Appropriate modelling: Application of Sobek 1D2D for dike ... · Chapter 2 The Elbe DSS and modelling area ... consists of a variety of models. This means that, for the realisation

Appropriate modelling: Application of Sobek 1D2D for dike break and overtopping at the Elbe

R. Lomulder November 2004

Appropriate modelling: Application of Sobek 1D2D for dike break and overtopping at the Elbe

Master thesis of Robin Lomulder University of Twente Faculty of Engineering Technology Group Water Engineering and Management (WEM) Graduation committee: Dr. M.S. Krol (University of Twente) Dr. J.L. de Kok (University of Twente) Msc Mphl Y. Huang (University of Twente)

Table of contents Preface…………………………………………………………………………………………….I Summary…………………………………………………………………………………….…..III Table of contents ............................................................................................................1 Chapter 1 Introduction.................................................................................................3

1.1 Background of decision support systems.............................................................3 1.2 Problem definition, objectives and research question..........................................4 1.3 Outline..................................................................................................................5

Chapter 2 The Elbe DSS and modelling area ............................................................7

2.1 The river Elbe and the study area........................................................................7 2.1.1 The Elbe river-basin ......................................................................................7 2.1.2 The Sandau area...........................................................................................9

2.2 Elbe DSS ...........................................................................................................10 2.2.1 The layout of the DSS-model ......................................................................11 2.2.2 Channel module ..........................................................................................12 2.2.3 River section module ...................................................................................13

2.3 Data ...................................................................................................................14 Chapter 3 Methodology .............................................................................................17

3.1 Hydraulic models ...............................................................................................17 3.1.1 Hec 6 ...........................................................................................................17 3.1.2 Sobek1D2D and Sobek 2D .........................................................................20 3.1.3 Qualitative assessment of the most appropriate hydraulic model ...............22

3.2 Damage models.................................................................................................23 3.2.1 Statistical damage model; based on Hec 6 .................................................23 3.2.2 Event-based damage model; connected to Sobek......................................26

3.3 Methodology ......................................................................................................27 Chapter 4 Case study ................................................................................................29

4.1 Data ...................................................................................................................29 4.1.1 Time series .................................................................................................29 4.1.2 Dike .............................................................................................................32

4.2 Sobek 2D calculations .......................................................................................34 4.2.1 Calibration and validation ............................................................................34 4.2.2 Simulations of artificial flood events ............................................................36 4.2.3 Damage modelling using Sobek 2D results.................................................40

4.3 Sobek 1D2D calculations...................................................................................42 4.4 Comparison and conclusions Sobek calculations..............................................47

Chapter 5 Uncertainty and sensitivity analysis.......................................................51

5.1 Uncertainty sources and proceedings................................................................51 5.1.1 Uncertainty identification .............................................................................51 5.1.2 Proceeding of UA/SA...................................................................................52

5.2 Results of the UA/SA for the Sobek/Damage model .........................................53 5.3 Results of the UA/SA based on Hec 6 ...............................................................57

R. Lomulder 12 November 2004

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5.4 Conclusions .......................................................................................................60 Chapter 6 Conclusions and recommendations.......................................................61

6.1 Conclusions .......................................................................................................61 6.2 Recommendations .............................................................................................63

References.....................................................................................................................65 Appendix I


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Chapter 1 Introduction Section 1.1 discusses the background of the research. The problem definition and objectives are presented in 1.2. An outline of the report is given in paragraph 1.3.

1.1 Background of decision support systems The state-of-the-art in system development has moved towards integrated multi-objective systems involving multi-processes. Decision support system (DSS) for river basin management is such an example. It typically involves processes of hydrology, hydraulics, water quality, flood risk, ecology and navigation assessment. In turn, model related activities have shifted from model development to selecting the most appropriate model in the system development [Snowling et al., 2001]. To answer the question of what model is the “best one among candidates”, a systematic approach which can present a guideline for model selection, namely as the appropriate modelling approach, is needed. This study focuses on the selection of the hydraulic model, which is one core of the river basin modelling, and it has many varieties in terms of complexity. It is known that under normal flow conditions a 1 dimensional hydrodynamic model is good enough, in terms of accuracy, to simulate the river flow. However, it is not applicable when more than one velocity components are involved, for example, in the cases of over-topping of dikes, or dike break. In those cases the ideal solution is to use higher dimensional models such as 2D or 3D [Huang, 2003]. However the drawbacks of such high dimensional models are large data requirements and excessive computing times, which prevent the application of these models to be used in an operational decision support system. Moreover, they might not provide significant improvement when further integration with other models is needed. In the case of using an integrated system for flood damage computation, the system uncertainty may be dominated by the damage function uncertainty rather than other sources. If that is true, a 2D model is not necessarily needed. Therefore, it makes great sense to access the applicability of an intermediate solution, such as Sobek 1D2D developed by Delft Hydraulics [reference]. This model consists of a 1D channel flow module and a 2D overland flow module. A third option is to extend an existing 1D model, such as Hec6, with modules that describe the amount of water that overtops the dike. The actual designing and building of a DSS is often a tedious process. One cause of the problem is that it is a multidisciplinary process, as mentioned above; the entire system consists of a variety of models. This means that, for the realisation of a DSS, different models have to be integrated. The scientists and system designers, with their different backgrounds, they should not only consult each other, but also to let the policy makers and the end-users participate into the design process [Kok et al., 2003]. In general, it can be concluded that, despite the effort invested in process modelling, data collection and the growing experience in developing integrated system models, practical application of decision support systems still runs behind the availability of these tools [Kok et al., 2003]. Obvious explanations could be a lack of user friendliness or a lack of familiarity of the persons responsible for taking decisions with these types of models [Kok et al., 2003]. However, such superficial observations probably pass over the more fundamental problems occurring during the design and application of decision support systems in the field of water management [Kok et al., 2003].


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1.2 Problem definition, objectives and research question Besides the problems during the design and building process for a DSS, described above, there is another difficulty, namely the choice and development of the hydrodynamic model itself. It can be summarised as: “By designing and building a DSS that contains a hydrodynamic model, there are no standards or guidelines developed for choosing the most appropriate model. The search for a hydrodynamic model is sort of an opportunistic affair, in which the outcome depends on the coincidental availability of data and/or models; hereby the integration with other models is neglected. The consequence is that the most appropriate model is often not selected.” The following research question is derived from the problem definition above: “Can hydrodynamic models simulate overtopping and dike break, with a satisfactory amount of accuracy, to be implemented in a DSS, without the data requirements and computation time rising at an exorbitant high level?” The most appropriate model should have a minimum complexity and still produce such a level of accuracy that it is possible to distinguish the results of the computations made for different measurements. Figure 1.1 below shows this optimum:

Figure 1.1 Relation between model power and complexity [Kok et al., 2003]

When the model complexity exceeds its optimum, at first the ability to distinguish the results of the computations rises. However the model has got a far greater accuracy than strictly needed, which makes the model unnecessarily expensive in terms of complexity and data requirement. Increasing the model complexity eventually results into reducing its decision-making power. Therefore, the main objective of this research is to assess the appropriateness - the applicability of hydrodynamic models for decision support system development. This assessment is based on an analysis of the model complexity, uncertainty and sensitivity. The second objective is to provide recommendations in defining an appropriate modelling approach based on the results.


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This study is based on a case study (in chapter 2), which is the development of a DSS for the Elbe [Bundesanstalt für Gewässerkunde, 2003]. The study area is around Sandau, which is a small part of the river basin.

1.3 Outline This report comprises the result of the Msc-research, entitled: ”Appropriate modelling: Application of Sobek 1D2D for dike break and overtopping at the Elbe”. Chapter 1 discusses the background of this research, including the problem definition and objectives. In order to examine the appropriateness of hydrodynamic models as the hydraulic “engine” for a DSS, several models are selected and tested. The chosen models are applied in a case study - the development of a DSS for the river Elbe. One of the main goals of this DSS is to obtain a quick insight in the behaviour of the river system, so that identified problem areas can be studied further. Several measures such as lowering floodplains and dike shifting, will be simulated by this system. Eventually the DSS will help the decision-makers (engineers, politicians) to find the right solutions. This research aims on a small selected part of the Elbe area instead of the entire river-basin area. Chapter 2 describes this case study, including the layout of that system, and an overview of the available data. The methodology is represented in chapter 3. Several hydraulic models, namely Hec 6, Sobek 1D2D, and Sobek 2D, are discussed. Furthermore it describes both of the available damage models and the methodology. Chapter 4 presents and discusses the results of the computations performed with the Sobek models. Several flood events are set up to simulate a dike overtopping and a dike break. Particularly dike break scenarios are interesting to simulate, due to the fact that it can be a measure to lower flood damages downstream. In case of a large flood a dike can be deliberately punctured in an area where the population density, and the economic value, is relative low. This will hopefully result into a lower peak, and thus a reduction to the damage downstream, where the population density and/or the economic value are higher. An important aspect of the evaluation of all the models is the uncertainty and sensitivity analysis. This topic is incorporated in chapter 5. Chapter 6 presents the conclusions and recommendations that are drawn from the research.


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Chapter 2 The Elbe DSS and modelling area This chapter describes the framework of the DSS developed for Elbe River. The DSS consists of several modules and in those were the University of Twente is involved (in paragraph 2.2), several flood events are set up to model an overtopping and a dike break. Next to the background of the Elbe project, the available data are described in section 2.3.

2.1 The river Elbe and the study area This paragraph gives a brief description of both the entire Elbe river-basin area that is modelled by the DSS, and the Sandau area, which is the main focus of the case study. This Sandau area is also a part of the DSS, with the difference that this region will be modelled with more detail.

2.1.1 The Elbe river-basin The Elbe is one of the largest rivers of Middle Europe, which largely determines the structure of the landscape in parts of the Czech Republic as well as in Germany. The source of the river lies in Krkonose, which is located at the high mountains in the Czech Republic, with an altitude of 1,383.60 meter above NN (the German reference level). The length of the Elbe, from Krkonose to the mouth at the North Sea, is 1,091.5 kilometre. The complete river-basin area is 148,268 km2, about two third of that surface (96,932 km2) is in Germany, the rest (50,176 km2) is in Czech with minor parts in Poland and Austria. The whole river-system contains several tributaries, the four most important ones are: the Moldau (river-basin area of 28,090 km2), the Eger (river-basin area of 5,614 km2), the Schwarze Elster (river-basin area of 5,541 km2), the Mulde (river-basin area of 7,400 km2), the Saale (river-basin area of 24,079 km2) and the Havel (river-basin area of 24,096 km2). The research area of the main part of the DSS, as discussed in paragraph 2.2.1, concentrates on the river, from the German-Czech border, to the weir at Geesthacht, which is located south of Hamburg. Geesthacht is considered to be the beginning of the tidally influenced stretch of the river. The map depicted in Figure 2.1 gives a description of the entire research area.


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Figure 2.1 Map of the research area of the entire DSS [Nestmann et al., 2002]

The average daily discharge (MQ) in the Elbe River depends on the location and varies between 327 m3/s at Dresden and 870 m3/s at Geesthacht [www.rivernet.org/elbe.htm]. In 2002 between August 11 and August 20, a massive flooding of the Elbe occurred, with a severity that has not been seen since the 17th century. The cause for the flooding was a rather rainy summer that culminated in a few days of extremely heavy rain which were uncommon for this area at that period [www.inf.tu-dresden.de/uml/html/floodinfo.html]. This caused altogether three effects, all of which hit the area badly [www.inf.tu-dresden.de/uml/html/floodinfo.html]:

1. Two small rivers, the Mueglitz and the Weisseritz, flowing into the river Elbe at Dresden, come from a mountain area that suffered from extremely heavy rain in an uncommon period of the year. These little rivers changed to torrents, destroying a


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significant part of the villages and small towns around Dresden, and damaging roads and railway lines. In Dresden, the Mueglitz a2. nd Weisseritz caused flooding and severe damage in

3. ays, water from the Czech Republic (which caused the flooding of

n example is the destruction of large parts of the city of Dresden. Figures 2.2 and 2.3

areas of the town nobody ever expected to flood. For example Dresden’s main railway station. In the following dPrague before) came down the Elbe and joined the high waters from the preceding flooding.

Agive a general image of what the effect was on Dresden.

Figure 2.2 and 2.3 The result of the floodi sden [www.inf.tu-dresden.de/uml/html/floodinfo.html]

ough cost estimates for the Elbe 2002 flood alone are +/- $3 billion in the Czech

l].

e

2.1.2 The Sandau area is located south of the city Havelberg. The altitude of the

e existence of a real problem; res are in effect or planned;

be significant; 2000

ng at Dre

RRepublic and more then $9 billion in Germany [www.glowa-elbe.de/presse_flut.htmTen extreme floods have been observed in Dresden since the 13th century, with floodpeak water levels between 8.2 and 8.8 metres. The August 2002 flood exceeds all theslevels with a peak of 9.4 metres. The corresponding peak discharge, estimated from stream flow measurements in Dresden, was about 4.680 m3/s. Surprisingly, in 1845, ahigher discharge (5.700 m3/s) was recorded, yet the peak water level (8.8 m) was lower; this can only be explained by reductions of the flow capacity of the flood plains below the Dresden gauge, e.g., as a result of settlement development [www.glowa-elbe.de/presse_flut.html].

The Sandau research arealandscape varies between 23 to 37 meters above NN. Figure 2.4 shows the Sandau area and its location in the entire research area. In the feasibility study for a prototypeDSS for the Elbe [Kok et al., 2000] the selection of this area is based on the following criteria: • Th• The fact that management measu• The fact that changes due to these measures are expected to • The readily availability of models and data from the Elbe Ecology and/or Elbe

programs.


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The Sandau area was selected because in this Elbe section hydraulic and groundwater models are available, an ecological study is conducted, and there are two dike shifting areas between kilometre 412 and 421 [Kok et al., 2000]. Moreover, the impacts of groyne shape modification are studied here [Kok et al., 2000]. The area of this region is 55.6 km2. The research area is restricted in the northern and western direction by the Elbe, from kilometre 411.4 to 422.4, and the river Havel. The eastern and southern borders are chosen in such a way that the water height measurements, with a time series since 1964, could be used as a boundary condition. The size of the Sandau area is 6.8 kilometres from east to west and 10.6 kilometres from north to east.

Figure 2.4 Map of the research area around Sandau [Bundesanstalt für Gewässerkunde, 2003]

This area is modelled with a greater level of detail in the DSS, it is also the area where this MSc-study focuses on.

2.2 Elbe DSS In order of the Bundesanstalt für Gewässerkunde (BfG) a feasibility study, for the building of a DSS for the river Elbe, has been made from 1999 until 2000 [Bundesanstalt für Gewässerkunde, 2003]. The outcome of this study was that the design of such a system is desirable. So after the positive recommendation, the development of a pilot-DSS started in March 2002. One of the goals of a DSS-development is to give a quick insight in the behaviour of the river system, so that problem areas can be identified. The system also makes it possible to investigate the consequences of several measures that can be taken, such as dike shifting, the construction of a side channel or lowering the floodplains. These changes in the river will have their effect on a number of quantities, like the water level and the morphology. The DSS-program helps the decision-makers (engineers, politicians) to come up with the right solutions. Therefore the DSS-program has to be easy to handle and not take too much computation time, without losing its accuracy.


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2.2.1 The layout of the DSS-model In order to develop the DSS the BfG called in a number of organisations. The partners in this project are: the Institut für Umweltsystemforschung, the University Osnabrück, the University of Twente, RIKS bv and Infram international bv. Together the participants have to design the entire DSS-program. The problem with the science of making strategies for coastal- and flood-areas is that the systems are dealing with factors, combing natural and anthropologic factors [Bundesanstalt für Gewässerkunde, 2003]. The knowledge of those processes is crucial for developing an effective strategy. Four aspects of these systems were appointed in the pilot phase to be particularly important [Bundesanstalt für Gewässerkunde,2003], are:

1. When the user can intervene in its own limited part of the system only, the possibility exists that the consequences of his/her actions can still be felt throughout the whole system. On the other hand problems the user has to solve in its own part can be caused in another part of the system.

2. The natural systems are dynamic and evolutionary. This means that a small intervention can have serious consequences.

3. The systems are structured in a geographical environment. This means that the context, in which the decisions take place, should not be ruled out.

4. The world is full of uncertainties. The plans and strategies have to be created in such a way, that they absorb these uncertainties.

In Figure 2.5 a scheme for a DSS-model is shown. The figure includes not only the natural (physical and ecological) systems, but also the anthropologic (social economic and institutional) ones.

External factors (External scenarios)

Decision maker

Projected state (Indicators)

System

Physical Ecological

Social-economical Institutional

Desired state

Measures

Figure 2.5 General scheme for a DSS-model [Kok et al., 2003] The feasibility study recommended that the pilot-DSS should fulfil four functions: a library function, an analysis function, a communication function and a learning function. The analysis function exists of four modules, namely “Einzugsgebiet”, “Fließgewässernetz”,


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“Hauptstrom” and “Flussabschnitt”. Both Universities (Osnabrück and Twente) took up the development of these four modules. Hereby the university Twente focuses on the channel (Hauptstrom) and the flooding (Flussabschnitt).

2.2.2 Channel module This module represents the flow of the river Elbe from the Czech border (km 0) to the weir at Geesthacht (km 586). A more detailed description of this 586 kilometre long route is given in section 2.1. The three most important functions of the channel module are [Bundesanstalt für Gewässerkunde, 2003]:

1. To give a description of the ecological connection in the floodplains. The ecological state of the floodplain is described by means of 15 kinds of biotopes and depends on the number of days per year that the plains are flooded. The model selected to perform this task is Mover.

2. To assess the risk of flooding, including the relative damage, the length and the height of the flooding. This can achieved by one of the hydraulic models mentioned in chapter 2.

3. To calculate the number of days per year that shipping is possible, as is done by the hydrostatic model Hec 6.

A detailed system-diagram of the channel module is depicted in Figure 2.6. As can be seen in the diagram, there are several measures, which can be simulated in this module. These measurements have their effects (positive and negative) on the safety and ecology. Possible interventions in the system include: • Changing the heights of the dikes; • Renaturing of the floodplains; • Increasing the retention volume, by means of dike shifting, lowering the

floodplains, weirs etc.; • Deepening the main channel to improve shipping; • Changing the transport capacity of the ships, so the minimum depth alters; • Altering the land use, to lower the flood risk.

The module must be able to calculate the effects of all kinds of interventions, but it also must take external changes into account. The relevant external scenarios, that have to be dealt with, are the changing land use in the future and changes in climate. A different land use has got a serious effect on the total damage inflicted by a flood. The second external scenario is the inevitable change of the climate, which causes more extreme flows, both higher and lower discharges. A 1D hydrostatic model is used as the hydraulic engine for this module. Most likely the Hec 6 model, which is discussed in the next chapter, will be selected to fulfil this task. The hydrostatic model will be connected with a damage model, which will be similar as the ones described in section 3.3.


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Figure 2.6 System diagram of the channel module [Bundesanstalt für Gewässerkunde, 2003]

2.2.3 River section module The second module the University Twente is involved in is quite similar to the channel module. The river section module has two objectives, first the ecological interaction between flood and plain, and in the second place the estimation of the flood damage risks. The distinction between the two modules is that some processes in the river section module are modelled in greater detail; a 2-dimensional hydrodynamic model is applied instead of a 1-dimensional steady flow hydraulic model. There is also a difference in the size of the study area. In the DSS the river section module will not be used to simulate the whole river channel, but restricts itself to a user defined smaller area such as river reaches. The river section


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module is bound to the Sandau area (km 412 – km 422) due to data availability. The Msc-research also focuses on this area that is discussed in section 2.1.2. According to the model requirement a more precise set-up is needed, i.e. smaller resolution for the modelling area. The system diagram is depicted in Figure 2.7:

Figure 2.7 System diagram of the flood module [Bundesanstalt für Gewässerkunde, 2003]

This module of the DSS comprises a hydraulic model that simulates peak discharges, after which it is fed into a damage model. This system is quite similar to the work performed in chapter 4.

2.3 Data The performance of every model, regardless its complexity, depends on the level of the available data. In general hydraulic models need at least the following input data to compute the water levels and the flow velocities: • Cross sections with different intervals; • Roughness of the river and the floodplain area; • Upstream boundary condition, Q(t) – discharge as the function of time; • Downstream boundary condition, Q(h) – rating curve.

2D hydrodynamic models do not need cross sections, but use 2D maps for the land level and the roughness. These maps consist of a 2D grid in which each cell has its own value


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for the level or the roughness. The digital elevation map (DEM) is also needed to obtain the inundation depth for the damage model. In order to assess the damage, the model needs the following data: • Inundation depth (provided by the hydraulic models); • Flow velocities (provided by the hydrodynamic models); • Land use.

The Bfg provides the cross sections and the DEM. The roughness of the riverbed itself can be begotten through literature study, to get some global values. After that the models are calibrated to fit the measured water levels in the river. The roughness outside the river channel; is obtained using the land use map. This map is the result of a European study where the land use of several countries is determined with the use of satellites [Bossard, 2000]. This so-called “remote sensing” is done with the IKONOS satellite for Germany; however the uncertainty of the map is unknown. A study for this topic would be so extensive that it is outside the scope of the MSc-research. The land use map is divided into 44 classes, each representing a different land use type; with16 classes are present in the study area. The total surface of the DEM is 37,237.50 hectares. By means of literature study each land use class can be attributed a roughness. Each land use class with its attributed roughness are shown in table 2.1.

Land use class Hectare % of total

Manning roughness

[s/m1/3] Reference

Discontinuous urban fabric

1,078.50 2.90 0.150 [Sande et al, 2004]

Road, railroad, and associated land

338.00 0.91 0.150 [Sande et al, 2004]

Mineral extraction sites 50.50 0.14 0.120 [Sande et al, 2004] Non-irrigated arable land 19,784.75 53.13 0.035 [Chow, 1959] Fruit trees and berry plantations

66.00 0.18 0.150 [Chow, 1959] [Sande et al, 2004]

Pastures 6,119.50 16.43 0.035 [Chow, 1959], [Meier et al., 1994], and [Sande et al, 2004]

Complex cultivation patterns

154.00 0.41 0.050 [Chow, 1959]

Land principally occupied by agriculture

595.25 1.60 0.050 [Chow, 1959]

Broad-leaved forest 365.00 0.98 0.120 [Chow, 1959] Coniferous forest 6,583.50 17.68 0.200 [Chow, 1959] [Sande et al,

2004] Mixed forest 135.00 0.36 0.200 [Chow, 1959], [Meier et al.,

1994] [Sande et al, 2004] Natural grassland 156.00 0.42 0.033 [Chow, 1959] Moors and heath land 252.00 0.68 0.033 [Chow, 1959] Inland marshes 221.00 0.59 0.050 [Chow, 1959] [Meier et al.,

1994] Water courses 1,243.50 3.34 0.030 [Chow, 1959] [Meier et al.,

1994] Water bodies 95.00 0.26 0.030 [Chow, 1959] and [Meier et

al., 1994] Table 2.1 Land use and attributed roughness in the research area


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Along the river Elbe several measurement stations are located which keep record of key hydraulic quantities, such as the discharge and the water level. Three stations are active in the research area, namely at (located at km 412), Sandau (located at km 416) and Havelberg (located at km 422). The time series of Tangermünde station can be used for the upstream boundary. The available time series starts at 1/11/1960 and ends at 31/10/1995, therefore the most recent flood in 2002 is not included. The Q-h relation obtained from the Havelberg station can provide the downstream boundary. The remaining third station at Sandau, which is established around the middle of the study area, can provide the water levels necessary for the calibration and validation of the models.


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Chapter 3 Methodology The Sandau research area is modelled using Sobek 1D2D . The performance of the 1D2D model is compared with the 2D module of Sobek and the 1D steady flow model Hec 6. Hec 6 has been extensively applied by the German government for previous research of the river Elbe, and is incorporated in the channel module of the DSS. Both types of models, steady state model and hydrodynamic model, are discussed in section 3.1. The results of the simulations of the hydraulic models are used as input for a damage model. Two types of risk/damage models are available; the statistical risk-analysis based approach, which uses results from Hec 6, and the event-based damage model, which uses inundation and velocity maps provided by Sobek. A more detailed description of the damage models is given in section 3.2.

3.1 Hydraulic models This section gives a brief introduction to the models used in this research. Their advantages and limitations are accordingly discussed. Section 3.1.1 describes the Hec 6 model and its underlying equations. Sobek is presented in section 3.1.2.

3.1.1 Hec 6 Developed in 1991 by the US army Corps of Engineers, Hec 6 is a one-dimensional movable boundary open channel flow numerical model. It was designed to simulate and predict changes in river profiles resulting from scour and/or deposition over moderate time periods (typically years, although application to single flood events are possible) [US Army Corps of Engineers, 1993]. The model is based on the standard step method and it can cope with steady non-uniform flows. This computational procedure calculates the water depth and velocities between the sections for which the data are available [Roberson et al., 1988]. The energy equation that needs to be solved is the Bernoulli-equation [US Army Corps of Engineers, 1993]:

ehgvWS

gvWS ++=+

22

211

1

222

2αα

3.1

Where: WS1, WS2 = water surface elevations at ends of reach [m]. In the original Bernoulli-

equation WS is split up in zb [m] (the distance between the bed level and the reference level) and in h [m] (the water level);

α1, α2 = velocity distribution coefficients for flow at ends of reach; v1, v2 = average velocities (total discharge divided by the total flow area) at ends of reach [m/s]; g = acceleration of gravity [m/s2]; he = energy loss [m]. The terms of the equation above are also shown in the picture on top of the next page. The energy losses consist of two kinds of losses, namely friction hf [m] and form ho [m].


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So the total energy loss is [US Army Corps of Engineers, 1993]:

ofe hhh += 3.2

Figure 3.1 Energy equation terms in the Hec 6 model [US Army Corps of Engineers, 1993]

To approximate the transverse distribution of flow, the river is divided into sections with similar hydraulic properties in the direction of the flow. Each cross section is subdivided into portions that are referred to as subsections. The calculation methods used to obtain the friction loss is discussed in the Hec 6 manual [US Army Corps of Engineers, 1993]. It is clear that Hec 6 is limited to steady flow computation. This simplicity has some advantages, for example the computation time is very low and in addition to this, due to low level of complexity, the model doesn’t require a large data input. It makes Hec 6 cheap to implement and suitable for a rapid assessment of the water depths for a static situation. However this model has also several serious drawbacks according to the requirements of risk and damage modelling, they are: • First, the model does not consider the time dependent aspects. Due to the shear

stress and other hydraulic characters of the river, flood wave propagation consists of transportation and attenuation (Figure 3.2), which, however, cannot be simulated by a steady flow model [Abbott et al., 1998].

• HEC 6 is not feasible to simulate dike break where flow dynamics occur. Dike break is one of the main non-structural measures [Marchand et al., 2003] of the DSS. The dike break simulation aims for simulating scenarios that can provide flood damage and other consequent impact such as ecological changes.

• The third drawback of Hec 6 is that the model cannot calculate the water depth in case of a supercritical flow. In the standard step method for water surface profile computations, calculations proceed from downstream to upstream, based upon the reach’s starting water surface elevation [US Army Corps of Engineers, 1993]. When the flow is sub-critical, the computations proceed upstream. On the other hand when the flow is supercritical, then this procedure is no longer applicable. In this case Hec 6 will equate the water depth with the critical depth. An example of the simulations of these flows is given in Figure 3.3.


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The unfeasibility to simulate supercritical flows does not make Hec 6 unsuitable for implementation in the DSS. These flows only occur when the bed slope is very steep, or when the river is very narrow, which is not common in the Elbe, as most of the river it has got a mild bed-slope and a wide flow profile. However the more sophisticated damage models, like the event-based damage model discussed in section 3.2.2, Hec 6 is not feasible due to its lack of dynamics computation.

Dampening flood wave

Time [days]

Dis

char

ge [m

^3/s

]

Discharge at x = 0Discharge at x + n

Figure 3.2 Dampening of a flood wave due to friction

Figure 3.3 Examples of sub- and supercritical flows in Hec 6

[US Army Corps of Engineers, 1993]


19

3.1.2 Sobek1D2D and Sobek 2D Another model option for application in the DSS is Sobek Rural. It is a software package which consists of different modules, namely 1D2D and 2D. As the name indicates, the 1D2D model consists of two components, i.e. a 1 dimensional and a 2 dimensional module. In the 1 dimensional module the model takes that the velocity in the main flow direction (x direction) as normative. For the water depths in the main channel this is no problem, but when an overtopping or a dike break occurs the 1 dimensional assumption is no longer correct. To cope with that, Sobek offers the possibility to model the flows in the floodplains in two dimensions. Next to the 1D2D variant, Sobek offers a complete 2 dimensional module for both the main channel and floodplains. Due to the fact that both components compute the water depths, by solving the equations for the continuity and the momentum, the explanation of how Sobek works applies for either of them. The continuity equation is based on the mass balance erected for a spatial element (∆x-∆y-∆z) of fluid. The incompressibility of water has the consequence that the mass of an element cannot change by in- or out flowing water. In other words the inflowing mass (or volume) of water must immediately be compensated by the same amount of out-flowing water [Ribberink et al., 2002]. In Figure 3.4, the mass flow rate is portrayed in and out of an elementary control volume.

Figure 3.4 Mass flow rate in and out of an elementary control volume [Abbott et al., 1998]

Due to the fact that the maximum number of dimensions the flow is modelled is two, the equations discussed below concentrates on the x-y plane. The continuity equation of a two dimensional flow is:

0)()(=

∂∂

+∂

∂+

∂∂

yvh

xuh

tζ

3.3

Where: ζ = water level above plane of reference [m]; t = time component [s]; h = total water depth (ζ + water level below plane of reference) [m]; u = velocity in x-direction [m/s]; v = velocity in y-direction [m/s];


20

The other basic equations are those for the momentum. These equations can be derived from the impulse balance for an element of fluid. The principle valid is that the change of impulse (mass times speed) must be in balance with the external forces that are working on the element. The external forces or accelerations can be caused by spatial variations in the pressure, and the gravity (acceleration g in z direction). In addition there are also internal friction forces active due to the viscous character of water. Besides these additional viscous forces flows are almost always turbulent, which creates stresses. When all these components are taken in account the continuity and momentum equations can be obtained. 1D flow:

Continuity equation: 0)(=

∂∂

+∂∂

xuh

tζ

3.4

Momentum equation: 02 =++∂∂

+∂∂

+∂∂ uau

hCuu

gx

gxuu

tu ζ

3.5

2D flow:

Continuity equation: 0)()(=

∂∂

+∂

∂+

∂∂

yvh

xuh

tζ

3.6

Momentum equations: 02 =++∂∂

+∂∂

+∂∂

+∂∂ uau

hCVu

gx

gyuv

xuu

tu ζ

3.7

02 =++∂∂

+∂∂

+∂∂

+∂∂ vav

hCVv

gx

gyvv

xvu

tv ζ

3.8

Where: V = velocity: V = (u2 + v2)1/2 [m/s]; C = Chezy coefficient [m1/2/s]; a = wall friction coefficient [1/m]. A finite difference number method, the “Delft Scheme” is applied to solve the equations above [Roberson et al., 1988]. Both the 1D2D and the 2D model have the drawback that it’s not possible to compute water depths when a supercritical flow occurs. Furthermore is the computational time with Sobek perhaps longer then Hec 6, because this model is not so sophisticated as Sobek is. Especially the 2 dimensional version can take longer, due to the fact that more equations have to be solved. Finally the Sobek 2 dimensional version needs more detailed and thus expensive input data.


21

3.1.3 Qualitative assessment of the most appropriate hydraulic model Having described the working and advantages/disadvantages of the models, the most appropriate one can be selected through a qualitative assessment. This assessment is a qualitative evaluation; a quantitative comparison of all the computations is presented in chapter 5. There are several criteria that can be used to investigate the overall performance of the models: • Complexity: which comprises both the equations and the numerical scheme. The

complexity must be minimal without losing its functionality to distinguish the effects of different scenarios (in Figure 1.1);

• Accuracy: the goodness-of-fit; • Computation time; • Feasibility to model dike break/overtopping.

Due to the fact that the criteria are not considered equally important, a weighting factor is introduced. According to the DSS development requirement, the most important feature of the hydraulic model is the possibility that a dike break/overtopping can be modelled. The second important criterion is the computation load (time) that is needed by the model. After that follows the accuracy, and complexity. The arrangement is chosen arbitrarily. The potential performance of the three models is ranked in the table below, where 1 denotes the best, and 3 is the poorest performance:

Criteria Hec 6 Sobek 1D2D Sobek 2D

Complexity 1 2 3 Accuracy 3 2 1 Computation time 1 2 3 Dike break/overtopping 3 1 1

Table 3.1 Ranking of the different criteria (1 is the best and 3 the poorest) There are several options to rank the appropriateness of the models; however most of them are only suitable for quantitative comparisons. A procedure that allows the user to classify qualitative values as well is the “expectation-value method”. First a number of qualitative effect scores are calculated using the formula 3.9. Where M1 is the best alternative, M3 is the least attractive one, and m is the number of alternatives [Pouwels].

)1(121

11

1

23

22

1

−−−=

−=

=

mmmM

mM

M

3.9

The weights are transformed to a vector, with the help of the next formula. C5 is the most important, C1 the least important criterion, and c the number of weights.


22

)3(1

)2(1

)1(11

)2(1

)1(11

)1(11

1

24

23

22

21

−+

−+

−+=

−+

−+=

−+=

=

cccccccC

cccccC

cccC

cC

3.10

Then a matrix is set up which quantifies the qualitative effect scores:

Criteria Hec 6 Sobek 1D2D Sobek 2D Weight

Complexity 1,00 0,89 0,61 0,09 Solution method 0,61 0,89 1,00 0,04 Accuracy 0,61 0,89 1,00 0,16 Computation time 1,00 0,89 0,61 0,26 Dike break/overtopping 0,61 1,00 1,00 0,46

Table 3.2 Qualitative matrix and weights Eventually the qualitative effect scores are multiplied by the weight vector and added up. Hec 6 scores 0.74, Sobek 1D2D 0.95, and Sobek 2D 0.87. This would appoint Sobek 1D2D on beforehand as the most appropriate model. However it must be noted that the qualitative assessment is an opinion.

3.2 Damage models Two types of damage models are tested in this study. The statistical model is a risk-analysis-based model that utilises results of Hec 6. The second model, an event-based damage model, utilises the output of the Sobek simulations, namely the maximum inundation depth and velocity maps. Both damage models are discussed in this section.

3.2.1 Statistical damage model; based on Hec 6 Flood risk is defined as the probability of failure of flood defence (for example failure as overtopping of the dike or a dike breach), and the consequence of the failure, namely the damage. Mathematically the risk R is expressed as the product of failure probability pfailure of river defences, and the estimation of the loss fdamage in case of failure:

damagefailure fpR ×= 3.11 Where failure is defined as overtopping of the dike. The damage function is expressed as follows:

∫∞

××=><*

)())((ijq

ij dqqfqhfdcijD 3.12


23

Where: <D>ij expectation value of relative flood damage at cell ij (%)

ijq * critical discharge, calculated using rating curve at cell ij (m3/s):

⎪⎪⎩

⎪⎪⎨

⎧

<=

>=

i

i

i

dikeijbdike

dikeijbij

ij

zza

z

zzaz

q/1

/1

)(

)(*

zij elevation at cell ij; a,b rating curve coefficients at row I; zdikei dike height at row i, applied for both left hand and right hand sides; c economic cost coefficient associate with landuse type; fd(h(q)) flood damage function, as a function of inundation depth (%); hij(q) inundation depth in cell (i,j); f(q) probability density function. For the probability density function the Gumbel distribution can be applied, because it is suited for extreme events [Shaw, 1999]:

( ))(exp)( aXbeXF −−−= 3.13 In which: F(X) is the chance that the peak discharge is smaller than X. The statistical risk model calculates the expected annual damage at each grid cell through the integration of the probability density function of discharge, and the flood damage functions. The damage is expressed as the expected value of percentage (%) damage proportional to the maximum damage. The integral of the Gumbel distribution provides the total chance the dike overtops. Therefore the lower boundary is equal to Qcritical. In principle the upper boundary is infinite in order to include all possible flood events. However the chance that the discharge reaches the infinity mark is very low. Due to the fact that the integral must be discretisized to solve it numerically, an arbitrary chosen upper boundary of 6,000 m3/s is used. The total damage is an integral of the damage function. The minimum discharge that would cause an overtopping is estimated by the Hec 6 model for every 100 meters along the river. Other parameters needed for the Gumbel distribution are from historical data at the gauge stations. There are three different damage functions available, namely: Elbe 2000 [Maiwald, 2001], Cur 1990 [Sande, 2001] and Pflunger 1995 [Sande, 2001]. The Elbe 2000 function is provided by the BfG. The other two are from the studies carried out in the Netherlands and are used as a comparison material to the German one. The damage functions distinguish two types of land use, namely agriculture and household. Depending on the land use, the model gives a maximum value of the potential damage if the inundation depth increases to 4 metres and above. Below that depth, the model interpolates percentage damage according to the inundation depth. The only significant difference between the three functions is that each model attributes other values to the maximum damage. The depth-damage curves for the household and the agriculture land use are depicted in Figure 3.5 and 3.6, respectively. The considerable differences in the progress between the three curves might be due to the fact that each damage function has its own maximum potential damage in monetary terms.


24

Depth-damage curve for household

0

10

20

30

40

50

60

70

80

90

100

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

Inundation depth [m]

Pot

entia

l dam

age

[%]

Elbe 2000Cur 1990Pflunger 1995

3.5 Household land use class depth-damage curves that represent the relation between the

inundation depth and the potential damage [%]

Depth-damage curve for agriculture

0

10

20

30

40

50

60

70

80

90

100

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0


Pote

ntia

l dam

age

[%]

Elbe 2000Cur 1990Pflunger 1995

3.6 Agriculture land use class depth-damage curves that represent the relation between the

inundation depth and the potential damage [%] The main drawback of this risk model is that the water level in the river is assumed equal to the inundation levels. This assumption makes the outcome of the model quite rough.


25

3.2.2 Event-based damage model; connected to Sobek The event-based damage model is developed to assess damage due to flood event associated with a certain return period, or flood duration. It uses the inundation depth and velocity as the model input, with other data such as land use, depth-damage curves and potential damage values (Euros/m2). The damage calculated in this study is expressed as percentage damage of the total potential damage, because of the uncertainty of the value of each land use type that differs for different locations. There is some literature available about the value in monetary units [Internationale Kommission zum Schutz des Rheins, 2001], these data are mostly for urban areas however and not valid for the entire Elbe, but restricted to their regions. As discussed in paragraph 2.3 there are 16 different land use types distinguished in the study area. However only the non-irrigated arable land class, has its own specified depth-damage curve. The rest of the land use types share another curve. Both depth-damage curves are depicted in Figure 3.7:

Depth-damage curves

0

10

20

30

40

50

60

70

80

90

100

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0


Pot

entia

l dam

age

[%]

non-irrigated arable landOther

Figure 3.7 Both depth-damage curves that represent the relation between the inundation

depth and the potential damage [%] Further a fixed number of people per cell, who are affected by the flood, is assumed for each land use type. This number is varying from 0, for nearly uninhabited land like moors, to 2000/km2 urban and industrial areas. Based on the people per land use the model estimates the number of affected people per cell. Finally the risk is for each cell is expressed in a qualitative way using the computed damage map and the maximum velocity map. Depending on the combination of the damage and velocity in a cell, the risk is classified into 5 distinctive classes, from 0 (no risk) to 4 (high risk). Next to the potential damage and affected people, the model predicts a risk level. Whether this is realistic and/or desirable can be up to discussion. Table 3.3 shows the ranking on which the risk is determined.


26

Damage (% of max)

Low velocity Medium velocity (>1/4 of max)

High velocity (>2/3 of max)

Very high velocity (>3/4 of max)

0 0 0 0 0 0-10 Risk class 1 Risk class 1 Risk class 1 Risk class 1 10-20 Risk class 1 Risk class 2 Risk class 2 Risk class 3 20-30 Risk class 2 Risk class 2 Risk class 3 Risk class 4 30-100 Risk class 4 Risk class 4 Risk class 4 Risk class 4

Table 3.3 Arrangement of the risk classification

3.3 Methodology The research investigates the performance of Hec 6 and Sobek models on their integrations with the flood risk assessment. All hydraulic models are connected with a damage model, which results into three types of combinations. These systems are illustrated in the research framework in Figure 3.8. The hydrodynamic models (Sobek 1D2D and 2D) are used to model a number of flood events, with and without dike break. Data availability is described in chapter 2. The models are set up, calibrated, and validated (chapter 4). A number of scenarios are run to provide maps of the maximum velocity and inundation depth. The results of the calibrations and the produced maps for the different hydrodynamic models are compared. The event-based damage model uses the hydraulic results. The most important output of the damage model is the relative damage as a percentage of the potential maximum damage. Further the number of people affected by the flood, and a number for the risk, based on the percentage damage and velocity. A more detailed description of the event-based damage model is given in chapter 4. The results of the computed damages for the different hydrodynamic models are compared. To pass judgement over the most appropriate combination hydraulic/damage model, an uncertainty and sensitivity analysis is carried out. The hydrostatic model Hec 6 is embedded into the statistic damage model, which provides the risk, rather than an estimation of the damage, expressed in for example money. The set up and fine-tuning of the model parameters in Hec 6 is previously been carried out by H. Holzhauer. In order to assess the functioning of this model, an uncertainty and sensitivity analysis is carried out.


27

• Roughness • DEM • Scenarios

Sobek 1D2D Sobek 2D

Obtain/prepare input data

Event-based damage model

Damage,risk and affected

people

UA/SA

Hec 6

Statistic damage model

Risk

UA/SA

Figure 3.8 Research framework


28

Chapter 4 Case study This chapter describes the results of the computations performed with both the hydrodynamic models Sobek1D2D and Sobek2D. Section 4.1 describes the input data for the models. The results of the Sobek 2D model are given in section 4.2 and section 4.3 represents the 1D2D computations.

4.1 Data Making the model ready for use comprises obtaining data for the boundary conditions (section 4.1.1) and completing the dike data (section 4.1.2).

4.1.1 Time series The first hydrodynamic model to be tested is the 2D version of Sobek. The input data needed for this model, as well to the 1D2D variant, is listed in paragraph 2.3. Some are not directly usable and need some modification. The data available from the Tangermünde gauge station, located at the upstream boundary of the research area, is used. The available time series of Tangermünde, covers 35 years of daily average discharge in the period of 1960-1995. Figure 4.1 presents the discharge time series of Tangermünde, and as a comparison the discharge of 200 year return period.

Time series Tangermunde

0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

nov-

60

nov-

65

nov-

70

nov-

75

nov-

80

nov-

85

nov-

90

nov-

95

Time [m/y]

Dis

char

ge [m

^3/s

]

Q(t)Q200

Figure 4.1 Discharge time series at Tangermünde station applied for the upstream boundary and a

Q200 flood event Due to the fact the models will be used to simulate relative large flood events, with return periods of up to 200 years, it is clear that the time series above is not sufficient. The highest discharge that is available from the time series (1/11/1960-31/10/1995) is 3,259 m3/s, occurred in September 1981. It is found that this event has a return period of 28


29

years, which is statistically a low flood. This Q28, together with a Q50 and a Q200 event corresponding to return period of 50 and 200 years, are used in the simulation of the hydrodynamic models. Two scenarios are set as; a) normal situation, b) situation with an artificial dike break. The Gumbel distribution is involved to obtain the discharges of Q50 and Q200 events, they are 3,573 m3/s and 4,303 m3/s, respectively. Next to the Gumbel distribution, many other probability distributions exist that have been analyzed for application to the extreme values produced by flood peak discharges. Literature shows that there is no general agreement on to which distribution, or distributions should be used for hydrologic frequency analysis of extreme rainfalls or floods [Nguyen, 2000]. The Gumbel distribution is suitable for peak discharges [Shaw, 1999] however, and because the needed parameters are known at any location of the Elbe, this distribution is selected. To satisfy the upstream boundary Sobek needs discharges of a daily base. Therefore, next to the peak discharge, the flood duration is needed. A single linear regression approach is used to obtain the flood duration. A relation between the size of a flood event and its duration can be found at literature [Yue et al., 1999]. The duration of peak events in the past is extrapolated from the available time series at Tangermünde. The length of the events can be measured with different methods. In this study threshold value of discharges are selected for the start and end of a flood event. This method is described in the literature [Shaw, 1999]. A threshold discharge of 1,479 m3/s corresponding to a Q1.5 event is used. To study this presumed relation, a linear regression model is set up with is the least-squares method. The result is expressed as:

xy 0.0111-8.9389+= Where: y is the duration [days]; x represents the size of the flood event [m3/s]. A method to quantify the goodness of fit is the Nash-Sutcliffe coefficient [Kok et al., 2004], expressed as:

∑

∑⎟⎠⎞

⎜⎝⎛ −

−−=

−

=

=2

1

212 )(

1ymym

ysymR

ni

ni 4.1

Where: ym is the measured water level; ys is the simulated water level. The R2 of the regression analysis is 0.52. It is rather poor and must be considered an important uncertainty source. The goodness of fit also consists of uncertainty introduced by the subjectivity of the choosing of the threshold value of the discharge.


30

There are alternative methods to generate a flood event, particularly on on the study of flood frequency analysis. However, most of these studies describe a flood event only by its instantaneous peak or its maximum daily flow [Javelle et al., 2001]. This provides only a limited assessment, while the solution of many hydrological problems requires the knowledge of complete information concerning the flood event (flood peak, flood volume, flood duration, or hydrograph shape) [Yue et al., 1999]. Only a limited number of researchers have addressed this topic. Basically three different methods can be distinguished: • Regionalization [Nguyen, 2000]; • Peak-volume analysis [Yue, 1999] and [Strupczewski et al., 2001]; • Flood-duration-frequency (QdF) analysis [Javelle et al., 2001].

To solve hydrological problems at sites where no, or very poor data are available, regionalization methods are frequently used. Data from hydrological similar sites are transferred to the problem area. These techniques are often criticized for the obvious subjectivity, in particular in the definition of hydrological similar sites or regions, and lack of theoretical justifications [Nguyen, 2000]. For each observed flood, a starting and an ending date are defined in peak-volume analysis. The volume and duration are determined and analysed as random variables. It is important to mention that in such an analysis approach the determination of the start and ending date contains a part of subjectivity and must be done with extreme care [Javelle et al., 2001]. The third method to completely describing a flood event is the QdF analysis. The main difference with the previous method is that the duration is not considered as a random variable but as a fixed parameter. Averaged discharges are computed over fixed durations. Then for each duration, a frequency distribution of maximum discharges is analysed [Javelle et al., 2001]. However due to time limitation, and the nature of importance, the approaches above are not studied in the present research. The duration of the Q50 and Q200 flood events is, with singe linear regression, estimated at respectively, 31 and 39 days. The hydrograph shape has been simplified, namely it is assumed to be parabolic. The Q50, Q200, and the largest flood ever measured, the Q28 (3,259 m3/s), are plotted in Figure 4.2.


31

Flood events

0

5001000

1500

2000

25003000

3500

40004500

5000

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39

Duration [days]

Dis

char

ge [m

^3/s

]Q28Q50Q200

Figure 4.2 Artificial flood events created with linear regression analysis

4.1.2 Dike Together with the Q-h relation based on the measurements at Havelberg, the station at the downstream boundary, both upstream and downstream conditions are satisfied. A flood damage model is used to calculate flood damage using the hydraulic results (section 2.3). The Sobek 2D model is set up for a simulation of a Q200 event with an artificial dike break. The location of the dike break is Northeast of Sandau station as shown in Figure 4.3. The dike breaks when the discharge reaches the Q10 level (2,707 m3/s). The created gap reaches its maximum width of 50 meters in 1 hour, and the crest level drops to the same level as the elevation next to the dike. The location of the break is not very realistic, due to the fact that the dikes west of the river, are considerably lower. However the lack of data, available for the DEM at the west riverbank, forces the break to be modelled as shown on the next page. To avoid such a problem, area with equal dike heights on both riverbanks should been chosen in future work. The DEM has a resolution of 50mx50m. At different locations of interests, under which the Sandau measurement station, data is collected by means of history points, which stores data for each time step throughout the simulations. Figure 4.3 demonstrates the locations of the Sandau station and the artificial dike break.


32

Dikes

Sandau station

Dike break

Figure 4.3 Layout of the 2D modelling area, including the location of the dike break, Sandau gauge station and the dikes. The brownish legend refers to the land levels [m+NN], the bluish legend represents the water depths [m].

Artificial interpolation to the dike data was used to fill in data gaps for the dike height in the original DEM. Figure 4.4 shows the situation, with the original DEM (i.e. no correction), for a Q200 event 45 minutes before the dike breaks, due to the gaps in the dike data, the area behind the dike is already flooded, with the result that the break makes no difference.


33

Figure 4.4 The research area is, 45 minutes before the dike breaks, already flooded due to a Q200 event

In order to overcome this problem, the dikes on both sides are manually closed. With the adapted DEM the water only flows into the area after the dike break occurs.

4.2 Sobek 2D calculations As described in section 4.2.1, the 2D model is calibrated and validated. The scenarios, consisting of three flood events, with and without dike break, are simulated. Inundation depths and flow velocities are simulated (section 4.2.2). With the Sobek output, the damage model calculates the damage, risk and the number of affected people by the flood (section 4.2.3).

4.2.1 Calibration and validation As mentioned in paragraph 2.3 the model needs a lot of input data. Most of them, the DEM, the upstream and the downstream boundary, are fixed. Roughness in the river channel is calibrated, but roughness outside of the river, based on the land use, is not calibrated due to the lack of measurements. A three month period is used for the calibration, namely from 1/2/1981 to 31/4/1981. This period is simulated by using the Q(t) time series as the upstream boundary condition. For the downstream boundary, the Q(h) relation at the Havelberg gauge station is used. It includes the maximum event that was ever measured (Q28) at 19/3/1981.


34

According to the literature, the average Manning’s roughness n for the entire river channel varies between 0.036 s/m1/3 and 0.076 s/m1/3 [www.rcamnl.wr.usgs.gov/sws/fieldmethods/]. Higher Manning n do occur, but only in rocky mountainous creeks. Other literature shows that the average roughness for the channel is about 0.035 s/m1/3, and the floodplains reach Manning n of 0.05 s/m1/3 [www.Imnoeng.com/manningn.htm]. During this iterative calibration process, simulations with Manning n roughness, varying from 0.01 s/m1/3 for the bottom to 0.05 s/m1/3 for the top of the bank proved to reach the highest R2. The values in between are interpolated. A R2 of 0.88 is obtained for the calibration. The maximum deviation between the computed and measured water depths is 0.47 meter. The error at peak level for Q28 flood event is 0.03 meter. The first day was not taken into account due to the fact that the calculation started with a complete dry system, with the result that this day was needed to fill the river with water. The computed water level is compared with the measured water levels at the Sandau station as shown in Figure 4.5:

Calibration Sobek 2D

23

24

25

26

27

28

29

30

2/1/

1981

2/8/

1981

2/15

/198

1

2/22

/198

1

3/1/

1981

3/8/

1981

3/15

/198

1

3/22

/198

1

3/29

/198

1

4/5/

1981

4/12

/198

1

4/19

/198

1

4/26

/198

1

Date [m/d/y]

Wat

er le

vel [

m+N

N]

MeasuredSimulated

Figure 4.5 Comparison between the by Sobek 2D computed and measured water levels. Note: the first

day was not taken in account for the determination of the goodness of fit The figure above shows that the simulated levels are higher than the measured ones during low discharges. The opposite occurs when the discharges are high while the measured water levels are higher. During a period with low discharges, the flow is concentrated at the lowest areas of the river. The results shown in figure 4.5 suggest that the roughness for the channel is lower than 0.01 s/m1/3. The opposite applies for the top of near the bank, the result suggests that the Manning n is larger than 0.05 s/m1/3. It must be noted that the roughness is the most sensitive parameter that can be adjusted to improve model result. The roughness is a lump parameter that may reflects model or data uncertainties.


35

The model was validated for two other periods. The first is from 12/24/1986 to 01/12/1987 and has got relative low discharges. R2 is 0.93 and the maximum error is 0.83 meter. The second validation period is from 11/20/1974 to 12/31/1974 with relative high discharges. R2 in this case is 0.92; the maximum deviation is 0.48 meter. The maximum difference between the simulation and the measurements, especially in the first series, is quite high. However it must be noticed that the maximum deviations occur when the discharges are relatively low. The deviations during higher discharges, for the first and second validation series, are 0.004 and 0.01 meters, respectively. The goodness-of-fit in both series is quite satisfying.

4.2.2 Simulations of artificial flood events The result for the Q200 flood event with dike break, based on the corrected DEM, is shown in Figure 4.6 and Figure 4.7. The dike is artificially broken when the discharge reaches the Q10 level, which is the overtopping level of the western dike. The left figure shows the situation 1 day before the dike break. The western dike is already overtopped, which is caused by insufficient dike height. The eastern dike however fulfils its duty until it is broken (figure 4.6). In a scenario without an artificial dike break the eastern side dike should theoretically provide protection against events up to Q100 (3938 m3/s). During the simulation of a Q200 event without dike break, the water however does not overtop the eastern dike. This is because the western dike is overtopped, and in turn, the water is stored outside of the river.

Figure 4.6 and 4.7 The results of a Q200 event, based on the corrected DEM, the day before (left figure)

and the day of the dike break (right figure) Sobek provides raster maps for the maximum inundation depths and the maximum flow velocities during the simulation period. These output files are analysed and a number of key parameters are obtained namely the mean depth, velocity, and the number of cells that remains dry. Table 4.1 represents the results of this analysis for the six scenarios.


36

Without dike break With dike break Flood event Spatial

avg. depth [m]

Spatial avg. velocity [m/s]

Σ ha of non flooded land (% of total)

Spatial avg. depth [m]



Q28 1.856 0.579 4,945 (13.28) 2.810 0.347 855 (2.30) Q50 1.972 0.611 4,919 (13.21) 3.224 0.354 638 (1.71) Q200 2.187 0.676 4,900 (13.16) 3.692 0.386 440 (1.18) Table 4.1 Inundation depths, flow velocities, and non-flooded land belonging to the

scenarios Logically the larger the flood event the bigger the inundation depth becomes. Also the number of cells that remains dry is decreasing as the events get bigger. The difference between a scenario with and without the artificial dike break is obvious. A scenario with dike break produces clearly higher average maximum depths, while the number of dry cells and the average maximum flow velocities are quite lower. It is because the western dike is considerable lower than the eastern dike, as a result of which all the water is either transported through the riverbed itself, or floods the land west of the dike. Therefore the land east of the river is not flooded, and therefore there are fewer cells inundated in a scenario without a dike break. Moreover, due to the bigger difference between flooded and dry cells, the spreading of the inundation depths in such a scenario is bigger. On the other hand the flow velocities are smaller, and the spreading of them is bigger, when the eastern dike brakes. Because there are more cells inundated, the average maximum flow velocity will decrease. Furthermore the flow is less uniform than in a scenario without dike break, which results in a larger standard deviation. As described above, during a scenario without dike break, the water overtops the eastern dike only. The available data in that part of the area is very limited, so the water reaches the border of the model quite quickly. The edges of the DEM in the Sobek model are like a “wall of infinite height”. When the water reaches this wall, the water level in the area will rise. However due to the effect large amount of dry cells that are protected at the eastern side of the river, the spatial average maximum inundation depths are lower than those of a scenario with a dike break. The difference between an event with and without dike break is studied. The dissimilarity between the two types of scenarios at Sandau, and at the downstream boundary, Havelberg, for Q50 and Q200 event are shown in Figure 4.8.


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Q50 and Q200 scenarios at Havelberg

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Figure 4.8 Difference in water levels between Q50 and Q200 events with and without dike break at

Havelberg Figure 4.8 shows that immediately after the artificial dike break, the water level does not rise as quickly as in a no-dike-break situation. Therefore the Q50 event results in a considerable lower maximum of the flood wave. The simulation of a Q200 event leads to a lower level during the period before the peak value of the flood. The maximum gap between an event with and without dike break is, for both Q50 and Q200 floods, 0.16 meters at Havelberg. The maximum discrepancies of the Q50 and Q200 flood events are reached respectively 5 and 4 days after the dike breaks. After some time the water levels, produced by both scenarios, converge. These results are not all positive, because the objective of the artificial dike break is to reduce the peak water levels, and store the water temporarily behind the dikes (chapter 2). Due to the fact that the peak water level is not lower, during a Q200 event with dike break, it is questionable if the damages downstream will decrease. There are a number of causes that are originating from the fact that the peak levels are not reduced. One of them is that due to a lack of knowledge of high floods, assumptions have to be made for the extrapolation of the existing rating curve at downstream boundary, at Havelberg. To prevent such an inadequacy of the data, an assumption is made to extend the rating curve, i.e. with water level increment of 0.01 is set to a discharge of 6000 m3/s. This solution is temporal. However, without such an adjustment, water levels with a dike break are higher than the levels computed in a scenario without a break. The problem with the downstream boundary can be categorised as a code problem, which has no relation with the modelling itself. Another cause is that the size of the DEM is not sufficient to hold the water that is flowing through and over the dike. Due to the relatively small dimensions of the available


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map, the area behind the dike floods so rapidly that there is no storage available when the flood reaches its peak. Changes to the model have been made in such a way that the latter two problems are diminished. A variety of widths of the dike break have been entered (up to 200 meters), however the results were identical to those with the original scenario. On the other hand altering the time of the break did lower the peak levels. By “trial and error” the moment of the dike break, for both Q50 and Q200 events, have been shifted in such way that the peak reduction is maximal. Figure 4.9 demonstrates that a controlled dike break leads to a reduction of the peak water level for both Q50 and Q200 events. In case of the Q50 scenario the dike breaks when the discharge reaches the Q30 level instead of the original Q10 level. Hereby the peak water level is reduced with 0.16 at Havelberg. Altering the time of the dike break, of the Q200 scenario, to the moment the discharge is equal to that of a Q75 event, results in a reduction of 0.17 meter for Havelberg. Previous research [Bundesanstalt für Gewässerkunde, 2003] shows similar results for reducing the peak water levels in the Elbe. At Pegel Wittenberge (km 450) the peak levels, resulting from different flood events, were reduced from 0.11 to 0.37 meter. Searching for the optimal time to break the dike leads to a significant improvement for both scenarios in term of damage reduction at downstream areas. Such a peak level reduction results into lower peak water levels downstream. Provided that the relation between the flood damage and the maximum inundation level is predominant, the damage in those of higher economic values can be reduced. However, as mentioned in paragraph 4.1 the western dike is considerably lower than the eastern one, where the dike is artificially broken, so that in reality the western dike will overtop/collapse long before the discharge reaches a Q75, or even a Q30 level. Therefore a more spatially extended DEM will improve the results. The DEM must preferably portray the area behind the lower western dike in order to locate an effective dike break there.

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Figure 4.9 Difference in water levels between Q50 and Q200 events with delayed and without dike break

at Havelberg


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4.2.3 Damage modelling using Sobek 2D results The results of the Sobek 2D simulations, the maximum inundation and maximum velocity maps, are used as the input of the flood damage model. The damage model is discussed in section 3.3. The results of the damage calculation are given in the table below:


avg. prop. damage

∑ ha with max. damage

∑ ha with no damage

Spatial avg. prop. damage



Q28 25.60 839 4,945 45.90 1,185 855 Q50 26.17 888 4,919 50.14 1,616 638 Q200 27.05 952 4,900 52.78 1,902 452

Table 4.2 Proportional damage (% of potential maximum damage) according to the different maximum inundation maps

As expected the damage is proportional to the scale of flood events. The difference between a scenario with and without a dike break is obvious. Even a relatively smaller flood event, like a Q28 event with dike break, causes a larger damage than a Q200 event without dike break. This is due to the fact that there are more “high-value” land use types (such as urban areas) flooded, with a Q28 event with dike break, than with a Q200 event without dike break. The difference between a Q200 event with a dike break and a Q28 event without dike break is presented in the damage maps as shown in Figure 4.10 and Figure 4.11.

Figure 4.10 Proportional damage (%) map Q200 event with dike break

The area depicted is that of Sandau (km 410.0 – km 422.5)


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Figure 4.11 Proportional damage (%) map Q28 event without dike break

The area depicted is that of Sandau (km 410.0 – km 422.5) The table below presents the number of people who are affected by the floods:

Without dike break With dike break Flood event Spatial avg.

[people/ha] ∑ ha with no aff. people

Total aff. people

Spatial avg. [people/ha]

∑ ha with no aff. people

Total aff. people

Q28 1.72 5,948 16,103 3.64 2,556 34,306 Q50 1.72 5,926 16,205 3.76 2,357 35,292 Q200 1.72 5,909 16,292 3.84 2,174 36,053

Table 4.3 Number of affected people A similar pattern can be seen for the damage, i.e. the larger the flood event, the more people are affected. Due to the fact that high-value land use types contain many potentially affected people, there is a large difference between the scenarios with and without dike break. Table 4.4 shows the risk levels obtained from the flood damage model. The arrangement of the risk classes is discussed in paragraph 3.2.2.


avg. risk level

∑ ha with max. risk

∑ ha with no risk

Spatial avg. risk level


∑ ha with no risk

Q28 1.82 4,121 4,946 3.36 7,369 863 Q50 1.86 4,258 4,919 3.55 7,994 645 Q200 3.55 7,994 645 3.69 8,447 454

Table 4.4 Risk levels according to the Sobek 2D output Except that the risk level of a Q50 event with dike break is equal to that of a Q200 event with no dike break, the results do not differ from the previous two calculations. Again


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scenarios with dike break leads to higher risk levels than scenarios with no dike break. Remarkable is that, the risk level of a Q200 event is much higher, than those of a Q28 or Q50 event, in case of the no dike break scenarios. This in contrast to the results presented in table 4.2, where the damages rise more gradually.

4.3 Sobek 1D2D calculations This paragraph describes the modeling with Sobek 1D2D. The same 6 scenarios as set up in section 4.1 have been simulated. As well as the modeling with Sobek 2D in the previous paragraph, the results have been used in the damage model. A lay out of the 1D2D model is depicted in Figure 4.12. The model is set up with the same data, regarding the DEM and roughness map, as the 2D module. However there are two exceptions. The first concerns the DEM, namely the artificial dikes have been removed. This measure has been taken, because a lot of the 1D-river cross sections contain both dikes. Another problem with the connection between the 1D and 2D part of the model is that due to data preparation problems of the 1D cross sections, the water does not flow correctly from the 1D into the 2D model. This problem causes a higher water level in the 2D model and is indicated in Figure 4.12 as “double storage”. By comparing the computed totals of water that flows in and out the model, with the measured totals, available from the time series, the deviation amounts to 33%. Due to technical reasons using rating curve, as downstream boundary for the 1D part, did not work. Therefore this model uses a water level time series as downstream boundary for the 1D part, and uses rating curve for the 2D boundary. The water levels belonging to a certain discharge (up to a Q28 event), can be obtained from the available time series at the Havelberg gauge station. The regression model from section 4.1 is used to create the levels caused by the Q50 and Q200 events. The drawback is that using linear regression adds an additional uncertainty source, due to the poor goodness of fit of the model.


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Calculation point Sandau

Dike break

1D part

Double storage

Figure 4.12 Layout of the 1D2D modelling area, including the location ofSandau gauge station and the double storage. The legend relevels [m+NN].

The Q28 event is used for calibration. The best fit is a roughness Mans/m1/3 for the main channel and 0.04 s/m1/3 for the floodplain. As for thvalues are interpolated. The difference between the measured and colevels is shown in Figure 4.13.

R. Lomulder

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the dike break, fers to the land

ning n of 0.01 e 2D model these mputed water

12 November 2004

Calibration Sobek 1D2D

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Figure 4.13 Comparison between the by Sobek 1D2D computed and measured water levels The R2 of this run is 0.86 and the maximum difference is 0.29 m. This is a quite reasonable fit, and at first sight it looks almost as good as the 2D model (the R2 of the 2D model is 0.88). However the computed water levels are obtained from the 1D calculation point that is nearest to the actual Sandau gauge station (as presented in figure 4.15). Which is in contrast to the 2D calibration, where the simulated water levels are begotten at the Sandau historical data point (as depicted in figure 4.3), hence the same location as the actual measurement station. This means that the deviations due to the interaction between the 1D and 2D modules are not taken in account. It can be concluded that despite the fact that the R2 of the 1D2D variant is good, the model is not plausible. The results of the simulations with the 1D2D model are given in table 4.5.


avg. depth [m]



Spatial avg. depth [m]



Q28 1.204 0.068 3,694 (9.92) 1.230 0.079 3,617 (9.71) Q50 1.308 0.041 3,109 (8.35) 1.337 0.053 3,085 (8.28) Q200 1.466 0.038 2,941 (7.89) 1.506 0.056 2,897 (7.78) Table 4.5 Inundation depths, flow velocities, and non-flooded land of two scenarios

Table 4.5 shows clearly, that a bigger flood event causes a bigger inundation depth. It also shows that an event with dike break results into a bigger depth, than the same event without dike break. But unlike the 2D simulations the differences, between these two types of scenarios, are not so large. The same applies for the flow velocities, the contrast between the dike break and no dike break scenarios, are smaller. Like the 2D results, the same pattern can be seen here, namely the bigger the event, the lower the velocity.


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In order to illustrate the results above, and as a comparison to Figure 4.8, the difference an event with and without dike break is depicted in Figure 4.14.

Q50 and Q200 scenarios at Havelberg

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Figure 4.14 Difference in water levels between a Q50 event with and without dike break at Sandau and

Havelberg. The results are obtained without optimisation of the dike break time. Similar to the 2D model, the scenario with an artificial dike break results into a slower rising of the water level, from the moment when the dike is broken. The maximum difference at Havelberg, between an event with and without dike break, is 0.04 and 0.06 meters for flood events of Q50 and Q200, respectively. These maximum discrepancies are reached 5 and 8 days after the dike break for respectively the Q50 and Q200 flood event. Due to the fact that the peak levels are already lowered, based on the original time of dike break, they have not been optimised. Therefore the results in figure 4.14 can only be compared with the 2D results in figure 4.8. The maximum inundation maps and the maximum velocity maps can be entered into the damage model. The result of the damage calculation is presented in table 4.6.


avg. prop. damage



Spatial avg. prop. damage



Q28 25.40 383 3,694 25.81 390 3,617 Q50 27.20 402 3,109 27.70 412 3,085 Q200 29.84 442 2,940 30.48 454 2,897 Table 4.6 Proportional damage (i.e. % of potential maximum damage) according to the

different maximum inundation maps As expected the damage grows as the peak discharge increases. The difference between a scenario with and without a dike break is much smaller than in the 2D


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computations. This can be explained by the different outcomes for the inundation depths. The difference between a Q200 event with a dike break and a Q28 event without dike break is presented in Figure 4.15 and 4.16. The table below shows the number of people who are affected by the floods:

Without dike break With dike break Flood event Spatial avg.

[people/ha] ∑ ha with no aff. people

Total aff. people

Spatial avg. [people/ha]

∑ ha with no aff. people

Total aff. people

Q28 2.56 4,691 24,188 2.60 4,634 24,465 Q50 2.80 4,217 26,229 2.80 4,197 26,348 Q200 2.88 4,091 26,970 2.88 4,059 27,145

Table 4.7 Number of affected people The same pattern can be seen as with the damage, namely the larger the flood event the more people are affected. Scenarios with dike break produce higher risks than the ones without.

Figure 4.15 Proportional damage (%) map Q200 event with dike break The area depicted is that of Sandau (km 410.0 – km 422.5)


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Figure 4.16 Proportional damage (%) map Q200 event with dike break The area depicted is that of Sandau (km 410.0 – km 422.5)

Finally the risk values can be obtained, which are represented in table 4.8.


avg. risk level


∑ ha with no risk

Spatial avg. risk level


∑ ha with no risk

Q28 2.01 3,928 3,725 2.03 3,971 3,649 Q50 2.14 4,063 3,126 2.16 4,114 3,100 Q200 2.36 4,844 2,963 2.40 4,917 2,909

Table 4.8 Risk levels according to the Sobek 2D output The results of the risk calculations don not differ from the previous two results. Again a scenario with a dike break leads to a higher risk a scenario with no dike break, and a bigger event causes a higher risk level.

4.4 Comparison and conclusions Sobek calculations The comparison of the computations executed with both the models leads to some remarkable results. In the first part of this section the hydraulic performance of both models is compared. The second part analyses the outcome of the damage model. The difference in the calculation of the maximum inundation depth maps is given in the tables 4.9 and 4.10.


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Without dike break With dike break Flood event 2D spatial

avg. depth 1D2D spatial avg. depth

Difference (2D-D2D)

2D spatial avg. depth

1D2D spatial avg. depth

Difference (2D-1D2D)

Q28 1.86 1.20 0.66 2.81 1.23 1.58 Q50 1.97 1.31 0.66 3.22 1.34 1.88 Q200 2.19 1.47 0.72 3.69 1.51 2.18

Table 4.9 Comparison inundation depths

Without dike break With dike break Flood event 2D spatial

avg. velocity

1D2D spatial avg. velocity


2D spatial avg. velocity

1D2D spatial avg. velocity


Q28 0.58 0.07 0.51 0.35 0.08 0.27 Q50 0.61 0.04 0.57 0.35 0.05 0.30 Q200 0.68 0.04 0.64 0.39 0.06 0.33

Table 4.10 Comparison flow velocities There are two striking differences between the 2D and 1D2D simulations. First the mean of the maximum inundation depth maps and the maximum velocity maps, of the Sobek 2D computations are clearly higher. The second distinction is that the 2D model, produces a higher mean inundation depth, and a lower velocity, with the scenarios with the artificial dike break, than without a dike break. For example a Q28 event with dike break produces a larger inundation depth than a Q200 event without dike break. These differences are much smaller with the 1D2D model. A bigger flood event, dike break or not, simply leads to a larger spatial averaged inundation depth, and a lower velocity. Secondly, the differences of the outcome of the damage model can be analyzed. In table 4.11 the values for the damage, affected people, and risk are compared, for both models. Apart from the simulations with the artificial dike break, the damage produced by the input of both hydraulic models, is quite similar. The gaps between the other two parameters, the number of affected people, and the risk, are relatively smaller than it was. The deviant behaviour of the 2D model with dike break can be accepted, due to the fact that this is the only 2D scenario, where the eastern land floods.

Flood event without dike break

2D Prop. damage

1D2D Prop. damage

2D Aff. People/ha

1D2D Aff. People/ha

2D Risk

1D2D Risk

Q28 25.60 25.40 1.72 2.56 1.82 2.01 Q50 26.17 27.20 1.72 2.80 1.86 2.14 Q200 27.05 29.84 1.72 2.88 3.55 2.36

Flood event with dike break

2D Prop. damage

1D2D Prop. damage

2D Aff. People/ha

1D2D Aff. People/ha

2D Risk

1D2D Risk

Q28 45.90 25.81 3.64 2.60 3.36 2.03 Q50 50.14 27.70 3.76 2.80 3.55 2.16 Q200 52.78 30.48 3.84 2.88 3.84 2.40

Table 4.11 Damage according to the different maximum inundation maps It can be concluded that the 1D2D model can be used only when the double storage problem is solved. However Sobek 1D2D itself is only partly to blame for the poor performance. Lack of and data preparation problems contribute largely to the results. Therefore the idea to incorporate a 1D2D model in the DSS, instead of a more complex and computation time consuming 2D model, is still good. The qualitative assessment in section 3.1.3 shows that Sobek 1D2D should be appropriate for simulating the different flood events.


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Provided that deficiencies, such as the artificially created double storage and the lack of data for the DEM, are repaired, both hydraulic models can be used to compute the data for the damage model. However both Sobek models require a large amount of computation time (up to 24 hours), and are therefore conflicting with one of the criteria set up by the BfG, namely to have a quick response. In order to overcome this problem is the application of meta-models. In general, the application of meta-modelling techniques has been focussed on sensitivity analysis, optimisation, and decision support system construction [Bendoly, 2004]. The employment of meta-models is interesting in cases when large memory requirements and slow response time prevent the use of simulation models [Meghabgab et al., 2000]. A Meta-model is a model of a model [Meghabgab et al., 2000]. Most of the meta-models are based on the result of literature, and estimate a regression equation with parameter values or elasticities as dependent variable and attributes, of the underlying studies and background variable as explanatory variables [Jong et al., 2003]. However meta-models have been constructed, which integrate results from runs with “underlying models” [Jong et al., 2003]. Therefore it would be possible to make a variety of runs with Sobek 2D, which has proven its ability to model flood events with and without dike break, and store the results of these runs in a database. Then, when a scenario must be simulated in the DSS, a less complex model (i.e. less computation load) can “pick a result from the shelf” that represents the scenario best.


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Chapter 5 Uncertainty and sensitivity analysis This chapter describes the uncertainty and sensitivity analysis (UA/SA) of the combined system, the hydrodynamic/damage model. The set up of the UA/SA is presented in paragraph 5.1. In 5.2 the results of the analysis are discussed. During an earlier stage of this research three damage functions have been tested. As shown in section 3.2.1, these models have been linked to a Gumbel distribution which estimates the annual risk. Various hydraulic values needed for these combined systems are based on modelling carried out with Hec 6. A summary of the UA/SA results of those systems is treated in section 5.3.

5.1 Uncertainty sources and proceedings Before the UA/SA is be carried out the uncertainty sources are identified in section 5.1.1. The proceedings of the UA/SA are discussed in subparagraph 5.1.2.

5.1.1 Uncertainty identification There are 7 uncertainty sources appointed, namely: • Land use; • Roughness; • DEM; • Inundation depth; • Velocity ; • Damage parameters; • Flood events.

Due to the fact that the land use is obtained through a European study of land cover classes [Bossard, 2000] that is carried out by hand of several satellites (remote sensing), it is nearly unfeasible to make a statement about the uncertainty of this source. Therefore the land use is left out of the UA/SA. However varying the land use for a particular cell, only affects the roughness assigned to that cell. Because of that the land use is indirectly still a factor in the UA/SA through the roughness. Because of the fact that it is nearly impracticable to take roughness into account, it is left out of the UA/SA. The flood events used during the computations contain a number of uncertainties. To create a flood event, information about a lot of parameters is needed, e.g. peak, volume, duration, and shape (paragraph 4.1.1). It is chosen to set up the flood events using the flood peak, the flood duration, assuming the hydrograph shape is parabolic. Leaving out the other parameters creates an uncertainty source. Furthermore the poor goodness of fit of the linear regression model, used to obtain the flood duration, also contributes to the uncertainty. However, due to inaccessibility of quantifying the uncertainty of those aspects, they are left out of the UA/SA. The probability distribution functions of the remaining parameters are unknown, but are assumed to be uniform. The relations between the uncertainty sources, the hydrodynamic and damage models can be visualised throughout the diagram in Figure 5.1. The value for the damage, number of affected people, and risk, estimated by the damage model, basically depends on three inputs: the damage parameters, the inundation depth, and velocity maps. Both maps are produced by Sobek, which in turn requires the DEM and roughness. In order to obtain a sample of both inundation depth and velocity maps, which represent the whole range of variables, a large number of runs


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with Sobek (>100) has to be carried out. This would involve a tremendous computation time (+/- 6 months) and therefore is unfeasible. To get a reasonable sample of these maps, with still a satisfactory coverage of their ranges, several scenarios for the DEM and roughness are set up. The DEM can be heightened or lowered with one fixed value. Choosing an interval of 1 meter, this results into 4 extra inundation depth and velocity maps (-2m, -1m, +1m, and +2m). Concerning the uncertainty of the roughness, a minimum and maximum roughness map has been produced based on the land use. These two scenarios are given in appendix I and are based on the available literature. Both DEM and roughness scenarios are simulated independently in Sobek.

Figure 5.1 Schematisation of the models and their uncertainty sources

Sobek 1D2D and 2D

DEM

Inundation depth/velocity maps

Damage model

Damage/affected people/risk

Damage parameters

Roughness (2D map)

The Q200 flood event with the artificial dike break is used for the Sobek computations. The model produces 7 inundation depth and velocity maps, for the further course of the UA/SA. For the 2D as well as the 1D2D UA/SA, a randomly selected inundation depth, and velocity maps are selected, and then combined with a set of damage parameters that is selected using Latin Hypercube Sampling (LHS). Finally the obtained scenarios results are entered into the damage model, where the output are analysed.

5.1.2 Proceeding of UA/SA As mentioned in paragraph 3.3 the UA/SA are carried out using Monte Carlo (MC) analysis. Other uncertainty analysis methods, like Sobol, FAST, and Response Surface Methods, were rejected because they demand too much computation time and/or are unnecessarily complex. The selected MC analysis is based on a number of specific


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steps, and the running of these, are discussed extensively by Granger Morgan et al. [Granger Morgan et al., 1990] and Saltelli et al. [Saltelli, 2001]. According to Saltelli et al. the MCS can be summarised and classified as:

1. Identifying uncertainty sources. These are the parameters that most likely have the largest contribution to the uncertainty and sensitivity.

2. Sampling. A sample that represents the full range of the possible input value of each uncertainty source needs to be acquired. There are a number of methods discussed in the preparation package report. The method that is used is Latin Hypercube Sampling (LHS), which is a form of stratified sampling, and widely used due to its better representative of the whole range of variables.

3. Running models with all sampled inputs. 4. Uncertainty analysis: a straightforward method to evaluate uncertainties is to

calculate the mean value and the variance (or standard deviation) of the model output.

5. Sensitivity analysis: Local sensitivity analysis (screening) is employed. The procedure that is used is named “one at a time”, which means that one of the uncertainty sources is allowed to change, while other parameters are fixedhave fixed values.

Determining the sample size there are basically two methods available:

1. Theoretical calculation; 2. Experimental approach: several sample numbers are used and the results are

compared, number of samples is determined when mean or variance converges. The theoretical calculation is discussed by Granger et al. [Granger et al., 1990], and is based on the confidence interval. After a test run based upon an arbitrary chosen number of scenarios, the mean and the standard deviation can be determined. Given a certain width ω between the low and high boundary value of the interval, the sample size can be calculated with:

22⎟⎠⎞

⎜⎝⎛>ωcsm 5.1

Where: s = the standard deviation; c = the deviation for the unit normal enclosing probability α; m = the sample size. The width can be acquired with:

−

= y*01.0ω 5.2

5.2 Results of the UA/SA for the Sobek/Damage model When the theoretical procedure for obtaining the sample size is executed for 50 runs, the sample size should be 463, hence another 413 scenarios should be computed. Due to the fact that these large samples require too much memory, and causes an unacceptable long computation time, this sample size is infeasible.


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The fist step in the experimental approach is to set up an arbitrary chosen number of scenarios and then calculate the mean and variance. After this, increase the number of scenarios, and again calculate the mean and variance. This operating procedure must be continued until the results tend to stabilise. The procedure above is repeated a number of times, namely for 1, 5, 50, 75, 100, and 150 distinctive samples. Larger sample sizes were not possible due to a too large memory requirement. Both the mean and standard deviation of the damage, number of affected people, and the risk, tend to stabilize after a run of 75 samples. The begotten results for the two systems, Sobek 2D/ damage model, and Sobek 17D2D/damage model, are depicted in table 5.1.

System Mean Damage [%]

Variance Mean Aff. People

Variance Mean Risk Variance

Sobek 2D 58.94 10.48 0.95 0.00 3.52 0.03 Sobek 1D2D 32.35 55.52 0.68 0.01 1.83 0.10 Table 5.1 Abstract of the uncertainty analysis for the combined Sobek/damage model system, including

the damage, affected people, and risk Due to the fact that the selection of the sample size is not entirely executed with LHS, the outcome could not be fitted with regression analysis into any probability density function. The combined system Sobek 2D/damage model seems to estimate all the parameters categorically higher. This is a direct effect of the differences between the functioning of the two Sobek models, which is discussed in the previous chapter. The deviations among the averages, calculated for the UA, and the results of the Q200 event with dike break, based on the normal maps and damage parameters (table 4.11), is quite small. The variance of all the outcome based on the 2D model is much smaller than that of the 1D2D model. Theoretically it means that the combination Sobek 2D/damage model has less uncertainty, and therefore is more stable. The higher estimates for the damage, risk, and the number of affected people, makes Sobek 2D/damage model more conservative. It could be a policy decision to select the more conservative, i.e. saver model as the appropriate one. The last part of the MC analysis is the sensitivity analysis. Sensitivity is defined as the rate of change of the output y with respect to the variation in an input x. The result of this examination is that the relation of the output of the damage model, to the different input parameters, becomes clearer. Accordingly the most important source to the uncertainty can be pointed out. The normalized sensitivity, i.e. the ratio of the relative change in y induced by a unit relative change in x, can be expressed with [Granger Morgan, 1990]:

0

0

*),(0 y

xxyyxU

XS ⎥⎦

⎤⎢⎣⎡∂∂

= 5.3

Where: US (x,y) = the sensitivity of input x on output y; dy = the change in output; dx = the change in input; x0 = the nominal value of x; y0 = the nominal value of y.


54

This normalized sensitivity has been calculated for both combinations of models. There are three uncertainty sources, namely the DEM, the roughness, and the damage parameters. Combined with the three output parameters of the damage model, the SA has been performed 9 times. Figure 5.2 and 5.3 shows the results of these analyses. It is clear that both systems are more sensitive on the changes of the DEM, which makes it the most dominating sensitivity factor. The roughness based on the land use classes, has a negligible effect (<1%) on any of the outcome of the two systems. To a certain extent, the damage parameters influence the damage and the risk, produced by the Sobek 2D/damage model. The Sobek 1D2D/damage model is insensitive to changes of the damage parameters. In general it can be stated that this system reacts less sensitive on changes of all the uncertainty sources than the 2D model does. The damage depends on the inundation depth and the potential damage associate with the land use classes (section 3.3). Obviously the DEM and the damage parameters are the two main factors that influence the damage. In addition to these two uncertainty sources, the roughness of the DEM, determines the flow velocity, hence the water depth. Yet the Q200 event, which is selected to perform the UA/SA, is so large that the change of roughness has a very small effect on the inundation depth. Due to the fact that the risk is largely based on the depth in each cell and the flow velocities (table 3.3), the DEM and indirectly the damage parameters are again the dominant sources. The number of affected people is determined whether or not a cell is inundated. Therefore it can be concluded that the DEM contributes the most to the sensitivity.

SA of the Sobek 2D/damage model

0

5

10

15

20

25

30

Damage Risk Aff. people

Nor

mal

ized

sen

sitiv

ity [%

]

Damage DEMDamage RoughnessDamage Dampar.Risk DEMRisk RoughnessRisk Dampar.Aff. people DEMAff. people RoughnessAff. people Dampar.

Figure 5.2 Results of the sensitivity analysis of the system Sobek 2D/damage model, for the uncertainty

sources: DEM, roughness and damage parameters


55

SA Sobek 1D2D/damage model

0

5

10

15

20

25

30

Damage Risk Aff. people

Nor

mal

ized

sen

sitiv

ity [%

]Damage DEMDamage RoughnessDamage Dampar.Risk DEMRisk RoughnessRisk Dampar.Aff. people DEMAff. people RoughnessAff. People Dampar.

Figure 5.3 Results of the sensitivity analysis of the system Sobek 2D/damage model, for the uncertainty sources: DEM, roughness and damage parameters

With the sensitivities the influence of each uncertainty source on the total system uncertainty can be attributed. The combination Sobek/damage model can be regarded as a function with the uncertainty sources as variables. The total error (i.e. standard deviation σ) of functions f with variables x1, x2,…,xn can be obtained with [Ortuzar et al., 1996]:

( ) ( )( )∑ ∑∑≠

∂∂∂∂+∂∂=i i ij

ijxjxijixiitot rxfxfxf σσσσ /// 222 5.4

Where: σtot = the total error; σxi = the error of input i; rij = the coefficient of correlation between xi and xj. Assuming that the DEM, roughness, and damage parameters are not correlated (rij = 0), the total error can be calculated with:

( )∑ ∂∂=i

xiitot xf 222 / σσ 5.5 5.5

Based on the total error and the sensitivities, the influence of each uncertainty source on the total uncertainty for the damage are shown in figure 5.4 and 5.5. Based on the total error and the sensitivities, the influence of each uncertainty source on the total uncertainty for the damage are shown in figure 5.4 and 5.5.


56

Influence of the uncertainty sources on the total Sobek 2D/damage model uncertainty

65%2%

33%

DEM Roughness Dampar.

Figure 5.4 The influence of the uncertainty sources on the total Sobek 2D/ damage model uncertainty

Influence of the uncertainty sources on the total Sobek 1D2D/damage model uncertainty

93%1%

6%

DEM Roughness Dampar.

Figure 5.5 The influence of the uncertainty sources on the total Sobek 1D2D/ damage model uncertainty

Figure 5.4 and 5.5 show that the DEM has the most significant influence on the uncertainty of both models. In contrast to the 2D model, the roughness and the damage parameters, have a small effect on the uncertainty of the 1D2D model.

5.3 Results of the UA/SA based on Hec 6 Next to the damage model linked to the Sobek models, three other damage models which are based on three different damage functions, namely: Elbe 2000 [Maiwald, 2001], Cur 1990 [Sande, 2001], and Pflunger 1995 [Sande, 2001] are tested. In principle the three models are identical, apart from the fact that each model assigns a different value for the maximum damage. Therefore the Elbe 2000 model estimates the damage higher than the other two, and the Pflunger 1995 model has the lowest damage parameters. A more extensive discussion of these models is given in section 3.3. Due to the low level of complexity of the statistical damage model, it is quite simple to identify the uncertainty sources, namely: • Dike height; • Critical discharge; • Damage parameters.


57

The first two sources are correlated, because both the dike height and the critical discharge, determine the moment the water starts to overtop the dike, and with that they influence the Gumbel distribution employed in the damage function (equation 3.12). Naturally the damage parameters affect the estimated risk directly. Similar to the sampling method used in the previous section, the sample size has been obtained with both methods. According to the theoretical approach 804 runs are needed, which consumes too much computer power. Therefore the experimental approach is used, resulting into 100 runs. The results of the UA are given in the table below:

Parameter Elbe 2000 Cur 1990 Pflunger 1995 Mean yearly risk (*10-3

%) 5.550 5.229 3.010 Variance (*10-7) 1.612 1.101 0.446 Table 5.2 Results of the uncertainty analysis of the three damage models,

with the mean and variance of the yearly risk, expressed in % of the potential damage

As expected the Pflunger 1995 model estimates the expected annual damage, due to its lower damage parameters, lower than the other two. Its variance is smaller too, which implies that the uncertainty of this function is smaller. The predicted mean expected annual damage, of the models Elbe 2000 and Cur 1990, have similar values. As a result there would be no crucial difference in using either of the two models. However the uncertainty of the Elbe 2000 model is slightly bigger than that of the Cur 1990. Deviations of the damage parameters are basically because of the differences between the three damage functions. Due to the fact that damage cannot reach negative values, the assumption is made that the begotten values are lognormal distributed. The lognormal distribution is fitted to the data and displayed in Figure 5.6.


58

Figure 5.6 Results of the uncertainty analysis fitted into lognormal probability distributions for each of

the damage models Figure 5.6 shows that the function Pflunger 1995 has a lower mean comparing with the other two. Without observation it is difficult to conclude which one is closer to the truth. The results show that Elbe2000 and CUR1990 agree with each other, which may provide more confidence of using one of them. These two functions overlap each other for a large part. Due to their apparently equality it seems that it does not matter which one is used. However the Elbe 2000 function estimates the damage higher, which makes it more conservative, but the Cur 1990 function, has a lesser variance, and therefore theoretically has less uncertainty. Next to the analysis of the whole map, a number of cells were selected, and the damages were likewise transformed to a normal probability distribution. The outcome of this cell by cell analysis is virtually identical to the results, as shown in Figure 5.6. The contribution of the dike height and the discharge to the sensitivity is negligible. The values of the normalised sensitivity of these two uncertainty sources are of the order of 10-6, for the discharge, and 10-5 for the dike height. An insensitive parameter indicates that a fixed average value can be taken as input, i.e. no extra effort must be made to reduce the uncertainty. Only a change in the flood damage parameters causes differences in the outcome of the model. The sensitivities vary from 16.8 % for the Pflunger 1995 function, to 18.9% for the Cur 1990 function.


59

5.4 Conclusions The UA/SA has been performed with a sample size that is determined by the experimental approach. According to the available theory the sample should be considerably larger, but regarding the fact that both mean and variance of the experimental runs were stable, it is unlikely that a larger sample results into a substantially different outcome. Sobek 2D model shows a lower uncertainty comparing to Sobek 1D2D. The more stable results make it more attractive to use. Also this combination estimates the mean damage higher than when the 1D2D model is linked to the damage model. However this is the direct result of the difference between how the two hydraulic models simulate a scenario with a dike break, which has been discussed in the previous chapter. The UA/SA is based on a Q200 event with an artificial dike break. Both Sobek/damage model combinations estimate roughly the same damages (table 4.14), the difference in this analysis would probably have been smaller, when an event without dike break was selected, or when the 1D2D model did not have the technical problems discussed in paragraph 4.3. Section 5.3 shows that the Elbe 2000 function contains the highest uncertainty, followed by the Cur 1990 and the Pflunger 1995 damage functions. Furthermore it can be concluded that the Pflunger 1995 model, estimates the damages significantly lower then the other two. It might be due to its different definition of the potential damage. The uncertainty distribution of other two damage functions overlap each other for a large part, while Cur 1990 model gives the user more confidence in its predictions. The SA for both the Sobek/damage model combinations shows one similarity, namely the DEM is for both systems the most important sensitivity source. Considering the SA based on the 2D hydrodynamic model, the damage parameters are, next to the DEM, another important uncertainty source for the damage and risk. The damage parameters in the Sobek 1D2D/damage model only influence the prediction of the damage. All three damage models that are used in the risk model show that the damage parameters are the only sensitivity source. Choosing either one of the combinations Sobek/damage model, or the risk model, the available resources (time, money, etc.) must be dedicated to eliminate uncertainties in the variables with the largest sensitivity. For the Sobek 2D/damage model the uncertainty of especially the DEM, and to a lesser extent the damage parameters should be reduced. For the Sobek 1D2D/damage model, the uncertainty of the DEM should be reduced, because it is the only sensitivity source. Regarding the Elbe 2000, Cur 1990, and Pflunger 1995 models, an additional research to more accurate damage parameters (the sole sensitivity source) is recommended. However it must be noted that all of the damage models utilise only the direct damage as a percentage of the potential damage. Although the model, connected to Sobek, also calculates the risk, and the number of affected people, it does not include damage due to loss of lives, irreparable environmental damage, loss of future production, or social effects. When these other aspects of the damage are included, the conclusion can possibly differ in such way.


60

Chapter 6 Conclusions and recommendations The state-of-the-art in system development has moved towards integrated multi-objective system involving multi-processes. Decision support system (DSS) for river basin management is such an example. In the integrated system, model selection is the trade off between model complexity and uncertainty. To look at model performance for model selection, a case study has been carried out, which was a part of the development of a DSS for the Elbe River in Germany (section 2.2). One of the main objectives of the Elbe DSS development is to give a quick insight in the behaviour of the river system, so that problem areas can be studied. The system must offer the possibility to investigate the consequences of several measures for flood management, such as dike shifting, the construction of a side channel, or lowering the floodplains or river channels. In order to do so, the BfG set up the criteria on that the DSS should be easy to handle, quick response, with acceptable accuracy. These criteria contradict each other, because a more complex model is in general considered as more accurate, however it requires higher computational loads comparing with a simpler model. To satisfy those requirements, in the Elbe DSS, the channel module that covers the entire German part of the Elbe, uses a steady state hydraulic model Hec 6, while the more detailed river section module uses a 2 dimensional hydrodynamic model. In order to assess the performance of hydrodynamic models for their implementation in the DSS, three models are tested. They are Hec 6, Sobek 1D2D, and Sobek 2D. Both Sobek models simulated three flood events in scenarios of situation with and without an artificial dike break. The results have been entered into an event-based damage model. Hec 6 is embedded in a statistical risk model. Finally, a Monte Carlo analysis propagated uncertainties through the integrated systems.

6.1 Conclusions The systematic modelling approach, known as appropriate modelling, involving qualitative analysis and quantitative analysis, is employed in this study. It has provided a useful technique for selecting the most appropriate model. The approach gives a clear specification of the guidelines a hydraulic model needs to satisfy in order for implementation in the DSS. Furthermore the method provides enough possibilities to compare the models to make a considerate model selection. When restricted to the three models used in this research, it is clear that due to its limitations, Hec 6 is not applicable for modelling dike break scenarios. The statistical risk model, with Hec 6 embedded, is more suitable for a long-term flood risk assessment. Despite the fact that the 1D2D model reaches a good value of R2 during the calibration process, the results of the model are not plausible. Lack of data and data processing problems are mainly the cause of the poor modelling results. Sobek 2D is found capable of simulating flood events with and without dike break, and delivering reliable results. However with computer loads of up to 24 hours per scenario, both Sobek models are not capable to give a quick insight in the behaviour of the river system as the component of an operational DSS. Therefore one of the main goals of the DSS cannot be accomplished with either Sobek 1D2D or Sobek 2D. The hydraulic simulations of both Sobek models are quite different but the differences become smaller when they are integrated with the event-based damage model.


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Differences between damage estimates using both model is small in case of a scenario without dike break. However damage estimates based on the 2D model remain more conservative. The two risk models that have been tested serve different purposes. The statistical risk model is suitable for long term planning. Short term flood mitigation operations and assessing flood loss for operational usage can be benefited by the event-based damage model. Apart from data problems the 1D2D model itself suffers from some technical flaws. For example the 1D part did not accept the rating curve as a downstream boundary. Therefore a water level time series had to be created. The rating curve in Sobek 2D model had to be adjusted in order to make the model work properly. The rating curve is however rather a problem of lack of data, than a model error. The 2D model reaches the largest reduction by choosing the optimal time of dike break. Also the Sobek 2D simulations show that controlled dike break is a successful measure, for lowering the peak water levels at the downstream area. Provided that the maximum inundation level is predominant for determining the damage, controlled dike break leads to lower damages at downstream of the research area. Hereby it must be noted that in practice, the size and duration of a flood event have to be forecasted with another model, in order to find the optimal time of dike break. Previous research for reducing the peak water levels in the Elbe agrees with the results obtained with Sobek 2D. Sobek 2D model has lower uncertainty comparing to the Sobek1D2D. This conclusion is based on an uncertainty analysis of a Q200 event with an artificial dike break. In a no-dike-break situation both models estimate roughly the same values for the damage, the differences in the uncertainty was expected to be smaller when the UA was based on such an extreme event. The DEM has been found the most sensitive input parameter for the event-based damage model. Considering the sensitivity analysis based on the 2D hydrodynamic model, the damage parameters are the second sensitive source for the damage and the risk. The SA for the Sobek 1D2D/damage model shows that the damage parameters are the only sensitivity source. Uncertainty analysis on the risk model shows that model based on the Elbe 2000 damage function contains the highest uncertainty, followed by Cur 1990 and Pflunger 1995, sequentially. The damage parameters are the most sensitive source in the risk model. The study shows that a complete and accurate DEM is very important for an appropriate flood risk assessment. The result is highly affected by the completion level of the DEM. Due to lack of dike data the dike break location had to be switched from the western to the eastern dike. Nevertheless the size of the DEM is not sufficient to hold the water in case of Q50 and Q200 flood events (Figure 4.8). Therefore the time of dike break is shifted for those two events. Furthermore the results suffer from a lack of detailed dike data. The dikes had to be artificially closed (Figure 4.4).


62

6.2 Recommendations Obviously neither Hec 6 nor Sobek are able to fulfil all the objectives of the Elbe DSS development, namely to give and a quick insight in the behaviour of the river system, and to be able to simulate dike break scenarios. To satisfy these conflicting demands an alternative approach is needed. One approach is to study the possibility to implement two hydraulic models, as is suggested in the feasibility study [Bundesanstalt für Gewässerkunde, 2003]. Hec 6 is imbedded in the channel module that covers the whole German part of the Elbe, and the river section module contains a hydrodynamic model like Sobek, to simulate scenarios in the Sandau area. A second approach is the application of meta-models, which are discussed in section 4.4. The study shows a very important role of an appropriate DEM in the development of a flood risk assessment system for river basin management. Therefore, the DEM must be extended in particular the area outside of the western dike. The extension needs to be sufficient to satisfy the requirement of a 200-year flood in terms of holding the amount of water. As the most important flood defence system, dike data needs to be more detailed, concerning the location and height of the dikes. In this study, due to a lack of data the dikes were manually interpolated. It was not sufficient to prevent the water escaping through the western dike. Actual and complete dike data should improve this problem properly. More flood data, such as the 2002 flood, would enable an extended calibration and validation process of the hydraulic models. The time series used in this research contains a maximum flood event equal to a Q28 event. Experts believe that the 2002 flooding was equal to a Q100 event or more. Whenever the inundation depths are obtained for the study area, both Sobek models can be calibrated outside the river making the damage estimates more accurate. With the 2002 data the Q(h) relation, applied for the downstream boundary in Sobek 2D, will be improved, by which the assumption for the extrapolation of the existing rating curves at Havelberg, would be redundant (section 4.2.2). Otherwise a different type of downstream boundary can be selected, in order to avoid adjustments to the rating curve. The data problem that causes the “double storage” in Sobek 1D2D needs to be solved. This artificially created storage is caused by data preparation problems. Due to technical reasons the 1D2D model does not accept the Q(H) relation as a downstream boundary, instead an H (t) relation is applied. This model error has to be solved as well. An additional study has to be carried out in order to predict the size, and shape of the hydrograph of flood events for dike break simulation of extreme floods. The following aspects are also important for future work: • Acquiring a more extensive and detailed DEM; • The date preparation problem that leads to the “double storage” error; • Unification of the downstream boundaries in Sobek 1D2D.

When the recommendations above are fulfilled a fairer comparison of these two hydrodynamic models can be made.


63


64

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2004).


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Preface This report presents results of the MSc-research that is carried out as the completion of my study Civil Engineering, Group Water Engineering and Management (WEM). The official title for the research is: ”Appropriate modelling: Application of Sobek 1D2D for dike break and overtopping at the Elbe”. My daily supervisor was Yan Huang and she is the first person I would like to thank for her enthusiasm and commitment. Of course I also would like to thank the rest of the graduation commission, Jean-Luc de Kok and Maarten Krol for their time and support during this research. Finally, I want to thank Harriette Holzhauer for helping me with numerous Matlab problems. Enschede, November 2004 Robin Lomulder


I


II

Summary The state-of-the-art in system development has moved towards integrated multi-objective systems involving multi-processes instead of a single process. Decision support systems (DSS) for river basin management are examples of these integrated multi-objective systems. It typically involves processes of hydrology, hydraulics, water quality, flood risk, ecology and navigation assessment. In turn, model-related activities have shifted from model development to selecting the most appropriate model for system development [Snowling et al., 2001]. To answer the question of what model is the “best one among candidates”, an appropriate modelling approach is needed. This study focuses on the selection of the hydraulic model, which metaphorically can be seen as the “engine” that propels the entire system, containing a variety of models. The main objective of this research is to assess the appropriateness, and the applicability of hydrodynamic models for decision support system development. This assessment is based on an analysis of the model complexity, uncertainty and sensitivity. A second objective is to provide recommendations for an appropriate modelling approach based on the studied results. To achieve the objectives above three models are selected and tested. These are the hydrodynamic models Sobek 1D2D and its 2D counterpart. The performances of these models are compared among themselves, and with the 1D steady flow model Hec 6. The selected models are deployed in order to execute a case study, namely the development of a DSS for the river Elbe. This research focuses on a small selected part of the Elbe area, rather than on the entire river basin. The study area is the region around Sandau, and is located south of the city Havelberg. The levels of the landscape vary between 23 to 37 meters above sea level. The area of this region is 55.6 km2. The research area is bounded in the northern and western area by the Elbe, from kilometre 411.4 to 422.4, and the river Havel. The size of the Sandau area is 6.8 kilometres from east to west and 10.6 kilometres from north to east. Both Sobek models are deployed to simulate three typical flood events, with the return periods of 28, 50 and 200 years. All flood events are simulated with and without a dike break. Particularly dike break scenarios are interesting to simulate, due to the fact that this can be a measure to lower flood damages downstream. In case of a large flood the dike can be deliberately punctured creating a retention area. This area must be located where the population density, and the economic value, is relatively low. This strategy aims to lower the peak water level, and thus a lower damage downstream, where the population density and/or the value of the land are higher. Based on the output of the hydrodynamic models, a damage model estimates the damage, the number of affected people, and the risk level. Hec 6 is integrated in a similar damage model. However, Hec 6 is not suitable for dike break scenarios, and the model cannot simulate actual floods accurately. The work with the Sobek models demonstrates some serious flaws in both input data and model. First the elevation data is not extensive enough to properly simulate a dike break scenario. The map is not sufficiently detailed regarding the dike data. Due to a lack of data, assumptions had to be made, in order to extend the rating curve for the downstream boundary. Data preparation problems result into difficulties in the connection between the 1D and 2D part of Sobek 1D2D. By comparing the computed


III

totals of water that flows in and out the model, with the measured totals, available from the time series, deviations of 33% occur. Despite the high goodness of fit (0.86) of the 1D2D model, the model is not plausible. The other hydrodynamic model, Sobek 2D, is quite accurate with a goodness of fit of 0.88. The scenarios with a dike break result in lower flood water levels (up to 0.19 m) in the river. This measure can help lowering flood damages downstream. Sobek 2D computes higher inundation depths and velocities than its 1D2D counterpart. After entering the Sobek results into the damage model, it appears that the differences between the two model combinations are strongly reduced, at least for the estimation of the most important parameter, namely the damage, for the no dike break scenarios. The differences between the other two parameters, the number of affected people, and the risk, are relative smaller than it was during the comparison of the hydraulic output. The uncertainty and sensitivity analysis carried out in conformance with the method of Monte Carlo, shows that the Sobek 2D/damage model has lower uncertainty than the Sobek 1D2D/damage model, making it more attractive to use. Regarding the sensitivity, the DEM is for both Sobek/damage models the most important investigated sensitivity source. Considering the SA based on the 2D hydrodynamic model, the damage parameters are, next to the DEM, an important source for the damage and risk. The damage parameters in the Sobek 1D2D/damage model only influence the prediction of the damage. For the alternative damage model, with the integrated Hec 6 model, the damage parameters are the only sensitivity source. The systematic modelling approach, known as appropriate modelling, involving qualitative analysis and quantitative analysis, is employed in this study. It has provided a useful technique for selecting the most appropriate model. The approach gives a clear specification of the guidelines a hydraulic model needs to satisfy in order for implementation in the DSS. Furthermore the method provides enough possibilities to compare the models to make a considerate model selection. When restricted to the three models used in this research, it is clear that due to its limitations, Hec 6 is not applicable for modelling dike break scenarios. The statistical risk model, with Hec 6 embedded, is more suitable for a long-term flood risk assessment. Despite the fact that the 1D2D model reaches a good value of R2 during the calibration process, the results of the model are not plausible. Lack of data and data processing problems are mainly the cause of the poor modelling results. Sobek 2D is found capable of simulating flood events with and without dike break, and delivering reliable results. However with computer loads of up to 24 hours per scenario, both Sobek models are not capable to give a quick insight in the behaviour of the river system as the component of an operational DSS. Therefore one of the main goals of the DSS cannot be accomplished with either Sobek 1D2D or Sobek 2D. It is recommended to perform further study to some important aspects. In order to improve the calibration and validation process, the 2002 flood data can be added to the time series. This would reduce the problems with the time series, and influence the height and duration of the flood events. Secondly, the size of the DEM must be increased to enhance the dike break simulations. The quality of the dike data (height and location) must improve as well. Also model errors, like the downstream boundary problem in the 1D2D, should be researched more extensively.


IV

Appendix I

Appendix I Roughness based on land use class In Sobek the roughness is assigned as Manning’s n [s/m1/3]. The roughness for most of the land use types are obtained through the available literature. Assumptions have been made for the land use types were the roughness was unavailable. Some sources express the roughness in Nikuradse’s k [m]. The Manning and Nikuradse roughness are related as:

nRC

6/1

= I.1

Where: C = Chézy coefficient [m1/2/s]; R = hydraulic radius [m]. Using the Strickler approximation for the Chézy value, the Nikuradse roughness can be converted into Manning’s n with the equation below:

25

6/1kn = I.2

The roughness for each land use type, including their minimum and maximum values for the UA/SA, is depicted in the table below:

Land use class Mean roughness

[s/m1/3]

Maximum roughness

[s/m1/3]

Minimum roughness

[s/m1/3]

Reference:

Discontinuous urban fabric 0.150 0.017 0.013 [Sande et al, 2004] Road, railroad, and associated land

0.150 0.020 0.013 [Sande et al, 2004]

Mineral extraction sites 0.120 0.140 0.100 [Sande et al, 2004] Non-irrigated arable land 0.035 0.407 0.293 [Chow, 1959] Fruit trees and berry plantations

0.150 0.200 0.100 [Chow, 1959] [Sande et al, 2004]

Pastures 0.035 0.407 0.29 [Chow, 1959], [Meier et al., 1994], and [Sande et al, 2004]

Complex cultivation patterns

0.050 0.058 0.042 [Chow, 1959]

Land principally occupied by agriculture

0.050 0.058 0.042 [Chow, 1959]

Broad-leaved forest 0.120 0.140 0.100 [Chow, 1959] Coniferous forest 0.200 0.250 0.150 [Chow, 1959] [Sande et al,

2004] Mixed forest 0.200 0.250 0.150 [Chow, 1959], [Meier et al.,

1994] [Sande et al, 2004] Natural grassland 0.033 0.035 0.030 [Chow, 1959] Moors and heath land 0.033 0.035 0.030 [Chow, 1959] Inland marshes 0.050 0.058 0.042 [Chow, 1959] [Meier et al.,

1994] Water courses 0.030 0.033 0.027 [Chow, 1959] [Meier et al.,

1994] Water bodies 0.030 0.033 0.027 [Chow, 1959] and [Meier et

al., 1994] Table I.1 Manning roughness based on land use type

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