1 Introduction

Transformation of the biophysical system alters the hydrological cycle, consequently changing the processes associated with water run-off, infiltration, and recharge, which can likely increase the frequency and intensity of flood events (Stocker et al. 2013; Wijesekara et al. 2012). Pluvial floods are common in urban areas due to reduced infiltration on the impervious surface or lack of appropriate drainage system commonly having the characteristics of a flash flood (Monrose and Tota-Maharaj 2018). Fluvial floods (riverine floods) are caused when the riverbanks fail to contain the water, resulting in the banks’ overtopping during heavy precipitation events. Coastal flooding results from compounded effects of floods and storm surge due to high tides and sea-level rise and is influenced by elevated wave heights (Vitousek et al. 2017).

Flood risk assessment and management (FRMA) comprises a two-part approach, one which deals with risk analysis, and the other deals with risk mitigation (Vojtek and Vojteková 2016). Hydrological (flood) risk analysis has generally been conducted with physically-based models (Buzacott et al. 2019; Huang et al. 2017) and statistical or data-driven models (Anshuka et al. 2020; Kundu et al. 2017). Flood risk management can comprise preparedness and a high degree of response to risk, which is geared more towards communications, policies, and human behaviour (Plate 2002). The second strategy pertains to managing the flood hazard by using flood control measures such as dykes and levees to redirect the floodwaters (Green et al. 2000). Flood management is one aspect of flood risk management, which encompasses understanding both the hazard characteristics and the system’s vulnerability (Tariq et al. 2020).

It is essential to understand that risks do not have a static path and will continue to evolve with other developmental issues such as rapid urbanisation, population growth, and changing climate and land-use scenarios (Haer et al. 2019). However, it is also essential to consider the dynamic adaptive behaviour of humans. Humans continuously show cognitive changes as they learn and adapt to the changing risks and often modify the hydrological cycle in response. The human or the social system and the natural (biophysical) systems are connected; feedback from one system affects another (Troy et al. 2015).

Given human and natural systems do not exist independently, integrating both aspects are critical to understanding risk. A systems approach is needed to holistically look at the challenges faced in an evolving risk environment (Sahin et al. 2019). This has given rise to several systems-based modelling tools which can be utilised to understand complex interactions within a system (Karami et al. 2017), such as random trees (LaValle et al. 2001), Bayesian networks (Ranganathan et al. 2014), systems dynamics models (Feofilovs et al. 2020) and agent-based models (Janssen and Ostrom 2006).

Recently, one method gaining more attention in hydrology is the agent-based modelling (ABM) approach, which considers hierarchy, heterogeneity, spatially explicit features, and represents feedback loops in human-natural systems (Dawson et al. 2011). Emerging from the field of computer science and artificial intelligence, ABMs can be described as a large Markov Chain (Fonoberova et al. 2013). Simply put, an ABM is a computerised simulation based on the different number of decision-makers called agents. Agents are autonomous entities capable of dynamically responding to problems defined by a set of behaviour rules or functions. These agents can process new information and adapt when situated in an interactive environment with simultaneous occurrence of multiple dynamic processes (An 2012). Human behaviour, interaction and feedback loops can be captured in an ABM model, together with a flood model, to better understand flood risk assessment and management. Decisions made by agents can affect the entire system, which puts ABM superior to just using physical or traditional equation models in FRMA (Matthews et al. 2007).

The application of ABM in FRMA is an emerging field and has gained attention from 2000 onwards. Outputs from ABMs have been used to understand the implications of different policies, land use planning and development (Liu et al. 2005), communication, decision-making, and system response to hazards. Several reviews on ABMs are available for land-use applications (Matthews et al. 2007), human-decision making (An 2012), traffic and transport (Bazzan and Klügl 2014), animal movement (Tang and Bennett 2010), and non-communicable disease (Nianogo and Arah 2015). However, with the growth of the application of ABMs in hydrology, it is essential and timely to review the use of agent-based models for FRMA.

Recently, reviews specific to the use of ABMs in the area of FRMA have been published by Aerts (2020), Taberna et al. (2020), Zhuo and Han (2020), and Simmonds et al. (2020). Aerts (2020) compared trends among other system dynamic models and discussed the decision-making process associated with human behaviour. Taberna et al. (2020), looked at ABM implementation across disciplines (from an economic and a flood viewpoint) and sheds light on different spatio-temporal scales, and the learning process in agents to change adaptive behaviour. Zhuo and Han (2020), identified spatial distributions of the studies, different ABM platforms, their applications and advantages. Notably, the study identified three main challenges of ABM simulation: model development, assessment, and documentation. A review of ABMs and multi-agent simulations by Simmonds et al. (2020) identified several improvement areas. For example, a modeller must ensure that the model outputs align with the study’s intended purpose and provide sufficient model details to ensure reproducibility. The review also highlighted the absence of validated models and lack of comprehensive information to understand model development. To address the lack of model documentation and improve model transparency, this review applies the standard ‘Overview, Design, and Detail (ODD) protocol’ to assess flood-ABM papers. It explores whether the protocol can be applied to characterise existing papers and encourage its use as a protocol in future studies.

The ODD was developed by Grimm et al. (2010) to deal with the considerable variation originating from ABM simulations for social science research. The field was rapidly growing, but the variation did not allow for further reproducibility of research, undermining the scientific process. The ODD aimed to develop an exhaustive description of ABMs in a standardised manner to ensure transparency in the development of the methods. Since 2010 the ODD protocol has undergone multiple revisions to be inclusively applied across different disciplines. Ultimately, the goal of ODD is to promote communication, replication of methods, comparison of results, and cross-disciplinary dialogue in the use of ABMs.

The purpose of this review is to first understand the model development process in the area of FRMA. The novelty of this review lies in adapting the ODD protocol as a framework to evaluate ABM-hydrological simulations. ODD has been previously used to assist the review of agent-based models. Examples include the work by Groeneveld et al. (2017) on agent-based land-use change models, Kremmydas et al. (2018) on ABMs for agricultural policy, and Jing et al. (2020) on ABM simulations of autonomous vehicles. ODD, however, has not been explicitly explored for flood-ABM models, which will be employed in this review.

2 Methodology

2.1 Systematic selection of studies using the PRISMA Method

This review was conducted to better understand the model development process for applications of ABM in FRMA, guided by the five steps proposed by Khan et al. (2003). These are framing a question, identifying relevant work, assessing the quality of studies, summarising the evidence, and interpreting the findings.

To achieve this goal, the first step was to pose the following questions:

  1. 1.

    What does a flood-ABM model development process entail, and how well is this documented?

  2. 2.

    What are the main areas of applications and overall trends of agent-based models for flood risk and management?

  3. 3.

    How does the design and structure of the agent-based models for flood risk and management vary for the main application areas?

The second step entailed an assemblage of literature using different term combinations. Boolean search techniques were applied, and an exhaustive literature search was conducted on the Web of Science database. Based on the research questions, the following search terms were selected: “floods” AND “agent based model*” OR “agent-based simulation*”. The web search was conducted in October 2021, which rendered 183 results in total. As seen in Fig. 1, between 2006 and 2014, there were, on average, three or fewer publications per year for ABM in the area of FRMA. From 2015 onwards, the number of publications increased to about 20 on average per year.

Fig. 1
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Number of publications on ABM and FRMA across years based on the initial search terms in the Web of Science database

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The third step of the systematic review used the PRISMA method (Moher et al. 2015) to further narrow down the studies included in the review (Fig. 2). To maintain the quality of the study, conference papers were excluded, and only peer-reviewed articles were included in the study. The search results also contained reviews on ABM; although these gave helpful information about the studies, they were not included in the systematic review (n = 118). The paper titles, abstract and authors’ names of the 118 studies were extracted for initial screening. The sample size contained studies in the area of disease management, seismic activity, computer network security, which were not a focus area in the review and hence were omitted.

Fig. 2
figure 2

PRISMA method flowchart for selection of studies

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Thereafter, n = 75 studies were checked for eligibility to be included in the review, which was the fourth step. The main inclusion criteria of the search were based on studies that focused on the use of an agent-based model for flood risks related assessment. Therefore, studies that did not use an agent-based model or focused on droughts or studies that looked at an agent-based model with applications to emergency management without a specific focus on floods were excluded. The authors carefully reviewed the identified studies and agreed on their incorporation in the review. Application of the inclusion and exclusion criteria reduced the total number of articles (n = 39). Subsequently, the 39 relevant articles were included for review, for which the full text was obtained and read by all the authors. The last step entailed an assessment of the articles based on the ODD protocol as described in the following section.

2.2 Assessment of the studies using the overview, design, detail protocol

2.2.1 Background on ODD protocol

The ODD protocol is used to describe individual agent-based simulations. The nature of ABM is such that there are many elements, often leading to confusion on the different terms, variables, and attributes. As proposed by the ODD, a more guided and standardised structure to document model processes enables reproducibility of research (Grimm et al. 2020) and increases its methodological rigour (Polhill 2010).

The initial ODD protocol was written from an ecology perspective and has evolved over the years. A review in 2010 showed the relevant research community widely adopted the ODD. However, Giske and Railsback (2010), Polhill (2010) state that modellers tend to eliminate certain components of the models’ description due to repetition. Lack of clarity on the explanations regarding individual components identified by Matthews et al. (2007) through a review on land-use models with ABM was another deterrent for adoption, together with inaccurate and incomplete use of the ODD. This led to an update in the protocol, which not only provided more clarity on the explanations, but some components were expanded so that its applicability is inclusive of all disciplines and not just ecology.

Further, Müller et al. (2013) adapted the ODD and improved some components which required more clarity, particularly for human decision making. Reinhardt et al. (2018), attempted to improve the ODD by complementing it with a provenance component to reflect the incorporation of data on artefacts, people and activities. To capture further intricacies within the ABM, the ODD has been improved by developing an outline to incorporate empirical data (Laatabi et al. 2018). The ODD protocol can be a valuable tool for practitioners in the socio-hydrology domain to familiarise themselves with the structure of models and know where to look for crucial information for the models’ constituents (Grimm et al. 2017).

2.2.2 Components of the ODD

The ODD protocol has an inverted pyramid structure that broadly describes the goal of the simulation, and then gradually progresses into finer details. The protocol has three categories (Overview, Design and Details) and several sub-components within each category. Table 1 presents the ODD protocol’s overall structure (Grimm et al. 2010; Muller et al. 2013) and indicates in highlight the categories used in this review to analyse the body of work in flood-ABM for each selected sub-component. This selection was driven by the research questions posed in Sect. 2.1. Moreover, because the protocol was developed in a manner to include all disciplines, not all aspects of the ODD may be necessary for describing flood-ABMs.

Table 1 ODD protocol: the highlighted sub-components are used in this review to evaluate the selected flood-ABMs
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2.2.2.1 Overview

The Overview component of the ODD protocol is related to our research question, which aims to understand the overall trends and main application areas for ABMs in the domain of FRMA. The two first sub-components of the Overview have been transformed into five review categories. They are described below.

  • Purpose and patterns: Information obtained from the purpose was used to categorise studies based on their focus on risk and adaptation or emergency management in FRMA.

  • Entities: refer to overarching characteristics of the ABM, which are defined as a balance between the problem being addressed and data availability. The main entity considered in this review were agents, such as humans or institutions.

  • State variables: Agents have distinct attributes that set them apart from other entities. For this review, the attributes which define the agent were categorised as physical, psychological and socio-economic.

  • Temporal Resolution: ABMs are a platform for dynamic spatio-temporal simulation. The temporal resolution refers to the discrete-time units of each simulation run in which rules, action, and changes in agent properties or environment are defined (Hammond 2015), which were categorised into minutes, hours, months or years.

  • Spatial Scales: Space in ABMs can be explicitly defined - geographically, or implicitly defined – abstract or hypothetical, not necessarily representing a real-world place. As most ABMs use a grid system to represent the entire simulation environment, the spatial resolution refers to the size of the grid unit within which agents are based. Since most of the Digital Elevation Model data for flood studies has a 30m by 30 m resolution, for this study, we have categorised spatial resolution into i) Equal and above 30m or ii) Below 30m.

  • Process and overview sub-component have not been included here because it is described in the Details component under subsection sub-models and process.

2.2.2.2 Design

The ‘Design’ component is related to the research question, which aims to understand how the models are developed, and how their design and structure vary according to different purposes. The design concepts allow the development of justifiable models, not on an ad-hoc basis (Grimm et al. 2017). There are eleven sub-components associated with design concepts (Table 1), not all are applicable in the area of FRMA. For this review, we have selected the following five sub-components:

  • Basic principles refer to guiding principles used at the system or agent level and describe the theory for agent behaviour. In this review, we have specifically used it to describe agent behaviour. Agent behaviour can be categorised based on theories (economic or cognitive), real-world observations (empirical data), or ad-hoc rules. Because adaptation is part of individual decision-making, it has not been assessed as a separate category but considered within the basic principles category.

  • Learning refers to how agents change their decision-making, where learners can update their strategies based on previous decisions. Learning is different from adaptation in that learning is considered a more active and cognitive behaviour that can change the behavioural rules within an ABM (Müller et al. 2013). We reported those studies that had instances of learning with a binary ‘Yes or No’ indicator for this study.

  • Sensing refers to how agents perceive the other agents and the environment around them, gathering information for their decisions. This systematic review has documented whether sensing occurs locally (endogenous) or globally (exogenous).

  • Stochasticity refers to introducing randomness in some part of the model, either in agent decision-making or the initial states of the variables, to make the models more suitable for depicting real-world variations. This review has documented whether stochasticity has been included using a yes or no indicator.

  • Collectives refers to categorisation within the model, which could be grouped within agents or behaviour rules for agents. This review has documented whether stochasticity has been included using a yes or no indicator.

2.2.2.3 Details

The ‘Details’ component is also related to the second research question, which aims to understand how the models are developed. Its three sub-components are described below.

  • Initialization refers to the initial state of different variables for agents and the environment before the main simulation starts. For the review, this sub-component has been categorised how initialisation occurs, based on existing data, probabilistically determined or using a combination of those.

  • Sub-models refer to sub-processes that together form the ABM. Often some processes need to be run independently and then programmatically interrelated. This is because some processes have different parameters, spatial or temporal scales. This is particularly relevant for the FRMA domain, which brings together large-scale weather dynamics that can be translated into localised disaster events and then associated with regional human and institutional dynamics. Frequent sub-model processes used for FRMA include flood simulation, urban systems, and transport and traffic networks.

  • Model Analysis and Accessibility while not part of the ODD protocol, model analysis is often suggested as a mandatory step to calibrate, verify, validate, and analyse the model results. Verification entails setting the model parameters in the conceptualisation phase (can be referred to as calibration). Validation occurs in the post-simulation phase. Two validation approaches are, comparing model outputs to observed data and through sensitivity analysis. We have also documented if the studies have provided accessible code in our review.

3 Results

Some of the studies selected for the systematic review have used the ODD protocol to describe their proposed ABMs (~ 24%). On the other hand, even though not explicitly stating the use of the ODD protocol, most of the studies (~51%) included in this review have relevant information which fulfills the ODD components and sub-components. Few of the reviewed studies (~25%) had a poor description of the model development process, allowing only partial completion of the ODD components. Below the analysed studies are described under the respective ODD categories.

3.1 Overview

3.1.1 Application type and timestep

Of the reviewed articles, 51% were based on emergency management, and 49% focused on risk and adaptation. Emergency management involved studies in the area of response to flood warning-related communication and evacuation. Risk and adaptation studies include identifying long-term risks and associated adaptive strategies. Agent-based models are spatio-temporal simulations, as such simulations have discrete time steps and an associated total duration of the simulation. For instance, simulations could be run at a yearly time step for a period of 30 years. This review finds that most emergency management-related studies have a short discrete time step (Fig. 3), ranging from minutes to hours (Coates et al. 2019, 2020; Du et al. 2017b). In comparison, most studies on risk and adaptation strategies tend to have longer discrete time step ranging from months to years (Haer et al. 2020; Tonn and Guikema 2018).The discrete time step is used to link flood simulation with the ABM; for example, Abebe et al. (2019a, b) assumes a maximum of one flood in a given time step. Similarly, Haer et al. (2019), updated the flood volume and inundation heights for each return period in each model time-step.

Fig. 3
figure 3

Mosaic plot of the two Application types: Emergency Management and Risk and Adaptation with Discrete timestep: minute, hour, month, year

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3.1.2 Space and spatial scale

Space in ABM can be explicitly or implicitly defined. All agents have a specific location for spatially explicit defined space, and their movement is a key variable (Abebe 2018; Abebe et al. 2019a, 2019b). Space can also be implicitly defined in an XY coordinate plane, such as the location of the parcels in which agents move about; however, the specific geographic location of agents within the parcels is not stated. The review indicated that overall, around 79% of the studies had explicitly defined space, 14% had implicitly defined space, and in 7% of the studies, it could not be identified how space was defined. Moreover, approximately 93% have explicitly defined space for emergency management studies, and 7% have implicitly defined space. In risk and adaptation studies, in 75% of the studies, space is explicitly defined, and 19% had implicitly defined space (Fig. 4a).

Fig. 4
figure 4

Space and Spatial resolution characteristics of the reviewed studies shown in percentages between the two application types: Emergency Management and Risk & Adaptation

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Generally, a study area is divided into a set of regularly shaped grid cells connected by adjacent cells. Individual grid cells have a specific resolution showing how fine or coarse the model is. In this review, 31% had a spatial resolution equal to and above 30m, 26% had a resolution of below 30m, while in 43% of the studies, the spatial resolution was not stated. In risk and adaption studies, ~38% have a spatial resolution of ‘Equal or above 30m’, while 25% have a resolution of below 30m (Fig. 4b). This in emergency management studies is higher, where 38% had a spatial resolution of Below 30m.

3.1.3 Agents and attributes

This review found that the agents comprised households in most studies, followed by a combination of households and institutions. A household can include an entire family or (a) single person(s). Institutions can be private or public bodies, such as government, developers, or private firms. In 90% of emergency management studies reviewed, the agents were households, and in the remaining studies, the agents were institutions or a combination of those (Fig. 5a). Fifty percent of the studies had households as agents in risk and adaptation studies, and the other 51% had a combination of households and institutions as agents (Fig. 5a). It was noted from the review that agents often have different attributes attached to them. Household agents were represented by a combination of physical, psychological and socio-economic attributes. However, institutions as agents were mainly represented with physical attributes (Fig. 5b).

Fig. 5
figure 5

Shows the different application types, agent types, and the attributes agents have. a Application type has been plotted with the different types of agents. b Shows the different attributes agents can have such as physical, psychological and socio-economic

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Physical attributes comprise building location, height, and distance from road networks (Abebe et al. 2019a, 2019b; Lumbroso and Davison 2018). The agents’ psychological attributes include risk perception, coping capacity, and risk tolerance thresholds (Michaelis 2020; Tonn 2019). There are also instances where agents' socioeconomic attributes such as income, education level, employment type, gender and age were included in studies (Dawson et al. 2011; Yang et al. 2018; Zhu et al. 2018). Some agent attributes can be static such as building height, and others can be dynamic such as location.

3.2 Design

3.2.1 Basic principles

Decision making in ABM simulations is based on different rationales or assumptions. The justification for agents’ decision-making can be founded on theories, empirical data collected through literature, and real-world observations, or it can be based on ad-hoc rules. Most of the decision making in ABMs was governed by ad-hoc rules 61%, followed by theories (26%), and 10% using real-world observations. In emergency management, related studies, rule-based decision making is commonly applied (39%), and none of the studies had used theories. The use of theories is more common in risk and adaptation studies (26%). The expected utility theory is frequently used where individuals seek out the best strategy with increased rationality and desire to reduce risks (Michaelis et al. 2020; Haer et al. 2019; Haer et al. 2017; Han et al. 2019). Prospect theory, another commonly applied theory, where individuals’ decisions are governed by bounded rationality, and decisions are made on limited information and processing capabilities.

Several reviewed papers have used past empirical studies or experience-based approaches to assign agent decisions. Interviews, questionnaires, and previous literature are generally used for data collection. For example, using participatory approaches, stakeholders or experts can work directly with the modeller to explain how decisions will be made and verify agents’ decisions (Nakanishi et al. 2019). In another study, community visits were made, and workshops were held to explore the senses of water, and variables to be included in the model were identified. The workshop employed various qualitative research techniques; social cartographies were made with children, and community discussions were held (Villefas Gonzálazez et al. 2016).

3.2.2 Learning

According to the review, in only 21% of the papers, agents can learn and dynamically change their decision-making process, while 71% did not incorporate learning. Most of the learning can be seen in risk and adaptation studies (Fig. 6a); on the other hand, emergency management-related studies do not incorporate learning as often. Furthermore, although some studies have both institutions and households as agents, learning was only noted among household agents (Fig. 6b). Most of the learning occurs amongst those agents who had a psychological attribute. One way learning was incorporated was through ‘Bayesian prospect theory’, where an individual continues to learn as new information becomes available (Haer et al. 2017). This method can be categorised as more cognitive and psychological. Du et al. (2017a) used opinion dynamics modelling to determine the final decisions made by agents where multiple sources of information are available, and agents have varying learning capabilities. Learning was also included using the Bass diffusion model which shows how new information gets adopted in a population, which then classifies these learners as “innovators” or “imitators of an action (O'Shea et al. 2020).

Fig. 6
figure 6

Learning indicated with a Yes/No response plotted with a application and b agent type

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3.2.3 Sensing

The environment in an agent-based model determines the flow of information amongst agents in a spatial and a temporal domain (Tang and Bennett 2010). Sensing refers to how agents perceive the environment around them. Sensing occurred endogenously (locally) in about 38% of the studies, exogenously in 10% of the studies, and 8 % used a combination of both. Most of the exogenous sensing occurs in emergency management studies. The sensing type could not be determined in around 25% of the studies.

In endogenous sensing, the agent senses risks or the changes in their own environment by observing changing attributes or cues within the local environment. For instance, an agent senses flood risk when the floodwater level exceeds building heights. In an example of endogenous sensing by Nakanishi et al. (2020), agents observe their surrounding environment, updating their knowledge of the relative safety of different locations. Moreover, individuals sense a flood warning issued by the local authority and sense an impending flood at a distance of 100m (Alonso Vicario et al. 2020).

In exogenous sensing, the agents receive information from a set of global variables, not within the local environment of the agent. In some studies, the flood onset or flood warning depends on the initialisation of global variables, and therefore changes (Alonso Vicario et al. 2020). Moreover, a flood warning can be released as a global forecast, and agents are assumed to have received the warning without sensing any changes in their local environment. Haer et al. 2016, used two global settings that influence the communication strategy, defined by the percentage of people reached, and the success rate of the communication strategy in changing the attitude of a household.

3.2.4 Stochasticity

Stochasticity was present in 70% of studies. Stochasticity can be incorporated through agent decisions or model simulation. For instance, in Abebe 2019, agents’ compliance rates and locations of new houses are stochastic and drawn from a random uniform distribution. The Monte Carlo sampling method was also used to incorporate stochasticity (Wang et al. 2020). This was done by executing the model 500 times per scenario to stabilise numerical results. Similarly, Lumbroso and Davison (2018), used Monte Carlo simulation to represent the probability distributions for critical flood depths and velocities that affect loss of life. Alonso Vicario et al. (2020) used different probabilities to add randomness in daily routines and behavioural parameters. Nakanishi et al. (2020), also incorporated stochasticity, where agents probabilistically adjust their willingness to evacuate based.

3.2.5 Collectives

Collectives were included in around 28% of the reviewed studies. The instances of collectives were mainly noted in the emergency management-related studies (~73%), primarily to define different categories within agents. For example, Dawson 2011, used collectives to distinguish household agents as males and females, and different age categories to derive travel patterns. Similarly, Shirvani et al. (2020) used different body heights and weight to reflect pedestrians’ walking speed in floodwater through additional behavioural rules.

3.3 Details

3.3.1 Initialization

This review finds, that in most studies (54%), had initialised values probabilistically through uniform distributions or by randomly assigning values within a range for agents’ state variables. Approximately 18% of the studies used existing or empirical data, and about 13% of the studies used a combination of methods. For instance, the factors which affect agents’ psychological state, such as risk perception or coping capacity, are determined from the literature. Each factor affecting an agent’s decision can be randomly assigned a value drawn from probability distributions. Nakanishi et al. (2020) use regional demographic information and evacuation policies outlined from survey data, initialising a synthetic population (Nakanishi et al. 2020). Han et al. (2019) determined decisions based on risk perception and prospect utility using a subjective weighting parameter calculated based on equations. In around 15% of the studies, how the values were initialised could not be determined.

3.3.2 Sub-models and processes

3.3.2.1 Flood hazard and risk

For hydrological applications in an agent-based environment, flood simulation has been carried out in several ways. Most studies have used a hydrodynamic model for flood simulation ~51 %. In hydrodynamic modelling, 1D models are used to understand river channels, and 2D component models water flow on the ground (overland flow) (Villefas Gonzálazez et al. 2016). The flood simulation occurs in two steps; first, flood hazard is modelled, and second, flood risk is calculated. Flood hazard modelling shows the inundation of water depths, whereas flood risk measures damage and loss (Tsakiris and Sciences 2014). Commonly used hydrodynamic models are MIKE-FLOOD and LISFLOOD-FP (Abebe et al. 2019a). The second step entails determining flood risk through damage assessments. Most studies have used flood water depth to calculate damage and loss. Dawson et al. (2011) used inundation information as a function of the probability of a flood event using an economic damage function. The flood damage in this study was calculated based on the residential damage function, whereby risk was expressed for each property. Mustafa et al. (2018) computed water depth for varying flood return periods; after that, the susceptibility of a building to flooding was assessed by a stage-damage function giving the relative damage with monetary value for each return period of the flood.

Other types of modelling include deterministic models (7%) and numerical models (3%). Where a conventional flood model has not been set up, stochastic modelling (such as extreme value analysis) has been done to represent flood simulation (17%). For instance, Tonn et al. (2019) derived flood elevations from a dataset of peak annual floods and thereafter used a Weibull distribution to obtain a 1 in a 100-year flood event. In other cases, existing data has been used, which provided information such as flood extent and water depth height (Li and Lim 2016). In about 15% of the studies, explicit flood simulation has not been conducted, but flood risk is only perceived through the agents’ psychological attributes, and no actual flood modelling has been done (Erdlenbruch and Bonté 2018; Haer et al. 2016; Nakanishi et al. 2019).

3.3.2.2 Urban systems process

For urban system processes, two common approaches have been seen, where the first approach entails undertaking flood simulation specifically for urban areas as described in the preceding section. For instance, Dubbelboer et al. (2017), simulated flood events using time series in an urban spatial weather generator.

The second approach entails simulating the urbanisation process, densification, or urban expansion. Mustafa 2018, used existing urban land use data to extrapolate observed demand rates for future scenarios. New urban cells were developed within the spatial ABM and then allocated to agents. Thereafter, the urban density indices were classified into six density classes to show the least and most dense areas due to urban expansion.

Löwe et al. (2017) used a DAnCE4Water model where urban development is implemented based on population projections that result in new households being developed in the catchment yearly. The urban development model is implemented as GIS layers in an SQLite database. The zoning policies were implemented as rules for developer agents to develop specific areas based on factors such as distance to transport routes, service centres, or green spaces. The planning horizon of 50 years in 5-year intervals was used for urban development, making this a risk and adaptation study with a long-time scale.

Abebe (2019a, 2019b) simulated the urban housing expansion process based on existing building permits to determine the number and location of new houses and future housing parcels. Building data and Open Street Map residential building surface data are commonly used as input data for urban systems related sub-process.

3.3.2.3 Traffic modelling

Traffic modelling entails using a traffic network system comprising connected lines and points indicating the road network and the movement rules within those road networks. It can account for the interactions of people and vehicles. The Nagel-Schrenberg model has been most used to simulate the movement in the reviewed studies. There are instances where the agent-based environment has been used to make the traffic simulation (Zhu et al. 2018). The traffic simulation considers vehicle acceleration, deceleration and checks for speed to avoid a collision. Speeds of the vehicle is mostly a randomly selected parameter to exhibit different agent driving behaviour. The Dijkstra method has been commonly used to determine the shortest path route in a connected network. Li and Lim (2016) used an Urban Network Analysis toolbox (Sevtsuk and Mekonnen 2012), designed to examine cities' spatial configurations and a redundancy tool that calculates the second shortest paths for the nearest evacuation buildings within a specific distance. These were used to establish the evacuation paths and time for emergency management studies.

3.4 Model analysis and accessibility

ABM model analysis happens in two parts, i.e., at the micro and macro level. This means that verification occurs at the model design or conceptualisation phase (micro) and validation occurs in the output or the simulation phase (macro). For model analysis, 48% of the studies have used sensitivity and uncertainty analysis, 7% validation using other methods, 14% verification, 14% used a combination of verification and validation. In comparison, 17% did not state any information regarding the model analysis. For verification, empirical-based studies and data extracted from surveys and interviews were used to determine agent actions in the conceptualisation phase. For instance, Erdlenbruch and Bonté 2018, used data based on a survey of 331 households in South of France to determine the surveyed households' distribution, location and previous experience with floods.

In the validation approach, Nakanishi et al. (2019) evaluated evacuation time for different scenarios and validated the results using local knowledge undertaken in a comprehensive interview-based data collection exercise. Yang et al. (2018) undertook uncertainty and sensitivity analysis of key variables that impact model results, namely rain scenarios, exposure of households, functions of depth-damage curves, and the value of household properties using a one-at-a-time-analysis technique (looks at the effect of one variable at a time, while keeping the other variables fixed) to see how it affects the model results. Dziubanski et al. (2020) also used a stratified sampling approach, i.e., randomly assigned values using a predefined normal distribution for sensitivity analysis.

Out of the 39 reviewed studies, only four had made the codes available online. Some studies had part of the pseudo-code available in the paper.

3.5 Thematic applications

3.5.1 Risk and adaptation

3.5.1.1 Policy analysis and long-term risks

In the review, approximately 35% of the studies pertained to understanding the implications of different policies and long-term risks under climatic scenarios. For instance, in the US, investigations revealed that voucher subsidies provided by the government for flood insurance policy coupled with house elevation policy are considered one of the best options for risk mitigation (Han et al. 2020, 2019). In the Netherlands, it was found that with the pro-active approach of government and households, flood risks will decrease by 80%; however, under future climate scenarios, the current policies will only mitigate 40% of the risks indicating a need for a policy upgrade (Haer et al. 2019). Tonn et al. (2019) stated that under the median climate scenario, total damage was generally higher than under the historical scenario; however, this was contingent on the risk perception of agents as high risk perception channels into mitigative procedures.

Lipiec et al. (2018) determined the quantitative impacts of current and alternative coastal adaptation policies. Consequently, the most beneficial approach, such as hard structural changes, are the hardest to implement. For each adaptative strategy, it is vital to consider the investment cost of implementation and the reduction in flood damage. Whilst a strategy may be efficient in reducing risks; however, the heavy costs associated with the strategy may not make the option viable. Important considerations by the government are whether they should invest in new infrastructure where it is lacking or prioritise maintenance of existing infrastructure. Haer et al. (2020) investigated the safe development paradox using ABM – where large engineering structures are considered to provide a false sense of security, leading to reduced adaptation efforts from people.

Abebe et al. (2019a) looked at the effects of household and government decisions. Flood risk levels were quantified based on the number of flooded houses, and those that were elevated or built far from the coastline, and these emerged from the behaviour of household agents. The study found that the impact of zoning policies will not have an immediate impact but will become evident gradually. Yang et al. (2018) stated that policies for risk mitigation should be geared at a household level rather than at a public level, where policies for risk mitigation should aim to increase individuals' capacities.

3.5.1.2 Urban applications

Approximately 17% of the reviewed studies focused on urban applications for flood risks in an agent-based environment. Mustafa et al. (2018) tested the different urbanisation scenarios on flood risk. They concluded that with increased new developments and no regulations on urbanisation, flood risk would increase by 6%. The study further concludes that eventually, densification of existing urban areas is more detrimental than the increased number of urban areas.

Another study in the UK used a coupled agent-based model to show urban expansion scenarios (Sanchez et al. 2014). An interconnected drainage model was also used, which showed that it was imperative to increase the drainage network as urbanisation increased to combat the issue of flooding. Analysing the effect of different structures on flood risk revealed that widening stormwater pipes would be the most efficient strategy to reduce urban floods (Löwe et al. 2017). The same study further inferred that installing a rainwater harvesting tank in urban buildings has minimal flood risk reduction.

According to Jenkins et al. (2017), investment in property-level flood protection and sustainable urban drainage systems reduce surface water flood risk, however, the benefits can be outweighed by continued development in high risk areas and under the effects of changing climate scenarios. As noted previously, this can be attributed to risk perception. Low risk perception may lead to continued development and urban growth in floodplains, and high risk perceptions may deter urban expansion (Michaelis et al. 2020).

3.5.2 Emergency management

3.5.2.1 Evacuation response

About 33% of the reviewed studies looked at evacuation during flood events. For example, Dawson 2011, looked at flood exposure for travel behaviour and concluded that agents’ experiences and locations on the weekdays versus weekends influence exposure. Since people are more likely to be at home during the night and at work during the day, should a flood event occur while agents are at work, they are more prone to traffic congestion. Nakanishi et al. (2019), found that social media information towards risk perception makes evacuation decisions more uncertain due to the rapidly changing nature of social media.

Higher density communities generally have high evacuation times; however, if the population comprises a higher number of vulnerable agents, the evacuation time also increases for low-density neighbourhoods (Wang et al. 2020). In developed nations, evacuation usually takes place in private cars, and in developing countries, evacuation takes place on foot (Nakanishi et al. 2019). Shirvani et al. (2020), Shirvani et al. (2021) linked a hydrodynamic model to a pedestrian model to demonstrate evacuation times from a shopping centre in case of a flood.

Zhu et al. (2018) used ABM to show the effect of flooding on traffic and deduced that as rainfall increases, so does crowding degree, with more traffic congestion occurring on weekdays than on weekends. Furthermore, staying home was not the best individual choice, so residents' response behaviour based on their subjective consciousness during floods may result in increased overall exposure (Zhu et al. 2019).

Shelter assignment information on different evacuation centres, reasonable accessibility in terms of a road network, cost, impedance, travel along with the network and the best possible routes, are essential factors to consider in car-based evacuations.

3.5.2.2 Flood warning communication

Approximately 15% of the studies focused on warning, communication, and response. In Australia, a study used different flood warnings and levels of awareness to understand evacuation times during floods (Liu and Lim 2018). Results indicated that evacuation preparation starts when a warning signal is received, but agents act only after receiving information about the nearest evacuation shelter. Inaccurate flood forecasts may cause delays or inadequate response in agents to make evacuation-based decisions (Du et al. 2017a).

Different warning levels and suitable lead times are essential components of flood warning systems. Short warning interval with a high frequency of warnings gives households more opportunities to take action in a long flood duration (Yang et al. 2018). Damages are shown to increase with a longer lead time. Longer lead times may mean more uncertainty, leading to a loss of trust and confidence in the warnings provided (Du et al. 2017b).

However, a shorter warning time intervals with higher lead times are more effective, such as having bulletins every hour (Yang et al. 2018), may assist in reducing risk. In high-density communities, warnings with longer lead times are more beneficial to give agents more time to evacuate (avoid traffic build-up).

With a poor flood warning system, exposure of agents to floods increase. Warning information should have a reasonable probability indicating the certainty of floods, a long enough lead time warning interval to show the development of the flood or indicate the flood status (Yang et al. 2018). For instance, if the likelihood of flood is indicated, an 80% chance of having a surge in two hours holds more credibility than a warning with low probability. This shows the types of warning information agents are likely to be taken into account.

Distinct levels of warning, disseminated at incremental intervals, probability of flood (certainty of the event), and suitable lead time are essential components of flood warning systems. In developing a flood warning system, these are some essential considerations that will help attain the highest levels of efficacy.

4 Discussion

The overall findings from this review are that generally, in risk and adaptation studies, the flood model drives the design of the ABMs (hydrology-driven models). In this case, the hydrological model's spatial and temporal characteristics are given, and other ABM components are aligned to that. However, there are cases where the social process drives the design of ABMs, and the flood simulations are “accommodated” into them. In this case, the spatial and temporal characteristics of the model are determined by the social process being simulated, for example, emergency management related studies. The flood model is aligned or adapted to the scale of the social process.

4.1 Overview

Spatio-temporal specifications are important components of the model development process, and the different scales can affect the model results. For modelling with ABMs, a fine spatial resolution is required, however, respective fine resolution for hydrological parameters such as digital elevation will mean a computationally expensive hydrodynamic model must be employed. On the other hand, if the spatial discretisation is too large for a flood model, then important information such as flood velocities and depths will be averaged over a large area leading to a loss of information, which impacts the reliability of the results (Lumbroso and Davison 2018). There is a trade-off between making the model real versus understanding the agent behaviour, where focusing on one may compromise the other (Filatova 2015). It was also noted from the review that most studies were applied to a case study area at a smaller scale. Importantly, behavioural adaptation by actors that appear to be successful on a small scale (or in one part of a system) should not be generalised. This may produce negligible or even have adverse effects for larger spatial areas (Hammond 2015). ABMs are often criticised for lack of ability to depict the natural world system; however, this study found that most of the studies had used explicit space, indicating that the models are calibrated for realistic settings.

The temporal scale and the discrete time-step also impact the simulation results. A flood is a rapidly changing phenomenon; therefore, selecting the appropriate time step could significantly affect the results. For example, if the flood model is simulated at a three-hourly scale, and the discrete-time step for ABM simulation is at an hourly scale, there is a lag time of three hours when new flood update information is passed to the agents. In the studies, most of the model development process occurs so that agents endogenously or locally sense their environment by observing changes in local parameters assigned, which may get updated every third hour. In contrast, the flood scenario in the real world is a rapidly changing phenomenon, but this may not be captured adequately by an ABM when the flood information is available at three hourly timescales, which is a limitation of the model. The interaction of agents with the flood event at each time step affects the decisions and risks people will encounter (Lumbroso and Davison 2018).

This also points to the finding that most reviewed flood studies are single event-based per year. This may be attributed to the computational demands of the model as simulating a hydrological model for multiple flood events per year for a 30-year period may increase computational resources. Importantly, this may be appropriate for emergency management-related studies where one event can shape people’s decisions or behaviour; however, numerous flood events per year will likely influence the agent’s long-term behaviour and decision-making particularly for risk and adaptation studies.

Most of the model outcomes in the reviewed studies are based on single space-time scales. Sensitivity analysis can be carried out to see the impact of multiple space-time scales on model results; however, in most studies, it is carried out for factors that pertain to human decision making. Therefore, multiple space-time scales should be considered in the model development stage to determine the most suitable time applicable for a given system, thus increasing model reliability and applicability (Kang and Aldstadt 2019).

4.2 Design

The review finds that most studies have households or a combination of households and institutions as agents. Households are represented by a combination of all three attributes (physical, psychological and socio-economic); however, institutions are mainly represented with physical attributes. Among households, the decisions were justified mainly by economic theories, while few used cognitive theories such as belief-desire-intervention (Taillandier et al. 2021). The review finds that the basic principles of decision making for emergency-related studies mainly comprise ad-hoc rules. In contrast, risk and adaptation studies had a combination of rule-based and theories for agent decisions. Human behaviour is complex, particularly in a crisis where decision making may occur as a ‘reflex’ reaction to a disaster; these have not been captured well in emergency management studies and have been simplified. Agents’ decisions and interactions can be highly random, leading to non-linearity and non-continuity in the model simulation. Most studies introduce stochasticity in the model design to reflect this randomness in decision-making studies and address the issue. Machine learning techniques are often well suited to deal with non-linear and non-stationary data in other domains of research (Anshuka et al. 2019; Dramsch et al. 2021), and these can be applied to overcome some of the challenges associated with human decision making (Bastani et al. 2021.).

In addition, the basic principles of decision making for institutions was mainly based on cost-benefit analysis (CBA) (Michaelis et al. 2020; O’Connell and O’Donnell 2014) and not justified by a range of options such as economic or cognitive theories as is the case in among household agents. From a government point of view, economic efficiency is important; however, CBA has a few challenges. It does not account for the impact of floods on human welfare and the ecosystems; there are discrepancies in quantifying the actual economic cost of flood damage and, it does not account for cultural and individual factors that play important roles in determining the willingness of individuals to invest in risk preparedness (O'Connell and O'Donnell 2014) This opens an avenue for further research on trying to understand different ways in which decisions are made by institutional agents such as governments in FRMA and not just limit to CBA. In addition, there is an avenue to expand research on how other institutions such as NGOs play a role in the flood risk reduction process. Heterogeneity in the types of agents that are important in a system’s behaviour and decision-making process can be critical in assessing interventions (Hammond 2015).

Based on the ODD, the review found that agents’ decisions are direct or indirect objective seeking where agents rank different measures and follow the rules for economic theories. The ranking process for risk perception is influenced by several factors such as social interactions, prior knowledge, and experiences are to name some (Sattler et al. 2018). However, the risk perception will be biased towards the more heavily weighted factor during the model conceptualisation process. The critical factors in the decision-making process are determined through literature and supported with empirical evidence wherever possible in most studies. However, it is unclear how the weightings are assigned to these factors or not always justified by literature in some studies.

Social interactions in the real world are common and can lead to a higher level of awareness and materialise into a decision. This can be incorporated into the design process of the models, where agents can dynamically learn. However, the ability of agents to learn dynamically has been rarely included in the study designs reviewed. Most of the learning can be seen in risk and adaptation studies attributed to long-term decision-making, which requires agents to assess risk and make the best choice. On the other hand, emergency management-related studies do not incorporate learning as often, as the motive is to take a reactive approach and quickly respond to the risk. Because learning entails changing the adaptive rules, it also increases the complexity of the model.

Similar to learning, collectives have been minimally used in the model design process among the reviewed studies. To include learning, the tension occurs again in the balance between parsimony and breadth of the model.

The review also found that the models are designed so that agents locally or endogenously sense the environment in most studies. An exogenous variable’s value is determined outside the model and is imposed on the model (without it being affected by other variables). In contrast, in endogenous sensing, agent can sense information only based on the attributes assigned to them. It has values determined by the model, which is affected by other model variables. This can be attributed to how models are programmed. For instance, in an object-oriented paradigm, operations and data (or behaviour and state) are grouped into modular units called objects (An et al. 2005), leading to the formation of a structured network (Larkin and Wilson 1995). Making the variables global and changing these variables at each time step may increase the computational resources required for the models.

A parsimonious model allows for effective tracing from inputs to the simulation outcome and has a low computational demand. However, to reflect the real-world complex-system models, there is often pressure to include as much realism as possible (Hammond 2015). Making a model complex may even derail the modeller from the initial motivation of model development, and the outcome may not align with what the model was supposed to do.

4.3 Details

From the review, it can be noted that a large majority of the studies use hydrodynamic models and stochastic models for flood simulation. In risk and adaptation study types, hydrodynamic models are more common. Emergency related management studies also utilised hydrodynamic models, albeit slightly less than risk and adaptation studies. Using deterministic models, existing data, simplified non-physics-based models, and including flood risk through psychological attributes is more prevalent in emergency management related studies. This could be because social processes such as traffic modelling in evacuation exercises require a higher spatio-temporal resolution, and modelling flood as such a fine resolution is computationally demanding.

Input variables in a flood loss model usually consider a range of factors such as water depth, duration, inundation, building characteristics and socio-economic factors (Gerl et al. 2016). The final value of damage assessment is subject to the damage curve functions used for analyses and the parameters used (Löwe et al. 2017). Water depth has been most commonly used in the reviewed studies to calculate damage risk. However, other parameters, such as the rising rate of floodwater and flow velocity, are minimally used. In flash floods, water can rise within a matter of minutes to a few hours (Kobiyama and Goerl 2007); and empirical studies show that despite the warnings, people still have difficulty in anticipating the rate of floodwater rise, putting their lives at risk (Ali et al. 2017; Anshuka et al. 2021). Therefore, incorporating other parameters to calculate damage assessment can be an essential criterion, notably for evacuation and early warning related studies.

The flood simulation process can be captured in the ‘sub-model process’ component of the ODD. It was noted that those studies that did not use ODD protocol for model description had a comprehensive description of the flood model, albeit done in a non-standardised way. Specific components of the sub-models are not currently well-captured by the ODD. The ODD protocol’s sub-model process component is presently explained by providing a factual description of a sub-model, i.e., “..the model parameters, dimensions, and reference values? How were sub-models designed or chosen, and how were they parameterised and tested?” As we see the application of ABM in conjunction with other complex models such as traffic and urban process models, understanding the development of different processes is as important as understanding the ABM. Therefore, we recommend that the ODD protocols and sub-model processes be improved so that it is better able to capture the functionality of flood models and models in other disciplines. This will consequently allow the process to be captured more systematically and facilitate comparison across the studies, a purpose on which ODD is based.

Most studies use sensitivity and uncertainty analysis to analyse model results. Other validation approaches, such as comparing the simulated ABM outcome with real-world observation, is generally challenging because of the lack of existing data. For instance, to validate the results and calculate a metric such as the R2 score, existing data must show how people/systems behave, which is difficult to quantify. In these cases, sensitivity analysis is a potential solution. Few studies did not analyse the model results. As a recommendation, model analysis can become part of the ODD protocol, which will compel modellers to think of ways to validate model outputs. Validated model outputs will increase the certainty of the results, and this may channel into higher applicability of ABMs for studies and policy-related work.

The studies which used the ODD protocol for the model description process made it easier to compare the model design process. The studies that did not use the ODD protocol did not have detailed information to fulfil the ODD components. Therefore, the model design process lacked information on different components, which does not facilitate the comparison of models and their results. Generally, with the use of ODD, the protocol was applied well with few instances of incorrect use, likely attributed to lack of proper interpretation of the component definitions.

5 Conclusion

For the FRMA domain, the use of the ODD protocol was only seen in 25% of the studies. The studies which did not explicitly use the ODD had a comprehensive description of the models, albeit done in a non-standardised way, making it difficult to compare these descriptions across studies. The hydrological component is mainly captured in the sub-model process. Presently, this sub-component is not as comprehensive to adequately describe the hydrological process, particularly for the flood models that can allow for comparison of model results. The studies showed promise in calibrating the simulation with explicit space and use of hydrodynamic models. Human decision making is a well-researched area, and the justifications for human decision-making have been well provided. However, institutions’ decision-making warrants further research to understand how they make these decisions. For the design of ABMs, a trade-off between model complexity and simplicity was noted, bearing in mind that the papers simulate other complex processes such as traffic modelling. Before implementing an agent-based model, it is crucial to understand the system to be studied, which will guide the model’s conceptualisation and the requirements for the model development process. Applications of ABMs in the different thematic areas show the effectiveness of flood warnings, evacuation routes, or different policies in a given system setting. The direction of work through ABM can bring hydrological experts and social scientists to work together to have a more significant impact. One of the limitations of the review was that in some papers, it was not possible to get information at a very detailed level. In addition, there was not enough differentiation in the results for some ODD categories, particularly for the design process to include the components as a distinct category.