FLOOD RISK ASSESSMENT IN THE VICINITY OF KARTENA TOWN USING HEC-RAS 1D-2D MODELS

Transkriptas

1 ALEKSANDRAS STULGINSKIS UNIVERSITY FACULTY OF WATER AND LAND MANAGEMENT INSTITUTE OF WATER RESOURCES ENGINEERING Federico Rubiu FLOOD RISK ASSESSMENT IN THE VICINITY OF KARTENA TOWN USING HEC-RAS 1D-2D MODELS Master's degree thesis Field of studies: Technological sciences Area of studies: Civil engineering Branch of studies: Water resources engineering Study program: Hydraulic engineering

2 2 Akademija, 2018 Committee members: (Approved by the Rector's Order No 209-PA, April 25, 2018) Chairman: Dr. Kazys Sivickis, President of the Association of Lithuanian Engineers of Water and Land Management Members: Prof. Dr. Arvydas Povilaitis, Institute of Water Resources Engineering, ASU Assoc. Prof. Dr. Algirdas Radzevičius, Institute of Hydraulic Engineering, ASU Assoc. Prof. Dr. Rytis Skominas, Institute of Hydraulic Engineering, ASU Paulius Vaitelis, senior project manager at thetechnical Projects Division of Kauno Vandenys Adviser Assoc. Prof. Dr. A. Dumbrauskas, Aleksandras Stulginskis university Reviewer Prof. Dr. P. Punys, Aleksandras Stulginskis university Opponent Assoc. Prof. Dr. R. Šadzevičius, Aleksandras Stulginskis university Institute director Prof. Dr. A. Povilaitis, Aleksandras Stulginskis university

3 3 Summary Hydraulic models can be used to predict the consequences of flooding events. In this project, three hydraulic models were constructed using the software HEC-RAS and compared through a case study on Minija river. The models include (i) a 1-dimensional (1D) model, where river and floodplain flow is modeled in 1D, (ii) a combined 1D-2D model, where river flow is modeled in 1D and floodplain flow is modeled in 2D, and (iii) a pure 2D model, where river and floodplain flow is modeled in 2D. Important differences between data requirements, preprocessing, model set-up and results were highlighted and summarized, and a rough guide that may be used when deciding the appropriate type of model for a project, was presented. In addition, the sub-grid technique used in 2D HEC-RAS modelling was studied by investigating the influence of computational mesh structure and coupling between 1D and 2D areas. The results showed that all three models might successfully reproduce a historic flooding event. The 2D and 1D-2Ds model could also provide more detailed information regarding flood propagation and velocities on the floodplain. The results from the 2D mesh analysis show that model result is very sensitive to mesh alignment along barriers. In rural floodplains with clear barriers, computational cell alignment is more important than computational cell size. With regards to the 1D-2D model, the results showed that the parameters describing the coupling between the 1D and 2D domain have large impact on model results.

4 4 Santrauka Hidraulinis modeliavimas sėkmingai ir plačiai naudojamas prognozuojant potvynius ir jų daromą žalą. Šiame darbe naudojant HEC-RAS programinės įrangos paketą, sukurti trys hidrodinamikos modeliai ir tarpusavyje palyginti Minijos ruožo ties Kartena praktiniu pavyzdžiu: vienmatis (1D), dvimatis (2D) ir hibridinis - kai upės vaga ir didesnė salpa modeliuojama vienmačiu modeliu, o atskira svarbi teritorija modeliuojama dvimačiu modeliu. Modelius lyginant tarpusavyje siekiama nustatyti ir įvertinti kiekvieno varianto privalumus ir trūkumus, aptarti kada kuris modeliavimo variantas priimtinesnis žiūrint kompiuterinio laiko sąnaudų ir gaunamų rezultatų atžvilgiu. Pradinių duomenų rengimo skirtumai, reikalingų išeities duomenų surinkimas, jų apdorojimas ir modelio duomenų bazės suformavimas. Darbe išdėstyta patirtis visais trimis atvejais turės atitinkamą praktinę naudą atliekant modeliavimą tiek su šia tieks su panašia modeliavimo sistema. Modeliuojant ypač svarbus dėmesys skirtas 1D modelio kalibravimui. Tam panaudoti ankstesnių magistrinių darbų metu sukaupti lauko tyrimai tirtame upės ruože. Taikant 1D modelį tėkmė modeliuota esant nusistovėjusiai (tada atliktas ir kalibravimo procedūra) ir nenusistovėjusiai tėkmei. 2D atveju ir kombinuotu atveju modeliuota tik nenusistovėjusi tėkmė. Rezultatų liginimas atliktas pagal nenusistovėjusios tėkmės ręžimo rezultatus. Aptarta 2D modelio gardelių dydžio įtaka skaičiavimo laikui ir rezultatų detalumui. Gauti rezultatai parodė, kad visais trimis modeliais galima sėkmingai atkurti tiek istorinių potvynių vandens lygius ir tėkmės dinamiką tiek sumodeliuoti norimos tikimybės potvynio eigą. Kokį hidrodinamikos modelio variantą naudoti visuomet priklausys nuo projekto tikslų. Pavyzdžiui 2D ir 1D-2D modeliai gali suteikti daug informacijos apie planinį tėkmės greičių pasiskirstymą ties svarbiais objektai kaip antai ties tiltų atramomis, gyvenamais pastatais ir pan. Modeliavimas parodė, kad rezultatai itin jautrūs ne tik gardelės dydžiui kai modeliuojame su 2D modeliu, bet ir gardelių išlyginimas ties barjerais (kaip antai pylimais). Salpoje su aiškiais barjerais, modeliavimo tinkle gardelių išlyginimas išilgai barjero dažnai yra svarbesnis nei gardelės dydis.

5 5 CONTENTS 1. INTRODUCTION LITERATURE REVIEW Floods and their impacts How to tackle flood events Modelling overview and methodology adopted Benefits of hydraulic modelling for flood mapping PURPOSE OF THE STUDY AND TASKS Aim of the study Undertaken tasks RESEARCH SUBJECT AND METHODOLOGY Research subject Research methods Theoretical background D Steady flow D unsteady flow D Unsteady flow Modelling simplifications Diffusive wave approximation Solving techniques HEC-RAS D modelling in HEC-RAS Geometric data Bridges and hydraulic structures Boundary conditions Hydraulic calculations D HEC-RAS modelling... 32

6 6 5.3 Mesh assembly and cardinal features Sub-grid terrain representation Hydraulic structures Boundary conditions Combined 1D-2D HEC-RAS modelling Connecting 1D river with a 2D Flow area through a lateral structure Direct connection of 1D river reach and 2D flow area RESULTS D model setup Geometry data manipulation Calibration D Model set-up D Geometry set-up manipulation Combined 1D-2D model setup Geometry set-up manipulation Discussion D model D model Combined 1D-2D Graphical overview of model comparisons CONCLUSION AND RECCOMENDATIONS PUBLICATION BIBLIOGRAPHY... 55

7 1. INTRODUCTION Flooding events are some of the world s most significant natural hazards. The EM-DAT Disaster Database has documented 266 flood disasters in Europe (excluding Russia but including Turkey) from 2000 to These floods have caused 1080 fatalities, affected more than 2.8 million people and caused economic damages amounting to more than 48 billion euro. (European Environment Agency, 2012). Meanwhile, an increase in floods is expected in the future. The mean global sea water level is expected to rise by up to 0.98 meters by 2100, threatening coastal areas (Church et al., 2013). In urban areas, the damage from heavy rain is expected to increase as a result of urbanization and increases in the intensity and frequency of heavy rainfall (Anonymous). Flood risks could be greatly reduced by avoiding building and other development close to rivers. Floods are usually broken down in several types even if any classification it is somewhat arbitrary. Let s list and describe them separately: Fluvial flooding occurs when water levels in a channel, lake or reservoir rise so that water covers nearby areas, which normally are dry land. A fluvial flood may be caused by heavy or persistent rain, snowmelt or ice jam, sometimes also by debris jam, landslide or another blockage of the channel. Flooding can be a regular feature of the yearly hydrological cycle, but rivers have different patterns of flow and the severity of flooding varies. Forecasting fluvial floods is generally easier than for other flood types. Pluvial flooding is caused by intense localized rainfall. Pluvial floods often cause damages in urban environments in combination with overflowing sewers and high runoff in small catchments. Urban pluvial floods often arise due to a combination of land sealing and insufficient capacities of sewers and drainage systems. They are difficult to predict due to the difficulty in predicting local rainfall patterns, lack of data on the actual hydrological status, and the short lead-times. Coastal flooding occurs when sea level exceeds normal levels due to storm surges, exceptional tides or tsunamis. Forecasting is difficult, but risk analyses can be performed using models. Lastly, flash flooding is characterized by very rapid inundation. Some pluvial floods can be classified as flash floods, particularly if heavy rain in the upper part of the catchment creates flood wave surges downstream where it may not have rained at all. The forecasting of flash floods is often extremely difficult due to the same factors as mentioned under pluvial flooding. 7

8 8 Due to the topography and the patterns of rainfall the risk of flash floods is highest in Mediterranean and mountain areas, besides the first three flood types are characterized by their source and the two first may occur almost everywhere in Europe. In order to predict flooding events as reliably as possible two main modelling approaches are applied. Basically, river flow is estimated by hydrological modelling, while hydraulic modelling is required to simulate water depths and velocities with the purpose of assessing the actual impacts of a certain river flow either overland flow. Over the last decades, the performance of hydraulic models has improved tremendously as a result of more powerful computers, while techniques such as remote sensing and radar has improved the detail of the input data (e.g. rainfall, topography and land use), therefore nowadays choosing to model it s a standard in design and paramount for decision-making processes establishing how and what kind of interventions has to be made for every specific case study. Although it is a promising and innovative instrument, modelers still tackle problems with lack of reliable data. In addition, current models are still far from being capable to correctly represent the complexity of natural and urban environments. Relevant improvements have to be done in performance and also in the features placed at the disposal of the modeler, which sometimes has to spend a lot of time in setting up and running the model itself. Fluvial flooding can be modeled in several ways. Traditionally, the river and the surrounding floodplains are depicted by a set of cross sections, in which the flow is modeled only in one dimension (1D-models). Whilst such models seem to thoroughly perform straight rivers where the flow is constrained to flow in 1D direction even during elevated water levels, instead, rivers that have flat and/or complex floodplains require a 2-dimension (2D) flow representation to account for the many individual 2D flow paths that will arise when the river is flooded (e.g. Horritt and Bates (2002) and Tayefi et al. (2007)). This has led to the development of coupled 1D-2D models, where the river is represented by 1D flow between cross sections, and the floodplain is represented by a computational mesh where flow modeled is in 2D. Pure 2D models also exist, with both river and floodplain flow is modelled in 2D. However, such models require detailed representation of the river bathymetry, which significantly increases computation times. Furthermore, river systems often contain bridges, weirs and culverts, lateral structures etc. and methods for presenting such structures are only robust for 1D modelling purposes (Ball, Babister and Retallick 2012). While the coupled 1D (river)-2d (floodplain) is preferred in literature, the connection between the two model descriptions is problematic with respect to setup, stability and description of the flow. Furthermore, by using models that incorporate terrain representation that are smaller than the computational mesh (so called sub-grid models), such

9 9 as the hydraulic modelling software HEC-RAS, computation times for pure 2D applications might be reduced substantially, making pure 2D modelling a potentially interesting alternative to 1D-2D. The performance of sub-grid models is not well studied, neither in rural, nor urban areas. Important questions regarding suitable mesh size and mesh orientation remains. Overall, comparisons between the use of 1D, 1D-2D and 2D models are rarely cited in literature. In addition, most studies target calibration and validation of the models and do not incorporate important differences and considerations during model set-up. With this background, this study aims to investigate important differences between 1D, 2D and coupled 1D-2D modelling in HEC-RAS. The study is based on a case study of the Minija river crossing the small town of Kartena located in the Klaipeda s County. The general purpose with this project, is to analyze and compare different methods for flood modelling and inundation mapping. The aim is to identify differences, potentials, and limitations of 1D, 2D and 1D-2D HEC-RAS models for the modelling of fluvial flooding events. Furthermore, the study aims at investigating model specific aspects regarding the use of 1D, 2D and 1D-2D models in HEC-RAS, which was the software used throughout the whole project. The study is carried out through a stretch of Minija river flowing across Kartena s town. We performed three different scenarios including, (1) a 1D model where the flow is modeled within the river and on the floodplains, (2) a paired 1D-2D model where the river is modeled in one dimension and the floodplains are conversely in two dimensions, lastly (3) which a pure 2D model where both river and floodplains are exclusively modeled in two dimensions. Specific peculiarities and outcomes of each model will be described during the text. This study aims essentially, to compare 1D and 2D models performed by using HEC- RAS. None other software has been used for simulations. In addition, no hydrological model is performed in the study, and it doesn t also deepen the modelling features for the hydraulic structures. Only those regarding the bridges will be briefly exposed since a bridge was included in the model geometry.

10 2. LITERATURE REVIEW Floods and their impacts The risk of flooding has always existed, and they are part of the natural hydrological cycle, but since humankind has favored the expansion of the urban areas, mostly surrounding the riverine system, the probability occurring inundations has dramatically raised. Talking about Europe, between 1998 and 2002, Europe suffered over 100 major damaging floods, including the catastrophic floods along the Danube and Elbe rivers in Between 1998 and 2004, floods caused something like 700 fatalities, the displacement of about half a million people and at least 25 billion in insured economic losses (European Environment Agency). Several EEA reports, over recent years, have displayed that between flooding and storms were still the costliest hazards, and that by 2009, the number of fatalities had reached 1126 in 213 recorded flood events. The overall losses recorded for this period, added up to about EUR 52 billion for floods and EUR 44 billion for storms. The assets at risk of flooding can be innumerable. For example, more than 10 million people live nearby areas at risk of extreme floods along the Rhine, and the potential damage from floods amounts to 165 billion. Coastal areas are also at risk of flooding. The total value of economic assets located within 500 metres of the European coastline, including beaches, agricultural land and industrial facilities, is currently estimated at 500 to 1,000 billion. (Authors: N. Lenôtre et al. ) In addition to economic and social damage, floods may have severe environmental consequences as for example when waste water treatment plants are inundated or when factories storing large quantities of toxic chemicals are also affected. Floods may also destroy wetland areas and reduce biodiversity. Floods are natural phenomena which cannot be prevented. However, human activity is contributing to an increase in the likelihood and adverse impacts of extreme flood events. Firstly, the scale and frequency of floods are likely to increase due to climate change, which will bring higher intensity of rainfall and rising sea levels, as well as to inappropriate river management and construction in floodplains which reducing their capacity of draining flood

11 11 waters. Secondly, the number of people and economic assets located in flood risk zones continues to grow. Recent studies have suggested that climate change can add significantly to the expected Fig. 1. Number of flood disasters documented in the EM-DAT-data-base for in Europe, excluding Russia but including Turkey (Oct Data version: v12.07). damages in some parts of Europe over the coming decades. (Hildén Mikael et al. ) For all these reasons, the EU Directive on the Assessment and Management of flood risks (Floods Directive, Directive 2007/60/EC) specifically addresses this problem at the EU level. The white paper "Adapting to climate change: Towards a European framework for action" (EC 2009a) also identifies flooding as one of the issues that need to be considered in planning for the future (Hildén Mikael et al. ) According to the European Environment Agency (EEA) State of the Environment Report in 2010, a further major potential impact of climate change, in combination with landuse changes and water management practices, is going to intensify the hydrological cycle, due to changes in temperature, precipitation, glaciers and snow cover. In general, annual river flows are increasing in the north and decreasing in the south, a trend that is projected to increase with

12 12 future global warming. Large changes in seasonality are also projected, with lower flows in summer and higher flows in winter. Consequently, droughts and water stress are expected to increase, especially in southern Europe and particularly in summer. Flood events are projected to occur more frequently in many river basins, particularly in winter and spring, although estimates of changes in flood frequency and magnitude remain uncertain. Basically, uncertainties in climate change projections are still the most limiting factor to succeed in providing a trustworthy system to predict at best the hazardous floods. Europe is striving to create a coordinated action involving all the member states for improving the overall level of flood protection in throughout Europe. Most of the states have already taken protection measures but only cooperatively can be reached the goals that EU commission has set itself for the coming years. 2.2 How to tackle flood events There are essentially two cardinal ways to prevent high flood events: Structural mitigations Non-structural mitigations First category embraces all those systems which act either by creating barriers for stopping the water flows or diverting flows themselves further from most populated districts and in general zones where are located significant industrial areas. Typical hydraulic structures used in flood risk management are the dams, dikes, embankments, canalization and related works, flood diversion channel or tunnels, storage ponds of flood attenuation. As it is generally known this kind of mitigation measures were widely used over recent decades as primary protection method against floods. By developing new technologies, such as flood-mapping software and new hydraulic programs, the approach in decision-making of how combat the climate change and therefore the escalation of flood events, has completely changed. Within non-structural approach are included all those mitigation s actions such as: integrated river basin management (IRBM), preparation of guidelines and design standard resettlement of population, flood forecasting and warning system. (Mohit and Sellu 2013, ) Nevertheless, structural approaches remain important in solving flooding issues, studies have shown that adequate undertaking of semi-structural and non-structural measures can considerably decrease the costs of floods for households (Poussin et al. 2012, ). Furthermore, nowadays the market is populated by freeware capable in simulations of floods, favoring even more the diffusion of non-structural methods employment. Non-structural mitigation besides, allow to the designers and subsequently to the stakeholders involved in

13 13 decision-making process, to better estimate the overall condition accounting for every aspect including social partners, surrounding environment, further developments after the risk assessment, to finally come to the decision of what measure should be taken to safeguard the area threatened by floods or by hydraulic risks in general. Concluding, the most effective fact with regards to non-structural methods is that they provide reliable solutions, granting a major saving on the costs than structural approaches. 2.3 Modelling overview and methodology adopted Hydraulic modelling potentials represent the core of this study, therefore now will be outlined how, through modelling, have been performed the various steps to obtain our results. First of all, we chose HEC-RAS (version 5.0.3) as a modelling tool to undertake hydraulic simulations and in addition we used ArcGIS, more specifically ArcMap (version 10.2) for the setting up of the geometry and the creation of all layers and sub-layers necessary before exporting the edited map on HEC-RAS for the hydraulic computation. It comes clear the we use the coupling between these two software, since HEC-RAS geometry editor functionalities falls short to the necessities of the users of depicting accurately all the elements contained in the map to achieve a reliable representation of the riverine system. It has to be mentioned that to model the river s scheme we exploited a HEC-RAS plug-in, namely HEC Geo-RAS, which allows to create hydrological layers gathering all elevation data coming from the DEM terrain. Moreover, has to be reported that in our terrain file the standard error is about 20 centimeters, which enables to maintain a robust accuracy of data needed. Indeed, there are studies showing that significant time savings are achieved throughout the modelling process and that filtering to four degrees can be performed without compromising cross sectional geometry, hydraulic model results, or floodplain delineation results (Omer, James, and Zundel 2003, ). Our terrain file was provided from EPA of Lithuania and data for model calibration and river bad geometry control points by former graduate student (Batavičius, 2017) who collected data in Flow rate for the same day provided by Hidrometeorological service. Proceeding in order, were primary implemented all the geometry parts of the river system, as: Main channel; Cross-sections; Overbanks; Bridge; Manning s table containing the coefficients for each surface displayed in the map;

14 14 Storage areas; Then, after having created and drawn all the features, were determined all the attributes corresponding to each item edited. Subsequently, all the geometry file created through ArcMap was exported to HEC-RAS by using a converted file made the HEC Geo-RAS plug-in itself. ArcGIS is a massive and really powerful software suite which offers an extensive variety of functions and toolboxes which can likely perform any kind of user s requests, and it is perfectly integrated with HEC based software. Only downside is not a free-of-charge hence, freeware solution can be QGIS with RiverGIS plug-in for example, which is also widely used worldwide, providing manuals and tutorials for learning the main capabilities and tools. Going backwards to description, the exported file containing all the necessary data for the hydraulic computations was imported on HEC-RAS, so were started the hydraulic models by simulating the 1D, combined 1D/2D and at last only 2D. The core of our investigation was to compare the overall features supported by the application to analyze the current and further condition at Minija river along Kartena. Let s just introduce what have been done for every model. 1D model is described by the main channel, cross-sections and overbanks. Then we set up the boundary conditions both for steady flow and unsteady flow conditions. For the steady flow, we set a subcritical flow regime, so we have just input a downstream boundary condition. We chose the Normal depth, option commonly be used. This option is simple, and the users must have an estimate of the friction slope at the downstream boundary. Typically, the slope of the channel will be used in lieu of the friction slope (Alzahrani 2017). At the downstream HEC- RAS will use the Manning s equation to compute the stage based on the flows obtained from (Batavičius, 2017) and probabilistic Weibull s curves of the flow rate at Minija gauge station. Friction slope is estimated through the rearranged Manning s formula for the open channels. In our case we obtained a friction slope value of selecting a roughness coefficient of for the river bed. Furthermore, we input a set of observed WS elevations to estimate at best the simulations and then compare observed water surface with simulated ones. The effective calibration was performed exploiting a land use shapefile containing the contours for each surface. Land use shapefile was taken from CORINE database. In 1985 the Corine programme was initiated in the European Union. Corine means 'coordination of information on the environment' and it was a prototype project working on many different environmental issues. The Corine databases and several of its programmes have been taken over by the EEA. The shapefile has been processed by HEC Geo-RAS and then included in the exported file used for the hydraulic modelling. The calibration of roughness coefficients has played a crucial role in the delineation of the floodplain mapping. After having input all data

15 required we run the simulation and we will carefully examine the results in the dedicated chapter. Calibration procedure will me illustrated more accurately in the (Chapter 6 Results). 15 Fig. 2. Table of Manning coefficient used to perform calibration (Brunner 2016, 547). As for the 1D, we repeated similar routine with 2D model, but in this case have been adopted different flow analysis (unsteady again, since steady isn t allowed), flow data (we used a flow hydrograph including discharges from 7 August 2005 to 26 August 2005 with daily time step interval) and also another geometry including a 2D flow area on the right side of the channel and two additional storage areas simulating ponds on the left side following the downstream direction of the river flow. In the two-dimensional analysis pre-processor calculates the stage-storage curve base on the terrain data for each cell. The stage-storage curve is developed at the pre-processor step; also, we can check out 2D flow area hydraulic table from RAS Mapper. Each cell has a center and the water surface elevation is computed at these

16 16 centers. The cell face is evaluated likewise to a cross section and this entails the creation of hydraulic property tables of each cell, plotting the relationship between elevation versus Area, Roughness, and wetted-perimeter. Currently, the result of 2D model can be observed in RAS Mapper. The dynamic mapping in RAS Mapper became the easiest way to show the results coming from each analysis. In the results section, on the left side of the RAS Mapper are listed all the simulation results and from the indented entries the most important three layers will be Depth, Velocity, and Water Surface Elevation. The accuracy of this dynamic mapping depends on several factors, but the most relevant factors is the cell size. The cell size should be appropriate for the terrain layer and flow over the terrain itself. Summarizing, as smaller will be the cell size as more accurate will be the depiction of the water surface extension. Finally, for the combined 1D/2D model we used the same geometry as for the 2D (we only reduced the dimension of the 2D flow area) but we connected the river modelled in 1D with the 2D flow area through a Lateral structure which was located in proximity of an existing embankment constructed to protect the neighbouring residential area. We used the weir equation to simulate if the flow was capable to overflow the retaining wall. Exposition of the results will be given in the dedicated chapter. 2.4 Benefits of hydraulic modelling for flood mapping There are essentially two ways for estimating the flood risk in vulnerable areas to a flood disaster and they are physical models and precisely the computational models. A physical model is a physical copy of an object, often built at a smaller scale. Although fascinating, physical models are costly (Gartner et al. 2016). Furthermore, our river system is not so complex to require an additional implementation of physical modelling, therefore proceeding with a computational model approach was the best and most suitable solution for our study. Talking about mathematical modelling instead, we can point out two main types: Hydrologic modelling is used to determine the amount of flow discharge at a given location for a given recurrence interval, and in this use it is one of several methods used in flow frequency analysis. Hydraulic modelling can be used to determine the elevation and lateral extent of water and other hydraulic parameters at a given location for a given discharge (Gartner et al. 2016). The scales of these two types of modelling differ. Hydrologic modelling often has a basin-wide view because the conditions throughout a contributing area can affect the amount of water delivered to the location of interest while hydraulic modelling focuses on the reach

17 17 scale (i.e., a given length of a river or stream), often taking the amount of water delivered to a reach as a given input and then simulating the hydraulic properties of the water and showing how it displaces on the river system area. In our study, as already mentioned, we opted for the hydraulic modelling since we investigated a river scale area. Should be mentioned few more annotation as to why we have preferred HEC suite software. First, HEC-RAS is free and broadly used hydraulic program, secondly it is perfectly integrated to GIS ecosystem due to the HEC Geo-RAS plug-in which enhances visualization of riverine systems in concert with digital elevation models (DEMs) and remotely sensed imagery allowing interpolation of model results between surveyed cross sections (Gartner et al. 2016). We know also there are nowadays many freeware on the market for hydraulic modelling as WSPRO, software as FLO-2D, DHI suite (MIKE 11 and MIKE 21 i.e.), Bentley software are solid in computing floods and river scale systems but they aren t for public domain, and usually have an annual license cost. Outlining instead the differences among the model types we can surely underline that 1D are undoubtedly easy and fast to build and to run, but the results of such models may have significant inaccuracies in the floodplains. However, 2D models can correct this problem but it needs much more time for the flows implementation and simulations (Gharbi et al. 2016, 13). Concluding the choice has fallen on HEC-RAS since the US Army Corps of Engineers has been developing a thorough experience in solving the toughest engineering and environmental challenges.

18 18 3 PURPOSE OF THE STUDY AND TASKS 3.1 Aim of the study The general purpose with this project is to analyze and compare different methods for flood modelling and inundation mapping. The aim is to identify differences, potentials, and limitations of 1D, 2D and 1D-2D HEC-RAS models for the modelling of fluvial flooding events. Furthermore, the study aims at investigating model specific aspects regarding the use of 1D, 2D and 1D-2D models in HEC-RAS, which was the software used throughout the whole project. This work is aiming to disseminate a better understanding of modelling and how modelling capabilities can be exploited for social necessities, since flooding is getting over the years one of the most tremendous causes of fatalities and structural damages throughout the world. 3.2 Undertaken tasks More specifically this study will investigate: 1. Creation of three different hydraulic models, including 1D model, 2D model and coupled 1D-2D. 2. The concepts and theoretical background behind modelling, eviscerating the main physical and mathematical rules governing the hydraulic processes through the software. 3. Comparison the capabilities of each model, highlighting pros and cons in terms of data requirements, pre-processing, model set-up, and simulated results. 4. Analysis of the obtained results, checking out the accuracy produced by each model and thus determining which are the most suitable in computing the flooding events. 5. Finally, as well as the discussion of the obtained results.

19 4 RESEARCH SUBJECT AND METHODOLOGY Research subject As mentioned before, the subject of this study is to investigate the differences among the types of models made accessible by the hydraulic software HEC-RAS. Our study area is located in Kartena. The Minija s river stretch crosses the town nearby a residential area protected by an embankment extending for about 350 m and rises for approximately 23 m. That embankment was built to prevent flooding events in the surrounding residential area. There is one more relevant structure, the bridge crossing the river in Atlanto g. which is part of the A11 highway connecting Kartena with the main city of Telsiai. The first Kartena bridge over the Minija river, built about 1910, during the dry season of the river, then it was raised over the riverbed, through scaffoldings. Even though for our study the bridge will not be analysed thoroughly with regards to the modelling features provided by HEC-RAS it is interesting to Minija river Fig. 3. Picture shows the study area crossed by Minija river ( point out that this bridge is quite old, but by he years is fulfilling all requirements yet, even thank to periodical maintenance to the present day. This study is going to figure out whether the current structures and measures already taken to prevent the flood risk can be still considered effective.

20 4.2 Research methods 20 HEC-RAS software has been chosen for modelling all the likely scenarios with the three different types of models available in the software itself. The 1990s brought with it development of Microsoft Windows and HEC s Next Generation software. Version 1.0 of HEC-RAS was released in August of 1995 with subsequent updated versions being released every few years thereafter. Many individuals from HEC and other branches of the Army Corps of Engineers have contributed to HEC-RAS development. The HEC-RAS software was designed by Gary Brunner, leader of the HEC-RAS software development team. The user interface and graphics were programmed by Mark Jensen. The steady flow water surface profiles computations, sediment transport computations, and a large portion of the unsteady flow computations were developed by Steven Piper. Dr. Robert Barkau (developer of the unsteady flow engine UNET) developed the unsteady flow equation solver. The sediment transport interface was developed by Stanford Gibson. Tony Thomas, the software developer of HEC-6 (a sediment transport version of HEC-2), assisted in sediment transport computations used in HEC-RAS. The water quality computations were developed Dr. Cindy Lowney and Mark Jensen. The user interface for the channel design and modifications was developed by Cameron Ackerman. The stable channel design computations were developed by Chris Goodell. Importing of HEC-2 models into HEC-RAS was developed by Joan Klipsch. Steve Daly developed the computations for modelling ice cover and wide river ice jams. The current HEC-RAS software builds upon all the engineering advances from previous generations of computer software. The software can be used for both 1-D and 2-D flow simulations, steady flow or unsteady flow boundary conditions, sediment transport, and water quality modelling. It can account for subcritical, supercritical, and mixed flow regimes. The software can be used to perform flood studies, analyse backwater effects at roadway crossings (i.e., bridges and culverts), compute bridge scour, perform dam or levee failure analysis, and a whole host of other complex river hydraulic analyses. We will use the version 5.0.3, namely the latest released. 4.3 Theoretical background This chapter will introduce the basic equations governing 1D and 2D unsteady flow, as well as a simplification of these equations, and some basics regarding the numerical solution of these equations. Unsteady fluid flow varies in both space and time. The flow is governed by the conservation of mass and momentum, which can be described by a set of equations referred to

21 as the Shallow Water Equations (also referred to as the St Venants equations). The following 21 sections presents the 1D and 2D formulations of these equations. Both 1D and 2D models builds upon a set of assumptions, since they are important for a better understanding of how HEC-RAS is developed and carries out certain functions, therefore let s list them briefly: The fluid is incompressible: it refers to a flow in which the material density is constant within a fluid parcel that moves with the flow velocity The pressure distribution is hydrostatic: vertical accelerations are neglected The flow is one- or two-dimensional, vertical variations in flow and velocity are neglected. The wave lengths are much larger than the water depth. The average channel bed slope is small. Bed friction can be calculated using Manning s equation, which has been derived for steady flow conditions. The flow can be described as continuous functions of the velocity and the water surface elevation H. Let s describe for each kind of flow the formulas and mechanisms which allow the implementation D Steady flow The steady flow in one-dimension it is described by HEC-RAS through the water surfaces profiles which are computed from one cross-section to the next one by using the energy equation with an iterative procedure called standard step method (). Where: 2 2 α 2 V 2 Z 2 + Y 2 2g = Z α 1 V Y 1 2g + h e Z1, Z2 = elevation of the main channel Y1, Y2 = water depth at each cross section V1, V2 = mean velocities α1, α2 = velocities weighting coefficients g = gravitational acceleration he = energy head loss

22 22 Fig. 4. Representation in terms of Energy equation () At each cross-section HEC-RAS uses several parameters to depict at best the terrain framework, determining river stations, left and right banks locations, reach lengths among the left overbank, stream centreline, and right overbank of adjacent cross-sections, Manning s roughness coefficients, geometric description of any hydraulic structure present along the river. Second parameter which will be part of the solution to find the water surface elevation is the energy head loss, which can be obtained from the equation below: where: h ce = LS f + C α 2 1 V 1 2g α 2 2 V 2 2g Sf = friction slope between two cross section C = expansion/contraction loss coefficient Another important aspect with regards to the computations, is the subdivision of the cross sections for determining the conveyance, which is indeed calculated within each subdivision, exploiting a modified version of Manning s equation: K = 1 n AR2 3

23 23 the overall conveyance for the cross sections is computed by summing up conveyances coming from each subdivision. The method just explained is the default approach in HEC-RAS in determining the total conveyance. Various set of water surface profiles were tested, and the default method usually produced highly computed water surface elevations. It can be asserted Fig. 5. Subdivided cross section for obtaining the conveyance. () that the default method is the most accurate, but it can be assessed is the most fitting the Manning s equation. Continuing the description of the 1D steady model features, it has to be mentioned the composite Manning coefficient within the main channel. Generally, the channel is not subdivided but if the Manning s coefficient varies either vertically or horizontally in it, composite value is required to describe more consistently the surface of the main channel. Others important parameters are the friction losses and the coefficients of contraction/expansion which are respectively computed as the product of the friction slope Sf and the weighted length of the river and the first, and solving the following equation the second: h ce = C α 2 1 V 1 2g α 2 2 V 2 2g The unknown water surface elevation is determined by solving iteratively the two equations of energy and energy head loss. The criterion used to assume water surface elevations in the iterative procedure varies from trial to trial. The first trial water surface is based on projecting the previous cross section's water depth onto the current cross section. The second trial water surface elevation is set to the assumed water surface elevation plus 70% of the error from the first trial (computed W.S. assumed W.S.). In other words, W.S. new = W.S. assumed * (W.S. computed - W.S. assumed). The third and subsequent trials are generally based on a "Secant" method of projecting the rate of change of the difference between computed and assumed elevations for the previous two trials. (BRUNNER, Gary. HEC-RAS, River Analysis System Hydraulic Reference Manual. Davies, p.)

24 24 Concluding, should be pointed out the limitations of one-dimensional steady flow: (1) the flow is steady, (2) flow is gradually varied, except at hydraulic structure as bridges where the variations are abrupt, this requires the application of momentum equation or some other empirical equations. (3) flow is one dimensional, so velocities and their directions aren t accounted for D unsteady flow Based on the assumption which the water flow in a stream is basically governed by two principles: (1) the conservation of mass and (2) the conservation of momentum. These laws are expressed mathematically in the form of partial differential equations. The law of conservation of mass states that for any system closed to all transfers of matter and energy, the mass of the system must remain constant over time because system s mass cannot change. Below it is shown how the equation of continuity can be written: (Q) x + A τ + q = 0 where Q is the flow rate, A the cross-section area and q represent the lateral inflow. Hereunder it is described the momentum equation which is based upon Newton s second law of motion, stating that the sum of the forces acting on an element equals the rate of change of momentum. The formulation of the momentum equation can vary depending on what forces that are being chosen. Considering pressure, gravity and frictional resistance, the 1-dimensional continuity equation can be expressed as: v t + g x (v2 2g + h) = g(s 0 S f ) where V is the flow velocity, g is the gravitational acceleration, h is the water depth S0 is the bed slope, and Sf is the friction slope D Unsteady flow The 2D form of the continuity equation states, as the 1D form, that the net mass flux into the control volume equals the change in storage in the control volume, with the only difference that the mass fluxes are now calculated in 2 dimensions. The 2-dimensional continuity equation can be written as: H t + (hu) x + (hv) y + q = 0

25 25 Where H is the water surface elevation, h is the water depth, u and v are the depth averaged velocities in the x- and y-direction, and q is the source term, representing inflow from external sources such as precipitation (Chaudhry, 2008). Subsequently, the momentum balance is based on the principle that the sum of forces acting on an element equals the rate of change of momentum. Considering forcing from gravity, eddy viscosity, friction and the Coriolis effect, the 2D momentum balance equations can be written as follows: Momentum balance in the x direction While in the y direction: u u u H + u + v = g t x y x + ν t ( 2 u x u y 2) c fu + f v v v v H + u + v = g t x y y + ν t ( 2 v x v y 2) c fv + f u where H is the water surface elevation, νt is the eddy viscosity coefficient, cf is the friction coefficient, f is the Coriolis parameter and v and u are depth averaged velocities in the x and y directions respectively (Brunner, 2016). The first term in the momentum equations represents the local acceleration the second term is the convective acceleration, the further terms describes the forcing from gravity, eddy viscosity, bed friction, and Coriolis force. Using the Manning s formula, the friction coefficient cf can be expressed as following (in the x-direction): c f = n2 g u R 4 3 where n is Manning s coefficient, g the gravitational constant, u the velocity in the x-direction and R the hydraulic radius.

26 4.4 Modelling simplifications 26 Diffusion Wave Approximation of the Shallow Water Equations asserts a relation between barotropic pressure gradient and the bottom friction. This relation results highly effective due to its simplicity. It will be shown furtherly that under certain condition the Diffusion Wave equation can be exploited in place of the momentum equation. Another important simplification which fits with the numerical methods pre-announced regards the grid framework. Indeed, for speeding up the computations HEC-RAS uses, instead of fine grid, a sub-grid which is capable to keep enough information so that this coarser numerical method can account for the fine bathymetry through mass conservation equation. The orthogonality among the cells also will increase the performance of the solver for calculations. Since various simplification are available for users, this report will only outline the main approximation, i.e. the Diffusion Wave Approximation Diffusive wave approximation When the velocity is determined by a balance between barotropic pressure gradient and bottom friction, the Diffusion Wave form of the Momentum equation can be used in place of the full momentum equation and the corresponding system of equations can in fact be simplified to a one equation model (Brunner 2016). In the diffusive wave approximation of the momentum equation the acceleration terms, eddy viscosity and Coriolis terms are neglected, and the momentum balance is written as a balance between gravitation and bottom friction forces. Therefore, considering the bottom friction and the gravity, the equation becomes: g H = c f V where V is the flow velocity in vector form V=(u,v) and cf is the bottom friction. If the bottom friction is considered evaluating the Manning formula, the equation can be rewritten as: V = (R(H))2 3 n H H 1 2 Where R(H) is the hydraulic radius at the water surface elevation H, is the differential operator, and n is the Manning friction coefficient. Rearranging the inserting the last equation into the continuity equation and writing it in vector form is obtained: H t + β H + q = 0

27 Where β is equal to: 27 β = (R(H))2 3 n Basically, the diffusive wave approximation it is summed up with the second-last equation. Using this method, the vertical momentum scales are small relative to those of the horizontal momentum, that is, due to depth restrictions the velocity structures in the horizontal direction are much larger than the ones in the vertical one. It was also noticed that DSW equation assumes that the horizontal momentum can be linked to the water height by an empirical relation such as Manning s equation. Thus, the DSW reduces to a scalar equation which resembles nonlinear diffusion. While the nonlinearities present challenges, the DSW equation is a simpler framework with which economically simulate shallow flows (Collier et al. 2011, ). Fig. 6. Grid nodes and edges are represented by dots and continue lines; the dual grid nodes and edges are represented by crosses and dashed lines. 4.5 Solving techniques Let s outline the approaches to solve the Shallow Water Equations, since they return a set of partial differential equation to be integrated analytically. To get the variables at stake, a hybrid discretization combining finite volume and finite differences is used to profit of the orthogonality obtained among original grid and sub-grid to make computation quicker. Because of second order derivative terms and the differential nature of the relationship between variables, a dual grid will be necessary in addition to the regular grid in order to numerically model the differential equations (Brunner 2016). The framework with the addition of the sub-grid creates a dual pattern which has some fruitful properties. For instance, the one-to-one relation between the grid cells and the dual nodes and vice versa.

28 28 Obviously, this scheme has its limitation, dual grid is therefore truncated by adding dual nodes on the center of the boundary edges and dual edges along the boundary joining the boundary dual nodes (Brunner 2016). Proceeding with numerical methods, finite difference scheme expresses a derivative as the difference of two quantities, whilst finite volume approach is used to discretize the equation of DSW accounting for the sub-grid bathymetry 1 when the grid is not locally orthogonal. Moreover, the finite volume technique will also be used to approximate other differential terms such as eddy viscosity (Brunner 2016). Streamlining the topic, finite differences are used to discretize time derivatives and hybrid approximations are used to discretize spatial derivatives and Crank-Nicolson method is used to weight the contribution of variables at time steps n and n+1. The SW equations express volume and momentum conservation. The continuity equation is discretized using finite volume approximations. For the momentum equation, the type of discretization will vary depending on the term. Again, as seen formerly for the DSW equations, the Crank-Nicolson method is used to weight the contribution of variables at time steps n and n+1. However, the different nature of the equations will demand the use of a more elaborate solver scheme. 1 The equation abovementioned is the following: Ω(H n+1 ) Ω(H n ) α H n + Q = 0 Δt where α = α(h) = (R(H))2 3 A k (H) n H 1 2 Ω(H n ) is the cell volume at time n and A k is the area of face k, as functions of water elevation. k

29 5 HEC-RAS HEC-RAS (Hydraulic Engineering Centre River Analysis System) is a hydraulic engineering software which was developed by Us Army Corps of Engineers. This tool can perform steady flow simulations for computing water surface elevations within the area of interest or by uploading hydrographs to the systems is capable to simulate unsteady flows. Moreover, with regards to unsteady flow analysis, this tool can accomplish both 1D and 2D flow simulations. Even though in this study they will not be outlined, HEC-RAS is capable to make a sediment transport modelling and water quality modelling D modelling in HEC-RAS The 1D unsteady computation engine solves the 1D continuity and momentum equations presented in the former sections using a semi-implicit finite difference solution scheme. In this section the basics of the HEC-RAS 1D program is presented, along with the data necessary to set up and run an unsteady flow model. All the features which have to be modelled in this section consists of geometric data, flow and/or stage data that lead to the boundary conditions of the model Geometric data The geometry framework is paramount in order to properly depict the river system parts, as the river, junctions and additional hydraulic structures present along the stream. The cornerstone in the geometry scheme is represented by the cross sections, a set of station-elevation points which describes the terrain profile of the river. Each cross section 29 Fig. 7. Typical HEC-RAS cross section geometry. With red dots are marked the bank stations defining the subdivision among main channel and overbanks.

30 30 results perpendicular to the flow direction. Within each cross section there is a subdivision among, main channel, left and right overbanks each of which has their own roughness coefficients. Finally, the hydraulic properties of the river system are strictly depending on cross sections resulting essential in the simulation step. Fig. 8. Property table associted with a cross section. The graph shows how the overall conveyance and area change with the elevation. In addition to each cross section is associated a property table plotting the relationship between cross sectional area and elevations. Below it is hown how it looks a property table after the software has performed the calculations Bridges and hydraulic structures Since in this project it is present a bridge, this study will briefly explain how HEC-RAS is able to develop a bridge modelling. Such hydraulic structures may have large influence on flow dynamics due to the contraction and expansion of the flow around the structure. The program is capable of computing energy losses due to contraction and expansion of the flow, as well as due to submergence of the structure. It is also possible to model pressurized flow through a culvert or under a bridge (Brunner 2016). Bridges are only modelled in 1D and based on four cross sections playing a role in the schematization of the hydraulic structure. There are two cross section upstream and two downstream. Respectively, those collocated most upstream and most downstream should be placed far enough where the flow is supposed to be maximally expanded. Instead, the remaining cross-sections in the proximity of the bridge should be located near the toe of the downstream road embankment to allow the software to calculate energy losses due to the contraction/expansion of the flow.

31 31 Into the bridge editor, the user has to insert all the parameters to sketch the bridge, as deck roadway, elevation of lower and upper chord and width of the bridge. In this study for bridge computation analysis was chosen the energy equation, nevertheless HEC-RAS has at his disposal several methods. It will not deepen this topic, because it goes beyond the aim of the study itself Boundary conditions HEC-RAS requires the setting of boundary conditions, both at the upstream and at the downstream. According to the flow regime and the time dependency, the boundary conditions may be required either at one location or both upstream and downstream ends of the reach. For example, when unsteady flow simulation is undertaken both conditions must be specified. Boundary condition included at the upstream are the stage hydrograph, flow hydrograph and coupled stage/hydrograph. Additionally, the downstream boundary conditions incorporate the normal depth and the rating curve. In our case it has been adopted the normal depth, which estimates a water depth. Aside from the boundary conditions necessary to perform the calculations, flow hydrographs can be entered laterally along a reach. Lateral inflows can be added as a flow hydrograph entering at a single cross section, or as a hydrograph that is uniformly distributed over several cross sections. (Brunner 2016) Hydraulic calculations The unsteady computation engine solves the continuity and momentum equations using a discretized finite difference approximation. For each cross section, a water surface elevation and flow velocities at the different portions of the river (overbanks and main channel) is calculated. For a reach consisting of N nodes, the momentum and continuity equations develop a system of 2N-2 equations. Since there are 2N unknowns that need to be solved for, namely Q and h in each cross section, two more equations are required to solve the system of equations. The two equations needed are exactly the upstream and downstream boundary conditions. The system of equations is solved iteratively until a satisfying solution is obtained for all cross sections, or until the maximum number of iterations is reached. Furthermore, the user is required to decide a time step Δt and the implicit weighting factor θ. The default value is 1.0, but the user can define a value of theta anywhere between 1.0 and 0.6. A value of 0.5 represents a half weighting explicit to the previous time step s known solution, and a half weighting implicit to the current time step s unknown. A value of 1.0 gives a fully implicit formula that is highly diffusive, improving on one hand model stability, but on

32 32 the other hand producing less accuracy in the solution. The opposite is true for lower values of Theta, which can make the model more sensitive to errors and lead to oscillations. Anyway, factors as cross-sectional properties, abrupt slope changes, flood wave characteristics, and complex hydraulic structures are the most influencing the stability of the model simulation. Therefore, they must be carefully evaluated before thinking of getting a stabilized model only by modifying the theta weighting factor D HEC-RAS modelling Released in 2014, the 2D modelling function is pretty recent in the landscape of HEC software. It enables users to undertake pure 2D models either combined 1D/2D. in this section will be shortly outlined the main features available in the latest version Mesh assembly and cardinal features The 2D geometry is built up by a computational mesh (or computational grid), illustrated in figure. Each mesh is built up by interconnected cells that may vary in size and shape, although one cell cannot have more than 8 cell faces (edges). Cell faces are similar to 1D cross sections and are used to compute flow between cells, except at the outer boundaries of the mesh (purple). Cell points (red), located at the connection between cell faces, are used to connect the mesh to 1D structures and 2D boundary conditions. The cell center (blue) is where the water surface elevation is computed for each cell but doesn t necessarily correspond to the cell centroid. Besides, underlying terrain and the computational mesh are pre-processed in order to develop detailed hydraulic property tables for the cells and the cell faces.

33 33 Fig. 9. 2D computational mesh in HEC-RAS showing specific terms for each element. HEC-RAS can manage orthogonal and non-orthogonal grids, but profiting of the orthogonality, computation time and formulation will be reduced, whereas grid orthogonality is where the centers of two adjacent cells are perpendicular to the face between them Sub-grid terrain representation Each cell and cell face of the computational mesh is pre-processed in order to obtain high resolution property table based on the terrain used during the process. Each face of a computational cell is pre-processed into detailed hydraulic property tables where elevation is compared with other parameters as, wetted perimeter, area, roughness, etc. Additionally, HEC- RAS doesn t have only one elevation for each cell, thus produces better results than other models retaining great hydraulic details within a cell. To fix some lacks in the sub-grid mesh the user can draw the breaklines which can be used to force alignment of computational cell faces along barriers or other features that will significantly affect the flow disposition.

34 34 Fig. 10. Detail of a computational mesh with cells aligned along a breakline. (Fragment of Minija model) Hydraulic structures Modelling structures in 2D is not as well developed and researched as in the 1D analysis. Weirs, culverts and gates can be added inside the 2D mesh but are modeled in 1D using the same equations as for the 1D case. The 2D equations will handle flow contraction and separation as long as the full momentum equations are used, with regards to ineffective flow areas, they are considered as long as cell faces are aligned with the top of bridges and other barriers (Brunner and CEIWR-HEC 2016, 171). Bridges cannot be modeled in as for 1D. They can be integrated by (1) modifying the terrain to capture bathymetry and banks underneath bridge. Unfortunately, this option cannot include the bridge deck, thus it will fail to restrict the flow when the water surface reaches the bottom of the bridge deck. A more detailed representation of bridges can instead be implemented by editing them as either (2) culverts or (3) gates. Using these options will require additional work during calibration. Moreover, the geometry of bridge openings is often hard to capture using culverts and gates (Brunner and CEIWR-HEC 2016, 171) Boundary conditions Have been used the same boundary condition of 1D, so Flow hydrograph upstream and Normal depth downstream. Stage hydrograph, rating curve are also available for the 2D model.

35 35 Internal boundary conditions are set-up as BC (boundary condition) lines which are connected to one or more cells through the cell face points. Boundary conditions can only be put at the perimeter of the mesh and not inside the mesh. 5.4 Combined 1D-2D HEC-RAS modelling Fig D river reach connected to a 2D flow area using a lateral structure. HEC-RAS, among many things can do, is also capable of combining 1D-2D models, where some areas can be modeled in 1D and others in 2D. When developing a coupled 1D-2D model, the crucial input data is the same as when developing a pure 2D model. A Digital Elevation Model (DEM) is required to set up the model geometry, and flow and water level data are required to set up the boundary conditions. A combined 1D-2D modelling can be performed in two different ways. The first option is to design a lateral connection where 2D flow areas are associated to 1D cross sections adding a lateral structure (we used this solution). The second option is to model the upstream (or downstream) reach of the river in pure 1D and connecting the most downstream (or upstream) cross section with a 2D area Connecting 1D river with a 2D Flow area through a lateral structure The flow between the two models is computed as flow overflowing a lateral structure. The 1D part of the model consists of cross sections just as in a pure 1D model. The 2D part of the model consist of a mesh, which is implemented in the same way of a pure 2D model. The lateral structure connecting the two models contains elevation data which can be extracted from the underlying terrain model using the Measure tool (Ctrl key). When the water level in the 1D cross section or 2D cell exceeds the elevation of the lateral structure, water

36 flows over the structure. The overflow can be calculated either using a weir equation or using the 2D flow equations (Brunner 2016, 547). When the 2D equations are used, the 1D water surface profile is added as a stage boundary condition to the 2D cells. When the weir equation is used the flow is calculated based on the difference between water surface elevation and the elevation of the structure. 36 Let s explicit the standard weir equation for major clarity: Where: dq = C(y ws y w ) 2 3dx dq is the flow over the structure over the length element dx, yws is the water surface elevation, yw is the elevation of the structure, and C is the weir coefficient. When the water surface and the lateral structure are not parallel, HEC-RAS uses a modified version of this equation (Brunner 2016, 547) Direct connection of 1D river reach and 2D flow area This connection allows 1D river streams to be directly connected to 2D flow areas by dint of connecting a cross section to a 2D area. Flow rate coming from the 1D-model is distributed in the 2D-model based on the conveyance distribution in the connected cross section. Flow diffusion is thereafter modeled using the standard 2D equations. This type of connection should be set up where the flow does extremely emulate 1D conditions (Brunner and CEIWR- HEC 2016, 171).

37 6 RESULTS D model setup Geometry data manipulation In the figure below is represented the complete extension of the 1D geometry. The main channel and overbanks are represented in blue and in red respectively while the cross-sections describing the river are depicted in yellow. Fig. 12. Overview of the 1D model. The geometric data is processed in ArcGIS using the extension HEC-GeoRAS, developed by US Army Corps of Engineers. The initial input data for developing the 1D geometry of the Minija River model is the DEM from Hydrometeorological service. The first step of creating the 1D geometry file is to digitize the river centerline, banklines and flow path lines. The river centerline is used by the program to calculate the length of the river reach, the stationing of the cross sections as well as the distance between consecutive cross sections. River centerline should be drawn from upstream to downstream following the direction of flow. The bank lines are used to calculate the location of the bank stations for each

38 38 cross section while the flow path lines are used to compute the overbank reach lengths between consecutive cross sections. Cross-sections also should carefully follow the rule of being digitized form the left overbank to the right overbank, otherwise hydraulic computation will give bed results. The abovementioned features are created as polylines in ArcMap (version 10.2) by using the available GeoRAS tools. After having created the layers, all necessary attributes are assigned to the features. A cross section cut line is a line describing the location of the cross section. Since the hydraulic computations are 1D, the cross sections should be perpendicular to the flow direction to accurately depict the hydraulic properties of the river. The cross-section polylines are thereafter converted to polyline Z features, namely polylines containing elevation data. The elevation data is extracted from the DEM. In our work we didn t use bathymetry since we haven t considered any additional shapefile containing bathymetry data. 6.2 Calibration First, calibration is a process which requires the adjustment of certain model parameters to achieve the best performance of the model for specific locations and applications. The model calibration must express:(a) express the level of agreement achieved; (b) express how realistic is the representation of the processes, and (c) define the criteria by which it has been judged as being fit for purpose. Fig. 13. Cross-section editor window showing all data of each cross-section as well as the additional column for the horizontally varied Manning s coefficients circled in red.

39 39 The quantitative assessment of data error, accuracy, and uncertainty in models then defines metrics against which model performance can be judged (Jon J. Williams and Luciana S. Esteves 2017, 25). Critical parameters affecting model performance (e.g., bed roughness) are then adjusted to achieve the best possible agreement between model predictions and measurements. A useful first step in the calibration and validation process is the determination of the most sensitive parameters in the model. While expert judgment can be helpful, less-experienced model users should undertake sensitivity analyses. The second step in the calibration process is undertaken to reduce the uncertainty in the model predictions. Normally, this uses carefully selected values for model input parameters and compares model predictions with observed data for the same conditions. In common with the process described in step 1, this is often done iteratively without any fixed rule and is guided by the experience of the user and knowledge of the model (Jon J. Williams and Luciana S. Esteves 2017, 25). Manning s n is a friction parameter reflecting the resistance against flow from the riverbed. The higher is a Manning s n value the more resistant will result the bottom of the river, thus producing a slower flow and higher water levels, whereas a lower Manning s n will allow more rapid flow and lower stage. The impact on stage and flow hydrographs and inundation extent of changing Manning s n was investigated. Manning s n is often used as a calibration parameter. Below it s illustrated clearly how we calibrated the model. Procedure of calibration was carried out only for the 1D model as follows: We used a DEM terrain containing bathymetry data from 2011, was undertaken a sensitivity analysis measuring differences in elevations from several selected points, thus was possible adjust the dataset(batavicius,2016). We used a shapefile coming from CORINE database. Shapefile contains contours of each surface polygon. Polygons are named with the kind of terrain. Then, we chose per each polygon an averaged valued which was at best fitting the situation. We started selecting values from tables of Manning s coefficient from user manual (Brunner 2016, 547). Thereafter, we adjusted coefficients accordingly to the observed WSE taken form (Batavicius,2016) and we selected our definitive parameters. For the river channel was found a best fit with roughness of About calibration of grid spacing setup, it has been chosen a resolution of 10x10 according to my personal requirements and capabilities of my computer machine. Indeed, very accurate grids requires powerful engines.

40 40 Any validation was performed for the model since we had at our disposal only data coming from one measured event by a former graduate student (Batavicius,2016). Below is shown a picture from HEC-RAS profile of WS, to give a first look at the agreement of the outcomes. Fig. 14. Profile plot showing differences between observed and simulated data. We demonstrated goodness of fit between observed and modelled data by statistical calculations and graphs, as: standard error, correlation and lastly with RSME.

41 41 Calibration should aim to minimize discrepancies; therefore, statistical analysis should be used to quantify the goodness of fit. Were used simple statistics demonstrating the level of agreement between measured/observed data D Model set-up Here will be explained guidelines to perform a correct 2D model. After this, the set-up of the 2D model is shown. Any sensitivity analysis is conducted, since doesn t fall into our purposes. Finally, 2D modelling in HEC-RAS is discussed in terms of geometric set-up, possibilities and current limitations. Fig. 15. Entire 2D area for the two dimensional modelling.

42 D Geometry set-up manipulation A comprehensive 2D Flow area was designed to be extended throughout the river including also floodplains and the populated area on the right side. Breaklines were edited along few ridges, banks and other features that may act as important barriers to the flow In order to set suitable cell sizes for the breaklines and the overall 2D area, a geometric sensitivity analysis was conducted (see section 8.2). Manning s n values were assigned as for the 1D model through the imported shapefile from ArcGIS containing all the coefficients calibrated per each polygon represented in the Land Cover. Fig. 16. Representation in detail how the 2D mesh is refined by using breaklines along ridges. The boundary conditions were set up likewise the 1D analysis, but since we used a wide 2D Flow area we drew them at the upstream and at the downstream end of the meshed area respectively. Both upstream and downstream 2D boundary conditions have the same hydrograph and the normal depth used in the already input formerly for the 1D modelling. A 2D flow area was designed to cover the extent of the flooding during all events, a process that was modified during calibration. Breaklines were introduced along ridges, bridges, banks and other features that may act as important barriers to the flow. Breaklines provides extra cells allowing a more accurate representation of variations on the terrain. Manning s n values were assigned to the river and the floodplain respectively, using polygons created through the shapefile of CORINE database.

43 43 The cell size and alignment needed to sufficiently represent the river and riverbanks was chosen according to our personal requirements. Mesh construction is quite important component for achieving good results. As already mentioned, it was chosen a resolution for the whole 2D area of 10x10 grid spacing with a terrain resolution of 1 meter. A time step of 1 seconds was used for all simulation, according to the Courant number condition. Lastly, a Mapping output interval of 30 minutes was adopted for the computations. 6.4 Combined 1D-2D model setup This paragraph will describe the set-up and running of the coupled 1D-2D model. The process of setting up the model geometry is outlined. Results will be paired along with the other models for a better comparison overview Geometry set-up manipulation The initial processing of the geometry data is performed in ArcMap using the GeoRAS extension. If a 1D geometry has been developed in GeoRAS it is pretty straightforward to set-up the 1D-2D geometry using the 1D model as a groundwork. It was decided to model the hypothetical flood around the residential area in 2D, and the rest of the domain was model purely in 1D. The 2D areas are connected to the 1D model using a lateral structure, which should ideally represent the embankment protecting the area itself. The stretch of the lateral structures was determined using the DEM. Using GeoRAS, the structures were digitized and assigned elevation data from the DEM. Thereafter, the 2D flow area was digitized as polygons, directly on HEC-RAS by the dedicated function in the geometry editor. The last step was to set the lateral structure parameters as well as weir coefficient, width, centerline length and equation to be used for computation. It was used the Weir equation. Also important is to carefully locate the positioning of the lateral structure, which in our case resulted on next to the right overbank. Thus, hydraulic structures can be added to the combined 1D-2D model in the same way that they are added to the pure 1D and 2D models. Differences between the model used can be showed graphically for the 1D and the 2D through the extension of the flooded area. From the picture below, we can see the differences. Anyway, variations encountered aren t influencing the stage of water surface computed from both models.

44 44 Fig. 17. Comparison between the WSE elevation map of 1D (to the left) and combined 1D-2D (to the right) 6.5 Discussion D model The main advantage with the 1D model approach is that the computation times are very quick, a month-long simulation period can be calculated in less than a couple of minutes. It is possible to set up very large models without ending up with long computation times Fig. 18. Differences between WSE inundation displacement between pure 1D and combined model Modelling bridges and other hydraulic structures is relatively easy in 1D. There exists a variety of different methods for modelling flow under bridges, through culverts and gates and over weirs. Adding the required data is straightforward, given that the modeler has access to ground plan and elevation data. The modelling of bridges and structures was not studied in detail in this project., and not to give a detailed description of the flow around the bridges in Minija river. In this study we tried to reproduce the modelling procedure described in the literature to only determine any unexpected WS variation. When the computed 1D results are displayed in RAS-mapper or in a GIS, the results has to be interpolated to a continuous surface, and displayed on a terrain model In 1D also it s possible to determine mapping velocity distribution but should be underlined that the velocity maps are based exclusively on interpolation of 1D results (Brunner 2016), and that it is not possible to map velocities around features represented between cross sections. Therefore, the velocity distribution is not realistic or even trustworthy D model Pre-processing of data for 2D modelling is relatively easy. Using river bathymetry measurements, the river can be incorporated into the DEM using a few simple steps

45 45 in HEC-RAS. Meanwhile, large uncertainties remain regarding the interpolation technique used by HEC-RAS, and current bugs require additional work using GIS software. Another consideration regarding pure 2D modelling are boundary conditions. Adding uniform lateral inflow to river reaches where floodplain flooding is to be modelled is not possible and may be hard to get around for certain applications. Modelling structures seems to be one of the largest current issues for pure fluvial 2D modelling in HEC-RAS. While bridges can be modelled using gates or culverts, we didn t opt for those alternatives. Indeed, from literature it is well-known that for avoiding all those uncertainties and instability issues occurring, it s suggested to model the bridge only in 1D, since the robustness of one dimensional modelling produces more reliable results. Mesh construction was shown to be very important regarding the model outcome. Result sensitivity to mesh construction should thus be investigated in all projects. Results from this study highlight the importance of correct river representation in flat, rural areas. Important barriers, both next to river and in the floodplain, has to be correctly represented using breaklines. When barriers are thin, steep and long (such as the barriers at the golf course), capturing the highest part can be difficult and requires precise work. It also requires high precision elevation data, and field surveys may have to complement LIDAR data. As a result, modifications may have to be done to the DEM in a GIS-software. Being familiar with GIS software and the many uncertainties included in GIS-operations is thus of great importance when constructing a pure 2D model. Floodplain cell size is likely much less important than breakline placement if reasonable computation times are to be kept Combined 1D-2D When the 2D equations are used a time step smaller than 10s was required for the model not to crash. Without iterations, the time step had to be smaller than 5s. The mass balance errors are significantly larger compared to when the weir equation is used. When flow is calculated using the 2D equations the model results are much affected by the choice of time step. Inundation extent increased with increased time step. Flow and stage hydrographs in the river as well as flow over the lateral structure was affected by the choice of model time step and whether the program could iterate. When the weir equation is being used to calculate flow over the structure, the user is required to specify a weir coefficient. We used a couple of coefficients to figure out any change in results. The HEC-RAS user manual recommends a weir coefficient between 0.11-

46 when modelling overland flow escaping the main channel over non-elevated terrain, and between when modelling flow over elevated natural ground (US-ACE, 2015). All simulations were performed using a time step of 1s, since this time step provided the most stable solution. Definitely, it was confirmed that weir coefficient wasn t an affecting parameter for the combined analysis. Any flow was found over later structure. These results give rise to the even after changing weir coefficients, meaning that the actual protections safeguard the area from a potential flood over 1000 years return period Set-up and pre-processing The coupled 1D-2D model with lateral structures is more complex to set up compared to the pure 1D and 2D models, since set-up of both 1D and 2D geometries and coupling between the two models is required. The 1D-2D model requires more user-specified parameters compared to the pure 1D and 2D models, which leads to more sources of uncertainty Advantages and limitations An advantage with the coupled 1D-2D approach is that the terrain model does not have to be modified to include channel bathymetry. Channel flow is modeled purely in 1D, and the channel is only represented in the cross sections. The coupled 1D-2D approach takes away the issues with representing the channel bathymetry in the 2D mesh, and there is no need to use a finer mesh cell size in the river to accurately model river flow. This reduces the complexity of the 2D mesh, and the total number of 2D cells, which could reduce the computation time. 6.6 Graphical overview of model comparisons First, it should be mentioned that we decided to make comparisons between 1D and 2D, excluding the combined, given that 1D and combined 1D-2D showed the same results and variations. Graphs outlined are coming form outputs obtained in three different cross-sections selected along the river. One was chosen at the upstream, another one approximately at the middle of the river and the last at the downstream near the bridge.

47 Graphs from section : 47 Fig. 19. Graph showing variations between models. Most affected parameter by the kind of modelling is clearly the velocity.

48 48 Let s proceed now with the graphs of cross-section : Fig. 20. Subsequent comparison at cross-section in the middle of river approximately.

49 Finally, is shown the last cross-section at the downstream 49 Fig. 21. Last cross-section compared at the downstream. Also interesting is the graph showing the velocity distribution along the bridge which was obtained form the pure 2D simulation. This graph shows that regardless 2D model isn t the most suitable for analyzing river stretches crossed by bridges, acceptability of modelled outputs is satisfied for our purposes, since we excluded to perform a thorough hydraulic analysis at the bridge location.

50 50 Fig. 23. Graph showing the velocity distribution along the bridge cross-section. 2D model It is also very engaging, the representation of velocity through animation of the water particles moving downstream. With this feature on RAS Mapper it is possible to evaluate which are the most sensitive areas of the banks influenced by erosion i.e. Contraction scour occurs as a result of the reduction in the channel s cross-sectional area that arises due to the construction of structures such as bridge piers and abutments. It manifests itself as an increase in flow velocity and resulting bed shear stresses, caused by a reduction in the channel s cross-sectional area at the location of a bridge. The increasing shear stresses can overcome the channel bed s threshold shear stress and mobilize the sediments (Prendergast and Gavin 2014, ). in this study wasn t conducted any deep analysis about erosion at hydraulic structures. Fig. 22. How velocity is impacting sensitive areas at bridges. (Fragment detail)