Flood Forecasting, Conterol and Modeling for Flood Risk Management Systems

Table of Contents

Abstract

Acknowledgements

Table of Contents

List of Figures

List of Tables

1 Introduction
1.1 Background
1.2 Problem description
1.3 Significance of the study
1.4 Research objectives
1.5 Research questions

2 Literature Review
2.1 Introduction
2.2 Hydrological modeling approaches
2.2.1 Reservoir inflow simulation
2.2.2 Reservoir operation approaches
2.2.3 Reservoir operation rule curves
2.3 Flood modeling approaches
2.3.1 Model parameterization
2.3.2 Boundary conditions
2.3.3 Sources of uncertainties
2.3.4 Calibration and sensitivity analysis
2.4 Previous studies

3 Study Area Description
3.1 Location and topography
3.2 Climate, vegetation and land use
3.3 Hydrology and flooding

4 Methods and Materials
4.1 Research methodology
4.2 Hydrological modeling using HEC-HMS
4.2.1 HEC-HMS model setup
4.2.1.1 Basin model
4.2.1.2 Meteorologic model
4.2.1.3 Control specification and HEC-DSSVue
4.2.2 Model requirements
4.2.3 Model parameters
4.2.4 Model calibration and validation
4.3 Reservoir operation rule curves
4.4 HEC-HMS modeling with reservoirs
4.4.1 Reservoir routing method
4.4.2 Storage method
4.4.3 Initial condition
4.5 Hydrodynamic flood model with SOBEK 1D/2D
4.5.1 Channel flow equations
4.5.2 Overland flow equations
4.5.3 SOBEK model setup
4.5.3.1 Digital Elevation Model
4.5.3.2 1D/2D connections

5 Data Preparation
5.1 Data collection and preprocessing
5.2 Meteorological data
5.2.1 Rainfall data
5.2.2 Evaporation data
5.3 Hydrological data
5.3.1 Data screening
5.4 Land use and soil types
5.5 Conclusions and discussion on data processing

6 Flood Frequency Analysis
6.1 Introduction
6.1.1 Log-Pearson Type III, LP3 distribution
6.1.2 Extreme Value Type I, EVI distribution
6.2 Shape of hydrographs
6.3 Results and discussion on frequency analysis

7 Hydrological Modeling
7.1 Data preparation using Arc GIS
7.2 Hydrological modeling with HEC-HMS
7.2.1 Model input requirements
7.2.2 Model efficiency assessment
7.2.3 Statistical assessment measures
7.2.4 Sensitive parameters
7.3 Results and discussion on hydrological modeling of existing conditions

8 Reservoir Simulations with HEC-HMS
8.1 Reservoir operation rule curves
8.1.1 Reservoir losses
8.1.2 Reservoir releases
8.1.3 Steady state rule curves
8.2 Reservoir model setup and simulation
8.3 Results and discussion on reservoir operation
8.3.1 Simulation and rule curve results
8.3.2 Flow differences and impact on flood modeling

9 Hydrodynamic Flood Modeling with SOBEK 1D/2D
9.1 Introduction
9.1.1 Initial conditions
9.1.2 Boundary conditions
9.1.3 Surface roughness
9.1.4 Cross section profile
9.2 River network
9.3 Validation satellite map
9.4 Results and discussion on SOBEK 1D/2D
9.4.1 Flows in 1D channel
9.4.2 Flood extent, depth and velocity
9.4.3 Flood extent prediction
9.4.4 Flood mitigation measures
9.4.5 Engineering measures
9.4.6 Non-engineering measures
9.4.7 Flood risk management practices

10 Conclusions and Recommendations
10.1 Conclusions
10.2 Recommendations

References

Annexes

List of Figures

Figure 3. 1. Watersheds, river networks, S. Gumara and Ribb dams and the floodplain

Figure 4. 1. The flowchart showing methodologies in the study area

Figure 4. 2. Typical representation of watershed runoff processes (Feldman, 2000)

Figure 4. 3. Connections between 1D network and 2D grid cell (www.sobek.nl)

Figure 5. 1. Annual seasonal rainfall of Gumara (a) and Ribb (b) watershed

Figure 5. 2. Annual seasonal rainfall of Bahir Dar and Gonder stations

Figure 5. 3. Frequency of monthly rainfall in Gumara (a) and Ribb (b) watersheds

Figure 5. 4. Average monthly evaporation of Bahir Dar station

Figure 5. 5. Watersheds, river networks, gauging stations, and Fogera plain

Figure 5. 6. Historical daily flows of Gumara and Ribb rivers (1959-2009)

Figure 5. 7. Daily flows of Gumara and Ribb rivers (1992-2009)

Figure 5. 8. Daily flows of Gumara (a) and Ribb (b) Rivers for wet seasons

Figure 5. 9. Unlikely daily peak flows of Ribb River in August

Figure 5. 10. Daily flows of Gumara and Ribb River for 2006

Figure 5. 11. Gumara and Ribb watersheds Land uses (a) and soil types (b)

Figure 6. 1. Plots of annual peak stream flow on the Gumara and Ribb Rivers

Figure 6. 2. Shape of hydrographs of Gumara (a) and Ribb (b) for observed flows

Figure 6. 3. Shape of hydrographs of Gumara (a) and Ribb (b) for 2, 5, 10, 25, 50 and 100 year return periods

Figure 6. 4. Return periods and probability exceedence of annual peak flows

Figure 6. 5. Confidence limit for Gumara (a) and Ribb (b) Rivers flows

Figure 7. 1. Schematic input data processing using Arc GIS

Figure 7. 2. Gumara and Ribb GeoHMS extracted results from Arc GIS

Figure 7. 3. Comparison hydrographs of Gumara (a) and Ribb (b) watersheds

Figure 7. 4. Inflow hydrographs into S. Gumara (a) and Ribb (b) reservoirs

Figure 7. 5. Calibration results for Gumara (a) and Ribb (b) Rivers flows

Figure 7. 6. Correlation relations of model and observations for Gumara and Ribb (b)

Figure 7. 7. Validation results for Gumara (a) and Ribb (b) river flows

Figure 7. 8. Correlation relations of model and observations for Gumara and Ribb (b)

Figure 8. 1. Rule curves for S. Gumara (a) and Ribb (b) reservoir operations

Figure 8. 2. Developed operation curves for S. Gumara (a) and Ribb (b) reservoirs

Figure 8. 3. Inflows from w240, w241 and w390 sub basins to S.Gumara and Ribb reservoirs

Figure 8. 4. Elevation-storage-discharge based simulation results in HEC-HMS

Figure 8. 5. S. Gumara reservoir level (a) and inflows/ outflows (b) using HEC-HMS and rule curves

Figure 8. 6. Ribb reservoir level (a) and inflows/ outflows (b) using HEC-HMS and Rule curves

Figure 8. 7. Flows at outlet of Gumara (a) and Ribb (b) watersheds

Figure 9. 1. Gumara and Ribb flows and Lake Tana levels as boundary conditions

Figure 9. 2. Cross section profiles of Gumara (a) and Ribb (b) stations

Figure 9. 3. Schematized 1D flow modules of Gumara and Ribb rivers

Figure 9. 4. Satellite image (a) and model result (b) showing the flood extents

Figure 9. 5. 1D channel flows of Gumara (a) and Ribb (b) Rivers

Figure 9. 6. Flood extents and depths in Fogera floodplain of August 2006

Figure 9. 7. History data showing water depths in Fogera floodplain

Figure 9. 8. History data showing water depths in Fogera floodplain

Figure 9. 9. Flood extent and depths in Fogera floodplain

Figure 9. 10. Flood extent and depths in the floodplain for the existing condition

Figure 9. 11. History data showing water depths (3 days) in Fogera floodplain

Figure 9. 12. Flood extents (a) and available evacuation route (b)

List of Tables

Table 3. 1. S. Gumara and Ribb reservoirs average and design flows

Table 4. 1. Soil groups and infiltration rates (FAO, 1998, Feldman, 2000, Natural Resources ConservationService, 210-VI-NEH, July 2004)

Table 5. 1. TRMM correlation with ground station, (Assefa, Andel and Jonoski, 2008)

Table 5. 2. Correlation of different stations in the study area

Table 5. 3. Missing flow records of Gumara and Ribb rivers in dry seasons

Table 5. 4. Screened hydrological and meteorological data for trends

Table 5. 5. Land uses and soil types in Gumara and Ribb watershed sub-basins

Table 6. 1. Summarized result for Gumara and Ribb rivers observed flows

Table 6. 2. Flood flow estimates using LP3 and EVI distribution methods

Table 7. 1. Some characteristic feature outputs of the watershed extracted from GIS

Table 7. 2. MAP distribution of Gumara and Ribb watersheds, August 2006

Table 7. 3. Model input parameters (before calibration)

Table 7. 4. Objective function for Gumara watershed

Table 7. 5. Objective function for Ribb watershed

Table 7. 6. Optimized parameters for Gumara watershed sub basins

Table 7. 7. Optimized parameters for Ribb watershed sub basins

Table 7. 8. Efficiency of calibration results of Gumara and Ribb flows

Table 7. 9. Efficiency of validation results of Gumara and Ribb flows of 2003

Table 8. 1. Different targets for the duration of each season t for S. Gumara reservoir

Table 8. 2. Different targets for the duration of each season t for Ribb reservoir

Table 8. 3. Operating policy to Sendega-Gumara reservoir

Table 8. 4. Operating policy to Ribb reservoir

Table 8. 5. Elevation-storage paired data of S. Gumara and Ribb reservoirs

Table 8. 6. Inflows and storage capacity of the proposed reservoirs

Table 9. 1. Flood extents in Fogera floodplain for the two scenarios

Table 9. 2. History data showing maximum water depths in Fogera floodplain

Abstract

A brief overview of flood control in Fogera plain, upper Blue Nile, Ethiopia is presented as the context of understanding the causes of flood problems and their solutions. The runoff from upstream Gumara and Ribb watersheds, runoff from direct rainfall, and overflows from Lake Tana along the shoreline are the main causes of flooding in the area. Some of the problems caused are damage of farm lands, crops and livestock, and loss of housing and life-threatening situation for the people living in the area. Furthermore, the frequency of floods has increased in recent years since mid of 1990's according to the statistics. The most likely reasons are related to the frequent changes of catchment characteristics, agricultural development of the area, population growth and other interrelated factors. Owing to the adverse nature of flooding events, this study was focused on developing a flood control strategy under regulatory operations of the proposed reservoirs and understanding the flood behavior to reduce flood risks. Sendega-Gumara and Ribb reservoirs are two planned reservoirs for future irrigation purposes. However, it is helpful to use them for flood control purposes during flood seasons as well.

To research how deal with flooding problems, three basic steps were addressed. The first step was to understand and quantify the runoff generated in the watersheds of the existing systems using a hydrological model in HEC-HMS. The second step was reservoir simulations. In this task, flows to the proposed reservoirs were identified and simulated the corresponding releases from each reservoir by imposing a separately developed reservoir operation rule curves. Reservoir operating rule curves play a significant role to control floods downstream. The rule curves are developed using DDP programming. The third step was focused on the floodplain where the actual flood occurs. In this part of the research, a coupled one- and two-dimensional hydrodynamic flood modeling with SOBEK 1D/2D was used in order to understand the flow dynamics and flood characteristics such as flood extent, inundation depth and flow velocity that enables to implement possible flood protections.

According to this study, results show that for the event based simulation period of 27th July to 16th of August 2006, the peak flows to S. Gumara reservoir is about 234 Mm3/day and for the Ribb reservoir it was about 160 Mm3/day within this simulation period. The average daily inflow to S. Gumara reservoir during this period is about 135 Mm3 and 95 Mm3 to Ribb reservoir. The maximum storage capacity of S. Gumara reservoir is 59.69 Mm3 which is 5 times smaller than the storage capacity of Ribb reservoir, 300 Mm3. On the other hand, the inflows to S. Gumara reservoir are much higher compared to the inflows of Ribb reservoir. The reservoir simulation results were then used as input data to the 1D/2D flood model. Therefore, model results show that the flood extent is reduced by approximately 26% compared to the simulated results of the existing condition though not significant.

Due to the limited storage capacity, mainly of the planned Gumara reservoir, and the runoff contributions of the proposed reservoirs have limited impacts (26%) to reduce the flood extent in the floodplain. Thus, if economically and technically feasible, it is recommended to reassess the design of S. Gumara reservoir in order to increase its storage capacity for peak flows. Moreover, some relevant mitigation measures, engineering and non-engineering, are required to reduce the flood risks. The engineering measures include construction of dykes, channel diversion, channel improvements, such as channel deepening, widening, and straightening. Non-engineering measures, including flood forecasting and early warning systems, improved land use policies, and educate local people are important. Either technically or scientifically integrated systems are also needed that supports in solving flooding problems by taking into account the significance of economic, social and different modeling approaches.

Keywords: Flood control, reservoir operation, flood extent, upper Blue Nile, Ethiopia

Acknowledgements

First of all, thanks to all members of Hydro-informatics and Knowledge Management department at UNESCO-IHE for making my stay in the Netherlands pleasant and blissful. I also would like to make a special reference to my fellowships WMO and UNESCO-IHE for making my study productive and being in this position.

I would like to thank my first supervisor Dr. Schalk Jan van Andel for his guidance, discussions, comments and supports he has given me ever since the beginning of my research work. It was with his encouragements, advices and feedbacks this thesis come to the end. During these times, I learnt from him how to think and discover by myself the answers to the problems I had. This has enabled me to develop independent thinking and an ability to stand up for what I believe is right. I owe my deepest gratitude to him.

It is a pleasure to thank my second supervisor Dr. Ioana Popescu for the debates, critical comments and encouragements I had from her at different stages of my work. She made this thesis possible by giving me the ideas and possible methods in solving specific problems. I sincerely thank her for her kind helps. I would like to thank A. Prof. Arnold H. Lobbrecht who is my second supervisor too. I thank him for his overall supports.

I am very thankful to everyone who all supported me in providing relevant data and ideas from in the Ministry of Water Resources of Ethiopia, ENTRO, NBI, NMA, and dedicated staff members. Without their co-operation, I could not have gotten such relevant data to my research work. I am equally pleased to those who guided me and gave me moral support in different matters regarding the topic. I thank them all for their overall supports which helped me to complete my thesis successfully and on time.

I would like to thank the lenvis project (localized Environmental Services for all-EU FP7) for supporting me financially during my research work. The results of my research are used as a demonstrator for lenvis, a demonstrator on how Internet can present and integrate results of different models, in order to make them available and comprehensible to both citizens and water professionals.

Last but not the least, I would like to thank my families, my cousins and my friends who helped me a lot in gathering different information, collecting data and guiding me from time to time. They gave me spirit and effort to complete and make this thesis productive with the blessing almighty of God.

1 Introduction

1.1 Background

Flood risk is a significant issue in many countries all over the world. Ethiopia is one of such countries which have flooding problems. In different parts of the country, flood endangered life and damaged large number of properties in the past times, when flood water covers the surface of land temporarily and threatened people who live in flood vulnerable areas. Owing to the adverse nature of flooding events in the country, this study focused on developing flood controlling scheme under regulatory operations of proposed reservoirs to reduce flood risks in Fogera plain. The study area is located in the northern part of Ethiopia in Lake Tana sub-basin, upper Blue Nile.

Gumara and Ribb rivers are the two main tributaries in the eastern side of Lake Tana sub-basin flowing into Lake Tana. The total watershed area they covered is about 1893 and 1394 square kilometers respectively. The lower reaches of these rivers, near their confluences with Lake Tana, is subjected to flood inundation in wet seasons. The flood inundation is mainly due to heavy rainfall in the upper catchments resulting in runoff flowing down to the Fogera plain. Moreover, the local rainfall adds some impact, together with backwater effect from Lake Tana itself when its level rises towards its yearly maximum; 1787 masl.

1.2 Problem description

Fogera floodplain is situated along the eastern shoreline of Lake Tana and faces many flooding problems in rainy seasons. Some of the floods in the area including very severe floods of 1996, 1998, 1999, 2000, 2001, 2003 and 2006 (Wubshet and Dagnachew, 2008). Some of the problems caused due to these recurrent floods are the damages of farm lands, crops and livestock, and loss of housing and life-threatening situation for the people living in the area during every rainy season. Furthermore, the frequency of such floods has also increased in recent times according to the statistics. Some of the reasons are likely related to the human interventions on the natural systems such as deforestation, changes of catchment characteristics which increases the probability of runoff, increase of farm land needs, population growth, and agricultural development of the area. Fogera area covers about 1,095 square kilometers with a total population of 243,309 (SMEC 2006, as pointed out by (Assefa, et al., 2008)).

This research study is therefore focused on understanding of flood extents in the Fogera plain in order to control flood risks. In particular, how to control floods downstream under regulatory control of the proposed Sendega-Gumara (S. Gumara) and Ribb reservoirs. In order to be able to reduce downstream flood more effectively, reservoir controlling and flow forecasting are very important issues to consider. The main purpose of the reservoirs is to provide irrigation water supply during the dry seasons.

1.3 Significance of the study

The significance of this study is to provide essential information how to control flooding problems in Fogera plain by considering the economic importance of the area for its irrigation potential, securing life and safety, and to develop confidence to the local people by developing proper flood risk management systems using flood mitigation measures. Moreover, this pilot study might also be used to address the impact of flood preparedness and management activities in supporting of decision making issues in flood forecasting and early warning systems in broader sense.

1.4 Research objectives

Based on the background and research problems described, the research objectives are formulated accordingly as general and specific objectives as follows:

1.4.1 General objective

1. Analyze potential reduction of flood extents and inundation depths in Fogera floodplain under regulatory control of the proposed S. Gumara and Ribb reservoirs

1.4.2 Specific objectives

1. Perform flood frequency analysis to estimate the frequency with which floods of a certain magnitude may occur
2. Develop rule curves and decision strategies for reservoir operation by taking into account the use of inflow simulations or design flood hydrographs
3. Simulate expected flood extents and inundation depth in the vulnerable area based on the releases from the proposed reservoirs and selected return periods
4. Discuss feasible flood mitigation measures: engineering and non- engineering measures

1.5 Research questions

1. How frequent flood problems occurred in Fogera floodplain and what were the causes of flooding?
2. How to control flooding in Fogera area under regulatory control of the proposed S. Gumara and Ribb reservoirs?
3. What storage capacity of the proposed S. Gumara and Ribb reservoirs will be needed to control flooding?
4. How downstream flood peaks could be minimized by discharging less water than is coming into the reservoirs during peak inflows?
5. What flood mitigation measures, engineering and non- engineering, should be used to resolve flood problems in Fogera floodplain?

2 Literature Review

2.1 Introduction

In the history of human civilization, human societies have revealed a tendency to live in the lowlands adjacent to the river systems as they provide numerous benefits. These lands are part of the natural floodplain of rivers and settlements which are highly susceptible to the recurrent flooding events. In other words, despite the potential flooding risks, floodplain occupation will continue as long as those areas signify as a source of economic benefits.

There are many research works and analyses on flood control using a regulatory operation of reservoirs on the basis of reservoir operating rules together with flow forecasts. This research summarizes in the following sections how some techniques have been developed and applied in flood controlling measures. Section 2.2 describes hydrological modeling approaches and section 2.3 presents the flood modeling approaches. Finally, section 2.4 highlights some hydrodynamic flood modeling techniques from previous studies.

2.2 Hydrological modeling approaches

Hydrological models are simplified, conceptual or physical representations of part of the hydrologic cycle that are used for many hydrological problems, hydrologic predictions and hydrologic processes. Two major types of hydrologic models are distinguished, stochastic and process-based models (Chow, et al., 1988). Stochastic models are black box systems that link a certain input to model output, based on data and using mathematical and statistical concepts. However, process-based/ deterministic models represent the physical processes observed in the real world. These models can be subdivided into single-event and continuous models.

Distributive hydrological models are becoming a common place in a variety of applications (Vieux, 2004) in historical practices and it has been to use lumped representations because of computational limitations or insufficient datasets to physically-based models. The model is aimed at flood forecasting and long term hydrologic simulation using distributed precipitation data and different parameters such as interception, infiltration, evaporation, interflow, base flow, and overland and channel routing. In the following sections, reservoir inflow simulation (2.2.1), reservoir monitoring approaches (2.2.2) and reservoir operating rule curves (2.2.3) are introduced. These sub sections review how hydrological model and hydrodynamic models are combined and how reservoir operating rules were developed and used with these physically distributed models in order to control flooding.

2.2.1 Reservoir inflow simulation

In the past, it has been common practice to base reservoir operating rules on current reservoir storages information without direct use of inflow forecasts because of its uncertainties (Xiang Li, 2009). According to (Xiang Li, 2009), now days inflow forecast information are taken into account, including uncertainties, to improve levels of flood protection through more effective use of available reservoir capacity. This technique is applied to the China’s three gorges reservoir (TGR) case study. In this case study, inflow forecasting and the future inflows are derived from gauged records by assuming the inflow forecasting uncertainties.

Therefore, this work was tried to simulate upstream and downstream flows into and from the proposed reservoirs using rainfall-runoff model. Then by taking into account the rate of inflows (not strictly inflow forecasts), rule curves were built up for regulatory operation of the proposed reservoirs in such a way to control flooding downstream in the floodplain.

2.2.2 Reservoir operation approaches

Reservoirs are used to store water during high flow seasons and release it at a later time when river flow gets small. The operations of reservoirs for flood control also requires information that be made available in a form that can be understood by reservoir operators. In some cases, large flood releases have the potential to cause significant downstream damages and loss of life (Bowles, et al., 2004). Therefore, in order to protect such losses, basically reservoirs operating rule curves are used to control peak inflows by regulating the releases.

2.2.3 Reservoir operation rule curves

Reservoir operating rule curves are operating policies that specify either reservoir storage volumes (levels) or desired releases based on seasons and the existing storage capacity of the reservoirs. Reservoirs can have multiple rule curves made up of wet season refill curves and dry season drawdown curves (McCartney, et al., 2005).

Reservoir operators need to know the amount of water to release and when by taking into account the downstream situations. Reservoirs designed to meet demands for water supplies, recreation, hydropower, flood control, and the environment need to be operated in ways that meet those demands in the most reliable and effective manner (Loucks, 2005). However, it is difficult to determine the best reservoir releases for different possible conditions since the future inflows or storage volumes are uncertain. According to (Loucks, 2005), release rules are typically derived from trial and error simulations based on the expected impact of different alternative policies on various objectives. Discrete Dynamic Programming (DDP) is used to obtain initial estimates of reservoir operating policies that meet these objectives.

Rule curves are decision tools in the form of equations or graphs relating the outlet reservoir state parameters in different periods within the year. Rule curves are usually of two types (USACE, 1991) as cited by (Valdes and Marco, 1995). In common flood situations, releases are decided only as a function of the current reservoir water level and rate of inflows. On the other hand, inflows can be expressed as a rate of rise of the reservoir water surface. Both systems are equivalent but the latter option is operationally safer. This paper suggests that, however, the design flood hydrographs must be developed from hydro-meteorological information to reflect extreme flood situations. Otherwise, the performances of rule curves under moderate floods are weak and frequently results in serious flooding.

As pointed out on (Xiang Li, 2009) research works, dynamic control bound of flood limited water level (FLWL) is a fundamental key element for implementing reservoir dynamic control operation. Reservoir water levels generally are not allowed to exceed the FLWL during flood season in order to offer adequate storage for flood prevention. This method was applied to the China’s three gorges reservoir (TGR). According to this case study, results show that the dynamic control of reservoir operation using Monte Carlo simulation can effectively increase hydropower generation and the flood water utilization rate without increasing flood control risk.

Jain et al. (1998) adopted the simulation approach to develop operating rules for a multipurpose reservoir system in India as referred by (RAMIREZ, 2004). On this paper, it is clearly described that from the major flood control reservoir in the system, an analysis of flood regulation simulations was performed using the reservoir’s design flood hydrograph (DFH) in order to define an emergency level within the flood control pool and to develop the operating rules. Moreover, to protect the downstream areas from the DFH by keeping the storage below the maximum reservoir capacity, through simulations using different normal and emergency rules, different scenarios of safe channel capacities and initial reservoir storage.

In general, reservoir operating rules play significant roles to control flood risks downstream. Hence, these rule curves were developed for the proposed S. Gumara and Ribb reservoirs based on the storage targets and release constraints and the inflows. In order to obtain initial estimates of reservoir operating curves for these reservoirs, a DDP method was used.

2.3 Flood modeling approaches

Many research works on floodplain processes incorporates a hydrodynamic modeling of flow, the behavior of floodplains, water quality and sedimentation. The most important concept taken into consideration is to know and understand flood risks in the floodplain using hydrodynamic modeling techniques, computational facilities and theoretical developments in relation to the governing flow equations and their solutions.

There are many different hydrodynamic flood modeling approaches such as one-dimensional (1D) and two-dimensional (2D) and coupled 1D/2D models (Werner, 2005). For instance, St. Venant equations are solved using 1D or 2D numerical schemes by flood inundation model approaches. In 1D hydrodynamic model the change of stage, velocity and discharge are assumed in the longitudinal direction while the cross-sections taken at certain locations for constant geometry, hydraulic energy, pressure terms, flow depth and velocity are assumed in the transverse direction. On the other hand, 2D model approaches account for both direction of flows (longitudinal and transverse directions). The 2D approaches typically uses depth averaged velocity obtained by integrating the Reynolds averaged Navier-Stokes equations over the flow depth (PU, April 2007). Examples are the St. Venant equations, which assume a hydrostatic pressure distribution.

Thus, the upstream runoff was computed using a rainfall-runoff model. The flood frequency analysis was also carried out in a certain return periods in order to understand the trend of the flood based on observations. Then the runoff hydrographs were used in the hydrodynamic flood model. In order to estimate the time of flooding and characteristics of change of flow with time, flooding models require the shape of hydrographs in the upstream part of the floodplain (Haile, 2005). The shape of the hydrographs and the peak runoff were estimated based on the releases from each reservoir. However, to calibrate the flood model for the expected flood event was a challenging work to represent channel cross-section details for the 1D model and longer simulation time for the 2D flood model.

2.3.1 Model parameterization

Flood model requires some important input parameters such as topography (floodplain and river channel geometry), surface roughness coefficient, and initial and boundary conditions. The surface roughness depends on the land covers and type of bed material characteristics, channel alignment and other factors. The topography was obtained from different source centers such as ASTER, contour maps or surveying techniques (from ENTRO) and other sources. The initial conditions represent the initial hydraulic state of the system before the actual model simulation starts. It can be estimated by interpolation of the observations from available gauge levels or simulated from models. Lastly, boundary conditions were specified at the upstream and downstream ends of the system domain depending on the type of flows.

2.3.2 Boundary conditions

In flood modeling, specifications of the upstream and downstream boundary conditions are required for model setup. The downstream boundary conditions might be specified as stage level or flow hydrograph, or stage-discharge relationship (rating curve). On the other hand, the upstream boundary conditions are commonly specified as flow time series. More specifically, the annual maximum flows and design flood storms developed using frequency analysis were used as upstream boundary conditions. This may be defined based on probability or frequency with volume of flow which will be exceeded. In practice, the frequency analysis is a procedure to fit the hydrologic data to a mathematical model of distribution (Chow, Maidment and Mays, 1988). These distributions are based on a number of assumptions which might not be expressed the actual cases. Despite of these limitations, it is a common practice to associate peak discharges at least once with certain exceeded peak discharge or return period.

2.3.3 Sources of uncertainties

Beside the use and growth of hydrodynamic models, their reliability is becoming a challenging concern for users and modelers. In order to increase the reliability of models, the errors between observation and model results would be computed to the minimum.

Principally there are three different sources of errors experienced in practice such as errors from the input data (rainfall- a primary driving input data), models setup (equations and assumptions), and parameters (initial conditions and BCs). However, these uncertainties would be reduced and controlled through model calibration (Pappenberger, et al., 2005). For instance, uncertainty analysis of the unsteady flow component (UNET) of the 1D HEC-RAS model within the generalized likelihood uncertainty estimation (GLUE), the model performance runs with different sets of values of Manning roughness coefficients are compared to inundation data and outflow hydrograph.

2.3.4 Calibration and sensitivity analysis

Calibration is a technique used to adjust model parameters values to minimize errors deviations between model results and observations in order to increase the model efficiency. In flood models, the surface roughness parameter values are usually selected for calibration and its values are changed manually or automatically until a fixed calibration target has been met (Horritt and Bates, 2002). For instant, in statistics, root means squared error is one of such types of techniques which are used to evaluate and compare model results with observed values in a given objective criteria. Nevertheless, the complexities of river hydraulics make the setting of objective function for hydrodynamic flood modeling as difficult task (Haile, 2005).

1D and 2D models of flood hydraulics (HEC-RAS, LISFLOOD-FP and TELEMAC-2D) are tested on a 60 km reach of the river Severn, UK, using floodplain and channel friction as free parameters, against both the observed inundated area and records of downstream discharge for flood events in 1998 and 2000 (Horritt and Bates, 2002). The predictive power of the models calibrated against inundation extent or discharge for one event can thus be measured using independent validation data for the second event. The results show that for this reach both HEC-RAS and TELEMAC-2D models can be calibrated against discharge or inundated area data and give good predictions of inundated area, whereas the LISFLOOD-FP needs to be calibrated against independent inundated area data to produce acceptable results. The different predictive performances of the models stem from their different responses to changes in friction parameterization.

Therefore, the model performance acceptability depends on the objectives of the study area, sensitivity of the model results and reliability of observed data. Sensitivity analysis is often performed by changing the values of one or more parameters or input data at a time (Hall, et al., 2005). This helps to determine which parameter or input data has a dominant effect on the model results, and to understand its reliability. In general, hydrologic and hydrodynamic models are sensitive to DEM resolution, surface roughness, initial and boundary conditions, and numerical parameters as well.

Thus, a 1D/2D hydrodynamic flood model was used to know the dynamics of flows in the floodplain to determine the flood extents/ inundation depths by taking into account the issues of uncertainties and sensitivity of such key parameters.

2.4 Previous studies

The lack of literatures in Fogera area suggests that on flood risk mitigation did not necessarily have an overall strong basis because they were limited in some degree to address flood induced pressures.

However, previously some research works were carried out in Fogera floodplain to assess the causes of flooding events and its consequences. From those studies one was carried out by (Assefa, Andel and Jonoski, 2008) which focuses on flood forecasting and early warning decision tools to combat the recurrent flood problems. This study conducted an ensemble flood forecasting analysis by making use of different quantitative precipitation forecast (QPF) based flood forecasting model using HEC-HMS rainfall-runoff model.

The other study was on flood hazard and risk assessment using GIS and Remote sensing by (Wubshet and Dagnachew, 2008). In this study flood inundation map was developed for Ribb-Gumara catchment with a particular return period of flood levels which is computed from frequency analysis of river level data. Moreover, they also developed flood hazard map for the catchment and flood risk maps for the floodplain. The flood hazard map provides information about flood inundation corresponding to different probabilities in the catchment whereas the flood risk map provides quick information for the receptors at risk and probable damages during flooding. These two maps are used as a guide to find the predicted risk of flooding in the flood vulnerable area with different probable sources of flooding to reduce its impact easily and take measures under different probabilities.

(Tarekegn, 2009) research work focused on Ribb catchment to study the flood characteristics in the floodplain using a two-dimensional (2D) hydrodynamic modeling approach to simulate the August 2006 flood event. He uses 1D/2D SOBEK model to represent the topography with the proper applications of GIS. Result of this study shows that when the Lake Tana water level rise propagates to upstream and affects the flooding patterns of Ribb floodplain.

Nevertheless, this study outlines a general framework to control flooding using regulatory operations of the proposed reservoirs. Reservoir operation rules were developed using DDP and then hydrodynamic flood model was established. These make this research work new from the previous studies. The general modeling approach for flood simulation was presented by introducing and combining the hydrological model, HEC-HMS and the hydrodynamic flood model, SOBEK into application. Finally, discussion on results and conclusions were drawn. Suggestions for possible and integrated model application and extension concluded then after. In general, as a preliminary work, some of the aforementioned literature reviews helps to know and understand some characteristics of flooding in the study area.

3 Study Area Description

Gumara and Ribb catchments were selected as a case study in this research work. They are the two main watersheds in Lake Tana basin, Upper Blue Nile flowing into the lake from its eastern side. These catchments span from the eastern shore of Lake Tana to the foot slopes of Debre Tabor Mountain sharing a common water divide line. Respective to each of these watersheds, there are two proposed dams that will be built for future irrigation purposes in the area.

3.1 Location and topography

Gumara catchment falls between 1279718N and 1322260N and 0337186E and 0410859E of UTM. Gumara River is originated from Debre Tabor town about 3,050masl and flows generally in westerly direction for a length of 132.50 km till Lake Tana. The proposed S. Gumara dam site is situated across this river. The proposed dam center axis is at 1299415N and 0371598E having a catchment area of 385 km2. The maximum and minimum (riverbed level) S. Gumara reservoir water levels are 1930.00masl and 1900.00masl respectively. At about 28 km downstream of the dam a proposed diversion weir structure is located to regulate water for irrigation.

Ribb catchment falls between 11o 43' and 11o 53' N and 37o 47' and 37o 53' E. Ribb River, with its tributaries, drains from the western slope of the high mountainous area east of Debre Tabor town a length of 130 km long. The maximum and minimum Ribb reservoir water levels are 1945masl and 1873masl resp. The coordinate of Ribb dam site is 12°02'30"N and 37°59'45"E having catchment area of 685 km2. A proposed diversion weir structure is located downstream of the dam to regulate water for irrigation.

The topography of S. Gumara and Ribb dam sites are generally similar and characterized by rounded hills, cliffs, ridges and flat lands at their lower parts. That means, for instance, the upper and middle parts of Ribb river catchment are characterized by mountainous, highly rugged and dissect topography, with steep slopes. But the lower part of both of these catchments is more or less similar and characterized by a valley floor with flat to gentle channel slopes near to their confluence with Lake Tana.

3.2 Climate, vegetation and land use

The climate of Gumara and Ribb catchments is of tropical type of climate characteristics. It is warm during dry season and humid during rainy seasons. In the area, the heavy rainy season runs from June to September. There is also a short duration of seasonal rain between February and April with much lesser contribution than the normal rainy season. Gumara catchment has a temperature variation from 16.9oC in December to 21.6oC in May and its mean annual rainfall is about 1320 mm over the proposed development area (National Atlas of Ethiopia, 1981) as pointed out on (WWDSE, March, 2010). The mean annual rainfall of Ribb catchment is about 1400 mm in its upper part and 1200 mm in lower part.

The vegetation covers for both catchments are shrubs, small trees of acacia, grassland and eucalyptus trees. The vegetation cover is reduced radically from time to time owing to the deforestation habit of the local peasants.

3.3 Hydrology and flooding

The average flow of Ribb River without the dam is 31m3/s in August and 0.4m3/s in April. The mean flow from a catchment area of 677 km2 (at reservoir's inlet) discharged to the reservoir is about 11.6 m3/s. The peak floods discharged to the proposed Ribb reservoir for 100 and 10,000-year return periods are shown in Table 3.1 (WWDSE, October, 2010). The gross storage of Ribb reservoir is 300 Mm3. The mean annual flow from Gumara catchment is 27.18 m3/s (WWDSE, March, 2010). The peak floods discharged to the proposed S. Gumara reservoir is 818m3/s for 10,000-year return periods and the gross storage is 59.69 Mm3. The summaries of data are shown in Table 3.1.

Table 3. 1. S. Gumara and Ribb reservoirs average and design flows

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The lower down plain reaches of these two rivers, near the upstream of their confluences with Lake Tana, is subjected to flooding mainly due to runoffs resulted from continuous and heavy rainfall in rainy seasons. More than 79% annual rainfall contribution is from June through September (Tarekegn, 2009). The local rainfall together with some backwater effect from Lake Tana itself when the lake level rises above its maximum adds some impacts as already discussed in the introduction section.

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Figure 3. 1. Watersheds, river networks, S. Gumara and Ribb dams and the floodplain

4 Methods and Materials

The methods developed and used were hydrological and hydrodynamic models with the help of Geographical Information System (GIS) based on the available datasets.

4.1 Research methodology

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The following model approaches are issued to answer the lists of research questions through addressing the introduced objectives to resolve flooding problems in Fogera floodplain. The hydrological model using HEC-HMS and hydrodynamic flood model using SOBEK 1D/2D were developed in two scenarios: without and with the proposed reservoirs. The detailed steps of each model are presented the following flowchart as shown in Figure 4.1.

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Figure 4. 1. The flowchart showing methodologies in the study area

4.2 Hydrological modeling using HEC-HMS

Hydrological modeling was carried out in two scenarios as mentioned above. In Figure 4.1, Block 1 and Block 2, shows the hydrological modeling steps. Observed time series data were used in the simulations. Then after model results of the two scenarios were examined and compared in order to know and understand the degree of flood impacts downstream in the floodplain. Note that the flow forecasts to the proposed reservoirs were not used in the simulation since it is beyond the scope of this study and of course it needs more time to deal with. Nevertheless, it is shown in the flowchart to show how it is important component especially for real time simulations.

In this research work, a single event based hydrological model was adopted since peak runoffs are restricted to short periods after a storm and due to limited model input data sources such as soil and land use datasets.

HEC-HMS is currently limited to the analysis of runoff from rainfall within the watershed's land surface, vegetation and water bodies (Bennett and Peters, 2004). A simplified and conceptualized hydrological process of a catchment is illustrated in Figure 4.2.

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Figure 4. 2. Typical representation of watershed runoff processes (Feldman, 2000)

4.2.1 HEC-HMS model setup

Before the setup of HEC-HMS model done, the basic input rainfall and discharge data were prepared in addition to the spatial datasets extracted using GIS with its important functionalities.

Basin model, meteorological model, control specifications, and input data (time series and paired data) are the four important components of the HEC-HMS project model used for providing model inputs.

4.2.1.1 Basin model

The basin model is one of the most important components of HEC-HMS used to compute outflows from the meteorological data by deducting losses, transforming excess rainfall and adding base flows. This means, basin model converts some portions of rainfall into surface runoff at certain points within the watershed by considering losses. It also contains elements of the basin and their connectivity within the drainage system.

Initial and constant losses for loss method, Clark transformation method for direct-runoff transformation and Lag method for channel routing were conducted in basin model components. These methods were selected owing to the availability of data and the number of parameters required for simulation. In this work the base flow was not included in the simulation since it has insignificant impacts in the watersheds unlike to runoff.

4.2.1.1.1 Loss method

Losses are modeled in order to account for the chance of the precipitation and its potential to affect the hydrograph. Among the ten different loss methods provided in HEC-HMS model, initial and constant-rate loss model was selected to account for the cumulative losses. All these methods conserve mass. This means, the sum of infiltration and precipitation left on the surface will always be equal to total incoming precipitation.

The initial and constant rate loss methods are simplistic methods but they are appropriate methods for watersheds that lack detailed soil information. These parameters represent physical properties of the watershed soils and land use, and the antecedent conditions respectively. It is suggested that of initial losses ranges 10-20% of the total rainfall for forest and rural areas, and 1.0-2.0 inches (25-50 mm) for urban areas (SCS, 1986; Skaggs and Khaleel, 1982)(Feldman, 2000).

Table 4. 1. Soil groups and infiltration rates (FAO, 1998, Feldman, 2000, Natural Resources ConservationService, 210-VI-NEH, July 2004)

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* The type of soils coverage in the study area is grouped to soil group B and C and the ranges to loss rate is approximated as 1.27-7.62mm/hr (Table 7.2) for initial loss and the constant loss rate is as lower as the lower values in the given range.

4.2.1.1.2 Clark transformation method

The Clark Unit Hydrograph accounts for sub-basin shape, hydraulic length, surface roughness, and storage of a watershed. It is a synthetic unit hydrograph method that is not required to develop through the analysis of past observations. Instead it assumes and uses the concept of instantaneous unit hydrograph (IUH) resulting from one-unit of excess precipitation applied instantly over a watershed. Translation and attenuation are the two main concepts considered in Clark transformation method and implicitly represented with the relationship of time and area. Attenuation is represented by the outflow hydrograph which is caused by the basin storage properties.

The parameters used in Clark method are the time of concentration, tc and the storage coefficient, R. The time of concentration is the maximum travel time in the watershed and used to develop the translation hydrograph. The storage coefficient, R is an index of temporary storage of excess precipitation of a watershed as it drains to the outlet point. According to many studies, the storage coefficient, divided by the sum of time of concentration, is reasonably constant over a region (Feldman, 2000). The linear reservoir at the watershed's outlet is given by:

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The inflow, It, is obtained from multiplying the watershed area with a unit depth and divided by the computational time step, Δt. The linear reservoir model and the storage at time t are related to the outflow as follows:

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The average outflow (Ot, average) during period t is then given by:

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Where, S is the storage changes, t is the time rate of change of storages, It is average inflow and Ot is outflow from storage at time t, R is a constant linear reservoir parameter (known as K in Clark's method), Ca and Cb are routing coefficients.

4.2.1.1.3 Routing method

The lag method was chosen as the routing method to translate the flood waves from the upstream sub-basins to the downstream. The only input parameter is the lag time in minutes. This method does not account for attenuation of the peaks. Therefore, it is best suited to short stream segments with a predictable travel time that doesn't vary with flow depth. The lag time was computed hydraulically from upstream hydrographs, reach length, slopes and channel cross sections. It also computed from time of concentration and multiplying it with a constant.

Time of concentration, tc is the time required for water to move from the most remote point of the watershed to its outlet after once the soil has become saturated and minor depressions filled. It is computed using Kirpich /Ramser empirical formula:

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Where tc is time of concentration in minutes, L is the maximum flow length in meters and S is the watershed gradient in m/m (or the elevation difference between the outlet and the most remote point divided by the length L).

4.2.1.2 Meteorologic model

The main purpose of a meteorologic model is to prepare meteorologic boundary conditions for the sub-basins. These boundary conditions include precipitation and potential evapo-transpiration. HEC-HMS includes a meteorology model to compute the precipitation time series which is required for simulation. A user-specified gage weights method was used for input precipitation depths that were prepared from various gagging stations within and adjacent of the watersheds.

Precipitation is a primary input data for the hydrologic system. It is used in the form of average values as an input. The average values are often referred to as mean aerial precipitation (MAP) values and was estimated by a weighting scheme from point gage data using Thiessen polygon method. The MAP data for six stations in this project area were determined and used in the model. Some gages are more representative of the watershed and assigned a higher weight.

4.2.1.3 Control specification and HEC-DSSVue

The control specification is one of the main components of a HMS project main window and mainly used to control model simulations period. It integrates basin model, meteorologic model, and time series and paired data to create a simulation run. For instance, the event based simulation starts on 27th of July and ends on 16th of August 2006 based on daily time steps.

HEC-DSS uses a block of sequential data as the basic unit of storage of data and results for efficient retrieval. Therefore, HEC-DSSVue is efficient database management system storage for time series data and retrieves them to HEC-HMS model.

4.2.2 Model requirements

The mathematical models are solved equations with specific conditions and parameters; the model simulates and predicts what will happen within a watershed. The mathematical models that are included in the model describe how a watershed responds to direct precipitation or water flowing from upstream into it. Even though equations and the procedures of solution are vary, all models have various components required in common such as input parameters, initial conditions and boundary conditions. Hence, such components required for Gumara and Ribb hydrologic systems are discussed in brief below.

4.2.3 Model parameters

Model parameters are numerical measures of the properties of the real-world system. They control the relationship of the system input to system output. Initial and boundary conditions are important parameters to the hydrologic model.

Initial conditions are the known value and specified with which the simulation start. For instance, in the runoff models, the initial conditions represent the runoff at the start of the storm being analyzed.

Boundary conditions (BCs) are system input values that forces and acts on the hydrologic system and cause it to change. The precipitation that is applying and causes runoff in the watershed and the flow hydrograph generated from the runoff used as BCs to channel reaches for a routing model. All these values are quantified and managed by the model system itself.

4.2.4 Model calibration and validation

Calibration is the determination of the parameters that are initially unknown and used to reduce deviations between simulation results and observations. The procedure of calibration involves a combination of both manual and automated procedures. Calibration is carried out using one set of data whereas validation using another set of data with a period of similar length using the concept of split-sample test (Abbott and Refsgaard, 1996).

Validation is the representation of the actual system behavior that it reproduces with enough reliability to satisfy the objectives with an acceptable accuracy. It is usually achieved through calibration, an iterative process of comparing the model to actual system behavior. Therefore, in order to understand the performance of the model, the difference between simulation and observation values were compared quantitatively.

4.2.4.1 Objective function

Objective function is used to measure the goodness-of-fit between the computed and observed values. There are seven different functions are provided in HEC-HMS to measure the goodness-of-fit. Among those functions, the peak-weighted root mean square errors (RMSE) function was used during calibration. RMSE gives high weight to flows above the mean and gives high credits for this function since this study focused on peak flows. Details of formulas and descriptions are referred on the HEC-HMS user’s manual of USACE (Feldman, 2000).

4.2.4.2 Search methods

There are two search methods in HEC-HMS for minimizing the objective function and optimize parameter values. The first method is the univariate gradient (UG) method which evaluates and adjusts one parameter at a time by keeping other parameters constant. The second method is the Nelder and Mead method evaluates all parameters simultaneously and determines which parameter to adjust. The UG method was used in this study since it is easy to observe the search results. This search method is also based on the Newton’s theory and Taylor’s series to approximate the objective function.

4.3 Reservoir operation rule curves

The operation of reservoirs under flood conditions can be performed through rule curves or within a real time framework (Valdes and Marco, 1995). The latter approach uses as much real time and the near future information as possible. On the other hand, the former approach uses operation rule curves for multistage decision making issues. Hence, this approach was adopted in this work to develop rule curves for the two proposed reservoirs since the real time approach is beyond the scope of this study.

Reservoir operation rule curves were then developed by considering reservoir storage volumes (levels) and desired releases and inflows based on seasons of a year and the existing storage capacity of the proposed reservoirs. In other words, rule curves were built up through Elevation-Storage-Discharge relationship function based on a mass balance equation.

Rule curves were developed using a discrete dynamic programming (DDP) method by taking into account the simulated inflows determined from the HEC-HMS model (refer Figure 4.1, Block 2).

4.4 HEC-HMS modeling with reservoirs

All the model setup and the required parameters and data were prepared during existing system simulations. In this part of the research, reservoir simulations were carried out using HEC-HMS by imposing the developed rule curves. Steps showing reservoir simulations are presented in Figure 4.1 under Block 2. The developed rule curves are then used to control the releases from the reservoirs.

4.4.1 Reservoir routing method

There are three different reservoir routing methods available in HEC-HMS for the actual reservoir storage simulation. Outflow curve routing method was used in this work to compute the storages. This routing method represents the reservoir with a user-provided relationship between elevation, storage and discharge. The relationship between discharge and storage must be unique, which does not permit looped rating curves. Further, the relationship must be monotonically increasing with storage. This relationship was developed externally to the program considering all the possible outlets from the reservoir and combining them in a single storage relationship. The method can then be used to preserve the specified release and track the storage using the inflow, outflow, and conservation of mass (Feldman, 2000).

4.4.2 Storage method

Storage-Discharge and Elevation-Storage-Discharge, and Elevation-Area-Discharge are the three available options for specifying the storage relationships. Among these options, Elevation-Storage-Discharge option was used. In this option, elevation-storage curve and storage-discharge curve were defined in the paired data manager before they can be used in simulation. During computation time, these two curves were selected and are combined into a single routing table with three rows (elevation, storage, and discharge) by the model itself.

The primary curve used for this configuration was storage-discharge curve. This table is initially configured using the storage-discharge curve selected as the primary curve and the remaining column is interpolated from the elevation-storage curve (which is not selected as the primary curve). Finally the storage routing is completed from the combined table using the storage and outflow columns. After the routing is completed, the program computes the elevation, storage and discharge from the reservoirs for each time interval.

4.4.3 Initial condition

The initial condition sets the amount of storage in the reservoir at the beginning of simulation. There are different options available in HEC-HMS model to specify initial conditions such as elevation, discharge, storage, and inflow = outflow. Elevation was used as initial condition to this model.

4.5 Hydrodynamic flood model with SOBEK 1D/2D

SOBEK hydrodynamic flood model is a powerful tool for flow modeling in many areas such as irrigation systems, drainage systems, and natural streams in different areas. Applications are typically related to irrigation, flood control, canal automation, reservoir operation, and water quality control to solve problems (SOBEK online reference, www.sobek.nl). Therefore it gives high quality information to water managers in such different sectors. However, this study focused and taken the advantage of its application to flood control problems.

To SOBEK 1D/2D flood model, the upstream and downstream boundary conditions, such as flow hydrographs, channel cross section profiles and the lake level were identified and determined. Finally, the two scenarios model results, with and without the proposed reservoirs, and selected return periods were examined and compared to observe the flood extents and inundation depths in the floodplain. The detailed steps are shown in Figure 4.1 under Block 3.

The SOBEK is a coupled 1D/2D hydrodynamic flood model and the hydrodynamic simulation engine underneath is based upon the complete Saint Venant Equations. The water flow is computed by solving the complete De Saint Venant equations (Lomulder, 2004). For the 1D flow two equations and for the 2D flow, three equations are solved.

4.5.1 Channel flow equations

The flow in 1D is described by two equations: the continuity equation and the momentum equation. The continuity equation is given by:

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The momentum equation for 1D flow reads:

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Where, Q is discharge in m3/s, t is time in second, x is the distance along the river channel in meter, A f is the wetted area in m2, qlat is the lateral discharge per unit length in m2/s, g is gravity of acceleration in m/s2 (9.81), h is the water level in meter (with respect to the reference level), C is Chézy coefficient in m½/s, R is the hydraulic radius in meter, W f is the flow width in meter, t wi is the wind shear stress (N/m2), and r w is the water density (kg/m3).

4.5.2 Overland flow equations

The 2D flow is described by three equations: the continuity equation, the momentum equation for the x-direction and the y-direction would be computed, together with the continuity equation. The continuity equation ensures the conservation of fluid.

The continuity equation reads:

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The two momentum equation reads:

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These equations are non-linear and they are a subset of the well-known shallow water equations that describe water motion for which vertical accelerations are small compared to horizontal accelerations which applies to flood flow, river flow and tidal flow.

Where, u is velocity in x-direction (m/s), v is velocity in y-direction (m/s), V is velocity is water level above plane of reference (m), C is Chezy coefficient (m1/2/s), h is total water depth: +d (m), d is depth below plane of reference (m), a is wall friction coefficient (1/m).

4.5.3 SOBEK model setup

The model setup was performed by considering the important computational parameters, initial conditions and boundary conditions. The calculation of time steps, simulation period and initial water levels to the 1D flow and the water height to the 2D flow was used. This is because the values used in 2D grid cell are defined as heights in relation to the reference level.

The required input datasets for the SOBEK model environment are: The background map, the river networks and the DEM file in arc info format. DEM file is the most important input data for the 2D flow simulation. All these input datasets were prepared separately using arc GIS.

The next steps are schematization of the stream flow networks, setting the initial conditions, boundary conditions, cross-sectional profiles, and setting the friction factors for the channel cross-sections and 2D grid cells. The resolution of the 2D grid cell is used to investigate the altitude of the 2D grid at several places where one is interested to know the altitude of a point.

The flow cross section profile nodes are the most important data inputs to the hydrodynamic model simulation which defines the dimensions of the rivers channels. The discharges through a river channel are greatly determined by the shape of the river bed. From the cross section data, the bed levels and hydraulic radiuses are interpolated towards the calculation points, for which every time step water levels are calculated.

4.5.3.1 Digital Elevation Model

The 2D grid cell or DEM file is one of the most important building blocks to model the 2D systems. The DEM required for SOBEK flood model in ASCII format. Then the 1D channel flows is schematized into split vectors and coupled with the 2D flow after importing the DEM file.

4.5.3.2 1D/2D connections

The 1D network is linked with the 2D grid either connecting between the 1D connection Node and 2D grid cell or the 1D calculation Points and 2D grid cell. The following rules should be obeyed; only one connection per grid cell is allowed (www.sobek.nl). In other words, it cannot be allowed a connection node and calculation point in one grid cell at the same time, nor more than one connection node or calculation point per grid cell. It is simpler to assume that 1D and 2D networks are two independent map layers, with the 2D network map layer overlapping a 1D network. The computational code determines the connection points between 1D and 2D based on the map coordinates for the center of 2D grid cell and the 1D calculation node. If they fall within certain criteria, then the connection is made between them. This is expressed mathematically as follows:

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Where, X1 = x map coordinate for 1D point, X2 = x map coordinate for 2D grid cell, Y1 = y map coordinate for 1D point, Y2 = y map coordinate for 2D grid cell, DX = width of grid cell in X direction, DY = width of grid cell in Y direction (DX and DY are equal) then the 1D point is assumed to ly completely within the 2D grid cell.

For instance, the connection between the 2D cells and the 1D network is done as follows: (1) The center of 1D node is internally moved to match with the center of 2D grid cell, without changing the length of the connecting 1D branches, (2) The 2D grid cell is counted as part of 1D Node and (3) The flow in 1D channel below the 2D grid level is treated as 1D flow, while the flow above the 2D Grid level is treated as 2D flow with the area of 2D grid cell.

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Figure 4. 3. Connections between 1D network and 2D grid cell (www.sobek.nl)

4.5.3.3 History data observations

History station nodes are special kind of node used to determine the exact values of all variables on specific locations in the 2D grid cell. It is used in the format of incremental files in order to reduce the enormous amount of data generated by the 2D simulations. It works by defining a number of classes for every output variable which are then used in the output files instead of the actual data value itself. For instance, if a water depth in a certain 2D grid cell equals 0.33 m, it would fall between 0.3 and 0.4. Therefore, the incremental outputs were determined for all selected parameters such as the water depths, velocities of the overland.

In case a 2D-History node is located on a 2D grid cell that has a missing value for the bed elevation, this means no output for such 2D-History node will be available. This also yields in case a 2D-History node located on a 2D grid cell of a nested grid that has a missing value, while the underlying parent 2D grid might have a real value for its bed elevation.

5 Data Preparation

The major part of our knowledge and understanding on flooding behavior and forecasting of flood event has been gained and rather it is derived from many long-term observations.

5.1 Data collection and preprocessing

Different types of datasets such as rainfall, discharges, reservoir water levels and storage capacities, river cross-section profiles, river and lake water levels, land use/ land covers and DEM are some of the mainly required datasets were obtained from the Ministry of Water Resources of Ethiopia, ENTRO and other data sources as per their needs to the models.

The hydrological and metrological data were compiled, analyzed, prepared used as input to the model. During data processing the possible errors has to be reduced through validation in order to minimize model result errors or uncertainties. For instance, cross checking and plotting the Gumara river discharge/ water level with Ribb river discharge/ water level by taking into account their catchment characteristics.

5.2 Meteorological data

5.2.1 Rainfall data

The daily rainfall data from 2000 up to 2006 was available to this study. This data was semi-analyzed data from the previous study (Assefa, Andel and Jonoski, 2008). The missing data was filled by referencing class-1 stations at Gonder and Bahir Dar and a 0.25ox0.25o grid TRMM data sources. According (Assefa, Andel and Jonoski, 2008) analysis, class-1 source was not satisfactory source since these stations have missing data gaps in similar periods. However, the rainfall data from TRMM within a grid have better estimates for data filling than this class-1 stations. In fact, it is difficult to conclude that TRMM performance has good bases than ground stations. Rather it was used as alternative method. The correlation of the daily and monthly time series data from TRMM is tabulated below in table 5.1.

Table 5. 1. TRMM correlation with ground station, (Assefa, Andel and Jonoski, 2008)

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Using the filled data series, all stations were checked for their correlation relation in order to see their contribution to each watershed. For instance, D.Tabor, A.Zemen, Yifag and Woreta stations have better contribution to Ribb watershed and the rest stations contributes better to Gumara watershed as shown in Table 5.2. The annual seasonal rainfall distribution for Gumara and Ribb catchments and class-I stations are presented in Figure 5.1 and 5.2. Figure 5.3 shows the frequencies of the rainfall distribution in August where peak flood occurred.

Table 5. 2. Correlation of different stations in the study area

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Figure 5. 1. Annual seasonal rainfall of Gumara (a) and Ribb (b) watershed

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Figure 5. 2. Annual seasonal rainfall of Bahir Dar and Gonder stations

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Figure 5. 3. Frequency of monthly rainfall in Gumara (a) and Ribb (b) watersheds

5.2.2 Evaporation data

The daily evaporation time series data from 1992 up to 2006 was available to this study. The daily Evaporation data is measured using pitch instrument at Bahir Dar. This data was then converted to the monthly average using the pan coefficient and the result is plotted as shown in figure 5.4 below.

The potential evapo-transpiration was estimated by considering the pan coefficient (Kp) in the area as per categories given to class standards. Pan coefficients for Class A pan for different pan setting and environment and different levels of mean relative humidity and wind speed are tabulated in FAO Irrigation and Drainage Paper No. 24 (ALLEN, et al., 1998). The criteria required to choose the Kp value were the medium mean relative humidity of the area which ranges from 40% to70% and the wind speed of 2ms-1 to 5ms-1. Therefore, the Kp value taken from the table was 0.7 to estimate the potential evapo-transpiration used in simulation.

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Where ETo is evapo-transpiration , Kp is pan coefficient and EV is evaporation

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Figure 5. 4. Average monthly evaporation of Bahir Dar station

5.3 Hydrological data

The daily time series river flows for both Gumara and Ribb rivers with their respective channel cross-sections at each gauging stations were available. The physical location of these two stations and the river network systems are presented in Figure 5.5 below.

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Figure 5. 5. Watersheds, river networks, gauging stations, and Fogera plain

This study uses the annual peak flows for flood frequency analysis since the peak flows are abounded in the wet seasons. In daily historical flow records, there are many data gaps identified from one month up to four months (Table 5.3) which could not be filled easily. However, all these missing data gaps lay in the dry seasons of the year and not necessary and critical to be filled and analyzed for this specific study.

Table 5. 3. Missing flow records of Gumara and Ribb rivers in dry seasons

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Moreover, some missing records are also observed before 1992 as shown in Figure 5.6. But after this year there is no missing data records identified as shown below in Figure 5.7. Although, this study focuses on event based simulation, no need of filling the data gaps in the dry seasons (recession periods). The actual flooding events were recorded in 1966, 1996, 1998, 1999, 2000, 2001, 2003 and 2006 years (Wubshet and Dagnachew, 2008). From these flooding events, 2006 is more likely to be chosen and analyzed for model simulation owing to the availability of meteorological and hydrological data, the satellite image for floodplain inundation, and the magnitude of actual flows in the specified year.

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Figure 5. 6. Historical daily flows of Gumara and Ribb rivers (1959-2009)

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Figure 5. 7. Daily flows of Gumara and Ribb rivers (1992-2009)

The maximum peak flows, within the rainy season (Jul-Aug-Sep), are recorded in August compared to flows of July and September for both Gumara and Ribb rivers as shown in Figure 5.8 below. These peak flows are resulted from high rainfall distributions on each catchment owing to less infiltration capacity of the soil then a higher surface runoff generated.

When looking at deeply to the peak flows of Ribb which are recorded in August (1994, 1996 and 1998), they are unlikely peak flow records as shown in Figure 5.8 and 5.9. This might be happen most likely either due to the washing away of the staff gages by the flood and reading the maximum flood marks only. Or might be due to the fact that when the river bank reaches at its full level, it overflows and distributes over the surface of the land then the gage shows more or less similar reading. This means, when the guided channel flows transported to an overland flow, and then it covers larger area with infinite small depths. Nevertheless, avoiding these datasets from flood frequency analysis is not being logical and therefore they were incorporated in to the analysis. But they did not considered for the model simulation.

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Figure 5. 8. Daily flows of Gumara (a) and Ribb (b) Rivers for wet seasons

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Figure 5. 9. Unlikely daily peak flows of Ribb River in August

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Figure 5. 10. Daily flows of Gumara and Ribb River for 2006

5.3.1 Data screening

The data used for this analysis was selected from the peak flows between 27th of July and 16th of August 2006. Then the data was screened using the basic Data-Screening Procedure (Dahmen and Hall, l990). The procedure consists of four principal steps: (1) Screening of the data roughly and computing the totals for the period, (2) Plot the totals according to the chosen time step and identify any trends or discontinuities, (3) Test the time series for absence of trend with Spearman’s rank-correlation method and (4) Apply the F-test for stability of variance and the t-test for stability of mean to split, non-overlapping, sub-sets of the time series. The method is based on the Spearman rank-correlation coefficient, Rsp, which is defined as:

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Where n is the total number of data, D is difference, and i is the chronological order number. The difference between rankings is computed with:

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Where, Kx is the rank of the variable, x, which is the chronological order number of the observations. The series of observations, y, is transformed to its rank equivalent, Ky, by assigning the chronological order number in the original series to the corresponding order number in the ranked series, y. If there are two or more ranked observations, y, with the same value, the convention is to take Kx as the average rank. Then compute the statistic test using:

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Where t, has Student’s t-distribution with v = n-2 degrees of freedom. Student’s t-distribution is symmetrical around t = O. Details of computation are on (Dahmen and Hall, l990) including the distribution table (it is present in many hydrological reference books). Therefore, if t is not contained in the critical region, then the time series data has no trend and given by:

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Following these steps for the chosen time period (n=21 datasets), there was no trends found for both hydrological and meteorological data series as shown below in Table 5.4 and in Annex 1 graphically for both Gumara and Ribb watersheds respectively.

Table 5. 4. Screened hydrological and meteorological data for trends

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5.4 Land use and soil types

The soil groups and the land use/ land cover in Lake Tana basin are presented below in table 5.5. The major soils groups are Luvisols, Fluvisols, Leptosols, Litic leptosols, and Vertisols having a common property of clay, with slight varieties of clay loam and silt-clay.

Table 5. 5. Land uses and soil types in Gumara and Ribb watershed sub-basins

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* Where A= Agriculture, AP= Agro-pastoral, P= Pastoral, M=Marsh, 3= Chromic luvisols, 7=Eutric Fluvisols, 8= Eutric Leptosols, 15= Haptic Luvisols, 24= urban (FAO, 1998, Natural Resources Conservation Service, 210-VI-NEH, July 2004)

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Figure 5. 11. Gumara and Ribb watersheds Land uses (a) and soil types (b)

5.5 Conclusions and discussion on data processing

This study was adopted an event based simulation method. Therefore, detailed data processes were focused on the annual peak flows, 27th of July to 16th of August 2006, which causes flooding in Fogera plain. Data were checked out for missing. As a result there is no missing data were observed. The data were also checked whether they have trends/ mean differences or not using the basic data screening procedures (Dahmen and Hall, l990). Results show that no trends were observed (see Table 5.4 above).

In conclusion, the hydrological and meteorological data records were used for farther studies such as for frequency analysis and different models. Hydrological model, HEC-HMS and hydrodynamic model, SOBEK 1D/2D are the two models were used in this research work including the flood frequency analysis.

It was also observed that Gumara watershed with its smaller catchment area contributes higher flows compared to the relatively higher Ribb catchment area. Principally the shape and catchment characteristics results such runoff differences generated from each catchment. Accordingly, Gumara watershed has a semi-rounded shape with smaller time of concentration yields higher runoff at its outlet compared to the elliptical shape of Ribb watershed having higher time of concentration (see Figure 5.5 above). Furthermore, the weighted spatial variation of the nearby and adjacent rainfall contribution of Gumara watershed is much higher compared to those rainfall stations which have contribution to Ribb watershed.

6 Flood Frequency Analysis

6.1 Introduction

The main objective of flood frequency analysis of hydrologic data is to relate the magnitude of extreme events to their frequency of occurrence through the use of probability distributions (Chow, Maidment and Mays, 1988). Principally, flood frequency analysis has two main applications. The first one is to predict the possible flood amount over a certain period and the second one is to estimate the frequency of floods may occurrences.

Flood frequency analysis uses historical peak flow data records to produce guidance about the expected behavior of possible future flood events. On the other hand, hydrologic models can also be used to generate data for frequency analysis to illustrate the estimation of exceedance probability and return periods. However, care should be taken while using models because of uncertainties due to many assumptions made. For instance, a 100-year event might happen once, more than once, or not at all. Nevertheless, there is a chance that it will only happen once, but there is no warranty to be occurred.

There are several methods of conducting flood frequency analysis on time basis to estimate probabilities and return periods. The common methods are: Normal, Log-Normal, Extreme Values and Log-Pearson Type III Distributions. However, Log-Pearson Type III (LP3) and Extreme Values (EVI) distributions are the most popular and commonly used methods. Therefore, among others, these two methods were chosen since they are used in many places around the world.

Although, before carrying out the flood frequency analysis, observed datasets were pre-processed and checked for extremities using outlier guidance. An outlier is an observation that deviates much from other observations (USGS, 1981). This might be due to measurement error and/or statistical sampling problems. Identifying outliers and dealing with them depends on understanding of the data and its sources (Bayliss and Reed, 2001). However, care should be taken again given that their presence or deletion from the population alters the statistics significantly. In other words, it might not be good to reject more than one point values.

In order to compute outliers, it is necessary to go through the following steps. First, determine the skew coefficient (Cs) of a station. If Cs is greater than +0.4, test for higher outliers and if it is less than -0.4 then test for lower outliers (USGS, 1981). If Cs is between -0.4 and +0.4 exclusive then test for both high and low threshold outliers. Secondly, the higher (equation 6.1) and lower (equation 6.2) outliers are computed respectively using:

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Where XH and XL are the higher and lower threshold outliers in log units, m is the mean, KN is value from table for N samples, and σ is standard deviation of the sample dataset.

From the computation, there are no outliers obtained. Results are shown in Table 6.1 below. In conclusion, the annual maximum flow observations from the population datasets were then used for flood frequency analysis.

Table 6. 1. Summarized result for Gumara and Ribb rivers observed flows

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As discussed above, the main objective of flood frequency analysis is to relate the magnitude of flood events to their frequency of occurrence through probability distribution. The historical annual peak flow records of Gumara and Ribb Rivers are shown in Figure 6.1 below.

Figure 6.1 shows some basic information about annual maximum observed flows for over the last 50 years and used in the frequency analysis. From the graphs, the peak flows are changing over time, either due to land use, stream channel deformation or some other reasons. However, peak flows are highly variable and changed unevenly from year-to-year. For instance, the Ribb river flows show a decreasing trend, below the mean value since 1980 unlike to Gumara flows. On the other hand, even if flows are decreased in both sub catchments the frequency of the flood events increases since mid of 1990's. The reason might be highly likely due to deforestation, poor agricultural practices, change of the river morphology and population growth. Despite the frequency analysis can only be applied to datasets with no detectable trend in hydrologic response. This means, the size of a different return period flow event is different for each watershed depending upon their catchment characteristics and probably climate conditions of the area.

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Figure 6. 1. Plots of annual peak stream flow on the Gumara and Ribb Rivers

6.1.1 Log-Pearson Type III, LP3 distribution

Flood frequency analysis using Log-Pearson Type III (LP3) method is a statistical technique for fitting frequency distribution data to predict the design flood at some selected points of a river (McMahon and Srikanthan, 1981). In this course, the annual peak flow data of Gumara and Ribb Rivers were used to calculate statistical information such as mean values (m), standard deviations (s), skew coefficient (Cs), and return periods (Tr). Once the statistical information is computed, then the frequency distribution is constructed and the probabilities of floods of various sizes are extracted from the curve of annual maximum data (Beran and Nozdryn-Plotnicki, 1977).

Given the historical annual peak flows of Gumara and Ribb rivers, the flood discharges were computed corresponding to 2, 5, 10, 25, 50 and 100 year of return periods. In order to compute the frequency of flood discharges (Q): first the given peak annual flows were ranked in descending order before log value computations of the given flows. Secondly, return periods were calculated for each discharge using (n+1) /m, where n is the number of data or years and m is the rank. Thirdly, the exceedence probability (1/Tr) of each discharge were computed, the K values are read or calculated from the frequency factor table, Bulletin 17B procedures (Rossi, et al., 1984, USGS, 1981) and discharges were calculated in log units using:

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Where k is the coefficient based on skew coefficient and return period. Lastly, the discharges corresponding to each return period were computed using antilog. The discharge with the corresponding return periods and exceedence probabilities were plotted as shown in Figure 6.4 below.

6.1.2 Extreme Value Type I, EVI distribution

The study of extreme hydrologic events involves the selection of a sequence of the largest or smallest observations from the data sets (Chow, Maidment and Mays, 1988). Flood frequency analysis often focuses on flood peak values, and hence, provides a limited assessment of flood events (Yue, et al., 1999). However, since this study deals with flooding, annual maximum flows were considered for the computation. The computation procedure are as follows: if N1, N2…, Nn be a set of daily stream flow, and let X = Max (Ni) be the maximum for the year. If Ni is independent and identically distributed, then for large n, X has an Extreme Value Type I (EVI) probability distribution function which is given by:

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To determine the values of xT for various values of return period T, it is convenient to use the reduced variate yT and then for the EVI distribution, xT is related to yT as:

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Where, f(x) is probability density function, F(x) is cumulative distribution function, u is the mode of the distribution (maximum probability density), y is a reduced variate.

6.2 Shape of hydrographs

Hydrographs are graphs which show the river flows over a given period of time as a function of the watershed's response time and its river to certain duration of rainfall. Therefore, the shape of a hydrograph is determined by the speed in which runoff flows are able to reach the river. There are multiple factors affecting the shape of hydrograph in a watershed such as slope of the area, land use which affects the response time of a watershed, soil types and amount and types of precipitation. For instance, the rate and intensity of the rainfall in the watershed affects directly the amount and rate of overland flow. And the soils which have larger particle sizes have larger infiltration capacities.

Taking into account such affecting factors, the shape of hydrographs of Gumara and Ribb rivers were identified and determined from the frequency analysis for different return periods with respective peak flows as shown in Figure 6.2 below. Hydrographs were then determined by using peak flows from the frequency curves and filling the observations before and after of the peaks. However, the ideal hydrographs shape were developed using one of the most well known methods called Soil Conservation Service (SCS), dimensionless unit hydrograph method, which is used to derive synthetic unit hydrographs as shown in Figure 6.3.

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Figure 6. 2. Shape of hydrographs of Gumara (a) and Ribb (b) for observed flows

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Figure 6. 3. Shape of hydrographs of Gumara (a) and Ribb (b) for 2, 5, 10, 25, 50 and 100 year return periods

6.3 Results and discussion on frequency analysis

The flow results obtained from the flood frequency analysis corresponding to 2, 5, 10, 25, 50 and 100 year return periods are presented in Table 6.2 and in Figure 6.4 below for both LP3 and EVI methods. The estimated flow results obtained using LP3 distribution method for a 100-year return period for Gumara River for instance is about 396.7m3/s and 232.8m3/s for Ribb River. On the other hand, these values are 412.5m3/s and 229.8m3/s respectively obtained using EVI distribution method as shown in Table 6.2 below. In general, based on observation and graphical inspections, LP3 method shows a better correlation results for Ribb stream flows while EVI method for Gumara stream flows.

Table 6. 2. Flood flow estimates using LP3 and EVI distribution methods

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Figure 6. 4. Return periods and probability exceedence of annual peak flows

In statistics, a confidence limit is a particular kind of interval estimation of a population parameter and is used to specify the reliability of estimation that used in the analysis (Chow, Maidment and Mays, 1988, CI, 2009). It is an observed interval computed from observations that frequently include parameters of interest. In general, the frequently observed interval which contains the parameter is determined by the confidence level. The 95% confidence limit calculated from the observations for Gumara and Ribb flow results are presented in Figure 6.5 below.

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Figure 6. 5. Confidence limit for Gumara (a) and Ribb (b) Rivers flows

In the frequency analysis, a 50 year flow observation data were used to relate the magnitude of extreme events to their frequency of occurrence in different return periods. This means, the number of observation is as long as half of the return periods that will be computed, and then the computed flood frequency results are more reasonable for application. For instance, to estimate a 100-year flood we should have at least a 50 year observed time series data. Otherwise, prediction beyond 100 year (say 200, 500 year) return period might not be good enough to get reliable results.

In general, from the frequency analysis, flood events are increased since 1995/6 in Fogera area (see Figure 6.1 above). However, the observations of flows are decreased in both watersheds since then. The reason is highly likely due to improper land use such as deforestation and poor agricultural practices, change of the river morphology and population growth in the area. These problems would be managed by taking into account many controlling measures such as improved land use policies.

7 Hydrological Modeling

7.1 Data preparation using Arc GIS

Arc GIS is an interacting model used to produce and organize input datasets to the hydrological models using DEM as an input file. The 30m by 30m DEM resolution file (tiles) was downloaded from GDEM-ASTER website, http://www.gdem.aster.ersdac.or.jp/. Since higher resolution DEMs is usually stored as tiles, they were merged together before use. As a result, a single DEM was drawn and suited for geo-processing and analysis tasks.

A step by step processing was carried out in arc GIS and the output results were stored for hydrological and hydrodynamic modeling. Terrain preprocessing, Basin processing and HMS model support are the main functionalities of HEC-GeoHMS. The purpose of HEC-GeoHMS is to facilitate the development of hydrologic models through GIS. It significantly reduces the effort and time required to develop the physical characteristics of the sub basins that are necessary for the HEC-HMS model.

In the terrain preprocessing, the DEM was used as input and computes the flow direction, flow accumulation, stream definition, stream delineation, watershed delineation, and watershed aggregation to generate the drainage networks. Each of this processes are explained in briefly in the next three consecutive paragraphs.

The flow direction defines the direction of flows to the steepest terrain cell. The flow accumulation determines the number of upstream cells from any given cell. The upstream drainage area at a given cell can be computed from the flow accumulation value by multiplying with the cell area. Stream definition classifies all cells with flow accumulation greater than the user-defined threshold point belonging to the stream networks.

Stream segmentation divides the stream into different segments that connects two successive junctions, a junction and an outlet or a junction and the watershed divide line. The catchment grid delineation delineates a sub-basin for each segment of the stream. Watershed polygon processing converts sub-basins into vector representation. And the stream segment processing converts stream in the grid representation of sub-basin into vector representation. In other words, stream segment processing operation vectorized the gridded stream into line segments.

The last step was extracting relevant spatial data from the main view and setup a hydrologic model. In this task all the necessary information were extracted from the spatial database and creates a HEC-HMS project database. After basin processing and setting some basin characteristics (slope, longest flow path and basin centroid) the result (with auto named sub-basins and rivers) are shown in Figure 7.1 and 7.2 below. For instance, the longest flow path is used to estimate the time of concentration in the sub basin.

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Figure 7. 1. Schematic input data processing using Arc GIS

The topographic and stream characteristics for Gumara and Ribb watersheds were computed from arc GIS using HMS tools. The Basin tools create specific stream basin and reach auto names. They also convert the physical characteristics of each sub basin and reach from the map to HMS units before extracting and creating a database file.

After the HMS schematization setup within arc GIS environment, the GeoHMS datasets were prepared and exported for the hydrologic model. The background map and basin model files are the two basic inputs to the lumped models and/ or mod file to physically distributed based model were exported. The spatial characteristics of both watersheds were retrieved from arc GIS attribute tables. The extracted results, spatial input datasets and other feature characteristics are presented in Table 7.1 and Figure 7.2 for each sub-basin and each reach.

Table 7. 1. Some characteristic feature outputs of the watershed extracted from GIS

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Figure 7. 2. Gumara and Ribb GeoHMS extracted results from Arc GIS

7.2 Hydrological modeling with HEC-HMS

In most cases, methods are chosen based on the availability of information for parameter estimation and model calibration, and of course based on experiences and preferences. In this study, HEC-HMS model was chosen with its basic concepts used and its application; a single event based method was adopted due to the limited input datasets in addition the peak runoffs are restricted to short periods after a storm in the area.

In hydrological modeling, the required input datasets, such as river networks and shape of the watersheds are prepared using arc GIS as discussed above. Once all the required model input data were prepared, the next important step is selecting appropriate methods of modeling.

7.2.1 Model input requirements

After the model setup was done, the required datasets such as observed rainfall and hydrological data, DEM file were collected to simulate flows in Gumara and Ribb watersheds and their perspective sub-basins. HEC-HMS model was used to estimate the runoff at a certain point for the un-gauged part of the catchment, say at inlet points of each proposed reservoir and flows at the outlet point of each watershed.

7.2.1.1 Input datasets

In hydrological model, the precipitation, evaporation and river discharge data are the main input datasets that were used. All these datasets used are observation data.

The average weighted precipitation was estimated from point gauge data using Thiessen polygon method; using (eq. 7.6) and results are shown in Table 7.3.

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Where, pa is MAP, Wi is weighting factor, ai is area of the polygon, Ai is the area covered by each sub basin and Pi is the gagging stations corresponding to the area, DWi is depth weight and TWi is time weight.

Table 7. 2. MAP distribution of Gumara and Ribb watersheds, August 2006

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The evaporation data was computed from a simple pan coefficient relation method to estimate the monthly evaporation in the region. The pan coefficient, Kp, was taken as 0.7 to the simulation, FAO Irrigation and Drainage Paper No. 24 table (ALLEN, Dirk and SMITH, 1998). This coefficient is selected based on some influencing factors of the catchment characteristics such as wind speed which ranges between 2m/s and 5m/s with 40% to 70% of moderate relative humidity.

7.2.1.2 Input parameters

The parameters for each sub-basin are determined and tabulated below: (1) Loss parameters, (2) Clark transform parameters and (3) Routing parameters are the most important model input parameters used in the simulations.

Table 7. 3. Model input parameters (before calibration)

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7.2.1.3 Optimal parameters

The set of optimized parameters and the summary of objective functions for each watershed with their respective sub-basins are tabulated in Table 7.5 and 7.6 below. According to model results, the simulated result is higher than the observed peak flow by 15% to Gumara and 29% to Ribb daily flows.

Table 7. 4. Objective function for Gumara watershed

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Table 7. 5. Objective function for Ribb watershed

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Table 7. 6. Optimized parameters for Gumara watershed sub basins

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Table 7. 7. Optimized parameters for Ribb watershed sub basins

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7.2.2 Model efficiency assessment

The optimized model results were evaluated using HEC-HMS model itself and statistical error assessment techniques. In HEC-HMS, the numerical as well as graphical evaluations are made using objective function, flow and hydrograph comparisons, and residual graphs.

7.2.2.1 Objective function graphs

The objective function graph, Annex 2, shows the objective function value of the search algorithm at each iteration. It gives some indication of how fast the search algorithm is able to converge to the optimal parameter values or not at all. This graph shows a convergence to the optimal parameter values.

7.2.2.2 Flow and hydrograph comparisons

The flow comparison graph shows the computed flow against the observed flow. If the computed flow is exactly equal to the observed flow, then the data will plot closely on a 45-degree line. However, in this actual case the match is scattered around the 45-degree line as shown in Annex 3. Data points before the time of peak flow are shown in red circles and in blue triangles after the time of peak flow.

Similarly, comparison hydrographs show the comparison between the computed and observed flows at the objective functions evaluation position. This allows to visually comparing how the computed and observed hydrographs matched well as shown in Figure 7.3 below. The degree to which the hydrographs match helps to indicate the quality of the parameter estimation.

7.2.2.3 Flow residuals graphs

The flow residuals graph shows the difference between computed and observed flow for each time step. It is determined as the computed flow minus the observed flow and may be positive or negative as shown in Annex 4. This means, positive value shows overestimated and negative value shows underestimated simulation values from observations. The magnitude of the residuals helps to indicate the quality of the parameter estimation deviations. The residuals also help to indicate biases in the agreement between the computed and observed flows.

Figure 7.4 shows flows from sub basin w240 (a) and junction J41 (b) that have flow contributions to each proposed reservoir, S. Gumara and Ribb. Therefore, these inflow results from each mentioned watershed were selected and used for basic interests of reservoir simulations.

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Figure 7. 3. Comparison hydrographs of Gumara (a) and Ribb (b) watersheds

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(a) Inflows from W240 sub basin

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(b) Inflows from Junction, J41

Figure 7. 4. Inflow hydrographs into S. Gumara (a) and Ribb (b) reservoirs

7.2.3 Statistical assessment measures

In statistics, there are various error metrics for proper model assessment. Some of the most widely used statistical measures were applied in this work such as the Root Mean Squared Error (RMSE), normalized form of RMSE, Nash-Sutcliffe efficiency (E) (Corzo and Solomatine, 2007) and coefficient of determination (R 2) as given in equations (7.8), (7.9), (7.10) and (7.11) respectively.

7.2.3.1 Root mean square error

The Root Mean Square Error (RMSE), also known as deviation (RMSD), is a statistical measure used to quantify deviations of model results from observations. It is given as:

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7.2.3.2 Normalized RMSE

Normalized RMSE (NRMSE or NRMSD) method is the most popular method to measure the mean deviation between the estimated and measured values. The value is often expressed as a percentage, where lower values indicate less residual variance.

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7.2.3.3 Nash-Sutcliffe efficiency

Nash-Sutcliffe Efficiency (E) method is used to assess the predictive power of hydrological models. It was proposed by Nash and Sutcliffe (1970) and is defined as:

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Nash-Sutcliffe efficiencies can range from negative ∞ to 1 (Nash and Sutcliffe, 1970). According to (Nash and Sutcliffe, 1970), if efficiency is equal to 1, it corresponds to a perfect match of modeled discharge to the observed data. If E is equal to 0, it indicates that the model predictions are as accurate as the mean of the observed data, whereas if E is less than 0, then the observed mean is a better predictor than the model.

7.2.3.4 Coefficient of determination

The coefficient of determination (R2) method is a measure of goodness-of-fit for the model and is the relative predictive power of a model. It is a descriptive measure between 0 and 1. The closer it is to 1, the better the model to provide perfect predictions. R2 is the squared value of correlation coefficient as defined by Bravais-Pearson (Zuse, 1998). It is calculated as:

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Where, is simulated value at ith time interval, is observed value, and the mean value, n is the number of observations.

7.2.4 Sensitive parameters

During model simulation and calibration some parameters are observed as more sensitive but some are not. The parameters such as the constant loss rate and the storage coefficient, initial loss, and lag time are identified sensitive model parameters. Constant loss rate is more sensitive parameter; others are far less sensitive parameters, say storage coefficient, K. For instance, if the constant rate of sub-basin W240 in Gumara watershed increased by 0.1mm/hr to 0.1003mm/hr from 0.003mm/hr, then the flow was decreased from 129.2m3/s to 118.6m3/s. Or when loss rate raises by 20%, the flow becomes 129.3m3/s and 129.1m3/s when it decreased by 20%. On the other hand, if the storage coefficient either increased or decreased by 20%, the flow remains the same as 129.2m3/s.

7.3 Results and discussion on hydrological modeling of existing conditions

The main objective of the hydrological analysis is to produce hydrographs at each hydrological station and/ or sub-basin of Gumara and Ribb watersheds in HEC-HMS model. In this task, flow hydrographs were generated using daily rainfall time series at the outlet of each watershed. The simulation results were compared with the storm events of 2006 observations and return periods in order to check the performance of the model. This means, the model results were verified to determine whether they agreed reasonably well with related analyses or not with the expected results.

The calibration results show that the model gave reasonable results by taking into account the number of data and methods used within the event based simulation period. Accordingly, the NRMSE shows lower residual variance of 25% for Gumara and higher variance of 45% to Ribb watershed (see Table 7.9 below). This means, the mean deviation between the estimated and measured values is larger in Ribb flows than Gumara flows (better result). The efficiency, E is equal to 0.08, is more loser to 0 than to 1 then model prediction is as accurate as the mean of measured data. On the other hand, the E value for Ribb watershed is less than 0 which is equal to -1.54. This implies that the observed mean predicts better than the model. The RMSE for Gumara watershed is about 53.35 which show that it has a better measure of precision of model performance unlike to Ribb watershed. The calibration and correlation results based on 21 days flows of 2006 are presented in Figure 7.5 and 7.6 respectively.

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Figure 7. 5. Calibration results for Gumara (a) and Ribb (b) Rivers flows

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Figure 7. 6. Correlation relations of model and observations for Gumara and Ribb (b)

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Table 7. 8. Efficiency of calibration results of Gumara and Ribb flows

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The validation results were generated based on 21 days of flood flows, 27th of July to 16th of August 2003. From the validation results, the NRMSE shows a lower residual variance of 30% for Gumara watershed which is better than the residual variance obtained from Ribb watershed which is about 67% (see Table 7.10 below). The efficiency, E of Gumara is equal to 0.47, which is closer to 0 than to 1, indicates that the model prediction is as accurate as the mean of the observed data. However, the E value is less than 0, -2.45 for Ribb watershed, implies the observed mean is much better predictor than the model does. The RMSE for Gumara watershed is about 45.40 which show that it has a better measure of precision of model performance unlike to Ribb cases having the value of 22.31.

It is noticed that, in both watersheds, the simulated flows are higher than the observations with few exceptions. Even though the model for Ribb watershed produced somehow acceptable validation results for the relatively high flow period. It did not respond well to peak rainfall which occurred between 9th and 13th of August (see Figure 7.7 (b)). This might be due to higher rainfall distributions occurred during this period. The validation and correlation results based on 21 days flows of 2003 are presented below in Figure 7.7 and 7.8 respectively.

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Figure 7. 7. Validation results for Gumara (a) and Ribb (b) river flows

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Figure 7. 8. Correlation relations of model and observations for Gumara and Ribb (b)

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Table 7. 9. Efficiency of validation results of Gumara and Ribb flows of 2003

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In general, accordingly to model efficiency results, Gumara watershed shows better results compared of Ribb watershed. For instance, the coefficient of determination of correlation increases from 59% to 71%. On the other hand, this value decreased from 51% to 43% for the Ribb watershed.

In addition, the time series hydrographs were attributed to the hydrodynamic flood model to study the flood extent problems downstream in Fogera floodplain. In this regard, the hydrologic model simulated by considering the proposed reservoirs with the advantages of reservoir operation rule curves in flood controlling system. In other words, after developing the reservoir operation rule curves, a hydrological model was simulated again by taking into account the developed rule curves. These rule curves govern optimal reservoir releases to get optimal flows at the outlets of each watershed. Hence, these optimal flows were used as input data to the SOBEK 1D/2D flood model to simulate the flood problems.

8 Reservoir Simulations with HEC-HMS

8.1 Reservoir operation rule curves

In order to develop rule curves, four seasons were considered within each year starting from January and ending at December, one season having three months. Season 1: Jan-Feb-Mar, Season 2: Apr-May-Jun, Season 3: Jul-Aug-Sep, and Season 4: Oct-Nov-Dec. This classification is based on the climatic conditions inhabited in the area (tropical climate).

Discrete Dynamic Programming (DDP) method was used to develop the rule curves and to obtain initial estimates of reservoir operating rules (Figure 7.11) to meet the objectives.

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Figure 8. 1. Rule curves for S. Gumara (a) and Ribb (b) reservoir operations

Dynamic Programming is an approach used to solve sequential or multistage decision problems and it is efficient in making a sequence of interrelated decisions (Nandalal and Bogárdi, 2007). Therefore dynamic programming is suitable to study reservoir operations.

To start with S. Gumara proposed reservoir has an active storage capacity of 23.99 Mm3 (24 Mm3 was used in the computation). This active storage volume in the reservoir assumed to be varied between 0 and 24. To use DDP, this range of possible storage volumes must be divided into a set of equal range of discrete values of 6 units. Hence, the initial storage volume, St, can assume values of 0, 6, 12, 18 and 24 for all periods, t. These values are then called as discrete state variable values.

In this formulation, the state variable is the reservoir storage St, at the beginning of a stage, while the decision variable is the reservoir release Rt, during the season t. Therefore, at the beginning of any season t, the storage volume can be in any of the five discrete states (0, 6, 12, 18 and 24) that used to make a release decision. This release depends on the state of initial storage volume and the mean inflow, as well as the losses. Storage volume continuity requires that in each period t the final active storage or equivalently the initial storage, St+1, in the following period t+1 for each period t is given as:

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Where, St+1 and St are the final and initial storages for each period t respectively, Qt is the mean inflow, Rt is the release, and Lt(St, St+1) is losses as a function of the storage volume. Each variable is expressed as volume units for the period t to make the computation easy.

Note: the approaches and some terminologies are adopted from "Water Resources System Planning and Management" reference book by (Loucks, 2005).

In the four seasons the peak inflow, Qt, was taken from HEC-HMS model results for W240 sub-basin which has a full flow contribution to S. Gumara reservoir with the area of coverage of 381.63 km2 and the area flooded at full reservoir level is 3.51km2 having an estimated mean annual inflow of 244.22 Mm3 (WWDSE, March, 2010). However, from the model 234Mm3 (129m3/s) of peak flow was obtained and this peak inflow was taken to develop the rule curve. Therefore, 12, 35, 234 and 59 values were considered as inflows for season 1, 2, 3 and 4 respectively. The assumptions of these portions of inflows were made based on the historical seasonal contributions of flows of the watershed. Then the respective seasonal flow is 5%, 15%, 100% and 25% of this peak flow. In addition, that portion of the peak flow is determined based on the storage capacity of the reservoirs. Likewise, 160 Mm3 of peak inflow was used for Ribb reservoir with a watershed area of 685 km2 at the proposed dam site. Hence, 8, 24, 160 and 40 values were taken respectively for each season.

8.1.1 Reservoir losses

The main losses in the reservoirs are evaporation and seepage losses. These losses were estimated based on the evaporation data available from the nearby station at Bahir Dar. The monthly seepage loss estimated as 25% of the monthly evaporation (WWDSE, October, 2010) for the initial and final storage volumes for each period t within a year. Computed results using equation (8.1) are presented in Annex 5 for both reservoirs.

8.1.2 Reservoir releases

The reservoir release which shows each of the discrete storage volume states for each of the feasible releases are presented in Annex 6 for the two proposed reservoirs given the initial storage volume, St, at the beginning of a season t, and an expected inflow of Qt during season t. A release decision from the proposed reservoirs is made based on the given state variable (St, Qt). This release depends on the initial storage volume, the mean inflow, and the losses and the objectives to be satisfied to accomplish.

The reservoir releases of the four seasons are also represented by network links showing the release links given the initial storage St and an expected inflow of Qt. A release decision is made based on the given state variable (at node), refer Annex 7 .

In order to achieve the downstream water users needs, such as for irrigation and flood protection, reservoir operators need to meet their flow targets. For instance, the flow targets for downstream irrigation water users and reservoir storage capacity for flood protection for individuals living on the downstream floodplain. These various targets that are to be met for the duration of each season t were assumed as given in Tables 8.1 and 8.2.

Table 8. 1. Different targets for the duration of each season t for S. Gumara reservoir

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Table 8. 2. Different targets for the duration of each season t for Ribb reservoir

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8.1.2.1 Weighted sum of squared deviations

In fact, it is difficult to meet all the storage volume and release targets in all four seasons, given inflows of 12, 35, 234 and 59 to S. Gumara reservoir for instance. Thus, the objective is then to do the best to minimize a weighted sum of squared deviations from each of these targets as much possible. According to (Loucks, 2005), the target deviations are squared to reflect the fact that the marginal "losses" associated with deviations increase with increasing deviations. In this theory, small deviations are not as serious as larger deviations, and it is better to have several small deviations rather than a single larger one.

During the irrigation season (periods 1, 2 and 4) or dry seasons, deviations below or above the irrigation storage volume targets are not damaging. During the flood season (period 3), any storage volume in excess of the flood control storage targets of 12Mm3 reduces the flood storage capacity. The deviations below that flood control target are not causing any problem.

The main objective is therefore to minimize the sum of total weighted squared deviations, TSD t , over all seasons, t and is given by:

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Where, ESt is the storage volume in excess of the flood storage target volume, TSft, DRt is the difference between the actual release, Rt, and the target release TRt, when the release is less than the target. The excess storage, ESt, at the beginning of each season t and the deficit release, DRt, during period t can be defined by the constraints (8.4) and (8.5) respectively.

The first component of equation (8.3), right hand side, defines the weighted squared deviations from irrigation storage target, TSIt, at the beginning and end of season t (periods 1, 2 and 4). This means, the weights wst associated with the irrigation component of the objective are 1 for periods 1, 2 and 4 but it is 0 for period 3. The second component is related to flood control. It defines the weighted squared deviations associated with storage volumes in excess of the flood control target volume, TSft, at the beginning and end of the flood season where period t=3. Therefore, the weights wfst are 1 for period 3 and 0 for periods 1, 2 and 4. The last component defines the weighted squared deficit deviations from a release target, TRt, and its weights wrt equal to 1 for all releases in all seasons.

The sum of weighted squared deviations, TSDt, was computed from the particular initial and final storage volumes, the target storage volumes and releases using equation (8.3). For this computation, the releases, Annex 6 and the targets, Tables 8.1 and 8.2, were used, for each feasible combination of initial storage, St, and final storage, St+1, volumes for each of the four seasons. The computed weighted squared deviations, TSDt, for each link are presented in the Annex 8 for S. Gumara and Ribb reservoirs respectively.

The path that minimizes the sum of the squared deviations associated with each of the network path links (Annex 7) are explored using the backward moving solution procedure of DDP. At each node (St, Qt), the release or final storage volume was computed in that period that minimizes the remaining sum of weighted squared deviations for all remaining seasons. This minimum sum of weighted squared deviations value for all n remaining seasons t is expressed in equation (8.6). This value is dependent on the state (St, Qt) and the number of remaining seasons, n but not a function of the decision Rt or St+1. This minimum sum of weighted squared deviations for all n remaining seasons t is given as:

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8.1.3 Steady state rule curves

A steady state policy will occur if the inflows, Q t, and objectives, TSD t ( St, Rt, St+ 1 ), remain the same from year to year. To find the steady state operating policy for S. Gumara and Ribb reservoirs, the operation assumed to end in some distant year at the end of season 4 of the network, refer Annex 7. At the end of this season the number of remaining seasons, n, equals 0. The values of the remaining minimum sums of weighted squared deviations, Ft 0 ( S 1 , Q 1 ) associated with each state ( S 1 , Q 1 ), equal 0.

Now the process of finding the best releases, Rt. in each successive season can begin moving backward to the beginning of stage t= 4, then to t = 3, t = 2, and t = 1, and then again to t= 4 of the preceding year, and so on. For each move to the left n increases by 1 to the remaining seasons. At each season, the release Rt (or equivalently the final storage volume St+ 1) were computed that minimizes the sums of weighted squared deviations using:

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Hence, the decision variable can be either the release Rt, or the final storage volume, St+ 1. If the decision variable is the release, then the constraints on that release Rt are:

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If the decision variable is the final storage volume, the constraints on that final storage volume St+ 1 are:

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In both cases, the storage volume s in each season are limited to discrete values 0, 6, 12, 18 and 24 for S. Gumara reservoir and 0, 68, 136, 204 and 272 for Ribb reservoir. The values obtained from solving the recursive equations for 17 successive seasons (4.25 years) are presented in Annex 9 for both proposed reservoirs. In these tables the recursion for season t, begins with t= 4 and the number of remaining seasons n= 1. The data in each table are obtained from Tables 8.1 and 8.2 above respectively for each reservoir. The last two columns of each table in Annex 9 represent the best release and final storage volume decisions associated with the initial storage volume and inflow.

Both S. Gumara and Ribb reservoirs operation policies defining the release or final storage for each discrete initial storage volume in season t= 4 (refer Annex 9) for n=1, 5, 13 and 17; for season t= 1 for n=8, 12 and 16 are obtained the same values (here in this case n=4 is omitted because it is different than others). Similarly for season t= 3 for n=2, 6, 10 and 14 and finally for season t= 2 for n=3, 7, 11 and 15 are similar values. According to the result obtained, the policy differs over each state and season but not from year to year for any specified state and season. Hence, from this analysis a steady state policy is achieved successfully. However, this policy is dependent on the initial storage volume and on the season t, but not on the year. This policy is summarized in Tables 8.3 and 8.4 for S. Gumara and Ribb reservoirs respectively.

Table 8. 3. Operating policy to Sendega-Gumara reservoir

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Table 8. 4. Operating policy to Ribb reservoir

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Therefore, these rule curves provides a first approximation of a reservoir release rules for each proposed reservoir. Tables 8.3 and 8.4 and Figure 8.2 define a policy that can be implemented for any initial storage volume condition at the beginning of any season t. However, this can be simulated under different flow patterns to determine just how well it satisfies the overall objective of minimizing the weighted sum of squared deviations from the desired.

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Figure 8. 2. Developed operation curves for S. Gumara (a) and Ribb (b) reservoirs

In Figure 8.2, each season is divided into storage volume zones and the releases associated with each storage zone are specified. It also shows the storage volumes that would result if in each year the actual inflows equaled the inflows used to derive these rule curves. The basic assumption made to derive these rule curves were that the amount of inflows were assumed to be similar that occurred each year, to find the storage volumes and releases that would occur in each period, year after year.

Once a steady state condition has been reached, the storage volumes and releases will be the same each year since the inflows are the same. The annual total squared deviations will also be the same each year. In other words, the annual difference of the accumulated minimum sum of squared deviations, Ftn (St, Qt), equals a constant value called the annual value of the objective function. Accordingly, 1508 and 25792 were the computed values for S. Gumara and Ribb reservoirs respectively using equation (8.15).

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Therefore, this condition indicates a steady state policy has been achieved and is applied only for the assumed inflows in each season. This means, it does not define what to do if the initial storage volumes or inflows differ from those for which the policy is defined. Initial storage volumes and inflows can and will vary from those specified in the solution of any deterministic model or the actual inflows will always differ.

In conclusion, a policy defined in Table 8.3 and 8.4, and Figure 8.3 are much more useful than considering the annual minimum weighted sum of squared deviation constant values. Thus, these developed rule curves were used and referred in the hydrological model during reservoir simulation.

8.2 Reservoir model setup and simulation

8.2.1 Introduction

The hydrological model simulation was already carried out without considering the proposed reservoirs as discussed above. However, in this second scenario, HEC-HMS was simulated considering the two proposed reservoirs and the developed rule curves.

The paired data manager component is used to manage and provide model input data and parameters in reservoir routing computation in addition to the four main components of the HEC-HMS project model used during existing condition simulations.

For this simulation, elevation was selected and used as initial condition and the storage value was interpolated from the elevation-storage curve. Accordingly, 1924.0 m and 1923.0 m reservoir level were specified for S. Gumara and Ribb reservoirs respectively as initial conditions at the start of each simulation.

The elevation-storage and storage-discharge curves were used in the simulation. They were prepared based on the information obtained from each reservoir designs as shown in Table 8.3.

Table 8. 5. Elevation-storage paired data of S. Gumara and Ribb reservoirs

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In addition, the inflows to the proposed reservoirs were determined and used in the simulation. Accordingly, the flows generated from sub basin W240 which flows to S. Gumara reservoir and W241 and W390 accumulated at J41 flows to Ribb reservoir were taken, see Figure 8.3 below. Based on these inflow results as a reference, the hydrological model incorporates the two proposed reservoirs in order to simulate the actual reservoir storage and releases within the simulation period.

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Figure 8. 3. Inflows from w240, w241 and w390 sub basins to S.Gumara and Ribb reservoirs

8.3 Results and discussion on reservoir operation

Gumara reservoir has smaller storage capacity with higher flow contributions compared to Ribb reservoir. Therefore, according to the simulation results, 27th of July to 16th of August 2006, more flows were released from S. Gumara reservoir than from Ribb reservoir as shown in Table 8.5. Similarly these differences are exhibited at the outlets of each watershed.

Table 8. 6. Inflows and storage capacity of the proposed reservoirs

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8.3.1 Simulation and rule curve results

The simulation results shown in Figure 8.4 shows the maximum holding capacities, inflows and releases into and from each reservoir. This means, during peak floods, each reservoir can store the peak flows in their emergency spaces and released later on when the peak drops. These flows are monitored by reservoir operating rule curves. Figure 8.5 (a) and Figure 8.6 (a) show the maximum S. Gumara and Ribb reservoir levels respectively due to peak inflows simulated by the model referencing the corresponding rule curves. Figure 8.5 (b) and Figure 8.6 (b) shows the inflows and outflows simulated by the HEC-HMS model and outflows computed using the rule curves for each reservoir.

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Figure 8. 4. Elevation-storage-discharge based simulation results in HEC-HMS

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Figure 8. 5. S. Gumara reservoir level (a) and inflows/ outflows (b) using HEC-HMS and rule curves

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Figure 8. 6. Ribb reservoir level (a) and inflows/ outflows (b) using HEC-HMS and Rule curves

8.3.2 Flow differences and impact on flood modeling

Flows at the outlets of each watershed with and without the proposed reservoirs are shown in Figure 8.7 below. As shown in this figure, flows from Gumara watershed have no significant impacts in reducing the flood extents in the floodplain. This impact is clearly observed from the SOBEK simulation results. On the other hand, flows from Ribb watershed have a better contribution in reducing the flood extents. This is mainly related with the storage holding capacity of each reservoir during peak flood events. For instance, the peak flows to S. Gumara reservoir is higher compared to its small storage capacity as discussed above. Figure 8.7 also clearly shows these influences at the outlet points of each watershed. On the other hand, peak inflows to Ribb reservoir are very small but the storage capacity of the reservoir is very high. For that matter it has the capability of storing all incoming peak flows.

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Figure 8. 7. Flows at outlet of Gumara (a) and Ribb (b) watersheds

In conclusion, results determined from the hydrological model in two scenarios, without and with the proposed reservoirs, were used as an input to the hydrodynamic flood model. SOBEK 1D/2D flood model would be used then after to simulate the flood extents and inundation depths in Fogera plain for the two scenarios. However, observed flows were used to simulate the existing system than using the calibrated flows. Therefore, understanding of the flood extents in the floodplain helps to prepare and protect the flood vulnerable area from the expected flood causing damages.

9 Hydrodynamic Flood Modeling with SOBEK 1D/2D

9.1 Introduction

The background map, the river networks and the DEM file in arc info format were the main required input datasets for the SOBEK model environment. DEM file is the most important input data for the 2D flow simulation. All these input data were prepared using arc GIS.

The next steps are schematization of the stream flow networks, setting the initial conditions, boundary conditions, cross-sectional profiles, and setting the friction factors for the channel cross-sections and 2D grid cells. The resolution of the 2D grid cell is used to investigate the altitude of the 2D grid at several places where one is interested to know the altitude of a point.

9.1.1 Initial conditions

In this work, the initial condition was introduced using the water depths and discharges at the beginning of the simulation. The initial conditions were defined as global value that is used at various calculation nodes for the water depth and reach segments for the discharge. The data used for simulation were from 3rd to 14th of August 2006. Then these 12 days of time series data was used in the simulation to keep a hydraulic gradient stable in the system of hydrodynamic flow behavior.

9.1.2 Boundary conditions

The upstream boundary conditions used were the flow hydrographs at Gumara and Ribb gauging stations to channel reach. The time series flow hydrographs (see Figure 9.1, below) considered was from 3rd to 14th of August 2006 for both rivers. But after 14th of August the peak flows are started to drop due to the variable river flow patterns and the decline of rainfall distribution as well.

The downstream boundary conditions used were the time series level of Lake Tana which is served as boundary conditions for the two channels at the edge of model network end boundary node and multiple 2D-line boundary conditions for the overland flows. The lake level is taken from the gage four times per day and averaged smoothly due to wave impacts on the lake surface. The minimum lake level is 1783.50 m amsl and the maximum yearly lake level is 1787 m amsl.

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Figure 9. 1. Gumara and Ribb flows and Lake Tana levels as boundary conditions

9.1.3 Surface roughness

The roughness values required for the model have been determined from the land use/ land cover map (FAO, 1998) and based on the dominant soil type (ALLEN, Dirk and SMITH, 1998). The land uses of the study area are dominated by agriculture, agro-pastoral and pastoral activities. The soil type is more of clay nature especially in the channel beds.

Accordingly, a constant manning friction value of 0.03 was considered for the overland flow and 0.02 for the river channel, and of course the vertical obstacle friction is kept at 0. Therefore, these constant roughness values were used in the model setup.

9.1.4 Cross section profile

Both rivers have their own cross-sectional profiles at their respective channels. A total of seventeen cross sections were used in model simulations, eight for Gumara and nine for Ribb river channels. The two cross sectional profiles at each river station (upstream point) are shown in figure 9.2.

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Figure 9. 2. Cross section profiles of Gumara (a) and Ribb (b) stations

9.2 River network

The 1D channel was prepared for the channel flow network and the 2D on the overland parts. However, the watershed maps, river networks, and the hydrological points were added before schematization. This was done first owing to have a better visualization during schematizing the 1D flow network modules as shown in Figure 9.3 below. This figure also shows that Ribb River channel changed its main channel since about 18 years ago, according to the local people. Hence, flows are only observed in this old channel during peak flows.

The network contains river channels in the 1D/2D coupled SOBEK flood model, four 1D boundary nodes, two upstream and two downstream, and seventeen channel cross section profiles and multiple 2D-line boundary conditions were used as shown in Figure 9.3.

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Figure 9. 3. Schematized 1D flow modules of Gumara and Ribb rivers

9.3 Validation satellite map

The satellite image from MODIS Rapid Response Flood Inundation map at the Dartmouth Flood Observatory (DFO) flood inundation map is available for validating the simulation results. This satellite image was taken on 14th of August 2006 flood inundation event in Fogera floodplain at this same day http://www.dartmouth.edu/~floods/2006174Nile.html. The satellite image and the model results are presented in Figure 9.4. The model result shows more or less approaching flood extents result to the satellite image (light red). This is mainly reasoned out due to the uncertainty of appropriate DEM files used in the model.

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Figure 9. 4. Satellite image (a) and model result (b) showing the flood extents

9.4 Results and discussion on SOBEK 1D/2D

Different simulation results were obtained for the existing condition and considering the proposed reservoirs. The simulation results showing the comparison of flood extents, inundation depths and flow velocities for the 1D and 2D flows at different selected reaches are presented below for the 12 days simulation from 3rd to 14th of August 2006.

However, some input data constraints and uncertainties were the big challenging factors to get better model results. Some of the constraints were related to the difficulty of selecting the appropriate 2D grid file. It is unlikely to get good fitting DEM file to the study area since the same DEM resolution obtained from GDEM, ASTER sources has different grid cell values. Extracting channel cross section profiles from the TIN file and the embedded surveyed profiles within is also difficult. The other difficulty was that there are no gauging stations at the inlet of each proposed reservoir for the purpose of this study.

9.4.1 Flows in 1D channel

Flows in 1D channel were dropped in considerable amounts from upstream to downstream reaches within the given boundary conditions. This means, when the river channel gets full by the continuously incoming upstream flows then it starts to overtop and flows to the 2D land surface. Accordingly, the peak flow of Gumara of 277.9m3/s was reduced up to the minimum value of 87m3/s at the downstream reaches. Similarly the peak flow of Ribb, 94.2m3/s, reduced to the minimum of 5m3/s in some reaches as is shown in Figure 9.5 below.

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Figure 9. 5. 1D channel flows of Gumara (a) and Ribb (b) Rivers

9.4.2 Flood extent, depth and velocity

Model results showing the flood extents, inundation depths and overland velocities are presented in the following consecutive figures and in the annex. Figure 9.6 shows the flood extents and the inundation depths for the existing system as well as when considering the proposed reservoirs.

According to the simulation results, the flood extent coverage for the existing condition is about 156 km2. This coverage is reduced to 115 km2 by approximately 26% when considering the reservoirs as shown in Table 9.1. The overland flood extent and velocity results for the two scenarios are also presented in Annex 10. Figure 9.9 shows flood extent and depths for 100 year return period in comparison with the existing condition. According to the result shown in this figure the two cases show more or less similar flood extents. Similarly information showing the flood extent and velocities is presented in Annex 11 for the 100 year return period.

Table 9. 1. Flood extents in Fogera floodplain for the two scenarios

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The 2D history data which showing the flood inundation depths at about twenty various locations for the two scenarios, for the existing system and with reservoirs, are presented in Figure 9.7. The history data showing the flood extent and depths for the 100 year return period is presented in Annex 12.

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(a) Existing conditions

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(b) With reservoirs

Figure 9. 6. Flood extents and depths in Fogera floodplain of August 2006

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(a) Existing conditions

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(b) With reservoirs

Figure 9. 7. History data showing water depths in Fogera floodplain

The history data that shows the maximum overland flood depths and flow velocities at different selected locations for simulation periods for both scenarios are tabulated in Table 9.2 below. This shows that within 12 days of simulation periods, the history data at each identified locations captured the maximum inundation depths and flow velocities. These values are also presented graphically in Figure 9.8 below.

Table 9. 2. History data showing maximum water depths in Fogera floodplain

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Figure 9. 8. History data showing water depths in Fogera floodplain

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(a) Existing conditions

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(b) 100 year storm

Figure 9. 9. Flood extent and depths in Fogera floodplain

In general, according to the model results, the flood extent reduced by approximately 26% owing to the presence of the two proposed reservoirs compared to the existing condition simulation result. However, the reduction is not significant since the incoming flows from the upstream watersheds are still very high. The comparison between the two model results are available in the Internet^[1], at https://docs.google.com/, and they constitute as well input as demonstrator for the lenvis, a demonstrator on how data can be made available to the public at large and to professionals. Lastly, based on the analysis of model results, an alternative flood mitigation measures are suggested in the area to reduce flood risks.

9.4.3 Flood extent prediction

Beside this research work, there are two other research works carried out in parallel; one is in titled "Precipitation Forecasts for Hydrologic Rainfall Runoff Prediction" (by M. Gizaw), to simulate and predict rainfall in Fogera area using MM5 and GFS techniques. The stream flows simulated in HEC-HMS, from the predicted rainfall made by MM5, are used here as an input to SOBEK 1D/2D flood model to simulate and predicate the flood extents in advance before the actual flood occurs. The model results for the next 3 days, starting on 12th of August 2006, are shown in Figure 9.10 in comparison with the 3 days observation simulation result. Therefore, prediction of flood extents in the floodplain gives a good indication and significant information ahead. This helps considerably to prepare and to take action before the actual flood occurred so as to reduce the consequences due to flooding.

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(a) 3 days observation

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(b) 3 days prediction

Figure 9. 10. Flood extent and depths in the floodplain for the existing condition

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(a) 3 days observation

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(b) 3 days prediction

Figure 9. 11. History data showing water depths (3 days) in Fogera floodplain

9.4.4 Flood mitigation measures

During the rainy season, there are three main sources of floods in the Fogera plain: runoff from the upper watersheds, runoff from direct rainfall and the wave propagations or fluctuations of Lake Tana level along the shore line. According to the model results, the two proposed reservoirs, S. Gumara and Ribb reservoirs are not sufficient to protect and reduce flood risks in the floodplain. Therefore, some alternative and feasible engineering and non-engineering flood mitigation measures should be required.

Moreover, a flood risk management for all causes of flooding, construction of physical flood defense infrastructure, implementation of forecasting and warning systems, land use planning and management within the catchment, discouragement of inappropriate development within the floodplain, and public communication and educating the local people and actions to take in a flood emergency are some of the vital measures to take place (www.floodsite.net).

Floods are always issued as threat, but it also has many benefits to the local people as a means of incomes. Since the soil is fertile, the local people accustomed to cultivate a short season crop and vegetable products after the flood retreats.

9.4.5 Engineering measures

River engineering such as channel improvements such as deepen, widen, and straighten, constructions of dykes or embankments and diversion channels are some of the measures used to protect floods in the study area.

There are two irrigation projects, Gumara irrigation project and Ribb irrigation project to each watershed that they proposed some flood protection measures. Accordingly to Gumara irrigation project (WWDSE, March, 2010), it proposes about 88.17km length of dykes provided for making the command area (14800 ha) safe from flooding either from Gumara river and/ or Lake Tana.

The Ribb irrigation project (WWDSE, October, 2010) suggests another alternatives using the main natural drainage channels. They designed layout of the proposed drainage and flood-protection systems to drain excess runoff and mitigate inundation and logging water from the project area. They also suggested additional drain systems above and parallel to the main canals, as diversion and interception drains to reduce crossings on the main canals protection.

9.4.6 Non-engineering measures

Implementation of flood forecasting and early warning systems, improved land use planning and management policy, educating the local people etc are some important measures used to mitigate flooding problems. Flood risk map is an important map used to get more detailed explanation to understand flood phenomenon in the floodplain. It gives important information that helps and shows possible measures and evacuation routes during flooding events. It is obvious and difficult to prevent flooding entirely, but it is possible to reduce the risks of flooding effects and reduce the damage it causes.

9.4.7 Flood risk management practices

An integrated management of flooding from the source, in the pathway and in the receptors is good to practice. Managing flooding from its source is difficult but it is possible and manageable at the receptor's side. The implementation of flood risk management practices such as pre-flood measures, flood event measures and post-flood measures practices gives an acceptable impact of flood events on the local society.

9.7.1 Pre-flood measures

This measure is a preventive measure using emergency planning, flood defense, preparedness, etc before the flood occurred. These measures are non-engineering measures to mitigate flood risks and its consequences.

9.7.2 Flood event measures

This is a real time risk management such as forecasting and warning, reservoir control, evacuation, etc activities should be taken. This measure combines both structural and non structural measures.

Reservoir control is one of the basic activities carried out before and during flooding events. The presence of the two proposed reservoirs reduces significant impacts of peak floods in the floodplain. This means, reservoirs allowed storing peak or extreme floods during emergency so as to reduce flood risks downstream. For instance, if the water level the reservoirs raise then the flood extent reduces, as a result flood risks reduce. In other words, the reservoir level and flood inundation depths/ extents have such relationships.

9.7.2.1 Evacuation routes

Identification and recommendation of some possible evacuation routes during flooding should be needed if all the measures failed to resolve the flood problems. Therefore, an emergency measures should be in hand before the consequences related to losses properties and damages. Flood risk map provides quick significant information for the receptors at risk and probable damages during flooding. It also shows some possible evacuation routes to closer villages and towns were identified based on the available transportation accesses as shown in Figure 9.12.

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Figure 9. 12. Flood extents and available evacuation route

9.7.3 Post-flood event measures

This measure is a measure taken for relief, clean up, and reconstructions of those damaged structures from flooding.

10 Conclusions and Recommendations

10.1 Conclusions

Flood risk is a significant issue in many countries all over the world including Ethiopia. In the past times, at different parts of the country flooding problems were experienced and it endangers many lives and causes enormous damage of properties.

In Ethiopian context, flood regulation and measurement is explicitly considered. In 1998, the Ministry of Water Resources of Ethiopia issued the water resource management policy that sets the guidelines for water resources planning, development and management (Cherre, 2006). Among many generalized policies one deals with drought and floods. In specific terms, one of the policy objective deals with floods " Combat and regulate floods through sustainable mitigation, prevention, rehabilitation and other practical measures ".

This research work was therefore focused to meet this specific objective to examine the repetitive flooding problems in Fogera floodplain, upper Blue Nile and analyze potential reservoir control measures. More specifically it was mainly aimed to achieve a flood control scheme under regulatory operations of reservoirs to control flood risks downstream. The floodplain is part of the lower plain reaches of Gumara and Ribb watersheds which is highly vulnerable to flood inundation problems during rainy seasons.

This thesis was structured in such a way to address the main flooding problems in Fogera floodplain. The first measure was the analysis of data and flood frequencies for different return periods to understand the impacts of peak floods and to relate the magnitude of recent extreme events to their frequency of occurrence. The second task was quantifying the runoffs generated from Gumara and Ribb watersheds and their perspective sub basins. This was done in two scenarios, with and without the proposed reservoirs, using hydrological model in HEC-HMS. Thirdly, reservoir operation rule curves were developed using DDP to regulate releases in order to reduce flood risks downstream. In other words, it is aimed to minimize downstream flood peaks by discharging less water from the reservoirs than coming into the reservoirs. Lastly, SOBEK 1D/2D flood model was used to simulate flood extent and inundation depths, to know and understand the impacts of floods and flood characteristics in the floodplain.

Though, some challenges were faced related to model input datasets, good results were obtained. Some of the problems that were faced are related to the cross sectional profiles, distribution of rainfall data within the watersheds and the uncertainty of DEM files used. For instance, selecting the appropriate DEM file for the flood model was one of the main challenges in the course of this research work. This means, different DEM files having the same coordinate system had different elevation values. As a result, the 2D flood model simulation results were validated in association with such uncertainties.

A control strategy with rule curves has been developed which manages to keep lower reservoir levels in the wet season to store temporarily part of the peak inflows. Model results showed that the flood extents and depths in the floodplain were reduced for regulated releases compared to the results obtained from the existing systems. The area covered by the simulated flood extent for the existing system is about 156 km2 where as this coverage reduced to 115 km2 when simulated using regulated releases from each reservoir. This reduction is approximately equal to 26%. The estimated 100 year storm simulation result shows closer flood extents with the existing system. Therefore, the overall contribution of the two proposed reservoirs in reducing the flood extents is not satisfactory. This is mainly due to the fact that the storage capacity and the location points of the reservoirs are not ideal. They are located at the upper most sub-basins so that their catchment area represents only small portion of the runoff generated. The analysis of flood extent also gives important information ahead for preparation and to take action before the actual flood occurs so as to reduce the consequences due to flooding.

The integration of different models increases our capability to understand, predict and manage flood events. To study and control flooding in Fogera area, a hydrological modeling with HEC-HMS, GIS, rule curve developing methods using DDP, and hydrodynamic flood modeling with SOBEK 1D/2D were used. Simulation results obtained from these combined models would then be ideally suited as an important part in decision making that can be efficiently applied for flood management aspects. In general, the recurrent flooding events in Fogera floodplain could be managed under regulatory operations of the proposed reservoirs upstream in addition to engineering and non-engineering flood mitigation measures.

10.2 Recommendations

From model efficiency analysis, the hydrological model gave reasonable results and showed a tendency of consistencies with observations, though further improvement is needed. The number of data and parameters used were too small in the event based model. However, if more datasets and parameters were incorporated into the model, this improves the model results. For this matter a continuous seasonal based model is highly recommended since it considers more input data to obtain better results. Moreover, the heterogeneous behavior of the hydrologic systems in relation to spatial distribution of rainfall, soil types and land use causes deviations in simulation results.

The two proposed reservoirs will be built for future irrigation purposes. However, it is highly recommended to use them for flood control purposes as well. According to the data analysis, flows from Gumara watershed are higher and its contribution to the flooding is also higher compared to the contribution by Ribb watershed. Unfortunately, the storage capacity of the planned S. Gumara reservoir is too small. As a result releases from the reservoir will still be very high and cause flooding. In contrast the storage capacity of Ribb reservoir is higher while the inflows are very small, thus the releases also will be reduced as much as possible, even to zero. Thus, it is reasonable to recheck the design works before launching the actual dam construction in order to try to increase the storage capacity of S. Gumara reservoir so as to store more water for irrigation in dry seasons and for flood control in the flood season.

The results of this study suggest that some flood protection and mitigation measures should be taken in the flood vulnerable area. The proposed reservoirs don't guarantee to protect the development area from flood damages unless additional protection measures are taken. Therefore, construction of dykes along the river banks, improving the channels and using flood forecasting and early warning systems and other relevant measures should be considered. This means, some protection measures, cares and awareness are needed during flooding seasons to protect the people from flood, causing harm to the people and damage to the irrigation area. In addition, improved land use should also be adopted in order to reduce deforestation, land degradation and channel deformation.

It is highly recommended that more detailed studies considering real time systems should be taken, such that during flood events, decision makers can take emergency actions at right time to reduce flood damage.

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Annexes

Annex 1. Rainfall and flow time series for Gumara (a) and Ribb (b) watersheds

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(a)

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(b)

Annex 2. Objective function graphs for Gumara (a) and Ribb (b) watersheds

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(a)

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(b)

Annex 3. Computed flow plotted against the observed flow Gumara (a) and Ribb (b) watersheds

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(a)

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(b)

Annex 4. Residuals graphs Gumara (a) and Ribb (b) watersheds

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(a)

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(b)

Annex 5. Losses (Evaporation and seepage) from S. Gumara (a) and Ribb (b) reservoirs

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(a)

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(b)

Annex 6. Discrete releases from S. Gumara (a) and Ribb (b) reservoirs

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(a)

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(b)

Annex 7. Network representation of release from S. Gumara (a) and (b) Ribb reservoirs

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(a)

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(b)

Annex 8. Weighted squared deviations (TDS) for S. Gumara (a) and Ribb (b) reservoirs

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(a)

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(b)

Annex 9. Minimum squared deviations from discrete storage states for S. Gumara (a) and Ribb (b) reservoir

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(a)

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(b)

Annex 10. Flood extents and overland flow velocities in the floodplain

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(a) Existing condition

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(b) With Reservoirs

Annex 11. Flood extents and velocities for 100 year return period

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Annex 12. Overland water depths at different locations for 100 year return period

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[...]

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