median 5 % quantile 95 % quantile Variance
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.
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Manual: EDF-R&D.
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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
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MIKE Powerred by DHI. MIKE 21. Retrieved from
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Description.
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Environment Food Rural Affairs. (2009). Desktop Review of 2D Hydraulic Modelling
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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
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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,
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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
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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
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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 ------")
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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
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
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