In the present work, we have modified the original PMT (Rogers, 1983) to use it in FRM and ABM contexts for the specific case of Wilhelmsburg. In the original theory, the sources of information initiate both the threat appraisal and coping appraisal processes. However, in the current study, the sources of information influence the threat appraisal only. We assume that if there is a threat and need to implement a coping measure, the agents know the type of measure they implement based on their house categories (see Table 1).

In the threat appraisal, the “maladaptive response” is the current behaviour of not implementing household-level flood vulnerability reduction measures. In the case of Wilhelmsburg, the maladaptive response is affected by flood experience, reliance on public protection (i.e. the dyke system), climate change perception and the source of information.

The flood experience refers to any experience of households being directly affected by flooding or witnessing flooding that affected others in Wilhelmsburg.

The reliance on public protection is related to the flood experience. Residents of Wilhelmsburg who have not experienced flooding have a high reliance on the dyke system. The fact of seeing the dykes on a daily basis gives residents a sense of protection and causes them to underestimate the flood threat. The reliance on public protection is also associated with the trust the residents have in the authorities when it comes to FRM. However, as some informants who experienced the 1962 flood described, the reliance on the dyke system drops if flooding occurs in the future (Birkholz, 2014).

We include agents' climate change perception as a factor as some residents of Wilhelmsburg described that sea level rise might increase the occurrence of flooding in future. The effects of climate change create some discomfort and stress, and hence, it is seen as a source of concern. Besides, Germans, in general, are concerned about climate change, whereby 86 % are “extremely to somewhat worried” (NatCen Social Research, 2017).

The source of information is an important factor that shapes residents' perception of flood risk. The municipal and state authorities have a firm belief that the dyke system is the primary flood protection measure and that there is no need to implement individual measures to protect properties. However, these authorities communicate evacuation strategies in the case that the dykes fail or are overtopped by a storm surge. On the other hand, other sources such as experts from the Technical University of Hamburg-Harburg organised flood risk awareness workshops presenting the flood risk in Wilhelmsburg and different adaptation measures that individuals could implement. Media also has a role in creating concern by showing flooding and its impacts in other German cities and even other countries.

In the coping appraisal, the “adaptive response” is developing a protection motivation behaviour to implement flood vulnerability reduction measure. The factors that affect the response probability in this conceptualisation are personal flood experience, house ownership, household income, subsidies from the state and social networks.

Personal flood experience refers to a direct flood experience in which an agent's house was flooded before. It is a major factor that drives the adaptive response (Bubeck et al., 2012). The factor is used as a proxy for behaviours in the case of near-miss flood events as agents tend to make riskier decisions if they escape damage while others are flooded (Tonn and Guikema, 2017).

We include house ownership as a factor, though it has a small to medium effect on the adaptive response (Bubeck et al., 2012). However, this factor is also used as a proxy for tenancy, which is an important factor since tenants tend not to implement measures. Hence, house ownership in this context specifies whether an owner or a tenant occupies a house at a given time.

Household income has a significant influence on the adaptive response, especially when agents implement measures that bring structural changes or adjustments to buildings such as flood proofing and installing utility systems at higher ground (Bubeck et al., 2013). Hence, this factor affects only those households that intend to implement structural measures.

Subsidies are any financial help the authorities may provide to encourage implementation of individual adaptation measures. Currently, the authorities do not provide subsidies as they only invest in public protection. But, the assumption is that if a future low-probability storm surge overtops or overflows the dyke system and flooding occurs, the authorities may take responsibility for the damage to properties, given their assurance that people are safe and do not need to implement individual measures. As subsidies are financial support, we conceptualise this factor similarly to the household income affecting household agents that implement structural measures.

The social network factor represents agents' relatives, friends or neighbours who have implemented any adaptation measure. Bubeck et al. (2013) showed that residents conform to the protection mitigation behaviour of others in their social network.

The state subsidy and the household income are proxy measures for the “financial response cost” of implementing the measures. In terms of other costs, such as time and effort, we assume that the agents have no limitation. The assumptions related to response efficacy are that agents implement the adaptation measure specified in the shared strategy based on the type of houses they own and that the measure is assumed to be effective in reducing flood damage. However, it does not necessarily imply that the measure is the best possible. Similarly, the assumption related to self-efficacy is that either agents need to hire technicians that are capable of successfully implementing the measures or they are capable of implementing the measures by themselves. Appendix A lists the assumptions made in conceptualising and developing the model.

Lastly, “protection motivation” is an intention to implement coping responses (Rogers, 1983), which may not necessarily lead to actual behaviour (Grothmann and Reusswig, 2006). In our conceptualisation, agents may delay the implementation of measures after they positively appraise coping. Agents may also change their behaviour through time and abandon temporary measures, affecting their protection motivation.

We will describe the FRM case of Wilhelmsburg using the agent, urban environment, and institution components of the CLAIM framework. Agents. We identified two types of agents – the household and the authority agents.

The household agents are representative of the residents of Wilhelmsburg. These agents live in residential houses. The actions they pursue include appraising the threat and coping, implementing adaptation measure and assessing direct damage. The agent attributes related to threat appraisal are flood experience, reliance on public protection, perception of climate change and the source of information about flooding. The attributes related to coping appraisal are direct flood experience, house ownership and household income. If agents decide to implement an adaptation measure, they know which measure to implement based on the institutions identified. The conceptualisation excludes businesses, industries, farmlands and other auxiliary buildings due to a lack of data.

Urban environment. The Wilhelmsburg quarter that is surrounded by the ring of dykes and walls defines the urban environment (see Fig. 1). The household and authority agents live and interact in this environment. In our conceptualisation, we focus only on household behaviour to protect their houses. Therefore, the only physical artefacts explicitly included in the conceptual model are residential houses, which spatially represent the household agents in the ABM. Their geographical location is represented by the use of polygon features, as illustrated in Fig. 1. These polygons are used to compute the area of the houses. Houses also have types, which are classified based on “the type of building, occupancy of the ground floor and the type of facing of the building.” (Ujeyl and Rose, 2015, p. 1540006-6). This study includes 31 types of houses, which we group into five categories: single-family houses, bungalows, IBA buildings, garden houses and apartment/high-rise buildings. Appendix C provides a complete list of the 31 types of houses.

If a house is flooded, the potential building and contents damages of the house are computed in monetary terms based on the house type. A raster file represents the urban environment, and if floods occur, agents obtain information about flood depth at their house from the environment. The adaptation measures that households may implement do not have physical representations in the model, though their impact is implicitly evaluated if a house is exposed to flooding.

Institutions. In Wilhelmsburg, there is a common understanding that it is the responsibility of the authorities to protect the people. There is no institution, formal or informal, that influences household behaviour to reduce vulnerability. As a result, we will test hypothetical shared strategies that may have some effect on household agents' flood risk. The conceptual model consists of five institutions of which one is related to the authority agent providing subsidies to household agents, and the rest are related to households implementing vulnerability reduction measures depending on the house categories.

Institutions in CLAIM are coded using the ADICO grammar, which refers to the five elements that institutional statements might contain: “Attributes”, “Deontic”, “aIm”, “Condition” and “Or else” (Crawford and Ostrom, 1995). Table 1 shows the five institutional statements that influence the implementation of individual flood risk reduction measures. When an agent is permitted to do an action (deontic “may”) with no explicit sanction (no “or else”) for failing to do the action, the statement is referred to as a “norm”. In this case, the last institutional statement related to the subsidies is conceptualised as a norm. The authority agent may give subsidies, but it is not obliged to do so and faces no sanction if it decides not to provide subsidies. When the deontic and “or else” components are absent from an ADICO statement, the statement is referred to as a “shared strategy”. Therefore, the first four statements in Table 1 are shared strategies as there are no sanctions for non-compliance with the statements (no “or else” component), and there is no deontic component. When a shared strategy drives a system, agents do what the majority in that system does. As a result, a household implements a measure when the majority of households implement the adaptation measure. However, the household also has the option not to implement the measure without incurring any punishment.

In our conceptualisation, households implement a specific primary measure or a secondary measure (stated in the “aim” component) based on the category of a house they occupy (stated in the “condition” component). Considering primary measures, as most single-family houses in Wilhelmsburg have two or three floors, household agents that live in such houses install utilities such as heating, energy, gas and water supply installations in higher floors. Household agents that live in bungalows and IBA buildings implement flood-adapted interior fittings such as walls and floors made of waterproof building materials. Agents that live in garden houses and apartment/high-rise buildings implement flood barriers. The barriers implemented by garden houses are sandbags and water-tight windows and door sealing, while the latter implement flood protection walls. Household agents that have already implemented a primary measure may also implement a secondary measure. This measure is adapted furnishings, which includes moving furniture and electrical appliances to higher floors. As most bungalows and garden houses are single-storey housings, they do not implement adapted furnishings.

Installing utilities in higher floors and flood-adapted interior fittings are permanent measures that alter the structure of the house, and we assume that once they are implemented, they will not be abandoned. Therefore, in PMT terminology, implementing these measures is a “single act” coping mode. In contrast, flood barriers and adapted furnishings are temporary measures which agents must decide whether to implement every time, just before a flood event. Therefore, implementing these measures is a “repeated act” coping mode. Implementing both primary and secondary measures is a “repeated, multiple act” coping mode.

External factors. There is no external institution conceptualised in this model. Although there is a European Union Floods Directive that requires member states such as Germany to take measures to reduce flood risk, it does not specify the type of measure implemented. In Wilhelmsburg, the authorities invest primarily in the dyke system; hence the implications of the Floods Directive for individual adaptation measures are not relevant in this study.

The model implementation flow chart shown in Fig. 3 lays out the actions agents perform at every time step. First, household agents assess if they perceive flood as a threat. If they do, they appraise coping that leads to protection motivation behaviour. Second, if there is the intention to implement a measure, they implement the adaptation measure specified in the institutional table. Lastly, if there is a flood event at a given time step, the house layer is overlaid with a flood map corresponding to the event. Households check the flood depth at their property and assess the building and contents damages. Agents' attributes are updated if the actions change their states. This process is performed until the end of the simulation time. We will describe below how the actions – threat appraisal, coping appraisal, adaptation measure implementation, damages assessment and the abandoning of measures – are evaluated in the model.

Hydrologic and hydrodynamic processes. Located in the Elbe estuary, the main physical hazard that poses a risk on Wilhelmsburg is storm surges from the North Sea. If the surge is high or strong enough to overtop, overflow or breach the dykes, a coastal flood occurs. The study only considers surge-induced coastal flooding due to dyke overtopping and overflows.

Urban environment. The dyke system is implicitly included in the hydrodynamic processes to set up the boundary conditions of overflow and overtopping discharge that causes coastal flooding. The conceptualisation does not include any other infrastructure.

The flood model in this study is based on extreme storm surge scenarios and two-dimensional (2D) hydrodynamic models explained in Naulin et al. (2012) and Ujeyl and Rose (2015). The storm surge is composed of wind surge, local tides and a possible external surge due to cyclones. The extreme storm surge events are computed by considering the highest observed occurrence of each component. The three storm surge events – Event A, Event B and Event C – used in this study have a peak water level of 8.00, 7.25 and 8.64 m, respectively (Naulin et al., 2012). Numerical 2D hydrodynamic models are used to calculate water levels and wave stages around the dyke ring. In turn, these data are used to compute the overflow and wave overtopping discharges for the three scenarios.

To assess the flood hazard from the three scenario events, flood models that simulate coastal flooding are implemented. The model is developed using the MIKE21 unstructured grid modelling software (DHI, 2017). The 2D model domain defines the computational mesh and bathymetry, the latter of which is based on a digital terrain model (see Fig. 7). The surface resistance is expressed using a space-dependent Manning number that is based on the current land use categories. The time-dependent overflow and overtopping discharges over the dykes described above are used as boundary conditions. The output of the hydrodynamic model relevant for the current study is the inundation map showing the maximum flood depth in Wilhelmsburg. This is because the main factor that significantly contributes to building and contents damages is the flood depth (Kreibich and Thieken, 2009). Further, as houses are represented by polygon features (see Fig. 1), the flood depth for a specific house is the maximum of the depths extracted for each vertex of the polygon that defines the house.

The input factors of the coupled ABM–flood model are presented in Table 2. The input factors are grouped into two. The first group includes the initial conditions and parameters that are regarded as control variables. Varying these factors is not of interest for the study; and hence, they are not included in the model experimentation. That said, a sensitivity analysis (SA) is carried out on these factors to assess which of them contribute more to the uncertainty of the model output. A detailed discussion of the SA we carried out is given in Appendix E. The second group comprises factors that are used to set up model experimentation and to evaluate the effect of household adaptation measures in FRM. In this group, the first three factors are related to the shared strategies defined in Table 1, while the last three are related to individual strategies. The flood event scenario is a randomly generated storm surge event series (see Fig. 8). The percentage base values in Table 2 are respective to the total number of agents.

Due to the lack of available data, most of the factors are parameterised based on our expert estimations. Some, however, are based on literature or census data. For example, since the last major flood occurred in 1962 and only 14 % of Wilhelmsburg's residents are older than the age of 65 (according to the 2011 census

Interactive maps for Hamburg for the 2011 census can be found at https://www.statistik-nord.de/fileadmin/maps/zensus2011_hh/index.html, last access: 3 June 2020

The response factors we use to measure the model outcome are the cumulative number of household agents that positively appraised coping (copingyes), that positively appraised coping due to the social network element (copingyes,SN), that implemented primary measures (PMimplemented), that abandoned primary measures (PMabandoned), that implemented secondary measures (SMimplemented) and that abandoned secondary measures (SMabandoned). In terms of damage, we focus on the building and contents damages mitigated rather than the total damage to highlight the benefits of household adaptation measures.

As mentioned in Sect. 4.2, the flood model we utilise in this study was developed and reported in a previous publication. Hence, we take the calibration and validation of the flood model at face value. Regarding the ABM, we carried out model verification by evaluating the relationship between agents' actions and expected response factors. For example, when agents implement measures, the system-level number of secondary measures implemented cannot be higher than the primary measures implemented. Or, in coping appraisal, with an increase in the number of agents with high income, we expect a system-level increase in the number of coping agents. However, the average number of agents that implement permanent measures should not be influenced as there is no relationship between income and permanent measures' implementation as specified in the conceptual model.

Regarding the model validation, we validated the conceptual model using expert and local knowledge of the study area. Currently, there is no practice of implementing household adaptation measures in Wilhelmsburg. The study is looking into the potential future direction of reducing vulnerability using a “what if” approach. Thus, due to the modelling approach performed, undertaking classical validation is not possible. Given the limitations, the practical purpose of the ABM is to showcase the benefits of household adaptation measures so that authorities and communities in Wilhelmsburg may consider implementing such measures to mitigate potential damages. Moreover, the model serves the purpose of advancing scientific understanding and modelling of socio-hydrologic systems, particularly human–flood interactions.

To evaluate the effect of the shared strategies listed in Table 1 and individual strategies such as delaying the implementation of measures, implementing secondary measures and abandoning measures, we set up simulations by varying the values of selected input factors as presented in Table 3. The subsidy levers 1, 2 and 3 represent no subsidy, subsidy only for flooded household agents and subsidy for all agents that consider flood as a threat, respectively. Considering the computational cost of simulations, we evaluate six flood event scenarios. The event series of the scenarios are randomly generated and shown in Fig. 8. In these batch of simulations, all the other input factors are set to their base values, as stated in Table 2.

The simulation period of the ABM is 50 time steps, each of which represents a year. The number of household agents is 7859. Every simulation of parameter combinations is replicated 3000 times. Hence, for the SA and policy-related experiments, simulation outputs are computed as averages of 3000 simulations per input factor setting. A detailed description of estimating the simulation replication is provided in Appendix D. All simulations in this study are performed using the SURFsara high-performance computing cloud facility (https://userinfo.surfsara.nl/systems/hpc-cloud, last access: 3 June 2020).

We have tested six different flood event scenarios, and the adaptation behaviours of agents are shown in Fig. 9. The plots show that each scenario results in a unique trajectory of adaptation measures. However, Scenarios 1, 3, 4 and 6 have similar curves of PMimplemented, while Scenarios 1 and 4 appear to overlap. The two curves appear to overlap because the effect of the first event in Scenario 1 (Event B) is very small, and the second and biggest flood event (Event C) of Scenario 1, which happens at the same time as that of Scenario 4, dictates the number of measures implemented. Irrespective of the subsidy lever, the four scenarios have a similar number of PMimplemented at the end of the simulation period. In these scenarios, the biggest event (Event C) occurs first or second. As this event is big enough to flood every agent's house directly, most agents tend to develop protection motivation behaviour earlier. On the other hand, Scenarios 2 and 5 display a lower number of the response factor, which improves with a subsidy. In these scenarios, Event C occurs last; and hence, the PMimplemented rises rapidly after time step =35. Furthermore, there are no major increases in the number of houses that implemented primary measures after the first flood events in the cases of Scenarios 1 and 2, i.e. after time step =7 and time step =2, respectively. The reason is that the first flood event in both scenarios (Event B) is a small event, and it only affects a few houses. Hence, its effect on the number of primary measures is minimal (but not zero). The curves appear flat, but there are minor increases in the slope of the curves after the time steps mentioned.

In terms of building damage mitigated, the scenarios with the two big events (C and A) occurring first and second and within a short time interval display the least damage mitigated (see Fig. 9b, Scenarios 4 and 6). These are considered to be the worst cases of the six scenarios as agents did not have a coping behaviour before the first big event, and most agents did not yet develop coping behaviour when the second big event occurred after 5 years. Only 21 % and 14 % of the agents implemented a measure in the cases of Scenarios 4 and 6, respectively, without subsidy. In contrast, in the case of Scenario 5, agents gradually develop coping behaviour after a first big event. By the time the second big event occurred after 37 years, about 45 % and 70 % of the agents already implemented a primary adaptation measure to flooded houses without subsidy and with a subsidy, respectively. Scenario 5 can be considered to be the best scenario in which household agents have time to adapt and significantly reduce the potential damage that may occur in the future.

The main lesson from the results of the scenario exercise is that agents should be prepared or adapt quickly after an event to mitigate considerable potential damages. Big events may occur within a short time interval, and households should be prepared to mitigate associated damages. It should be noted that in Fig. 9b there is no mitigated damage in the first event as we assumed that no mitigation measure was implemented initially.

The effects of the institutions are analysed in two categories. The first ones are the impacts of subsidies, and the second effects are that of the social network and shared strategy parameters.

In this section, we will analyse the effects of three factors that characterise individual strategies: the delay parameter, adaptation duration parameter and secondary measure parameter.