Hydrological risk: modeling ﬂ ood memory and human proximity to rivers

Recent literature in sociohydrology has shown the important role of ﬂ ood memory in shaping hydrological risk. In this paper, we present a system dynamics model of human – ﬂ ood interactions that simulates how the river proximity of human settlements is altered by changes in ﬂ ood memory. We also compare our model outcomes with an unprecedented dataset consisting of historical and archeological observations of human settlements in the Czech Republic that have been affected by major ﬂ ood events. This comparison allows us to evaluate the potentials and limitations of our sociohydrological model in capturing essential features of ﬂ ood risk changes, including the process of resettling farther and closer to the river. Our results show that the accumulation (and decay) of collective memory has potential in explaining temporal changes of ﬂ ood risk driven by the occurrence (or absence) of major events. As such, this study contributes to advancing knowledge about the complex dynamics of human – water systems, while providing useful insights in the ﬁ eld of ﬂ ood risk reduction. We explore how ﬂ ood memory shapes human settlements and their proximity to rivers. (cid:129) We develop a system dynamics model of human – ﬂ ood interactions that simulates how the settlements ’ proximity to rivers is altered by changes in ﬂ ood memory. (cid:129) We validate the model using a dataset of settlements location spanning eight centuries. (cid:129) Relocation of a community is effective in ﬂ ood risk mitigation if ﬂ ood memory is sustained in time.


INTRODUCTION
Throughout history, floods have been a major concern for numerous communities that have settled in the proximity of rivers (Ramesh ; Rosbjerg et al. ). UNISDR Most human societies adapt and respond to flood risk using a combination of hard and soft measures. Hard protection measures include large infrastructures, such as levees, which aim to decrease the frequency of floods. These structures tend to increase people's complacency and often enable intense urbanization of flood-prone areas. This process is widely known as the 'levee effect' (White, ), and it can lead to catastrophic outcomes when hard protection measures eventually fail, as seen in 2005 in New Orleans, USA (Kates et al. ). Soft adaptation measures aim at raising flood risk awareness and preparedness in the population living in flood-prone areas through, e.g. community education programs (Scolobig et al. ), or reducing flood exposure using risk-avoiding strategies, such as resettling away from rivers (e.g., Mård et al. ).
The process of resettling farther from the river as an informal (e.g. migration) or formal (e.g. relocation plan) response to flooding has been described in many cases around the world (e.g.  (Kreibich et al. ). Yet, it has also been shown that communities relying heavily on structural protection measures, such as levees, tend to stay in the same area after major flooding and respond by improving these structural protection measures, e.g. repairing, reinforcing or raising levees (Mård et al. ). Indeed, relocation after flooding is difficult, if not impossible, as it encounters resistance especially when high levels of structural protection are in place (Hino et al. ).
When dealing with the process of resettlement, the role of collective memory of floods is key (Viglione et al. ).
Indeed, resilience can be strongly affected by society's flood memory. It was found that a long interarrival time between flood events can fade the memory that the community built after the occurrence of a flood (Ullberg  Olick ). However, there is no clear definition of the concept itself, and the only defining characteristic is that 'it is a form of memory that transcends individuals and is shared by a group' (Wertsch & Roediger ). While individual memory is one's personal memory of a previous experience, collective memories can be seen as the remembering of the same experience but not necessarily in the same way (Van Dijck ). This feature of collective memory is particularly  value of W(t), ranging from 0 (no losses) to 1 (total destruction). The variable is given by the following equation (time dependence is omitted for brevity) describing the flood system: where α is a unitless parameter related to the topographic characteristics of the floodplain (Di Baldassarre et al. b), which determines to what extent flood damage reduces by increasing the vertical distance between the center of the human settlement and the river. Note that a near-total destruction of the settlement can occur if the water level is extremely high or if the vertical distance to the river is about zero.
The flood system (Equation (1)) is fully coupled with the human system:  Table 1.

MODEL APPLICATION AND RESULTS
Model results are compared with historical observations in order to assess whether changes in flood memory can explain the observed dynamics of human settlements. As we are inter-    Table 2. We assume that at the beginning of the simulation, i.e. at time t ¼ 0 in Figure 2 confirming that the proximity to rivers is often the result of a trade-off that may depend on the specific community.  It is worth noting that regarding three flood events (i.e., This work has a number of limitations. The human response to floods is complex and uncertain as it depends on many other aspectssuch as economic interests, cultural values and historical eventsthat were not considered here.

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Moreover, changes in both collective memory and vertical distance from the river are influenced by numerous factors and thus are more complex than what is described in our model.
As such, the concept of flood memory alone cannot adequately describe the complexity of the processes that lead to translate societal perceptions into policy action (Gober & Wheater ), especially because other variables involved, such as risk awareness and preparedness, have been shown to be multifaceted and non-trivial in various contexts (Scolobig et al. ). Still, it has been shown that being aware of exposure to flood risk remains a necessary step to be prepared to face the occurrence of a flood event (Kreibich et al. ).
Despite its simplicity, the model presented here is able to reproduce the key features of the dynamics generated by the interplay between floods and society. The process of resettling farther and closer to the river depending on the collective flood memory allowed us to perform a further step in disentangling the relationship between societal and hydrological processes.
Adaptation strategies such as resettling farther from the river may have a key role in reducing flood risk. However, a flood risk-averse attitude requires programs that sustain memory and awareness over time. As the link between societal perception and flood mitigation strategies is still not fully understood, testing the hypotheses of our model can inspire future research to further unravel the role of collective memory in shaping the dynamics of flood risk over time.