How Pluvial Floods in Urban Areas Vary with Rain Return Period A Pilot Study to Develop a Tool for Simplifying the Cloudburst Management in Gothenburg Master’s thesis in Master Programme Infrastructure and Environmental Engineering ALICIA COOPS AND FANNY KARLSSON DEPARTMENT OF ARCHITECTURE AND CIVIL ENGINEERING CHALMERS UNIVERSITY OF TECHNOLOGY Gothenburg, Sweden 2023 www.chalmers.se www.chalmers.se Master’s thesis 2023 How Pluvial Floods in Urban Areas Vary with Rain Return Period A Pilot Study to Develop a Tool for Simplifying the Cloudburst Management in Gothenburg ALICIA COOPS FANNY KARLSSON Department of Architecture and Civil Engineering Division of Water Environment Technology Chalmers University of Technology Gothenburg, Sweden 2023 How Pluvial Floods in Urban Areas Vary with Rain Return Period A Pilot Study to Develop a Tool for Simplifying The Cloudburst Management in Gothenburg ALICIA COOPS FANNY KARLSSON © ALICIA COOPS, FANNY KARLSSON 2023. Master’s Thesis 2023 Department of Architecture and Civil Engineering Chalmers University of Technology SE-412 96 Gothenburg Telephone +46 31 772 1000 Cover: Floods with depths above or equal to 0.2 m due to a 100-year rain within structure plan West in Gothenburg. Typeset in LATEX, template by Kyriaki Antoniadou-Plytaria Printed by Chalmers Reproservice Gothenburg, Sweden 2023 iii How Pluvial Floods in Urban Areas Vary with Rain Return Period Master’s thesis in Master Programme Infrastructure and Environmental Engineering ALICIA COOPS FANNY KARLSSON Department of Architecture and Civil Engineering Division of Water Environment Technology Chalmers University of Technology Abstract Urban floods are the most frequently occurring natural disasters, posing significant threats to cities worldwide. The risk for pluvial floods (i.e. floods due to intense rain- fall) is increasing, and thereby, several initiatives have been established worldwide. The aim of this study is to develop a tool to simplify the process of implementing a cloudburst area in different types of residential areas by estimating a manageable rain return period. The study evaluated floods generated by rain from return pe- riods in the range of 10-100 years, in four different residential areas with nearby cloudburst areas, all located in the City of Gothenburg. Further, the study included an evaluation of the site characteristics of each residential area. Ten rain events (each representing a different return period) were simulated using the hydrodynamic modeling software MIKE+. Simulations were conducted both without and with cloudburst areas. From the results of the simulations without cloudburst areas, a relation between flood and rain return period was established for each residential area separately. No general relation was identified for all inves- tigated areas. However, a correlation was found for two of the areas consisting of townhouses. Based on the correlation between the two areas, a framework for a tool was developed. The developed tool provides an estimation of the manageable rain return period due to the implementation of a cloudburst area in residential areas with townhouses. From the study, it is concluded that to accomplish full utilization of the cloudburst area it is necessary to evaluate both if other measures are required and the most suitable location of the cloudburst area. From the evaluation of site characteristics, different physical parameters were iden- tified to influence the resilience against floods in different areas, e.g. sewer network capacity, building structure, and depression storage capacity. Further, this study concluded that topography had a distinct impact on flooding in all areas. Keywords: flood management, hydrodynamic modeling, MIKE+, pluvial flood, rain return period, urban flood. iv Acknowledgements This thesis is the final part of the Master Programme Infrastructural and Environ- mental Engineering at Chalmers University of Technology in Gothenburg, Sweden. The thesis has been conducted at the Division of Water Environment Technology at the Department of Architecture and Civil Engineering. We would like to thank our examiner Mia Bondelind and our supervisor Sebastien Rauch for your guidance and support. Also, our opponents Klara Djerf and Josefin Hasselberg for helpful inputs and comments. This thesis would not have been possible without the guidance from Christofer Karlsson at DHI and Dick Karlsson at Stadsutveckling, Enheten för dagvatten och skyfall at the City of Gothenburg. We would like to thank you for your support and interest in our work and for giving us the possibility to be creative and shape the thesis following our interest. You have both supported us during the process and contributed with good discussions and new perspectives. We would also like to thank DHI for allowing us to use MIKE+ and contributing with student licenses, and for sharing the model of structure plan West with us. A special thanks to Lena Abrahamsson at IT support at Chalmers University of Technology in Gothenburg. Without your help with the student computers, this thesis would not have been possible. Alicia Coops & Fanny Karlsson, Gothenburg, June 2023 vi Acronyms Below is the list of acronyms that have been used throughout this thesis: CBA Cost-Benefit Analysis CDS Chicago Design Storm CRED Centre for Research on the Epidemiology of Disasters DHI Danish Hydraulic Institute EC European Commission EPA United States Environmental Protection Agency EPA-SWMM Environmental Protection Agency Storm Water Management Model EU European Union GIS Geographical Information System GUFIM GIS-based Urban Flood Inundation Model HFSA Hierarchical Filling-and-Spilling Algorithm IDF Intensity-Duration-Frequency IPCC International Panel of Climate Change LNHE Laboratoire National d’Hydraulique MCA Multi-Criteria Analysis MSB Myndigheten för Samhällsskydd och Beredskap (Swedish Authority for Social Security and Preparedness) SMHI Sveriges Meteorologiska och Hydrologiska Institut (Swedish Meteorological and Hydrological Institute) UN United Nations UNISDR United Nations Office for Disaster Risk Reduction USACE United States Army Corps of Engineering WHO World Health Organisation viii Nomenclature Below is the nomenclature of parameters and variables that have been used through- out this thesis: Parameters φ Runoff coefficient [-] φshort Runoff coefficient for short-term precipitation [-] φ10 Runoff coefficient for a 10-year rain [-] φ100 Runoff coefficient for a 100-year rain [-] cf Climate factor [-] F Return period [year] T Return period [year] Tr Duration [min] Variables dT Average of maximum depths for a T -year rain [m] d≥0.2m,T Average of maximum depths ≥ 0.2 m for a T -year rain [m] FImax,T Maximum flow intensity for a T -year rain [m3/s/m] iF Rain intensity [l/(s · ha)] R1,T Ratio of the runoff volume with depths ≥ 0.2 m for a T -year rain and the runoff volume with depths ≥ 0.2 m for a 100-year rain [-] R2,T Ratio of the runoff volume with depths ≥ 0.2 m for a T -year rain and the total runoff volume for a T -year rain [-] Vtot,T Total runoff volume for a T -year rain [m3] Vd≥0.2m,T Runoff volume with depths ≥ 0.2 m for a T -year rain [m3] x Contents List of Acronyms viii List of Nomenclature x List of Figures xiv List of Tables xvi 1 Introduction 1 1.1 Aim . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2 Background 4 2.1 Pluvial floods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.2 Rain concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2.1 Return period . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2.2 Statistical description of rain events . . . . . . . . . . . . . . . 5 2.2.3 Climate factor . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.3 Physical parameters influencing flooding . . . . . . . . . . . . . . . . 7 2.3.1 Topography . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.3.2 Infiltration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.3.3 Sewer network . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.3.4 Building structure . . . . . . . . . . . . . . . . . . . . . . . . 8 2.4 Flood management . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.5 Flood modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.5.1 Hydrodynamic models . . . . . . . . . . . . . . . . . . . . . . 10 2.5.1.1 Hydrodynamic software . . . . . . . . . . . . . . . . 11 2.5.2 GIS-based models . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.6 Previous research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 3 Methodology 17 3.1 Literature study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 3.2 Research design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 3.3 Case study area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 3.3.1 Selection of risk zones . . . . . . . . . . . . . . . . . . . . . . 21 3.3.2 Selection of site characteristics . . . . . . . . . . . . . . . . . . 23 3.3.2.1 Topography . . . . . . . . . . . . . . . . . . . . . . . 24 xi Contents 3.3.2.2 Infiltration . . . . . . . . . . . . . . . . . . . . . . . 27 3.3.2.3 Runoff coefficient . . . . . . . . . . . . . . . . . . . . 28 3.3.2.4 Sewer network . . . . . . . . . . . . . . . . . . . . . 29 3.4 Modeling in MIKE+ . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 3.4.1 Original model from DHI . . . . . . . . . . . . . . . . . . . . . 30 3.4.2 Simulations conducted in this thesis . . . . . . . . . . . . . . . 31 3.4.2.1 Selection of simulations . . . . . . . . . . . . . . . . 32 3.4.2.2 Modifications made in the original model . . . . . . . 32 3.4.2.3 Model uncertainties . . . . . . . . . . . . . . . . . . 33 3.5 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 3.5.1 Selection of results . . . . . . . . . . . . . . . . . . . . . . . . 34 3.5.2 Extraction of depth, d≥0.2m,T and dT . . . . . . . . . . . . . . 35 3.5.3 Calculation of flooded volume, Vd≥0.2m,T and Vtot,T . . . . . . . 36 3.5.4 Calculation of R1,T and R2,T . . . . . . . . . . . . . . . . . . . 36 3.5.5 Methodology to develop the tool . . . . . . . . . . . . . . . . . 37 4 Results & Discussion 40 4.1 Current situation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 4.1.1 Runoff coefficients . . . . . . . . . . . . . . . . . . . . . . . . . 40 4.1.2 Maximum flow intensities, FImax,T , current situation . . . . . 41 4.1.3 The flood in each risk zone, current situation . . . . . . . . . . 43 4.1.4 R1,T for each residential area . . . . . . . . . . . . . . . . . . . 45 4.1.5 R2,T for each residential area . . . . . . . . . . . . . . . . . . . 46 4.1.6 Discussion of current situation . . . . . . . . . . . . . . . . . . 47 4.1.6.1 Furåsen and Högen . . . . . . . . . . . . . . . . . . . 47 4.1.6.2 Majvallen . . . . . . . . . . . . . . . . . . . . . . . . 48 4.1.6.3 Såggatan . . . . . . . . . . . . . . . . . . . . . . . . 50 4.2 Future situation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 4.2.1 Maximum flow intensities, FImax,T , future situation . . . . . . 51 4.2.2 The flood in each risk zone, future situation . . . . . . . . . . 51 4.2.3 Vd≥0.2,100 and Vtot,100, current and future situations . . . . . . . 52 4.2.4 Discussion of future situation . . . . . . . . . . . . . . . . . . 53 4.3 Development of tool . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 4.3.1 Selection of risk zones to include in the tool . . . . . . . . . . 54 4.3.2 Final tool . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 4.4 Research uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . 57 5 Conclusion & further research 60 5.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 5.2 Further research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 References 63 A Appendix: Study visit I B Appendix: Catchment areas IX xii Contents C Appendix: Runoff coefficient XI D Appendix: Simulation details XIII xiii List of Figures 1.1 Number of flood disaster worldwide per year. . . . . . . . . . . . . . . 1 2.1 Example of a 100-year CDS rain. . . . . . . . . . . . . . . . . . . . . 6 2.2 Correlation between water depth and rain return period. . . . . . . . 14 2.3 Correlation between elements and rain return period. . . . . . . . . . 15 2.4 Correlation between flooded area and rain return period. . . . . . . . 16 3.1 A conceptual description of the research design used in this study. . . 19 3.2 Map over the structure plans in Gothenburg. . . . . . . . . . . . . . . 20 3.3 The selected risk zones with recommended cloudburst facilities. . . . 22 3.4 The selected risk zones dived by residential area and cloudburst area. 23 3.5 Topography of each risk zone. . . . . . . . . . . . . . . . . . . . . . . 25 3.6 Depressions within each risk zone. . . . . . . . . . . . . . . . . . . . . 27 3.7 The sewer network in each risk zone. . . . . . . . . . . . . . . . . . . 29 3.8 The simulation setup used in the original model. . . . . . . . . . . . . 31 3.9 A conceptual model of the tool. . . . . . . . . . . . . . . . . . . . . . 38 4.1 FImax,10 and FImax,100 for the current situation in Furåsen. . . . . . . 41 4.2 FImax,10 and FImax,100 for the current situation in Högen. . . . . . . . 42 4.3 FImax,10 and FImax,100 for the current situation in Majvallen. . . . . . 42 4.4 FImax,10 and FImax,100 for the current situation in Såggatan. . . . . . 43 4.5 Maximum flood depths ≥ 0.2 m for a 10- and 100-year rain for the current situation in Furåsen. . . . . . . . . . . . . . . . . . . . . . . . 43 4.6 Maximum flood depths ≥ 0.2 m for a 10- and 100-year rain for the current situation in Högen. . . . . . . . . . . . . . . . . . . . . . . . . 44 4.7 Maximum flood depths ≥ 0.2 m for a 10- and 100-year rain for the current situation in Majvallen. . . . . . . . . . . . . . . . . . . . . . . 44 4.8 Maximum flood depths ≥ 0.2 m for a 10- and 100-year rain for the current situation in Såggatan. . . . . . . . . . . . . . . . . . . . . . . 45 4.9 R1,T for each return period T and residential area separate. . . . . . . 46 4.10 R2,T for each return period T and residential area separate. . . . . . . 47 4.11 FImax,100 for all risk zones for the future situation. . . . . . . . . . . . 51 4.12 Maximum flood depths ≥ 0.2 m for each risk zone in the future situation. 52 4.13 Vd≥0.2m,100 in the residential before and after implementing cloudburst areas. Vtot,100 in the cloudburst area before and after implementation. 53 4.14 R1,T in relation to return period for Furåsen and Högen, and the interpolated trend. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 xiv List of Figures 4.15 The interface of the final tool. . . . . . . . . . . . . . . . . . . . . . . 56 A.1 Location and direction of images of Furåsen. . . . . . . . . . . . . . . I A.2 Images from the study visit to Furåsen. . . . . . . . . . . . . . . . . . II A.3 Location and direction of images of Högen. . . . . . . . . . . . . . . . III A.4 Images from the study visit to Högen. . . . . . . . . . . . . . . . . . . IV A.5 Location and direction of images of Majvallen. . . . . . . . . . . . . . V A.6 Images from the study visit to Majvallen. . . . . . . . . . . . . . . . . VI A.7 Location and direction of images of Såggatan. . . . . . . . . . . . . . VII A.8 Images from the study visit to Såggatan. . . . . . . . . . . . . . . . . VIII B.1 The catchment areas for Furåsen and Högen. . . . . . . . . . . . . . . IX B.2 The catchment area of Majvallen and Såggatan. . . . . . . . . . . . . X C.1 Graphs used to estimate φ10y and φ100y. . . . . . . . . . . . . . . . . XII xv List of Tables 2.1 Strengths and limitations for different hydrodynamic software. . . . . 12 3.1 Size of residential and cloudburst area in each risk zone. . . . . . . . 23 3.2 Catchment area characteristics for all risk zones. . . . . . . . . . . . . 24 3.3 The inclination of each risk zone. . . . . . . . . . . . . . . . . . . . . 26 3.4 Percentage of impermeable land cover in the catchment areas, risk zones, and residential areas for each risk zone. . . . . . . . . . . . . . 27 3.5 The modeled simulations for each situation. All return periods (T ) are simulated with cf = 1.2. . . . . . . . . . . . . . . . . . . . . . . . 32 3.6 Description of the variables used to describe the results. . . . . . . . . 35 3.7 Functions for the graphical representation and corresponding R2, for each risk zone. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 4.1 Runoff coefficients for each catchment area. . . . . . . . . . . . . . . . 40 4.2 Runoff coefficeint for each risk zone. . . . . . . . . . . . . . . . . . . . 41 4.3 Flooded volume Vd≥0.2m,T for each risk zone and simulated return period T (current situation). . . . . . . . . . . . . . . . . . . . . . . . 45 4.4 Flooded volume Vtot,T for each risk zone and simulated return period T (current situation). . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 C.1 Standard values of runoff coefficient for short-term precipitation. . . . XI C.2 Runoff coefficient used to calculate comprehensive values for, short- term precipitation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . XI D.1 Simulated rain loads for each return period. . . . . . . . . . . . . . . XIII D.2 Simulated rain volumes for each return period. . . . . . . . . . . . . . XIV D.3 Initial water content for each return period. . . . . . . . . . . . . . . XIV xvi 1 Introduction Floods are the natural disasters with the most severe consequences considering hu- man health and economic loss, according to the World Health Organization (WHO) (2013). The organization defines floods as "when an overflow of water submerges land that is usually dry" (WHO, 2013). Another definition, used by United Nations (UN) (2023), is "a general and temporary condition of partial or complete inundation of normally dry land areas from overflow of inland or tidal waters from the unusual and rapid accumulation or runoff of surface waters from any source". The initial cause for flooding to occur varies, however, the most common are intense rainfall, water-level rise, river flooding, or groundwater rise (Houston et al., 2011). Centre for Research on the Epidemiology of Disasters (CRED) has compiled the number of flood events classified as disasters (either at least 10 death or 100 people affected, or requiring international help (CRED, n.d.-a)), see Figure 1.1. In the figure, it can be seen that the frequency increases with time. According to the International Panel of Climate Change (IPCC) (2021), intensive rain will become more intensive and occur more often due to climate change. Consequently, the risk of floods has increased and is expected to increase even more in the future. Figure 1.1: Number of flood disasters worldwide per year, 1970-2022 (based on data from CRED (n.d.-b)). 1 1. Introduction Urban floods are the most frequently occurring natural disaster and pose a significant threat to cities all over the world (Eldho et al., 2018), resulting in disturbances to infrastructure services and socioeconomic activities (Zhou et al., 2019). Both more heavy precipitation but also urbanization will increase the risk of urban floods. Urbanization not only increases the area exposed to floods but also the amount of intensive rains falling on cities (IPCC, 2021). Due to the increased risk of floods, extensive initiatives have been implemented worldwide to increase resilience in cities and these highlight the vitality of addressing how floods will affect an urban area (European Commission, 2023; Jha et al., 2012; Koutsoyiannis & Papalexiou, 2017; UNISDR, 2002). For instance, to understand the correlation between cloudburst events and flood characteristics (Koutsoyiannis & Papalexiou, 2017). Gothenburg is one example of an urban area with an increased risk of flooding in the future due to increased precipitation, more cloudburst events, sea-level rise, and densification (Stadsbyggnadskontoret, 2019). To enable a dense city with increased resilience against flooding, the municipality has determined several objectives to strive for (Stadsbyggnadskontoret, 2019). Following these objectives, 15 structure plans have been established considering different geographical areas and these aim to concretize how extreme rain events will affect the area and how to prevent such scenarios (Kretslopp och vatten, 2021c). The plans are meant to work as guidance for stakeholders considering the implementation of cloudburst facilities to minimize the risk for and the consequences of flooding (Stadsbyggnadskontoret, 2019). As a complement to the structure plans, Rosén & Nimmermark (2018) developed Flood- Man - Sustainable Flood Management Assessment Tool, a tool that aims to simplify the process of performing cost benefits analysis (CBA) and multi-criteria analysis (MCA) when planning new flood infrastructure. In the design process today, the structure plans are used to evaluate the risk of floods while FloodMan is used to eval- uate the advantages and disadvantages of risk-reducing measures. However, there is no standardized method for evaluating the decrease in risk due to the implementa- tion of a risk-reducing measure. 1.1 Aim The aim of the thesis is to develop a tool to simplify the process of implementing a cloudburst area in different types of residential areas by estimating a manageable rain return period. The objective is to develop the tool by evaluating flooded volumes generated by rain from return periods in the range of 10-100 years, in different residential areas. The following research questions will be answered to achieve the aim of the thesis: • Is it possible to create a tool to estimate the increase in flood resilience due to the implementation of a cloudburst area? • Is there a general relationship between flooded volume and rain return period for the selected areas? • Which site characteristics impact the flooding in the areas? 2 1. Introduction 1.2 Limitations The following limitations have been made: • This study is limited to four residential areas from structure plan West in Gothenburg. All four areas include a cloudburst area that is not incorporated in larger cloudburst facility networks. • The types of residential areas are limited to three different types i.e. townhouse areas and apartment building areas with- and without enclosed yards. • The study only considers pluvial floods, i.e. floods that occur due to rainfall. • The study will evaluate the current situation (2023). The simulated rain events will be customized with a climate factor to include future climate changes in the cloudburst events investigated. 3 2 Background The following chapter will provide general information about pluvial flooding. Con- cepts that are used to describe rain and parameters that affect the severity of a flood will be described. Further, international and national flood management will be ex- plained. This chapter also includes a summary of the concept of flood modeling and some of the tools that are available. At the end of the chapter, previous research similar to this thesis is presented. 2.1 Pluvial floods The term flood includes coastal flood, flash flood, glacial lake outburst flood, pluvial flood, river flood (fluvial), sewer flood, and urban flood (Seneviratne et al., 2012). Pluvial floods occur due to intensive rain events and are described by Prokic et al. (2019) as floods that occur before the runoff can enter either a recipient, the sewer system, or be infiltrated into the ground. In research, pluvial floods are less studied than fluvial and coastal floods since these often are more extensive considering the affected area and duration (Prokić et al., 2019). The risk for pluvial floods has increased and will, according to IPCC (2021) continue to do so. In addition, Prokic et al. (2019) describe that pluvial floods often have larger economic consequences than fluvial and coastal floods. Extreme rain events can happen everywhere, however, serious consequences will most likely arise in urban areas (Douglas et al., 2010; Houston et al., 2011; Jha et al., 2012; The European Parliament and the Council, 2007). Walczykiewicz & Skonieczna (2020) presents several possible consequences of pluvial floods, for instance: • Damage to buildings, estates, and roads • A reduced capacity in transport- and infrastructure systems • Disturbances in waste- and drinking-water management Currently, most of the pluvial floods in Sweden occur during summer (SMHI, 2023). The yearly distribution of precipitation in Sweden will, according to the Swedish Authority for Social Security and Preparedness (MSB), change as a consequence of climate changes (MSB, 2013b). In the future, there will be less total precipitation during the summer months and more total precipitation for the winter months (MSB, 4 2. Background 2013b). However, extreme rain will occur more frequently all year (even during the summer months), and hence, the risk of pluvial floods will increase (MSB, 2013b; WHO, 2013). 2.2 Rain concepts This section will include a description of different concepts commonly used to de- scribe rain events. The selection of concepts is based on the methodology for this thesis, hence concepts that are required to understand to be able to follow the thesis. Other concepts might be mentioned but not further described. 2.2.1 Return period Return period is defined by a period of time (time interval) and used to describe the probability for an event to occur (Svenskt Vatten, 2016). The concept has several applications, for instance, to describe the probability of a specific rain intensity or volume (Svenskt Vatten, 2016), and is a central element in water management and flood assessment (Vogel & Castellarin, 2016). The Swedish Meteorological & Hydrological Institute (SMHI) (2021) describes re- turn period as the average time between two events, a statistical measurement based on historical data from observations of extreme weather and series of measurements. From the return period, it is possible to calculate the probability of an event to oc- cur, for instance, the probability of 100-year rain is 1 % each year, independently of other events. Simply explained, there is 1 % risk of a 100-year rain each year, regardless if there where a 100-year rain last year. However, this might also result in no extreme rain of this magnitude during a period of 100 years. 2.2.2 Statistical description of rain events To be able to statistically describe rain events with different return periods it is nec- essary to process data from historical rainfall observations (Svenskt Vatten, 2011). In Sweden, the process starts with the establishment of so-called block rains where the rain events are sorted into different blocks considering the maximum mean value of a given intensity. These block rains are thereafter used to develop Intensity- Duration-Frequency (IDF) diagrams (Svenskt Vatten, 2011). An IDF diagram de- scribes the mathematical relationship between rain intensity, rain duration, and return period (Sun et al., 2019). Based on the IDF diagrams, different equations to calculate rain intensity have been established (Svenskt Vatten, 2011). In Sweden, Equation 2.1 is recommended to use for a rain duration of up to 24 hours. (Svenskt Vatten, 2011; Svensson et al., 2020). iF = 190 · 3 √ (F · 12) · ln(Tr) T 0.98 r + 2 (2.1) iF : Rain intensity [l/s/ha] 5 2. Background F : Return period (T in this study) [year] Tr: Duration [min] To model rain it is required to describe how the rain intensity varies for a time serie. For this, a hyetograph is used which is a plot of the average intensity of rainfall against the time interval that is constructed based on either historical rains or design rains (Svenskt Vatten, 2011). A commonly used design rain from IDF diagrams is the Chicago Design Storm (CDS-rain), first established by Keifer & Chu (1957). The CDS-rain is designed using Equation 2.1 to establish a graph where the rain peak (intensity maximum) is located in the middle of the curve (Svenskt Vatten, 2011). The graph is constructed based on maximum rain intensities for different duration and relates to the occurrence of a peak during a rain event and the amount of rain before and after this peak (Marsalek & Watt, 1984) An example of a graph to present a CDS-rain can be seen in Figure 2.1. Figure 2.1: Example of a graph that presents the rain intensities (mm/h) for a 100-year CDS-rain with a duration of 240 min (based on Svenskt Vatten (2016)). 2.2.3 Climate factor Increased precipitation in the future is greatly associated with climate changes and according to SMHI, the rain intensity for a 10-year rain will increase by 15-30 % un- til the year 2100 (Eklund et al., 2015). To consider the impact of climate change in design rains, that are based on historical data, a climate factor (cf ) is used (Svenskt Vatten, 2016). Climate factors are established by estimations of future climate sce- narios and hence, the climate factor might differ depending on the scenario analysed. According to Svenskt Vatten (2016) and Gustafsson & Mårtensson (2017), it is suit- able to use a climate factor in the range of 1.2 to 1.5 when evaluating cloudburst in Sweden with a return period of 100 years and above. 6 2. Background 2.3 Physical parameters influencing flooding There are several physical parameters influencing the occurrence and characteristics of flooding (Jha et al., 2012; Prokić et al., 2019; SMHI, 2023). The following sections will present research regarding these parameters and their impact on floods in urban areas. 2.3.1 Topography Topographic factors include inclination, elevation, and depressions and are impor- tant spatial characteristics that affect urban flooding (Zhang, 2020; Huang et al., 2019). Topography affects both infiltration capacity and generation and charac- teristics of runoff (i.e. velocity, directions, and depths) (Qi et al., 2020). Further, the topography may contribute to increased flood volume by hindering water from reaching the sewer system if inlets are improperly located (Palla et al., 2018). Wal- czykiewicz & Skonieczna (2020) state topography as one of the two most significant aspects (in addition to surface properties) that influence the risk for urban flooding. Topography is especially important for low-lying areas and depressions with large contributing areas (Qi et al., 2020). Walczykiewicz & Skonieczna (2020) define de- pressions as the most vulnerable places in urban areas considering floods. The vul- nerability of depressions is defined by the size and slope of the area and surrounding areas that contribute to the flood (Qi et al., 2020). 2.3.2 Infiltration The influence of infiltration on urban flooding has been analyzed by several re- searchers (K. Luo & Zhang, 2022; Ren et al., 2020; Qi et al., 2020; Walczykiewicz & Skonieczna, 2020; Wang et al., 2022), and according to Alshammari et al. (2023) insufficient infiltration capacity is one of the dominant factors. Infiltration capacity depends on the characteristics of the soil, e.g. structure, porosity, land cover, and texture (Alshammari et al., 2023). Green areas are associated with a high infiltra- tion capacity, however, during intense rains the infiltration capacity will decrease due to saturation resulting in surface runoff (Svenskt Vatten, 2016). Impervious areas influence the urban water cycle processes resulting in decreased infiltration capacity and emerged urban floods (Ren et al., 2020). Since urban areas generally are covered by a large fraction of impervious surfaces (e.g. roads, asphalt surfaces, and buildings), a majority of the rain will result in surface runoff (Ren et al., 2020). Walczykiewicz & Skonieczna (2020) state that impervious surfaced areas are one of the main causes of urban flooding. In a study by Wang et al. (2022), imperviousness, and green-space-ratio were identified as the overall dominant factors influencing urban flooding. K. Luo & Zhang (2022) analysed how changes in land cover in China, between 1977 and 2018, have affected the risk of urban floods. According to the study, the amount of impervious surfaces has increased by 140 % for the observed period. The increase in imperviousness resulted in a decreased capacity of cities to reduce surface runoff, by 13 % (K. Luo & Zhang, 2022). 7 2. Background Urban areas in Sweden have, according to MSB (2013b), an infiltration capacity equivalent to a 10-years rain (no climate factor). This indicates an insufficient ca- pacity during heavy precipitation and hence, it is important to ensure that the infiltration capacity enhances or at least remains (MSB, 2013b). The Swedish Na- tional Board of Housing, Building, and Planning, Boverket, states that it might be required to restrict the increase of impermeable areas when establishing detailed developments plans and instead implement areas for enhanced infiltration to ensure resilient urban areas (Boverket, 2010). 2.3.3 Sewer network The sewer network influences urban flooding, mainly due to insufficient capacity in most urban areas (Prokić et al., 2019). Evans et al. (2013) state that urbanization, rapid population growth, and the expansion of impermeable surface areas have led to a significant surge in demand for sewer systems for most urban areas. Com- monly there are two methods used for sewer networks, combined and separated. A combined system is when all water (waste, runoff, and drainage) is collected in one system, and a separate system is when wastewater is collected in one system and the remaining water is collected in another (Jha et al., 2012). Combined sewer systems are common in old sewer networks and Prokic et al. (2019) describes that urban areas with combined sewer systems generally are more vulnerable to flooding than urban areas with separated systems. One of the reasons for the lack of sewer capacity is that the sewer network has not been updated to the same extent as cities have developed (Jha et al., 2012). The Swedish sewer system was developed in the 19th century and since the 1950s, mainly separate systems have been installed to ensure better management of stormwater (Svenskt Vatten, 2016). Although, approximately 13 % of the Swedish sewer network consists of combined systems and these are often located in central parts of urban areas (Räddningsverket, 1997; Svenskt Vatten, 2016). The general sewer network in Sweden is designed to manage normal precipitation and, according to MSB (2013b), a properly designed sewer network is capable to handle the volume of a 10-year rain. 2.3.4 Building structure Urban floods are highly influenced by spatial characteristics which commonly are associated with infiltration. However, urban forms, building structures, and density also influence urban flooding but have not received as much attention (X. Li et al., 2021). Urban forms (e.g. congestion, location in relation to streets, building height) strongly influence the mean flood depths in urban areas (Bruwier et al., 2020). The most important factor, according to Bruwier et al. (2020), is the building side setback (i.e. the distance between the building and the road) which influences both the water storage and outflow discharge (Bruwier et al., 2020). Further, building height and density are potential driving factors for urban floods since these are associated with impermeable areas and hence the generation of runoff (Qi et al., 2020; Wang et al., 2022). 8 2. Background 2.4 Flood management Inappropriate urban planning and lacking communication between stakeholders re- sult in an increased risk for hazardous floods (Jha et al., 2012). Hence, functioning flood management is important for urban areas that strive for resilience against floods. The following section presents an overview of the flood management agree- ments in the world, Europe, and Sweden followed by a brief description of the agreements set by the City of Gothenburg. In 2004, UN released a report on how to reduce losses due to flooding (UNISDR, 2002). The report aims to guide decision-makers to increase resilience against flood- ing (UNISDR, 2002). In 2012, the World Bank released Cities and Flooding with guidance for stakeholders considering urban flood risk management (Jha et al., 2012). Further, in 2015, the Sendai Framework for Disaster Risk Reduction: 2015- 2030, was established by the United Nations Office for Disaster Risk Reduction (UNISDR) to increase knowledge and reduce the risk of disaster globally (UNISDR, 2015). Considering floods, the framework defines the importance of simplifying flood risk management on a national and local level (UNISDR, 2015). In the European Union (EU), flood management is governed by the Floods Direc- tive 2007/60/EC which was established in 2007 (The European Parliament and the Council, 2007). Following the directive, each member state is obliged to (i) map areas vulnerable to floods, (ii) analyse the risks (considering human health, envi- ronment, cultural heritage, and economic loss) in each area, and (iii) establish an action plan to reduce the risks for the areas. Further, the directive gives guidance on which rain events and parameters to analyse, e,g rain events with a return period of 100 years or larger, and flood extension, depth, and flow (The European Parliament and the Council, 2007). The European Commission (EC) (2023) declares that the Floods Directive shall be an iterative process that should be continuously updated in six years cycles (i.e. all three steps should be accomplished every six years). In Sweden, the obligations stated by the Flood Directive are governed by several regulations. In 2009, the Regulation of flood risks (SFS 2009:956 ) (Försvarsdepartementet, 2009) was adopted which aims to reduce the negative im- pacts of floods. In SFS 2009:956, MSB is defined as responsible for the preliminary analysis of flood risks and flood mapping and the County Administrative Boards for the development of action plans considering flood risks. To guide the County Administrative Boards, MSB established regulations considering flood risk manage- ment (MSBFS 2013:1 ) in 2013 (MSB, 2013a). The municipalities are responsible for flood management when developing comprehensive and detailed development plans, according to PBL 2010:900 (Landsbygds- och infrastrukturdepartementet, 2010), and as property owners, according to Jordabalk 1970:994 (Justitiedepartementet, 1970). To guide the municipalities to fulfill their responsibilities, MSB released a report on how to work with cloudburst mapping and flood prevention in urban areas in 2016 (Gustafsson & Mårtensson, 2017). In the guidance the process of cloudburst management is divided into planning, cloudburst mapping, impact analysis, devel- oping structure plans, planning of measures, contingency planning, and follow-up, 9 2. Background and guidance on how to proceed is given for each part (Gustafsson & Mårtensson, 2017). The City of Gothenburg is, as the municipality, responsible for flood management when developing comprehensive and detailed development plans. Following this, a supplement to the comprehensive plan that considers flood risks was adopted in 2019 (Stadsbyggnadskontoret, 2019). In the supplement, current and future risks are described and strategies to reduce these (e.g. structure plans) are presented. In addition to the comprehensive plan, a cloudburst agreement was initiated between several departments in the city in 2021 (Göteborgs Stad, 2021). The agreement aims to divide the responsibilities considering cloudburst and flood management in the city and clarify the decision-making process (Göteborgs Stad, 2021). 2.5 Flood modeling To analyse floods, two tools are often mentioned, hydrodynamic models and Geo- graphical Information System (GIS) (Seenath et al., 2016). The difference between the tools is that hydrodynamic models involve water movement and GIS tools do not, instead GIS tools are used to display data by mapping (Seenath et al., 2016). GIS is mostly used for flood mapping, risk mapping, and hazard assessments (Seenath et al., 2016; Di Salvo et al., 2018). Hydrodynamic models are commonly used for flood-related engineering (e.g. flood forecasting) and are more suitable to be used for scenario analysis (Teng et al., 2017). The following sections will include a description of both tools and examples of software. 2.5.1 Hydrodynamic models Hydrodynamic models are mathematical models that simulate water movement, specific flow rates, and water depth distribution, by solving equations formulated by applying laws of physics (P. Luo et al., 2022; Teng et al., 2017; Randa et al., 2022). Hydrodynamic models could be applied for different dimensions: one dimensional (1D), two dimensional (2D), three dimensional (3D), and coupled 1D-2D (Randa et al., 2022). For 1D hydrodynamic models, it is assumed that the flow is in one direction, and the flow velocity is homogeneous (Randa et al., 2022). The basis for the model is to represent flow as a series of cross-sections towards the flow direction and the model uses the Shallow Water Equations (Randa et al., 2022; Teng et al., 2017). These models are the simplest representation of flow and can be used in various hydraulic situations where the flow is comparable to one dimension, e.g. open channels and pipes (Teng et al., 2017). One advantage with 1D models is due to the low input re- quirements resulting in a simple model structure (P. Luo et al., 2022). However, the low input requirements also limit the broad understanding of hydrological processes (Randa et al., 2022). The 2D hydrodynamic models are the most common setup for flood mapping and flood prediction (Randa et al., 2022). These models represent the floodplain as a 10 2. Background 2D field by using the two-dimensional Shallow Water Equations for estimating the horizontal velocity and the depth of the flow (Teng et al., 2017). In comparison to the 1D models, the 2D models provide more information resulting in increased accuracy (P. Luo et al., 2022). Additional advantages are the incorporation of small- scale topography in the model which has been demonstrated to impact the urban flooding (Randa et al., 2022). Coupled 1D-2D models combine the advantages of the two model types. An ap- plication for such models is by using the 2D models to model surface runoff and combining it with a 1D description of the pipe network (P. Luo et al., 2022). These types of models are more suitable for complex sites such as urban areas (P. Luo et al., 2022). The 3D models can be used to model vertical turbulence, spiral flow, and vortices (Teng et al., 2017). These models are more suitable for catastrophic floods such as tsunamis, flash floods, or dam breaks (P. Luo et al., 2022). The 3D models are complex and often stated to be unnecessary for urban flood modeling since 2D and 1D-2D models provide sufficient information (P. Luo et al., 2022). 2.5.1.1 Hydrodynamic software There are several hydrodynamic model software developed for pluvial modeling and it is possible to apply most of these for urban flood studies (Teng et al., 2017). However, the strength and limitations of each software need to be considered de- pending on the aim and application. Three examples of modeling software capable of modeling floods are MIKE+, TELEMAC, and HEC-RAS. Table 2.1 lists the lim- itations and strengths of the software based on literature obtained by Randa et al. (2022). MIKE+ is a hydraulic modeling software created by Danish Hydraulic Insti- tute (DH) in 2020, with the latest update in 2023, and is a combination of existing DHI software such as MIKE Urban and MIKE 21 (DHI, 2023a). Since MIKE+ is a new software, no studies have been accomplished considering the advantages and disadvantages of the software. Therefore, the strengths and limitations of MIKE Urban and MIKE 21 are presented. 11 2. Background Table 2.1: Summary of strengths and limitations for different hydrodynamic soft- ware (based on Randa et al. (2022)). (Published with CC BY-NC-ND 4.0.) Model name Developer Strength Limitations MIKE 21 DHI Capable of simulating flow characteristics. Applicable in flood dynamic simulations. Simulation time steps must be manually calibrated, to ensure model stability, more calibration needed. MIKE Urban DHI Integrated GIS capabilities. Applicable in simulating urban flows. Inability to capture some hydrodynamics such as shocks and supercritical flows during simulations. TELEMAC 2D LNHE Can simulate permanent and transient hydrodynamic conditions. Stable under specific conditions. HEC-RAS 2D USACE Wide references, wide range of applicability. Inability to perform water quality modeling in 2D flow areas. MIKE+ is based on the Shallow Water Equations and can be used as 1D, 2D, or coupled 1D-2D for modeling distribution-, wastewater- and stormwater networks, collection systems, river networks, and overland flows (DHI, 2023b). Since MIKE+ is a relatively new tool, there is limited literature on the application. However, there is extensive research found about MIKE 21 and MIKE Urban and their application in urban flooding. One example, similar to the objective of this thesis, is a study from Aalborg University where the aim was to analyze rainfall and flooding in relation to return periods in urban areas using both MIKE Urban and MIKE 21 (Tuyls et al., 2018). Apart from research applications, MIKE applications have been used by the City of Gothenburg to model flooding and establish the structure plans (Kretslopp och vatten, 2021c). TELEMAC-2D is a modeling software developed by Laboratoire National d’Hydraulique (LNHE) (Ata et al., 2014). The software is based on the Shallow Water Equations and the main application is for river and marine hydraulics (Ata et al., 2014). Since TELEMAC-2D commonly is used for coastal areas there is limited literature obtained about its application in urban areas (G. Li et al., 2022). There have been some studies conducted in urban areas though, an example is G. Li et al. (2022) where TELEMAC-2D was used for flood risk assessment. The research scope differs from the aim of this thesis, however, some similarities are found as different rain intensities depending on the return period are simulated. Some limitations are mentioned, such as not being able to model the drainage system. Although, Li et al. (2022) state that TELECMAC-2D is reliable for urban flood simulation. 12 2. Background The third example is HEC-RAS 2D which is a software developed by the US Army Corps of Engineering (USACE). The software can be used in either 1D, 2D, or cou- pled 1D-2D and solves the Shallow Water Equations and the Diffusion Wave Equa- tion (Brunner, 2023). There are several application possibilities for HEC-RAS-2D such as channel modeling, floodplain modeling, and dam breach modeling (Brunner, 2023). One advantage of HEC-RAS 2D is that it is free to access which could be a reason for its wide references (Randa et al., 2022). An application of HEC-RAS, similar to the topic of the thesis, is Rangari et al. (2019) who used it to analyse the flood risk in urban areas. Their aim was to develop a risk map of Hyderabad, India, by modeling rains with different return periods. Their result showed that, by using HEC-RAS, it is possible to create a general model used to generate risk maps applicable to any region with few input requirements. 2.5.2 GIS-based models GIS is used to display information, called spatial data, about the earth’s physical aspects in a geographical coordinate system (Unwin, 1996). Spatial data could be defined in different ways, such as vectors or rasters, and are used to describe the world with the help of lines and polygons (Unwin, 1996). GIS tools have multiple application possibilities and, in relation to flooding, it is mainly used for spatial analysis (Di Salvo et al., 2018). In contrast to hydrodynamic models, GIS tools are simpler and require less extensive information about the area of interest (Di Salvo et al., 2018). However, this also limits the applicability (Di Salvo et al., 2018). GIS is extensively adopted for flood modeling, however, not considered the most common method (Xing et al., 2022). Although, for flood mapping and flood risk as- sessments, GIS based models are commonly mentioned (Chen et al., 2009; Di Salvo et al., 2018; Xing et al., 2022). One example of such model is GIS based Urban Flood Inundation Model (GUFIM) that was developed by Chen et al. (2009). The study aimed to create a model for simplifying the identification of flood risks in urban areas. The model used standard data, IDF diagram, and contour maps, and resulted in a simplified less time-consuming model to be used for urban planning (Chen et al., 2009). Another GIS-based model is the more established Scalgo Live which is a browser-based modeling tool developed by the Danish company Scalgo in 2015 (SCALGO ApS, 2023). Scalgo Live is used by consultant companies and municipalities in Sweden and Denmark for urban planning, risk management, and climate adoption (SCALGO ApS, 2023). Scalgo Live has multiple application possi- bilities and uses topography and water volumes to determine the flooding in an area (SCALGO ApS, 2023). The Swedish consultant company Sweco used Scalgo Live for cloudburst mapping in Ängelholm municipality, Sweden (Theland, 2019) and described the limited computer times as advantageous. One limitation mentioned was that it does not provide details of water flow and no further analysis of rain duration as the analysis is static (Theland, 2019). 13 2. Background 2.6 Previous research This thesis aims to evaluate the relationship between the rain return period and floods in Gothenburg. During the literature review, few studies similar to this thesis have been found. This section will include an overview of the research available, similar to the aim of this thesis. Tuyls et al. (2018) analysed the correlation between rain return period and flooded volume and area in Lystrup, Denmark, using 35 historical extreme rain events in a 1D-2D coupled hydrodynamic model. The study defined the relation between rain intensity and flooded volume and area as complex and highly dependent on the characteristics of the studied area. Further, the identification of risk areas was stated as essential to enable efficient flood management (Tuyls et al., 2018). A limitation of the study was that just one area was analysed though, and Tuyls et al. (2018) recommend verifying these results for other areas as further research. Mediero et al. (2022) examined the correlation between the rain and flood return period in Pamplona, Spain, using a standard, and a stochastic approach. The stan- dard approach refers to the use of design rains in a 2D hydrodynamic flood mod- eling tool (Mediero et al., 2022). The stochastic approach analyses the probability of a specific water depth for each risk zone and storm event using a Hierarchical Filling-and-Spilling Algorithm (HFSA) called Safer_RAIN, developed by Samela et al. (2020). Figure 2.2 visualizes the results for one of the risk zones analysed as two graphs, one for each approach (Mediero et al., 2022). The graphs represent the correlation between the water depth and rain return period and show similar trends for the standard and stochastic approaches. Figure 2.2: The correlation between water depth (m) and rain return period (years) for a risk zone in Pamplona (Mediero et al., 2022). (Published with CC BY-NC-ND 4.0.) 14 2. Background Arosio et al. (2020) analysed flood risks in Mexico City using the 1D modeling tool EPA SWMM (a stormwater management model provided by the United States En- vironmental Protection Agency (EPA)). Figure 2.3 presents the results as a graph where the number of affected (directly or indirectly) elements are visualized in rela- tion to the rain return period. The elements considered were crossroads, fire stations, fuel stations, hospitals, schools, and blocks (Arosio et al., 2020). The graph shows an increasing trend for affected elements with an increasing rain return period. Figure 2.3: The correlation between elements affected (direct or indirect) (-) and rain return period (years), for Mexico City (Arosio et al., 2020). (Published with CC BY 4.0.) Following Arosio et al. (2020), Martina et al. (2020) examined the correlation between flooded areas and water levels for different rain return periods in Mexico City. The study was conducted by modeling CDS-rain for different return periods in EPA SWMM and by analysing water depths in GIS (Martina et al., 2020). Figure 2.4 visualizes the results where the graph shows that the flooded area increases with the rain return period. 15 2. Background Figure 2.4: The correlation between the flooded area (km2) and rain return period (years), for Mexico City (Martina et al., 2020). (Published with CC BY.) 16 3 Methodology This chapter outlines the methodology used in this master thesis. This thesis in- cluded a qualitative literature review, a case study, a quantitative data analysis of the results generated from modeling using MIKE+, and tool development. 3.1 Literature study This master thesis included a qualitative research part consisting of a systematic literature review to establish further knowledge in the research area. A qualitative research approach is beneficial for gaining more extensive knowledge in a research area (Bell et al., 2019). The literature search was accomplished using a set of key- words, e.g. cloudburst events, pluvial flooding, precipitation, return period, urban areas, topography, infiltration, sewer network, and hydrodynamic modeling. These keywords were used in different combinations and enabled both a more extensive knowledge in some specific areas (e.g. hydraulic modeling) and a broader under- standing in others (e.g. differences in how flooding affects urban areas). The search method snowballing was used to find additional literature. Snowballing is when new literature is collected from the sources of other relevant literature (Bell et al., 2019). The method was conducted on collected literature to increase the possibility of finding relevant information. The literature search was accomplished using Scopus and Google and included both articles from scientific journals and grey literature. Scientific articles were used to gather relevant knowledge within the research area. Also, to gain knowledge about studies with similar objectives as the thesis. Grey literature refers to materi- als from organizations, government departments, companies, consultants, and other non-academic associations (Kanu et al., 2020). Grey literature was required to estab- lish knowledge about the study area considering previous studies, local conditions, and the process of cloudburst infrastructure implementation in the city of Gothen- burg. Both primary and secondary sources were required to be able to answer the research questions. Primary sources include previous studies and the model with simulations received from Kretslopp och vatten while secondary sources included reviews. 17 3. Methodology 3.2 Research design The aim of this thesis is to develop a tool to simplify the process of implementing a cloudburst area in different types of residential areas by estimating a manageable rain return period. The tool is meant to be used for planning by providing the user an estimated return period of which a residential area is free from flooding if implementing a nearby cloudburst area. Since the tool aims to simplify the planning process when implementing cloudburst areas, it should be easy to use. Therefore, the tool is designed to require minor input information that is available. Following this, the tool was developed to be used with the flooded volume of a 100-year rain (with a climate factor of 1.2) since this can be extracted from the structure plans. The tool was developed by evaluating flooded volumes generated by rain from return periods in the range of 10-100 years, in different residential areas. The evaluation was conducted by establishing graphs which is a commonly used approach to describe the correlation between rain return period and other parameters (Arosio et al., 2020; Martina et al., 2020; Mediero et al., 2022). The tool was developed by following a research design that can be seen in Figure 3.1. The research design included the selection of areas and site characteristics to investigate. The selected areas were modeled in the hydrodynamic modeling software MIKE+. First, the areas were modeled without cloudburst areas and this is defined as the current situation, and secondly, with cloudburst areas defined as the future situation. For the current situation, different rain loads from rain return periods between 10 to 100 years were modeled, while for the future situation, only the rain load from a 100-year rain was modeled. The results from the simulation of the current situation were processed and analysed separately for each selected area. Further, an analysis of the site characteristics was conducted to provide an understanding of how these affected the results. From the results of the current situation, a correlation between rain return period and runoff volume was established and this was used to develop the tool. The results from the future situation were used to analyse the utilization of the cloudburst areas and hence, to evaluate the accuracy of the tool. 18 3. Methodology Figure 3.1: A conceptual description of the research design used in this study. The following sections include a description of all steps conducted in this study. An overview of the structure of the methodology and the content within each section is presented in the following list: • Case study area: The case study area is the City of Gothenburg and this section provides a brief description of the flood management in the city. • Selection of risk zones: In Gothenburg, four residential areas (defined as risk zones) were selected and used for the development of the tool. This section describes the process of choosing the risk zones and requirements that were considered. Further, this section includes a presentation of the selected risk zones. • Selection of site characteristics: To evaluate the similarities and dissim- ilarities between the results for the different risk zones, different site char- acteristics were analysed. In this section, the process of choosing which site characteristics to analyse is described. Further, a description of each site char- acteristic in each risk zone is presented coupled with observations from a study visit to all risk zones (conducted 9th of May, 2023). • Modeling in MIKE+: In this study, a MIKE+ model for flood mapping of Gothenburg was provided from DHI and Kretslopp och vatten. This section provides a general description of the provided model, the selections of simula- tions to model, and modifications made to the model for this study. Also, a description of the uncertainties in the model. 19 3. Methodology • Analysis: From the modeling, results were extracted and processed to develop the tool. This section includes a description of the extracted results, the methodology for processing the results, and the steps conducted to develop the final tool. 3.3 Case study area The City of Gothenburg serves as the case study in this thesis. Following the flood risk supplement to the comprehensive plan from 2019, the City of Gothenburg has initiated and developed several strategies to increase resilience against cloudbursts and floods. In Gothenburg, the department Kretslopp och vatten has developed 15 structure plans following the objectives defined in the comprehensive plan, see Figure 3.2 (Kretslopp och vatten, 2021c). The aim of structure plans is to clarify and support planning and to identify needed cloudburst infrastructure to minimize flood consequences (Kretslopp och vatten, 2021a). The structure plans include flood mapping due to a 100-year rain with a climate factor of 1.2 and also recommenda- tions for different cloudburst facilities (such as cloudburst areas, paths, and steering measures). Figure 3.2: Map over Gothenburg with the 15 structure plans displayed (Kretslopp och vatten, 2021b). (Published with approval from C. Karlsson DHI and D. Karlsson Kretslopp och vatten.) 20 3. Methodology 3.3.1 Selection of risk zones For each structure plan, a hydrodynamic model has been established to conduct flood mapping. In this thesis, the model from structure plan West (see number 13 in Figure 3.2) was used and hence, all risk zones are residential areas located within this structure plan. This structure plan was selected based on recommendations from DHI and Kretslopp och vatten (C. Karlsson & D. Karlsson, personal communication, January 23, 2023). Following the aim of this thesis, it was required to determine the number of risk zones to evaluate. Henrichs (2003) describes that a study should include an adequate number of perspectives, however, as few to avoid fatigue and to ensure that the process remains manageable. In this thesis, a total of four risk zones were selected based on evaluations of the structure plan West and in discussions with DHI and Kretslopp och vatten. The number of risk zones was considered suitable since it provided a diversity of types of residential areas which was required to fulfill the aim. Further, four risk zones enable an extensive comparison of the results and site characteristics of the zones. The risk zones were selected based on the following criteria: • Different types of residential areas. • A residential area with an adjacent recommended cloudburst area. • The cloudburst area decreases the flood within the residential area. • The cloudburst area is not included in a larger chain of cloudburst facilities. This means that the cloudburst area is designed to decrease the risk of flooding in the residential area without several other measures. The selected risk zones are Furåsen, Högen, Majvallen, and Såggatan. A study visit to each risk zone was carried out on the 9th of May 2023 and images of each zone can be seen in Figures A.2, A.4, A.6, and A.8 in Appendix A. Furåsen and Högen are located outside the city center while Majvallen and Såggatan are located in the central parts of Gothenburg. In Furåsen and Högen the main building type is townhouses with gardens. Majvallen and Såggatan consist of apartment buildings and planted courtyards near or enclosed by the buildings. The apartment buildings in Majvallen have an open structure while the apartment buildings in Såggatan have an enclosed structure. In Figure 3.3, all risk zones are visualized together with the cloudburst areas recommended by Kretslopp och vatten (2021b). In the figure, additional recommendations for cloudburst facilities near the residential area are visualized as well. 21 3. Methodology Cloudburst area Cloudburst path Steering measure (a) Furåsen Cloudburst area Cloudburst path Steering measure (b) Högen Cloudburst area Cloudburst path Steering measure (c) Majvallen Cloudburst area Cloudburst path Steering measure (d) Såggatan Figure 3.3: The selected risk zones with the cloudburst facilities recommended by Kretslopp och vatten (based on Kretslopp och vatten (2021b)). The legend describes the representation of cloudburst areas, paths, and steering measures. Each risk zone has been divided into a residential area and a cloudburst area, see Figure 3.4. The residential area was determined to be all buildings close to the recommended cloudburst area where the flood decreased when implementing the cloudburst area. The decrease in flood was evaluated using the tool Vatten i Staden (2023). Further, the cloudburst areas used in this study were the ones recommended in structure plan West. 22 3. Methodology Residential area Cloudburst area (a) Furåsen Residential area Cloudburst area (b) Högen Residential area Cloudburst area (c) Majvallen Residential area Cloudburst area (d) Såggatan Figure 3.4: The residential (pink outlined area) and cloudburst area (blue outlined area) within each risk zone. The size of all residential and cloudburst areas are presented in Table 3.1. The table displays similar sizes for all risk zones, however, Såggatan has the largest residential area and the smallest cloudburst area. Table 3.1: Size of residential and cloudburst area in each risk zone. Area Furåsen Högen Majvallen Såggatan Residential area [m2] 34924 47197 36983 50197 Cloudburst area [m2] 9152 12192 14672 7264 3.3.2 Selection of site characteristics The selection of site characteristics was determined based on the literature collected and presented in section 2.3. All characteristics that were determined to be analysed in this thesis have been identified by literature as important factors that influence urban floods. Further, these characteristics are commonly mentioned and used in flood analysis of urban areas. The selected characteristics are: 23 3. Methodology • Topography: Several studies state topography as one of the dominant factors influencing flooding (Huang et al., 2019; Qi et al., 2020; Walczykiewicz & Skonieczna, 2020; Zhang, 2020). • Infiltration: Infiltration highly influences urban floods and is associated with the high degree of imperviousness in cities (P. Luo et al., 2022; Ren et al., 2020; Qi et al., 2020; Walczykiewicz & Skonieczna, 2020; Wang et al., 2022). • Sewer network: Insufficient sewer networks increase urban floods and res- idential areas with combined sewer networks are more vulnerable (Evans & Orman, 2013; Jha et al., 2012; Prokić et al., 2019). The runoff coefficient is a factor used to describe the proportion of precipitation that results in runoff (Tegelberg & Svensson, 2013). The runoff coefficient is not a site characteristic, however, a parameter used to quantify different parameters (topography, infiltration, building structure). Thus, runoff coefficients provide easily comparable results, in terms of numbers, and therefore, runoff coefficients for all risk zones were calculated. In the following sections, the characteristics of all zones and the methodology used to calculate the runoff coefficient are described. 3.3.2.1 Topography The elevation of the catchment areas was analysed for each risk zone. The catchment area refers to the land area from which the runoff flow towards the same direction and in this case, ends up in the risk zone. Information (e.g. area, storage capacity, land use) regarding each catchment area was gathered in Scalgo Live and a shp-file was extracted for further analyse in QGIS. The inclination of each catchment area was calculated by dividing the difference in height (m) between the highest and lowest point of each catchment area by the shortest distance (m) between the points (both measured in QGIS). Table 3.2 displays the size, depression storage capacity, and inclination for the catchment area of each risk zone. The table shows large differences between the catchment areas where Furåsen is influenced by a catchment area that is significantly larger than the other areas, however, with the smallest inclination. Further, the table shows the smallest catchment area of Såggatan. The location and topography of the catchment areas are visualized in Figures B.1 and B.2, in Appendix B. Table 3.2: Catchment area characteristics for all risk zones. Furåsen Högen Majvallen Såggatan Area [m2] 3590000 300000 310000 130000 Depression storage capacity [m3] 129244 4765 783 4344 Inclination [%] 1.8 4.5 7.3 4.6 The topography within each zone was analysed using QGIS and can be seen in Figure 3.5. The common denominator for all zones is that the residential areas are 24 3. Methodology located in a depression when compared to the surroundings. The figures visualize a similar topography for Furåsen and Högen where the middle areas of each zone have the lowest elevation. In Majvallen, the residential area slopes towards the larger road on the west side, which is a low point, while Såggatan has the lowest point in the northern parts. Residential area Cloudburst area Building Road Elevation (a) Furåsen Residential area Cloudburst area Building Road Elevation (b) Högen Residential area Cloudburst area Building Road Elevation (c) Majvallen Residential area Cloudburst area Building Road Elevation (d) Såggatan Figure 3.5: Topography for each risk zone, arrows represent water flow direction © Lantmäteriet. The legend describes the representation of residential areas, cloud- burst areas, buildings, and roads. Also, the color legend is used to describe elevation reaching from +2 m (blue) to +100 m (red). In Figure 3.5 it is visualized that the proposed cloudburst areas in Furåsen and Högen (today larger grass areas) are situated upstream of the residential area. The topographical characteristics imply that runoff from northern upstream areas will pass the grass areas before entering the residential areas. Both Furåsen and Högen have the lowest elevation in the middle of the residential areas, and in Högen an additional cloudburst area is located here. This implies that the runoff entering the residential area of Högen will end up in this cloudburst area if it can flow unhindered. Majvallen is surrounded by steep areas with slopes directed against the zone in al- most all directions, see Figure 3.5. In the figure, it is visualized that the proposed cloudburst area (today a soccer field) in Majvallen is located upstream of the res- 25 3. Methodology idential area. The soccer field should therefore reduce the runoff flowing from the southern areas into the residential area. However, runoff from the southeastern and eastern areas will most likely end up in the residential area. The road west of the residential area is lower elevated than the residential area and will therefore hinder runoff from entering the residential area. The recommended cloudburst area (today a soccer field) at Såggatan is located downstream of the residential area. The topography in Figure 3.5 implies that runoff from all parts of the residential area will flow towards the soccer field. However, one building that extends over the entire area in the opposite direction from the inclination of the risk zone is visualized in Figure 3.5 and this building will hinder the runoff. The building was visited during the study visit where an opening in the middle of the apartment building was observed, hence runoff will be able to flow through the building, see Figure A.8 in Appendix A. The residential area in Såggatan is on the east side surrounded by higher elevated areas with slopes directed against the residential area. Runoff from these areas will most likely end up in the residential area since there is no upstream grass area that can reduce the runoff. The inclination of each risk zone was calculated using the same methodology as for the catchment areas and is presented in Table 3.3. Table 3.3: The inclination of each risk zone. Furåsen Högen Majvallen Såggatan Inclination [%] 1.0 1.4 2.8 2.6 Depressions larger than 20 m3 within each risk zone were evaluated in Scalgo Live. The information was exported to and illustrated in QGIS and could be obtained in Figure 3.6. The figure shows that a large part of the residential areas in especially Såggatan but also Högen are depressions. For Högen, the upstream grass area is also a depression. Furåsen has depressions in some parts of the upstream grass area and in the middle of the residential area. In Majvallen the figure shows no depression in the upstream soccer field and just smaller ones in the residential area. 26 3. Methodology (a) Furåsen (b) Högen (c) Majvallen (d) Såggatan Figure 3.6: Depressions (volume > 20 m3) within each risk zone © Lantmäteriet. The legend describes the representation of residential areas, cloudburst areas, and depressions. 3.3.2.2 Infiltration The land covers in the catchment areas, risk zones, and residential areas were anal- ysed. For the catchment areas, the amount of impermeable areas were extracted from Scalgo Live. For the risk zones and residential areas, the analyses were per- formed by observing the infiltration parameters used in the model. For both the risk zones and residential areas, the area that was classified as impermeable in the model where divided by the total area, and by this, the percentage of impermeable land cover in each area was calculated. The percentages of impermeable land cover in the catchment areas, risk zones, and residential areas are presented in Table 3.4. Table 3.4: Percentage of impermeable land cover in the catchment areas, risk zones, and residential areas for each risk zone. Impermeable land cover Furåsen Högen Majvallen Såggatan Catchment area [%] 36 37 19 50 Risk zone [%] 62 49 77 78 Residential area [%] 83 67 80 84 27 3. Methodology The results in Table 3.4 show the largest percentage of impermeable areas for Såg- gatan considering all areas. All zones show a similar trend where the catchment area has the lowest percentage of impermeable areas while the residential areas have the highest. 3.3.2.3 Runoff coefficient The runoff coefficient, φ, is a factor used to quantify the proportion of precipitation that results in runoff (Tegelberg & Svensson, 2013). The coefficient depends on evaporation, infiltration, and retention and is dependent on spatial characteristics (Hayes & Young, 2005). The runoff coefficient is a unitless factor with a ratio of 0-1 where 0 implies no runoff and 1 indicates that all rain falling over the area will generate runoff (Hayes & Young, 2005). In this thesis, three runoff coefficients were calculated for both the total and catchment area of each zone. First, a coefficient for short-term precipitation (φshort) was estimated by using the recommendations given in Svenskt Vatten (2016). Thereafter, runoff coefficients for 10- and 100-year rain (φ10y and φ100y) were calculated based on recommendations provided in Tegelberg & Svensson (2013). Svenskt Vatten has defined standard values for the runoff coefficient for short-term rains based on land use and topography, see Table C.1 in Appendix C (Svenskt Vatten, 2016). For areas that include different land use or topography, it is possible to calculate a comprehensive runoff coefficient by dividing a large area into smaller areas. This can be done by using Equation 3.1 together with the values presented in Table C.2 in Appendix C (Svenskt Vatten, 2016). φ = A1φ1 + A2φ2 + ... + Aiφi A1 + A2 + ... + Ai (3.1) Ai: Catchment area for the limited area [ha] φi: Runoff coefficient for each limited area [-] For the calculation of φshort, the residential areas and recommended cloudburst ar- eas were analysed separately, and summarized using Equation 3.1. The residential areas within each zone were defined as either open construction (Majvallen), closed construction with vegetation (Såggatan), or townhouses (Furåsen and Högen), see Table C.1. In Table C.1, the coefficient differs depending on the steepness, and fol- lowing the inclinations presented in Table 3.3 Furåsen was considered as flat, Högen as slightly steep, and Majvallen and Såggatan as steep. Further, all recommended cloudburst areas were defined as cultivated land, grass area etcetera, see Table C.2. In Såggatan, the cloudburst area consists of an artificial turf soccer plan though, however, a stormwater investigation performed by Sweco (Berntzon, 2019) defines the runoff coefficients of artificial turfs as 0.1. The runoff coefficients for the catch- ment areas were calculated using the areas of different land uses provided in Scalgo Live and the coefficients in Table C.2. 28 3. Methodology The φ10y and φ100y were estimated to enable an understanding of the increase in the generation of runoff for cloudburst events. The runoff coefficient for permeable areas increases during long and/or more intensive rains due to reduced infiltration capacity according to Svenskt Vatten (2016). To consider the reduced infiltration capacity during cloudburst events, a German methodology, included in Tegelberg & Svensson (2013), was used. The methodology includes the ratio of impermeable area (%), the gradient of the area (%), and the rain intensity (l/(s · ha)) to estimate the runoff coefficient. The graphs used for this methodology can be seen in Figure C.1 in Appendix C. The inclinations and imperviousness used as input to the graphs are presented in Tables 3.2, 3.3, and 3.4. Further, the rain intensities for both return periods were calculated by Equation 2.1 and using a duration of 30 minutes. 3.3.2.4 Sewer network The sewer network for each zone was extracted from the model and is illustrated in Figure 3.7. The figure shows the stormwater manholes and the pipe network. All zones except Majvallen contain a separated network, displayed as a stormwa- ter network in the figure, while Majvallen contains both combined and separated networks. (a) Furåsen (b) Högen (c) Majvallen (d) Såggatan Figure 3.7: The sewer network in each risk zone. The legend describes the represen- tation of the manholes and sewer networks based on the type of system. (Published with approval from C. Karlsson DHI and D. Karlsson Kretslopp och vatten.) 29 3. Methodology Figure 3.7 only includes the public network since this is the network included in the model. During the study visit to all risk zones, several additional manholes were identified for all risk zones. For instance, in the model, Högen includes just one pipe in the middle of the risk zone but in reality, several manholes were observed within the blocks of the residential area which most likely are connected to the pipe. 3.4 Modeling in MIKE+ To develop the tool, different rain events have been modeled in MIKE+. The model that was used in this study was originally developed by DHI and modified for this study. In the following sections, the original model is described followed by an explanation of the modifications for the purpose of this study. 3.4.1 Original model from DHI The original model was built in 2020 in MIKE 21 FM, and MIKE Urban and was used to construct structure plan West (number 13 in Figure 3.2). The model was designed as a coupled 1D/2D model where the collection system was defined by a 1D network and the overland by 2D grids (4 · 4 m2) (Kretslopp och vatten, 2021a). The collection system was based on the existing network, distributed by the City of Gothenburg, consisting of stormwater, wastewater, and combined sewer networks (Kretslopp och vatten, 2021a). The 2D domain (topography) was based on a to- pography model that was established in 2017 by height-scanning conducted by the City of Gothenburg (Kretslopp och vatten, 2021a). By using the grids in the 2D do- main, hydrodynamic processes such as surface runoff, infiltration, and rain intensity were included in the model (Kretslopp och vatten, 2021a). The infiltration capacity was determined based on soil properties and land use and defined by porosity, soil thickness, initial water content, infiltration rate, and leakage rate (Kretslopp och vatten, 2021a). The porosity and soil thickness were fixed values and permitted an infiltration capacity of 120 mm excluding the initial water content. The infiltration and leakage rate were also fixed values and dependent on the soil properties. The initial water content was not fixed and depended on both soil properties and rain intensity. To develop structure plan West, a 100-year rain with a climate factor of 1.2 was modeled. The 100-year rain was a CDS rain with a duration of six hours. The CDS rain was divided into three phases with varying rain intensities: pre-rain, peak-rain, and post-rain (Kretslopp och vatten, 2021a). The simulation was conducted in two steps: • Initial simulation: In the initial simulation, the 1D network and the pre-rain were included. The simulation was made to represent the conditions in the sewer network due to the pre-rain and resulted in a hotstart file (DHI, 2023a). • Main simulation: The main simulation included the coupled 1D/2D model and both the peak- and post-rain. Further, the simulation included the hot- start file created in the initial simulation and thereby, a representation of the 30 3. Methodology filling degree within the sewer network due to the pre-rain. From the main sim- ulation, two result files were generated, one containing the maximum values, and one containing a dynamic representation of the results over the simulated time. The result files included for instance depth and flow intensity. A conceptual model of the simulation setup with the rain phases and simulation steps is displayed in Figure 3.8. Figure 3.8: The simulation setup used in the original model with the rain intensities (mm/h) for each time step used for the simulation of the 100-year CDS rain (climate factor 1.2) (based on Kretslopp och vatten (2021c)). The figure also includes the division of the rain event and the two steps used for the simulation. 3.4.2 Simulations conducted in this thesis The original model created by DHI was converted from MIKE21 FM and MIKE Urban to MIKE+ in this study. The MIKE+ model was a coupled 1D/2D model and included structure plan West. The following sections include descriptions of the different simulations, the modifications made to the model, and the model uncer- tainties. 31 3. Methodology 3.4.2.1 Selection of simulations In this study, eleven simulations were modeled. Each simulation represented a return period (T ) and was simulated either with or without cloudburst areas. Ten of the simulations were used to develop the tool and did not include the cloudburst area (the current situation). The last simulation was used to analyse the improvement due to the implementation of cloudburst areas and, hence, included the recom- mended cloudburst areas (the future situation). An overview of the simulations is visualized in Table 3.5. Table 3.5: The modeled simulations for each situation. All return periods (T ) are simulated with cf = 1.2. Situation Description Return period T [years] Current Without cloudburst areas 10, 20, 30, 40, 50, 60, 70, 80, 90, 100 Future With cloudburst areas 100 The interval of simulations used to develop the tool was selected based on the struc- ture plans and guidance from DHI and Kretslopp och vatten (C. Karlsson & D. Karlsson, personal communication, February 16, 2023). A 100-year rain (climate factor 1.2) was determined to be used as the maximum return period since this is the return period evaluated in the structure plans. A 10-year rain (climate factor 1.2) was determined to be used as the minimum return period. Ten simulations within the selected interval were considered a sufficient number of simulations to evaluate the relation between flooded volume and rain return period. In addition, the number of ten simulations provided an evenly distributed range of T . 3.4.2.2 Modifications made in the original model The same simulation setup as in the original model (initial and main simulation) was used in this study, see Figure 3.8. Modifications were made in the input data and differed between the two situations (current and future). The modifications made in the model to simulate the current situation were related to the different return periods. For each return period, an associated rain load was used and represented by a CDS rain with a duration of six hours and a climate factor of 1.2. The rain loads were calculated based on the recommendation in P104 provided by Svenskt Vatten (2011) and are presented in Table D.1 in Appendix D. The rain loads were used as boundary conditions and assigned in two different parts in the model setup: • Boundary conditions: The rain load was inserted as a time series for the full duration. • 2D precipitation: The total pre-rain load was assigned to all grids to describe the water depths due to the pre-rain. The total pre-rain load for each return period is presented in Table D.2 in Appendix D. 32 3. Methodology Further, the rain loads for each return period were used to calculate the initial water content for different soil types using an Excel sheet provided by DHI. The initial water contents for different soil types were assigned as boundary conditions to each grid in the tab 2D infiltration. The initial water contents for each of the simulations are presented in Table D.3 in Appendix D. The simulation of the future situation only included a 100-year rain, equal to the original model, and thereby no modifications associated with the rain loads were required. However, modifications were made to the topography defined in the 2D domain. The topography was adjusted by lowering the surface of each cloudburst area within the risk zones to an infinite depth using MIKE Zero (a complementary software to MIKE+, developed by DHI). By using infinite depths, the cloudburst areas are assigned to be able to store all water that can enter the cloudburst area. 3.4.2.3 Model uncertainties The original model was used to simulate a 100-year rain and has been calibrated in comparison to rain events of a similar magnitude (Kretslopp och vatten, 2021a). No calibration has been conducted for rain events from return periods smaller than 100 years and hence, there are uncertainties regarding the accuracy of the results when modeling these scenarios. The uncertainties are associated with infiltration capacity, sewer network capacity, and manhole placements and increase for return periods with rain loads that approach the infiltration and sewer network capacity (Kretslopp och vatten, 2021c). By that, the model uncertainties increase when the rain intensity decrease. The model that has been used is a complex and large model, depending on a major amount of input data and settings. The model has been failing during some simu- lations, especially for high return periods with large rain loads. These simulations have therefore been simulated several times, without changing any settings or input data, until the whole simulation was finished. Consequently, there are uncertain- ties considering the model since the exact same simulation both failed and finished. Further, different simulations have been conducted on two different computers with different data performances and this is assumed to create variance within the results. During this thesis, two limitations have been identified in the model. First, simpli- fications consider the representation of manholes within all risk zones. During the study visit, the locations of manholes in the model were compared to the manholes observed at the risk zones, and several manholes were identified to be excluded from the model. This affected the sewer network capacity in the model, and hence, the magnitude of floods within the residential areas. Secondly, the representation of one of the apartment buildings located in Såggatan. For this apartment building, an opening that would allow for water to flow downstream has been excluded from the model. This influenced the magnitude of floods within the residential area in Såggatan. 33 3. Methodology 3.5 Analysis Several steps of processing and analyzing were required to develop the tool from the results provided in the modeling. An overview of the structure of the analysis and the content within each section is presented in the following list: • Selection of results: This section includes a description of the selection of results to use and also, the definition of flood used in this thesis. • Extraction of depth, d≥0.2m,T and dT : In this section, the methodology used to extract the depths from the simulations in MIKE+ is described. • Calculation of flooded volume, Vd≥0.2m,T and Vtot,T : In this study, two types of volumes were calculated. In this section, the methodology used to calculate these volumes is described. • Calculation of R1,T and R2,T : In this section, the variable R1,T and R2,T is described together with the methodology used to calculate these. R1,T was the variable used to develop the tool, and R2,T was the variable used for further understanding of the flooded volume. • Development of tool: This section includes a description of the methodology used to develop the tool. This includes the development of one graph for each risk zone based on R1,T , analyse of the graphs, and the development of the tool. 3.5.1 Selection of results To be able to develop the tool, it was required to determine the definition of flood to be used. The flood definition was determined in collaboration with DHI and Kret- slopp och vatten, and was influenced by the definition of flood used in the structure plans in Gothenburg (Kretslopp och vatten, 2021c, 2021b). In the structure plans, floods are divided by depth and location, and floods with depths above or equal to 0.2 m, either close to a building or on an asphalt surface, are considered unwanted (Kretslopp och vatten, 2021c). Following this, the results used to develop the tool were floods with depths above or equal to 0.2 m in the residential areas, thereby close to buildings. In this study, these floods were described by two variables: depth d≥0.2m,T and volume Vd≥0.2m,T . To enable an evaluation of the cloudburst areas, the total floods (i.e. with all depths) in the cloudburst areas were included in the anal- ysis. Further, the total floods were used to evaluate the flood characteristics within each residential area. The total floods were also described by two variables: depth dT and volume Vtot,T . Further, the maximum flow intensity FImax,T was included in the analysis to visualize the flow paths within each risk zone. From the volumes, two ratios were calculated for all residential areas for all return periods T for the current situation. The ratio between Vd≥0.2m,T and Vd≥0.2m,100 was named R1,T and was included in the development of the tool. The ratio between Vd≥0.2m,T and Vtot,T was named R2,T . and was not included in the development of the tool but included in the analysis. 34 3. Methodology For this thesis, only the maximum values for floods were considered, hence the result files with maximum values from the simulations were used. Further, the volumes, depths, and flow intensities were analysed for both the current and future situations while the ratios only were calculated for the current situation. The different variables included in the analysis of the current and future situations are summarized and visualized in Table 3.6 together with a description. Table 3.6: Description of the variables used to describe the results. All variables except R1,T and R2,T were analysed for both current and future situations. The ratios were calculated for the current situation. Variable Description Unit Area Simulations Collected by FImax,T Flow intensity m3/s/m R/C R: T=10&100 C: T=10&100 Result file d≥0.2m,T Average depth ≥ 0.2 m m R T=10-100 Extraction dT Average depth m R/C R: T=10-100 C: T=100 Extraction Vd≥0.2m,T Volume with depth ≥ 0.2m m3 R T=10-100 Calculated from d≥0.2m,T Vtot,T Total volume m3 R/C R: T=10-100 C: T=100 Calculated from dT R1,T Vd≥0.2,T /Vd≥0.2,100 - R T=10-100 Calculated from Vd≥0.2,T R2,T Vd≥0.2,T /Vtot,T - R T=10-100 Calculated from Vd≥0.2,T & Vtot,T C=Cloudburst area, R=Residential area, T=Return period [years] 3.5.2 Extraction of depth, d≥0.2m,T and dT The results from MIKE+ were processed using MIKE Zero. The model included the entire structure plan West, and hence, it was required to limit the results to the selected risk zones. Therefore, a selection was constructed for each residential area and each cloudburst area within the risk zones. The selections were created by importing shp-files of each area (created in QGIS) into MIKE Zero. By the development of selections, it was possible to evaluate the results within each specific area separately. The d≥0.2m,T and dT were extracted from the result files by using these selections. The depth (d≥0.2m,T ) was extracted for all residential areas in each simulation (both for the current and the future situation). In the residential area, all grids with depths ≥ 0.2 m were selected, and the average depth of these grids was extracted as d≥0.2m,T . The depth (dT ) was extracted for all residential areas for each simulation for the current situation and for all cloudburst areas for the 100-year rains simulations for 35 3. Methodology both current and future situations. This depth was extracted following the same methodology as for d≥0.2m,T , however, the average of all depths was used. 3.5.3 Calculation of flooded volume, Vd≥0.2m,T and Vtot,T The flooded volume Vd≥0.2m,T was calculated for all residential areas, for each sim- ulation of both current and future situations. The volume was calculated by the depth (d≥0.2m,T ), the number of grids with depths ≥ 0.2 m (nd≥0.2m,T ), and the area of the grids (Agrid) that were used in the model (4 · 4 m2) by using Equation 3.2. Vd≥0.2m,T = d≥0.2m,T · nd≥0.2m,T · Agrid (3.2) Vd≥0.2m,T : Flood volume with depths ≥ 0.2 m for a T -year rain [m3] d≥0.2m,T : Average depths ≥ 0.2 m for a T -year rain [m] nd≥0.2,T : Number of grids with depths ≥ 0.2 m for a T -year rain [−] Agrid: Area of grids (4 · 4 m2) [m2] T : Rain return period [year] The total volume (Vtot,T ) was calculated for all residential areas for each simulation for both current and future situations and for all cloudburst areas for the 100- year rain simulations for both the current situation and future situation. The total volume (Vtot,T ) was calculated by the depth (dT ), the number of grids with a flood (nT ), and the area of the grids (Agrid) by using Equation 3.3. Vtot,T = dT · nT · Agrid (3.3) Vtot,T : Total flood volume (all depths) for a T -year rain [m3] dT : Average depth for a T -year rain [m] nT : Number of grids with flood for a T -year rain [−] Agrid: Area of grids (4 · 4 m2) [m2] T : Rain return period [year] 3.5.4 Calculation of R1,T and R2,T The ratios R1,T , and R2,T were calculated for all the residential areas, for each T for the current situation. The ratio R1,T was calculated by Vd≥0.2m,T and Vd≥0.2m,100, see Equation 3.4. This enabled a comparison of Vd≥0.2m,T for different return periods, regardless of the size of the risk zone and the flood volume. 36 3. Methodology R1,T = Vd≥0.2m,T Vd≥0.2m,100 (3.4) R1,T : Ratio [-] Vd≥0.2m,T : Flood volume with depths ≥ 0.2 m for a T -year rain [m3] Vd≥0.2m,100: Flood volume with depths ≥ 0.2 m for a 100-year rain [m3] T : Rain return period [year] The ratio R2,T was calculated by Vd≥0.2m,T and Vtot,T , see Equation 3.5. R2,T = Vd≥0.2m,T Vtot,T (3.5) R2,T : Ratio [-] Vd≥0.2m,T : Flood volume with depths ≥ 0.2 m for a T -year rain [m3] Vtot,T : Total flood volume (all depths) for a T -year rain [m3] T : Rain return period [year] 3.5.5 Methodology to develop the tool To develop the tool, ten R1,T (one for each return period) were calculated for each risk zone. These were plotted as points in a diagram. Thereafter, a trend line was created for each risk zone by interpolating the points in Excel. For the interpolation, the trend line with the highest coefficient of determination, a.k.a R2, was selected for each risk zone separately. R2 is defined as the measure of the variation of dependent variables (Chicco et al., 2021), and a high R2 indicates low variation. Table 3.7 describes the function for the graphical representation used for each risk zone together with R2. Table 3.7: Functions for the graphical representation and corresponding R2, for each risk zone. Risk zone Function R2 Furåsen Power 0.998 Högen Polynomial of second degree 0.999 Majvallen Polynomial of second degree 0.998 Såggatan Power 0.996 The four graphs were all plotted in one diagram. By using R1,T for developing the graphs, the graphs approached each other for higher return periods, since R1,100 is 100% for all risk zones. Thereby, an analysis of the similarities and dissimilarities between the risk zones was conducted for lower return periods and especially fo- cused on R1,10. The lower ratios were compared along with an evaluation of the 37 3. Methodology site characteristics for all risk zones. Modeling uncertainties were also included in the evaluation. By this analysis, the risk zones with similar R1,T , and site charac- teristics were determined to be included in the development of the tool. The tool was developed by plotting the ratios from the selected risk zones in one diagram. From the ratios, an interpolated trend line was created by a polynomial equation of the third degree since this received the highest R2. The equation describes R1,T in relation to T and is the basis of the tool, see the yellow line (A) in Figure 3.9. Figure 3.9: A conceptual model of the tool where (A) represents R1,T , (B) repre- sents Ravailable, and (C) provides the manageable T-year rain. Ravailable was included in the tool to describe the ratio between available volume for a cloudburst area (Vavailable) and Vd≥0.2m,100 in the residential area, see the green line (B) in Figure 3.9. In the tool, Ravailable is calculated by Equation 3.6. Ravailable = Vavailable Vd≥0.2m,100 (3.6) Ravailable: Ratio [-] Vavailable: Available volume for a cloudburst area [m3] Vd≥0.2m,100: Flood volume with depths ≥ 0.2 m for a 100-year rain [m3] The tool was created in Excel and programmed to identify the intersection between lines A and B in Figure 3.9. The intersection is described by the blue line (C) which 38 3. Methodology provides the user with an estimated T -year rain. The estimated T describes the return period for which Vavailable is equal to Vd≥0.2m,T . By that, the tool provides the T where no flood will occur in the residential area if implementing the cloudburst area and enabling all Vd≥0.2m,T to reach the cloudburst area. 39 4 Results & Discussion The following chapter includes results from the quantitative data collection con- ducted using MIKE+ and MIKE Zero. The chapter is divided into three sections, current situation, implementation of cloudburst area, and final tool. Additionally, this chapter will include a discussion of the results. 4.1 Current situation The objective of this study is to develop a tool that describes the correlation between return period and flooding and that could be used in flood management considering the implementation of cloudburst areas in different residential areas. Based on the objective, the approach is to primarily evaluate the current situation (i.e. no cloudburst areas are implemented) as this is the situation analyzed when using the tool. 4.1.1 Runoff coefficients The calculated runoff coefficients for short-term precipitation (φshort) and 10- and 100-year rain (φ10y and φ100y) in each catchment area are presented in Table 4.1. The table visualizes the largest runoff coefficients for the catchment area of Såggatan considering all rain events. Further, the catchment area of Majvallen has the smallest φshort and φ10y, and Furåsen has the smallest φ100y. Table 4.1: Runoff coefficients for each catchment area, for short-term precipitation and cloudbursts with the intensities of 10- and 100-year rains (climate factor 1.2). Runoff coefficient φ [-] Furåsen Högen Majvallen Såggatan Short-term precipitation φshort 0.32 0.29