Agent‐based simulator of dynamic flood‐people interactions

Abstract

This article presents a simulator for the modelling of the two‐way interactions between flooding and people. The simulator links a hydrodynamic model to a pedestrian model in a single agent‐based modelling platform, Flexible Large‐scale Agent Modelling Environment for the Graphical Processing Unit (FLAMEGPU). Dynamic coupling is achieved by the simultaneous update and exchange of information across multiple agent types. Behavioural rules and states for the pedestrian agents are proposed to account for the pedestrians' presence/actions in/to floodwater. These are based on a commonly used hazard rate (HR) metric to evaluate the risk states of people in floodwater, and by considering two roles for the pedestrians: evacuees or responders for action during or before the flood event, respectively. The potential of the simulator is demonstrated in a case study of a flooded and busy shopping centre for two scenarios: (a) during a flood evacuation and (b) pre‐flood intervention to deploy a sandbag barrier. The evacuation scenario points to changes in floodwater hydrodynamics around congested areas, which either worsen (by 5–8%) or lessen (by 25%) the HR. The intervention scenario demonstrates the utility of the simulator to select an optimal barrier height and number of responders for safe and effective deployment. Accompanying details for software accessibility are provided.

Full text

ORIGINAL ARTICLE
Agent-based simulator of dynamic flood-people interactions
Mohammad Shirvani
1
| Georges Kesserwani
1
| Paul Richmond
2
1
Department of Civil and Structural
Engineering, University of Sheffield,
Mappin St, Sheffield City Centre,
Sheffield, UK
2
Department of Computer Science,
University of Sheffield, Mappin St,
Sheffield City Centre, Sheffield, UK
Correspondence
Georges Kesserwani, Department of Civil
and Structural Engineering, University of
Sheffield.
Email: g.kesserwani@sheffield.ac.uk
Funding information
Engineering and Physical Sciences
Research Council, Grant/Award Number:
EP/R007349/1
Abstract
This article presents a simulator for the modelling of the two-way interactions
between flooding and people. The simulator links a hydrodynamic model to a
pedestrian model in a single agent-based modelling platform, Flexible Large-
scale Agent Modelling Environment for the Graphical Processing Unit
(FLAMEGPU). Dynamic coupling is achieved by the simultaneous update and
exchange of information across multiple agent types. Behavioural rules and
states for the pedestrian agents are proposed to account for the pedestrians'
presence/actions in/to floodwater. These are based on a commonly used haz-
ard rate (HR) metric to evaluate the risk states of people in floodwater, and by
considering two roles for the pedestrians: evacuees or responders for action dur-
ing or before the flood event, respectively. The potential of the simulator is
demonstrated in a case study of a flooded and busy shopping centre for two
scenarios: (a) during a flood evacuation and (b) pre-flood intervention to
deploy a sandbag barrier. The evacuation scenario points to changes in flood-
water hydrodynamics around congested areas, which either worsen (by 5–8%)
or lessen (by 25%) the HR. The intervention scenario demonstrates the utility
of the simulator to select an optimal barrier height and number of responders
for safe and effective deployment. Accompanying details for software accessi-
bility are provided.
KEYWORDS
coupled agent-based models, evaluation of flood evacuation and mitigation strategies, flood risk
analysis, human response dynamics
1|INTRODUCTION
Flooding is a frequent hazard that can disrupt communi-
ties, in particular in small urban areas (<0.5 km ×0.5 km)
where people congregate. These areas usually include
important pedestrian hubs such as in or around shopping
centres, supermarkets, transport infrastructure, and foot-
ball stadiums (Becker et al., 2015). Although computa-
tional models have become central to mitigate, prepare
and manage flood risks (Kreibich, Seifert, Merz, &
Thieken, 2010; Kreibich, Bubeck, van Vliet, & de
Moel, 2015; Wedawatta & Ingirige, 2012), there is a partic-
ular strategic need to develop a simulation framework and
models for integrating human behaviour dynamics into
the flood risk analysis (Aerts et al., 2018; Lumbroso &
Vinet, 2012; McClymont, Morrison, Beevers, &
Carmen, 2019; Zischg, 2018).
Agent-based models (ABMs) offer a flexible method
to develop a computational model to simulate the co-
evolution of the actions and interactions of multiple
Received: 13 August 2019 Revised: 6 October 2020 Accepted: 16 December 2020
DOI: 10.1111/jfr3.12695
This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided
the original work is properly cited.
© 2021 The Authors. Journal of Flood Risk Management published by Chartered Institution of Water and Environmental Management and John Wiley & Sons Ltd.
J Flood Risk Management. 2021;14:e12695. wileyonlinelibrary.com/journal/jfr3 1of17
https://doi.org/10.1111/jfr3.12695

drivers that could lead to the emergent behaviour of
receptors (Bonabeau, 2002). This provides the ability to
dynamically explore the synergies between social and
physical dynamics and mitigation policies, making ABMs
ideally suited to support flood resilience studies at differ-
ent scales (spatial, temporal, and organisational). In
recent years, ABMs have been devised to support flood
risk management, most commonly at meso and macro
scales (Lumbroso, Gaume, Logtmeijer, Mens, & van der
Vat, 2008), to simulate and analyse various receptors'
response to floodwater. For example, ABMs have been
developed to evaluate: risk management strategies under
future climate change scenarios with multiple institu-
tional drivers (Abebe, Ghorbani, Nikolic, Vojinovic, &
Sanchez, 2019; Jenkins, Surminski, Hall, & Crick, 2017);
business loss and long-term effect of floods on economic
growth (Grames, Prskawetz, Grass, Viglione, &
Blöschl, 2016; Li & Coates, 2016); and, the effect of pro-
tection measures, individual behaviour and flood fre-
quency on the resilience of at-risk communities (Tonn &
Guikema, 2018). ABMs have also been built for flood
evacuation planning in coastal areas, to estimate evacua-
tion times for dam failures, and to estimate the number
of casualties and injuries (Aboelata & Bowles, 2008; Daw-
son, Peppe, & Wang, 2011; Liu & Lim, 2016; Lumbroso &
Davison, 2018; Lumbroso, Sakamoto, Johnstone, Tagg, &
Lence, 2011; Mas et al., 2015).
For flood risk analysis in small and congregated
urban areas, only a few ABMs have been designed for the
evaluation of evacuation strategies considering the emer-
gent behaviour of individual people in response to a
flood. Liu, Okada, Shen, and Li (2009) devised an ABM
to simulate the movement of up to five evacuees in an
underground station during a flash flood, while inter-
acting with each other and responding to the station's
layout and the flood information available. Bernardini
et al. (2017) designed “FloodPEDS”: an ABM incorporat-
ing a crowd of pedestrians responding to evolving flood-
water under evacuation scenarios. In FloodPEDS,
pedestrian movement in floodwater has been modelled
via (sparse) data processed from video footage of people
stuck in floodwater. The modelled data was incorporated
into a standard pedestrian simulation model. Such
models combine a local motion planning model
(i.e., social force model) with a global path planning
model (i.e., a navigation map). The social force model
accounts for the movements of each individual and by
modelling the interaction between individuals to derive
forces that avoid collisions with neighbours. Whereas,
the navigation map encodes the features of the walkable
area necessary for the individuals' way-finding decisions
(Jiang, Chen, Li, & Ding, 2020; Li, Wei, & Xu, 2019), for
example, terrain obstacles and walls that need to be
avoided as the individuals navigate and vector fields pro-
viding navigation to key destinations. More generally, the
life safety model (LSM, www.lifesafetymodel.net) has
been developed to assess the risk of flooding on people
while taking into account dynamic interactions between
multiple receptors across different scales. The LSM incor-
porates interactions between vehicles, via a traffic model,
and includes a pedestrian flow model accounting for peo-
ple movement as they relay warnings to each other
(Lumbroso & di Mauro, 2008; Lumbroso et al., 2011;
Lumbroso, Simm, Davison, White, & Durden, 2015;
Lumbroso & Davison, 2018). Similarly, the LifeSIM
model (www.hec.usace.army.mil/software/hec-lifesim)
was developed to include an individuals' response to
emergency warnings and their interaction with each
other and their surroundings, for example, urban layouts
and buildings, to estimate fatalities under flood-induced
evacuation conditions. However, these ABMs are applied
to support modelling problems at relatively large spatial
scales, where the presence of people will not have a sig-
nificant impact on floodwater depths and velocities
(>5 km ×5 km). Also, they are not dynamically coupled
to a hydrodynamic model. This may be needed to incor-
porate local changes in the floodwater hydrodynamics in
response to the people movement in confined areas of
mass gatherings, for example, groupings during an emer-
gency evacuation, or changes in the height of the ground
elevation in response to targeted people actions, for
example, as they act as sandbaggers. For small and con-
gregated urban areas, such people responses can actually
affect the floodwaters, and thus developing a fully
coupled “flood-pedestrian”simulator in a single ABM
platform is necessary to be able to capture two-way inter-
actions between people and flooding.
This article presents the development and evaluation
of a “flood-pedestrian”simulator, which dynamically
couples a hydrodynamic model to a pedestrian model on
the Flexible Large-scale Agent Modelling Environment
for the Graphical Processing Unit (FLAMEGPU)
(Section 2.1). The FLAMEGPU platform allows discrete
and continuous agent types to be defined, and to dynami-
cally give-and-take copies of the data stored across multi-
ple ABMs (Section 2.2). The hydrodynamic model is
incorporated on a grid of fixed agents (Section 2.3),
referred to as flood agents, which is coincident with the
navigation map of the pedestrian evacuation model
(Section 2.4). The latter involves continuous pedestrian
agents driven by a social force model and moving on the
navigation map spanned by a fixed grid of navigation
agents. Dynamic passing of information across the pedes-
trian and flood agents is facilitated by the navigation
agents (Section 2.5). Behaviour rules governing pedes-
trian interaction with/to the flood hydrodynamics are
2of17 SHIRVANI ET AL.

implemented based on one of the two different roles that
pedestrians can be assigned: evacuees moving in floodwa-
ter where the presence of individuals and groups of peo-
ple are incorporated by changing the surface roughness
coefficient in the hydrodynamic model; or, responders
participating in pre-event sandbagging where the sand-
bags are incorporated by changing the height of the gro-
und elevation parameter in the hydrodynamic model.
The dynamic coupling ability of the proposed simulator
is demonstrated over a synthetic case study of a flooded
and crowded shopping centre considering two scenarios:
(a) during a flood evacuation (Section 3.1), and (b) pre-
flood intervention to deploy a temporary flood barrier
(Section 3.2). Simulation results are discussed considering
the broader implications on flood evacuation and inter-
vention strategies for small and congregated urban stud-
ies. Conclusions are drawn reflecting on the future
research needs (Section 4), and the details for accessing
the simulator software are provided in the acknowledg-
ments section.
2|MATERIALS AND METHODS
2.1 |Overview of FLAMEGPU
FLAMEGPU is a computational platform for the simula-
tion of multiple agent interactions on CUDA Cores for
parallel processing on graphical processing units (GPUs)
(Chimeh & Richmond, 2018; Richmond, Coakley, &
Romano, 2009). It involves a standard procedure to create
and run a CUDA simulation program by processing three
inputs, as shown in Figure 1. The XMLModelFile.xml is
where a user defines formal agent specifications, includ-
ing their descriptive information, type, numbers, proper-
ties, etc. An agent can be specified in space as either
discrete or continuous (FLAMEGPU user guide). Discrete
agents have fixed coordinates and must be pre-allocated
in the memory of the GPU as two-dimensional (2D) grid
of size of a power of two numbers (e.g., 64 ×64,
128 ×128, 256 ×256, 512 ×512, etc.). Continuous agents
change their coordinates and their population; they can
be of any population size (within the limitations of avail-
able GPU memory). The input.xml file contains the initial
conditions of the variables of state of all the defined
agents. In a single C script, the behaviour rules to update
all agents are implemented, and include Transition func-
tions to achieve dynamic passing of the information
stored in the agents as they get simultaneously updated
(FLAMEGPU user guide). The implementation of the
coupled flood-pedestrian simulator on FLAMEGPU is
described next, with a focus on the agent specifications
and rules for interactions used across both the hydrody-
namic model and the pedestrian model.
2.2 |Agents specifications
The pedestrian model involves two agent types: naviga-
tion agents and pedestrian agents. Navigation agents are
defined to be discrete, that is, agents are located on a grid
encoding a navigation map detailing obstacles and navi-
gation fields for a given study area. Each singular naviga-
tion agent stores information that a pedestrian requires
to carry on with their movement at the discrete location
which it represents. This information in particular, con-
veys the direction to key destinations and their location
on the map (e.g., the entrances, exits, and walkable path-
ways), and obstacles that pedestrians must avoid
(e.g., walls and terrain blocks). For this study, a grid reso-
lution of 128 ×128 navigation agents is defined to pro-
vide pedestrian agents with the information on the
location and direction of the entrances/exits and the ter-
rain features in the study area. In this work, this
FIGURE 1 The process for
generating and running an
agent-based simulation program
on flexible large-scale agent
modelling environment for the
graphical processing unit
(FLAMEGPU) (http://www.
flamegpu.com/home). A
detailed list of the agents'
description and initial states is
available in the accompanying
“run guide”document of the
flood-pedestrian simulator
software (see also the
Acknowledgements section)
SHIRVANI ET AL.3of17

resolution was found sufficient to capture details of the
built environment.
Pedestrian agents are modelled as continuous space
agents as they can change position (represented as a con-
tinuous value) in space and over time. The space between
pedestrian agents is controlled by each one's perceptive
steering forces (Karmakharm, Richmond, &
Romano, 2010), which ensures that the pedestrian has a
physical radius given its continuous location position. In
the meantime, the pedestrian agents receive information
from the navigation agents that influence their way-
finding decisions from the navigation map. Multiple pedes-
trian agents can be presented at the same time over one
mutual navigation agent as they are of continuous type.
A hydrodynamic model, which describes flood agents,
is incorporated within FLAMEGPU pedestrian model to
enable the dynamic exchange of information between
navigation and flood agents. Flood agents are represented
using discrete agents, which are coincident with the grid
of navigation agents. Each flood agent stores its position
x(m) and y(m), terrain properties in terms of height
z(m) and Manning's roughness parameter n
M
(s m
−1/3
),
and the states of the floodwater variables in terms of
water depth h(m) and velocity components u(m/s) and
v(m/s). The states of floodwater variables in the flood
agent are affected by those stored in the adjacent neigh-
bours sharing its four interfaces. Therefore, each flood
agent is programmed to store and exchange information
with these four neighbours, in order to simultaneously
update the states of the floodwater variables in all the
flood agents (Section 2.3).
The information stored in the pedestrian agents and
in the flood agents is passed between them through the
navigation agents that act as shared communication
interfaces (Section 2.5). This means that each navigation
agent is set to receive the information of a pedestrian or
flood agent at their location and send back an update to
the flood agent. That is, a navigation agent converts the
information received from the flood agent into a flood
hazard rate (HR) quantity, which is retrieved by any
pedestrian agent walking in its spatial area. Estimating a
flood HR usually involves measuring a product quantity
of a water depth hto a velocity magnitude V(Costabile,
Costanzo, de Lorenzo, & Macchione, 2020). As in
Kvocˇka, Falconer, and Bray (2016) and Willis, Wright,
and Sleigh (2019), the degree of flood HR is estimated as
HR = (V+ 0.5) ×h, with V=max(juj,jvj), following the
risk to people method developed for the UK Environment
Agency (2006). Pedestrian agents therefore consider a
flood risk state and a walking speed state based on the
information of the flood HR they receive at their local
and temporal location. Pedestrian agents are also
assigned a role (Section 2.5) and accordingly pass certain
information to the navigation agent where they are
located at a certain time. This is to incorporates any local
change in the terrain properties caused by pedestrians'
presence or actions, namely: due to local and temporal
grouping of evacuees in certain zones leading to increas-
ingly higher surface roughness; or, due to sandbagging by
responders leading to a local change in the height of the
terrain. The navigation agent processes the information
on such changes, received by the pedestrian agents, and
passes them back to the hydrodynamic model to dynami-
cally updates the surface roughness's Manning's parame-
ter (n
M
) or the ground elevation (z) in the hydrodynamic
model. Then, it passes the updated terrain parameters
back to the flood agent at its equivalent position. Sec-
tion 2.5 follows up with the rules governing the interac-
tions between the flood, navigation, and pedestrian
agents.
2.3 |Update of the floodwater states
stored in the flood agents
As flood agents in the FLAMEGPU model are distributed
on a grid, their states of floodwater variables can be
updated by adopting a hydrodynamic numerical model
on a mesh formed by square elements (e.g., TUFLOW-
HPC, Wang, Liang, Kesserwani, & Hall, 2011). The
hydrodynamic model is re-implemented so as to suit the
non-sequential computation on FLAMEGPU such that it
dynamically updates the states of floodwater variables at
all the flood agents at the same time (i.e., in parallel).
A hydrodynamic model is selected based on an
explicit shock-capturing scheme (Wang et al., 2011), in a
first-order formulation to keep the calculation stencil lim-
ited to the information stored in the immediate neigh-
bours sharing its four interface (Figure 2). The scheme
numerically solves the 2D depth-averaged shallow water
equations, including the ground elevation and the Man-
ning's roughness parameter, written in the following vec-
torial form (Néelz & Pender, 2009):
∂tU+∂xF+∂yG=S ð1Þ
In Equation (1), tis the time, U=[h,hu,hv]
T
is the
flow vector containing the water depth and components
of the unit-width flow discharge, F=[hu,hu
2
+½gh
2
,
huv]
T
and G=[hv,huv,hv
2
+½gh
2
]
T
are the components
of the flux vectors with gbeing the gravity constant, and
S= [0, gh (S
0x
-S
fx
), gh (S
0y
-S
fy
)]
T
is the source vector
containing the terrain slopes from the ground elevation
(S
0x
=−∂
x
zand S
0y
=−∂
y
z) and friction terms (S
fx
and
S
fy
) expressed by the Manning's formula including n
M
.
4of17 SHIRVANI ET AL.

For a flood agent at position (x,y), their vector
Ucontains constant floodwater states at time iteration n,
which need elevating to iteration n+ 1 according to the
following formula (Figure 2).
Un+1
=Un−
Δt
ΔxFEAST −FWEST
ðÞ−
Δt
ΔyGNORTH −GSOUTH
ðÞ+S
ð2Þ
In Equation (2), Δt,Δxand Δydenote the time step
and dimensions of the flood agent. To update the states
of floodwater variables in the flow vector U
n
, the incom-
ing and outgoing spatial fluxes across the four interfaces,
denoted by F
EAST
,F
WEST
,G
NORTH
,G
SOUTH
, and the
source vector Sneed to be first evaluated. These evalua-
tion are performed while incorporating measures to
ensure robust treatments for wetting-and-drying and
terrain-slope terms (Wang et al., 2011). As each flood
agent (“dark blue,”Figure 2) receives the information
(“white message icons,”Figure 2) stored the four neigh-
bours sharing its four interfaces, the robustness treat-
ments alongside flux and source term evaluations can be
applied element-wise, that is, to simultaneously update
the states of floodwater variables in all the flood agents.
The non-sequential hydrodynamic ABM implementa-
tion on FLAMEGPU was verified in reproducing two 2D
dam-break flow tests (Huang, Zhang, & Pei, 2013; Wang
et al., 2011). In both tests, the hydrodynamic ABM on
FLAMEGPU reproduced the same predictions as the
sequential counterpart and shows close agreement alter-
native predictions (see Appendix for more details).
2.4 |Update of the pedestrian and
navigation agents
A pedestrian simulation model has already been
implemented in FLAMEGPU (Karmakharm et al., 2010),
which has been utilised by this study. It combines a social
force model, governing random walk movement of the
pedestrian agents and their interaction, alongside the nav-
igation agents of the navigation map that contains infor-
mation for the pedestrian agents to find their way in the
walkable zones within the study area (Jiang et al., 2020; Li
et al., 2019). When there is no floodwater, the walking
speed of the pedestrian agents is set to 1.4 m/s to represent
the average human walking speed (Mohler, Thompson,
Creem-Regehr, Pick, & Warren, 2007; Wirtz & Ries, 1992).
Nonetheless, the existing behavioural rules in both the
social force model and the navigation map allow the pedes-
trian agents to locally increase or decrease their walking
speed (e.g., when they need to abruptly change direction
to avoid collisions with each other or with existing obsta-
cles located in the study area). The pedestrian simulation
model has been adapted into a flood-pedestrian simulator
so as to enable exchange of information between the
pedestrian and flood agents. It is also adapted to inform
on pedestrians-related HR states, changes in local flood-
water dynamics as a result of the interactions between the
flood, navigation, and pedestrian agents as explained in
Section 2.5.
2.5 |Interactions between the flood,
navigation, and pedestrian agents
This section explains the behavioural rules programmed
to process the information dynamically exchanged
between the flood, navigation, and pedestrian agents.
Two different sets of pedestrian behavioural rules are
implemented depending on the role assigned to the
pedestrian agents, that is, either to be evacuees or
responders.Evacuee agents are pedestrian agents evacuat-
ing during a flood without a prior warning. Once a non-
zero water depth is received by any navigation agent on
the navigation map (i.e., from the flood agent at its same
location), the pedestrian agents will no longer be entering
the study area, and those remaining, that is, the evacuee
agents, will be leaving to an emergency exit destination
(specified by the user on the navigation map). Evacuee
agents in flooded zones receive the flood HR quantity
from the navigation agents where they are located.
FIGURE 2 A flood agent (“dark blue”) updating its states of
floodwater variables, U, from time iteration nto n+ 1. The process
is done simultaneously for all flood agents, facilitated by the
messages (“white message icons”) the flood agent receives to access
the states of floodwater variables of its neighbours sharing its four
interfaces
SHIRVANI ET AL.5of17

Aflood risk state is then assigned to each of these evacuee
agents based on the four HR ranges used by the UK Envi-
ronment Agency (2006) for identifying the level of flood
risk to people. These ranges define the low,medium,high
or highest flood risk state of HR (see Table 1). Evacuee
agents are also assigned a walking speed state that is
assumed
1
to be constant per flood risk state, such that:
•When an evacuee agent is in a low flood risk state, it is
able to accelerate its escape via a brisk walk that is on
average 1.8 m/s (Mohler et al., 2007).
•When an evacuee agent is in a medium to high HR
flood risk state, it needs to decelerate walking speed to
0.9 and 0.45 m/s, respectively. These walking speeds
are within the average range of human walking speeds
in floodwater (Lee, Hong, & Lee, 2019).
•When an evacuee agent is at the highest flood risk
state, it cannot walk in floodwater due to instability
issues and thus has a waking speed of 0 m/s.
Meanwhile, the evacuee agents that are present on
the flooded navigation agents are counted: their number,
N
p
, is used to locally update the Manning's roughness
coefficient n
M
in the hydrodynamic model as
n
M
=n
M
+N
p
n
M
(see Figure 3, left). The updated coeffi-
cient n
M
is then passed back to the flood agent at the nav-
igation agent's location to represent the effects of the
presence of individuals and groups of people on floodwa-
ter hydrodynamics. For this study, the initial n
M
parame-
ter is set to be equal to 0.01 s m
−1/3
, representative of
clear cement (Chow, 1959), and no more than 20 evacuee
agents are allowed to simultaneously occupy the area of a
navigation agent, which means that any local amend-
ment in n
M
cannot exceed 0.2 s m
−1/3
.
Responder agents form a group of the existing pedes-
trian agents, who are emergency first responders, taking
a series of actions to construct a flood barrier within a
specified time window due to an advanced flood warning.
A standard sandbagging procedure is implemented to
form the temporary barrier, which is an appropriate
choice to support this study.
2
To govern the movement
and actions of responder agents, destinations of the
sandbag storage and of the location of flood barrier are
initially specified on the navigation map (Figure 3, right).
Responder agents get information to walk to the location
of the sandbag storage. Once they reach it, they are set to
wait for half a minute representative of a picking up
duration (specified), and then pick up the information on
the dimension of a sandbag from the navigation agents
spanning the sandbag storage location (Figure 3, right).
Responder agents are then redirected to carry up this
information to the navigation agents spanning the tem-
porary flood barrier, which are set to receive it after a
wait of half a minute representative of a safe drop out
duration (specified). Responder agents are set to go and
share their information with one (specified) first naviga-
tion agent representative of the starting location for the
deployment. As the dimension of a sandbag is smaller
than the area of a navigation agent, the first navigation
agent is set to accumulate the received information until
it has enough to cover one horizontal layer of sandbags
all-over its area. Then, the first navigation agent
TABLE 1 Evacuee agent states in
floodwater selected based on the ranges
for HR tabulated in the flood hazard
matrix of the UK Environment
Agency (2006)
HR ranges
Flood risk state Walking speed stateFrom To
0 0.75 Low—safe to walk 1.8 m/s—brisk walk
0.75 1.5 Medium—mildly disrupted 0.9 m/s—slow walk
1.5 2.5 High—disrupted 0.45 m/s—slower walk
2.5 20 Highest—trapped 0.00 m/s—no walk
Abbreviation: HR, hazard rate.
FIGURE 3 Dynamic passing of stored information between a
flood agent and pedestrian agents (evacuees) facilitated via the
navigation agent that is aligned to the flood agent (left). Procedure
for pedestrian agents (responders) deploying a sandbag barrier
(right): red navigation agent represents a “sandbag storage”
destination and grey navigation agents represent the deployment
destination
6of17 SHIRVANI ET AL.

increments the ground elevation parameter, z, by one
unit of sandbag thickness. The process then moves to the
adjacent navigation agent spanning the flood barrier's
location, and so on until the single layer of sandbags
reach either a wall or an obstacle existing in the study
area. Responder agents then repeat the overall process N
L
times, until all the navigation agents spanning the flood
barrier's location are filled up with N
L
(specified) layers
of sandbags. After N
L
rounds, the height of the ground
elevation parameter at the navigation agents spanning
the flood barrier's location has become z×N
L
. This new
height for the ground evaluation is then passed to the
flood agents at their aligned location (Figure 3, left), that
is, to incorporate the changes from the presence of sand-
bags in the hydrodynamic model.
3|DEMONSTRATION ON A
SYNTHETIC CASE STUDY
A case study was developed to evaluate the flood-
pedestrian simulator for modelling dynamic interactions
between people and floodwater flows. The case study
utilised a shopping centre filled with people exposed to
flooding. It distinguished two independent scenarios one
with the pedestrians as evacuees, and another involving
them as responders. Scenario 1 assumed that there is no
early warning nor an early evacuation plan, and focused
on the behaviour of pedestrians as evacuees during the
propagation of the floodwater while moving to an emer-
gency exit (Figure 4a). Scenario 2 focused on mitigation
options on the number of the responders and thickness
of the flood barrier needed for a safe and effective deploy-
ment upstream of the emergency exit (Figure 4b). Sce-
nario 2 also requires a specified lead time, taken to be
12 hr. This time was selected assuming severe flood
warnings were issued for the areas surrounding the shop-
ping centre, though the shopping centre had remained
open (e.g., as with the case of Meadowhall shopping cen-
tre during November 2019 floods, which opened despite
an early warning of half-a-day [www.bbc.co.uk/news/uk-
50341846]).
The area of the shopping centre is
332 m ×332 m = 110,224 m
2
(Figure 4), chosen based on
the average area size of the UK's 43 largest shopping cen-
tres (Gibson, Percy, Yates, & Sykes, 2018; Globaldata
Consulting, 2018; Sen Nag, 2018; Tugba, 2018). The shop-
ping centre includes stores, located at the east and west
side, separated by corridors linking the entrance doors to
an open area. Through these corridors, pedestrians can
enter the open area and walk toward their destinations.
The open area was assumed to be occupied by a popula-
tion of 1,000 pedestrians (configurable by the user) when
there is no floodwater. This average population was
assumed in spite of an influx of people entering or leav-
ing from seven entrance doors with an equal probability
of one in seven. The total walkable area of the shopping
centre, including the open area and the corridors, is equal
FIGURE 4 Schematic description of the hypothetical shopping centre (Section 3) with the two scenarios: (a) during a flood evacuation;
and (b) pre-flood intervention. (a) Scenario 1 and (b) Scenario 2
SHIRVANI ET AL.7of17

to 70,350.8 m
2
. A population of 1,000 pedestrians was
selected to give an area of almost 8.4 ×8.4 m
2
for each
person. This area allows some areas of the pedestrian
space to not be crowded, based on a calculator toolbox of
the average space required for individuals in malls
(Engineering ToolBox, 2003). The flood propagation was
assumed to breach from the southern side along a 100 m
width (Figure 4), assuming floodwaters had reached the
shopping centre after a severe inundation from a river
nearby. When flooding started in Scenario 1, in response
to an announcement, pedestrians had started the evacua-
tion to the emergency exit located at the northern side
(Figure 4a), which was set to remain open during
evacuation.
In Scenario 2, a group of the pedestrians were
responders, tasked to deploy a local barrier at the loca-
tion specified in Figure 4b and within a time window that
did not exceed the specified lead time of 12 hr. The area
where the intended barrier was 168.6 m long and it has
the same width as a navigation agent (i.e., 2.59 m for a
grid of 128 ×128 navigation agents). The responders
were set to build the barrier by placing layers of sandbags
in this area. The dimension of a sandbag was based on
standard measurements (Padgham, Horne, Singh, &
Moore, 2014; Williamson, 2010), to be 40 cm long
×30 cm wide ×25 cm thick. This means that 3,484 sand-
bags were needed to form a one-layer thick barrier,
which is a close estimate to the sandbag numbers
predicted by online calculation tools (e.g., 3,318 sand-
bags, https://sandbaggy.com/blogs/articles/sandbag-
calculator), and recommended in the UK official guid-
ance (Environment Agency, 2009).
In both scenarios, the flood-pedestrian simulator
model within FLAMEGPU was executed with a resolu-
tion of 2.59 m ×2.59 m for the grids of navigation and
flood agents. When floodwaters occupy the study area,
the time-step is calculated dynamically from the hydrody-
namic model under the CFL condition (CFL num-
ber = 0.5), while otherwise the 1.0 s time-step of the
pedestrian model is selected by default.
3.1 |Flood condition selection based on
HR analysis
An equivalent triangular hydrograph was used to repre-
sent the flooding inflow. This is a standard method
reported in hydrology manuals (e.g., United States
Department of Agriculture, 2018) and computational
hydrology textbooks (e.g., Adrien, 2003). The inflow
hydrograph was characterised by a flow peak, Q
peak
, and
a duration, t
inflow
. Four choices of a flooding inflow
hydrograph were explored based on fixing the volume of
water that entered the shopping centre. The Norwich
inundation case study reported a population of 500 to
2000 individuals that were flooded in a residential area
located 50 m away from a river inundation (Section 6.3.3,
document FD2321/TR1, Environment Agency, 2006).
Because of its resemblance to the case of the shopping
centre, it was considered to calibrate the inflow hydro-
graphs, Q
peak
for 60 min of flooding, that is, estimated
according to initial water depth and velocity magnitude
of h
inflow
= 1 m and v
inflow
= 0.2 m/s, respectively. This
corresponds to an initial inflow hydrograph with (Q
peak
,
t
inflow
) = (20 m
3
/s, 60 min) for which Q
peak
=v
inflow
h
inflow
Bwhere B= 100 m is the length of the inflow breach.
The three other inflow hydrographs were formed to rep-
resent more severe flooding events, by recursive halving
of t
inflow
alongside doubling of v
inflow
(h
inflow
=1 m is
fixed), leading to inflow hydrographs with: (Q
peak
,
t
inflow
) = (40 m
3
/s, 30 min), (80 m
3
/s, 15 min) and
(160 m
3
/s, 7.5 min), respectively, which are shown in
Figure 5.
To analyse flood event severity resulting from the four
selected inflow hydrographs, the hydrodynamic model
within FLAMEGPU was executed with each of the
hydrographs. For all simulation runs, the model was
applied with slip boundary conditions for the northern
side and wall boundary conditions for the eastern and
western sides. Figure 6 shows the time history of the
maximum HR calculated from the model outputs during
60 min. The inflow hydrographs with (20 m
3
/s, 60 min),
(40 m
3
/s, 30 min), and (80 m
3
/s, 15 min), show a maxi-
mum HR below 2 and only exceeding 1 between 4 and
6 min. This indicates that these inflow hydrographs lead
to flooding that at worst disrupt a few pedestrians for a
very short duration of 2 min. In contrast, the inflow
hydrograph with (160 m
3
/s, 7.5 min) demonstrates the
most severe flooding event with significantly higher max-
imum HR values
3
occurring over a 10 min, that is, indica-
tive of potentially disruptive propagation of floodwaters
in the shopping centre. Hence, only the inflow hydro-
graph with (160 m
3
/s, 7.5 min) was considered when
exploring the flood-pedestrian simulator within
FLAMEGPU for the proposed Scenarios 1 and 2.
3.2 |Simulation of Scenario 1 (during a
flood evacuation)
The flood-pedestrian simulator was applied to simulate
Scenario 1. The pedestrian model was set to have a con-
stant rate of 10 entering/leaving pedestrians per
entrance/exit such that to maintain a total of 1,000 ran-
domly walking pedestrians before flooding happens. A
pre-flooding duration of t=−5 min was set in the
8of17 SHIRVANI ET AL.

hydrodynamic model, by zeroing Q
peak
, in order to allow
spreading of the pedestrians all over the walkable area
(blue zone in Figure 4a). When flooding entered the
walkable area, at t= 0 min, the pedestrian agents were
scheduled to become evacuees. The simulation was set to
terminate when all evacuees left the walkable area via
the emergency exit (Figure 4a). In a single run, the flood-
pedestrian simulator was set to record, every 0.1 min, the
information stored in the flood agents (coordinate, water
depth, water velocity and HR) and the pedestrian agents
(coordinate and the HR-related flood risk states). Two
runs were performed one “with”and one “without”the
effects of people on local floodwater hydrodynamics
(Section 2.5). The time history of the outputs produced by
the two runs is compared in Figure 7, in terms of statis-
tics of the flood risk states (Table 1) of evacuees.
Before 2.8 min, both runs led to almost similar statis-
tics indicating that 60% of the evacuees were either in a
dry zone or in a state of low HR, while the remaining
40% were at most in a medium HR state. After 2.8 min
and before 4.9 min, at least 55% of the evacuees had
medium to highest HR states, namely in the vicinity of
3.6 min where 5–8% more pedestrians were identified to
be in high to highest HR states for the run “with”the
effects of people on local floodwater hydrodynamics
(compare Figure 7a to Figure 7b). For the latter run,
more pedestrians with the highest HR states were noted,
and this was likely caused by the relative local increase
in the HR due to the grouping of pedestrians at critical
zones and times (see also Figure 8 and its discussions).
After 4.9 min and before 8.0 min, the majority of the
evacuees had a medium HR state, namely in the vicinity
of 6.3 min. Over this duration, 25% more pedestrians
were found to be in a state of low HR, for the same run
“with”the effects of people on local floodwater hydrody-
namics (compare Figure 7a to Figure 7b), due to a rela-
tively local decrease in the HR. After 8.0 min, all the
evacuees had a low HR state, irrespective of the run and
were able to continue the evacuation process until it
ended after 10 min. Notably, as the evacuees become con-
gested on their way to the emergency exit, they affect
their surrounding evacuees to become: either in a higher
risk state of HR when the evacuees were in a state of high
to highest HR,orinalower risk state of HR when the
evacuees were in a state of medium HR.
This aspect can be closely explored in the spatial plots
of Figure 8 for the runs “without”and “with”the effects
of people on local flood hydrodynamics, respectively,
after 3.6 and 6.3 min (Figure 8a,b). The plots include the
2D spatial flood maps in terms of HR and the evacuees.
FIGURE 5 Flooding inflow
hydrographs defined according
to four different flow peaks, by
fixing the volume of water that
can be released into the
shopping centre and, doubling
the discharge peak (Q
peak
) while
halving the duration of its
occurrence (t
inflow
)
FIGURE 6 Time history of
the maximum HR calculated
from the model outputs of the
hydrodynamic model on flexible
large-scale agent modelling
environment for the graphical
processing unit (FLAMEGPU)
run for the four selected inflow
hydrographs
SHIRVANI ET AL.9of17

Comparing the left and right columns in Figure 8a, a
clear difference can be observed between the distribution
of the evacuees and the flood maps in the crowded zones
of the shopping centre: around the middle, more evac-
uees had high to highest HR states and the local flood
hydrodynamics was relatively higher. Whereas, closer to
the emergency exit downstream, more evacuees had a
low HR state indicative of relatively lower local flood
hydrodynamics. The latter observation can also be
detected when comparing the left and right columns in
Figure 8b. Overall, these results indicate that the local
synergies between flood and evacuees can dramatically
affect flood impact on evacuee states in floodwater.
3.3 |Simulation of Scenario 2 (pre-flood
intervention)
The flood-pedestrian simulator was applied to simulate
Scenario 2, with the aim to identify a minimum required
number of people and thickness for the barrier for a safe
and effective deployment within a safety time window of
12 hr. Four group sizes for the responders were explored,
made of 50, 100, 200, and 300 pedestrians, respectively,
alongside six layers of thickness for the sandbag barrier.
Hence, a total of 24 simulations were run to estimate the
deployment time for a barrier up to six-layer thick and
considering the four group sizes. Per group size, a first
simulation started with the responders evacuating as
soon as they had completed a one-layer thick barrier for
flood risk analysis to be applied; then, by analogy, a sec-
ond simulation was run to analyse the case for a two-
layer thick barrier, and so on until the case of a six-layer
thick barrier was analysed. The analysis also considered
the respective changes in floodwater hydrodynamics in
relation to the water depth and maximum HR as the bar-
rier's thickness is increased. In Figure 9, the simulated
time taken to deploy up to a six-layer thick (sandbag) bar-
rier are shown for the four group sizes for the emergency
responders. As shown in Figure 9, within the safety time
FIGURE 7 A stack chart
illustrating the “flood risk
states”(Table 1) of the
pedestrians as they evacuate
during 10-min flooding, without
(a), and with (b) accounting for
the effects of people on local
floodwater hydrodynamics
10 of 17 SHIRVANI ET AL.

window (“green”area of less than 12 hr): the group of
50 responders could only deploy a one-layer thick barrier,
the groups of 100 and 200 responders could deploy a bar-
rier between three- to five-layer thick, respectively;
whereas, the group of 300 responders could deploy up to
six-layer thick barrier. It is worth noting that involving
higher group sizes may not be realistic and was found to
result in efficiency stagnation due to overcrowding.
4
Figure 10 shows the changes in water depth as the
barrier's thickness is increased: water depth downstream
of the barrier reduced to around 0.4 m with one-layer
thickness, to around 0.3 m with two-layer thickness and
FIGURE 8 Spatial flood
maps alongside the distribution
of evacuees at (a) t= 3.6 min
and (b) t= 6.3 min: Left and
right columns contain the plots
produced by the run “without”
and “with”the effects of people
on local flood hydrodynamics,
respectively
FIGURE 9 Simulated times
versus responders' group size for
deploying up to six-layer thick
(sandbag) barrier: “red line”
indicates flooding start time
below which is safe to deploy
(area shaded in “green”)or
otherwise unsafe (area shaded
in “red”)
SHIRVANI ET AL.11 of 17

to less than 0.2 m with tree-layer thickness and higher.
To help assess the level of safety attributed to these water
depths, it is further necessary to analyse their respective
velocity impacts as recommended by the Environment
Agency (2006, p. 13).
Figure 11 illustrates the relative change in maximum
HR downstream of the barrier with respect to the bar-
rier's thickness level in terms of number of sandbag
layers. After a one-layer thick barrier, a major drop of
91.2% in maximum HR is observed, which is quite
expected relative to having no barrier at all. After two-
and three-layer thickness, more relative reduction of 5.3
and 1.9%, respectively, is observed for the maximum
HR. After four-layer thickness, no further significant
reduction in maximum HR is noted (0.4%), suggesting
that there is no point in going beyond three layers to
reduce the flood risk to potentially walking pedestrians
downstream of the barrier.
Overall, the combined analyses of Figures 9–11
seem to suggest that a three-layer thick barrier (0.75 m
height) would be sufficient to alleviate the flood
impacts upstream of the emergency exit of the shopping
centre, and its deployment is feasible within less than
12 hr by involving a group of responders made up of
100 people.
4|CONCLUSIONS AND OUTLOOK
The FLAMEGPU platform was used to dynamically cou-
ple validated hydrodynamic and pedestrian models, for-
ming a “flood-pedestrian”simulator. The pedestrian
model involved continuous pedestrian agents moving
based on the information available on the navigation
map formed by a grid of navigation agents while follow-
ing a standard social force model. A grid of flood agents
was coincident with the grid of navigation agents, on
which the states of floodwater variables are stored and
updated by a hydrodynamic model. Dynamic passing of
information across the pedestrian and flood agents was
facilitated by the navigation agents. Behaviour rules
governing pedestrian interaction with/to the flood hydro-
dynamics were implemented for two roles that pedes-
trians can be assigned: evacuees moving in floodwater
where the presence of individuals and groups of people
was incorporated by changing the surface roughness
coefficient in the hydrodynamic model; and, responders
that participate in pre-event sandbagging where the sand-
bags were incorporated by changing the height of the gro-
und elevation parameter in the hydrodynamic model.
The functioning of the flood-pedestrian simulator was
demonstrated over a synthetic case study of a flooded and
densely populated shopping centre for two scenarios:
(a) during a flood evacuation to an emergency exit, and
(b) pre-flood intervention to deploy, from sandbags, a
temporary flood barrier. The simulation results of Sce-
nario 1 identified that incorporating local effects of
FIGURE 10 Centrelines of
two-dimensional (2D) water
depth maps along y-axis after
the deployment the sandbag
barrier (red dashed line)
considering up to six layers of
sandbag thickness
FIGURE 11 Cumulative percentage of maximum HR
reduction in line with increased thickness of the barrier in terms of
number of sandbag layers
12 of 17 SHIRVANI ET AL.

evacuees on floodwater hydrodynamics can dramatically
affect flood impact on the flood risk states of evacuee in
relatively confined areas. This dramatic change in
flooding impact was noted to be extreme: either reduced
the risk to the surrounding of a group of people when the
people were in low to medium state of flood HR, or
increased the risk when people were located in the
highest state of flood HR. The simulation results of Sce-
nario 2 provided evidence that the flood-pedestrian simu-
lator can also be used to decide on the required number
of people for emergency first responders and the required
minimum height for a temporary flood barrier for a safe
and effective deployment, alongside a quantification of
the resulting level of flood risk reduction. These simula-
tion results suggest a potential utility of the flood-
pedestrian simulator to inform emergency evacuation
and intervention strategies for relative small-scale and
congregated areas such as supermarkets, football stadi-
ums or shopping centres.
Work is ongoing to support the simulator with more
realistic in-model human behaviour rules to floodwater,
that is, variable body shapes and height for the pedes-
trians, variable people walking speeds and stability rules
(Shirvani et al., 2020), and to demonstrate its potential to
plan mass emergency evacuation for a real study site.
There is also a crucial need for interdisciplinary research
across social science and psychology, hydraulic engineer-
ing and modelling, computer science, and system engi-
neering to characterise and formulate hydro-social
behavioural rules that would feature in such a flood-
people simulator.
ACKNOWLEDGEMENTS AND SOFTWARE
ACCESSIBILITY
The authors declare that there is no conflict of interest.
This work was supported by the UK Engineering and
Physical Sciences Research Council (EPSRC) grant
EP/R007349/1. The authors thank Mozhgan Kabiri Chi-
meh and Peter Heywood from the Research Software Engi-
neering (https://rse.shef.ac.uk/) group for providing
technical support during the implementation of the flood-
pedestrian simulator on FLAMEGPU. The authors also
thank the two anonymous reviewers for their careful read-
ing and their insightful comments and suggestions that
greatly improved the quality of this article. The flood-
pedestrian simulator software is available on DAFNI
(https://dafni.ac.uk/project/flood-people-simulator/), where
it can be run from a graphical interface and supported by
a detailed “run guide”document. Further updates on
ongoing developments related to the flood-pedestrian simu-
lator can be found on www.seamlesswave.com/Flood_
Human_ABM.
ENDNOTES
1
This assumption is sufficient to support to scope of this investiga-
tion. Variable walking speed and stability rules are feasible
options (e.g., Bernardini, Quagliarini, D'Orazio, &
Brocchini, 2020; Chen, Xia, Falconer, & Guo, 2019). Exploring
their impact on pedestrian evacuation dynamics in floodwater
and recovery times is the subject of another study (Shirvani,
Kesserwani, & Richmond, 2020).
2
To demonstrate the feasibility of the coupled ABMs. More effi-
cient sandbag replacement systems (Lankenau, Massolle,
Koppe, & Krull, 2020) can also be implemented, tested and com-
pared in a future study.
3
Because the aim of this study aimed to explore people effects on
local flood hydrodynamics, considering inflow hydrographs that
would lead to HR > 7 (i.e., indicative of loss of life) was out of
scope.
4
No significant reduction in deployment times was observed as
people-group sizes is increase further. This is likely because lon-
ger waiting times were needed with higher number of responders.
DATA AVAILABILITY STATEMENT
Data sharing is not applicable to this article as no new
data were created or analysed in this study.
ORCID
Georges Kesserwani https://orcid.org/0000-0003-1125-
8384
REFERENCES
Abebe, Y. A., Ghorbani, A., Nikolic, I., Vojinovic, Z., & Sanchez, A.
(2019). A coupled flood-agent-institution modelling (CLAIM)
framework for urban flood risk anagement. Environmental
Modelling & Software,111, 483–492.
Aboelata, M., & Bowles, D. S. (2008). LIFESim: A tool for estimat-
ing and reducing life-loss resulting from dam and levee failures.
In Proceedings of the Association of State Dam Safety Officials
“Dam Safety 2008”Conference, pp. 533–547. 7–11 September
2008, Indian Wells, CA.
Adrien, N. G. (2003). Computational hydraulics and hydrology: An
illustrated dictionary. Boca Raton, FL: CRC Press.
Aerts, J. C., Botzen, W. J., Clarke, K. C., Cutter, S. L., Hall, J. W.,
Merz, B., …Kunreuther, H. (2018). Integrating human behav-
iour dynamics into flood disaster risk assessment. Nature Cli-
mate Change,8(3), 193.
Becker, J. S., Taylor, H. L., Doody, B. J., Wright, K. C.,
Gruntfest, E., & Webber, D. (2015). A review of people's behav-
ior in and around floodwater. Weather, Climate, and Society,7
(4), 321–332.
Bernardini, G., Postacchini, M., Quagliarini, E., Brocchini, M.,
Cianca, C., & D'Orazio, M. (2017). A preliminary combined
simulation tool for the risk assessment of pedestrians' flood-
induced evacuation. Environmental Modelling & Software,96,
14–29.
Bernardini, G., Quagliarini, E., D'Orazio, M., & Brocchini, M.
(2020). Towards the simulation of flood evacuation in urban
SHIRVANI ET AL.13 of 17

scenarios: Experiments to estimate human motion speed in
floodwaters. Safety Science,123, 104563.
Bonabeau, E. (2002). Agent-based modelling: Methods and tech-
niques for simulating human systems. Proceedings of the
National Academy of Sciences,99(Suppl 3), 7280–7287.
Chen, Q., Xia, J., Falconer, R. A., & Guo, P. (2019). Further
improvement in a criterion for human stability in floodwaters.
Journal of Flood Risk Management,12(3), e12486.
Chimeh, M. K., & Richmond, P. (2018). Simulating heterogeneous
behaviours in complex systems on GPUs. Simulation Modelling
Practice and Theory,83,3–17.
Chow, V. T. (1959). Open channel hydraulics. New York, NY:
McGraw-Hill.
Costabile, P., Costanzo, C., de Lorenzo, G., & Macchione, F. (2020).
Is local flood hazard assessment in urban areas significantly
influenced by the physical complexity of the hydrodynamic
inundation model? Journal of Hydrology,580, 124231.
Dawson, R. J., Peppe, R., & Wang, M. (2011). An agent-based model
for risk-based flood incident management. Natural Hazards,59
(1), 167–189.
Engineering ToolBox. (2003). Room Area per Person. [online].
Retrieved from https://www.engineeringtoolbox.com/number-
persons-buildings-d_118.html..
Environment Agency. (2009). Sandbags and how to use them prop-
erly for flood protection. Document FLHO0309BPSL-E-E.
Environment Agency/DEFRA. (2006). R&D outputs: Flood risks to
people: Phase 2 FD2321/TR1. The flood risks to people methodol-
ogy, Bristol: The Flood and Coastal Defence R&D Programme.
Gibson, A., Percy, J., Yates, D., & Sykes, T. (2018). UK Shopping
Centres the Development Story January 2018 [online].
Cushmanwakefield. Retrieved from http://www.cushmanwake
field.co.uk/en-gb/research-and-insight/2018/uk-shopping-centr
es-the-development-story-january-2018.
Globaldata Consulting. (2018). Top 50 UK Shopping Centres Report
[online]. GlobalData. Retrieved from https://www.globaldata.
com/ground-breaking-report-sheds-new-light-uks-best-
performing-shopping-centres.
Grames, J., Prskawetz, A., Grass, D., Viglione, A., & Blöschl, G.
(2016). Modelling the interaction between flooding events and
economic growth. Ecological Economics,129, 193–209.
Huang, Y., Zhang, N., & Pei, Y. (2013). Well-balanced finite volume
scheme for shallow water flooding and drying over arbitrary
topography. Engineering Applications of Computational Fluid
Mechanics,7(1), 40–54.
Jenkins, K., Surminski, S., Hall, J., & Crick, F. (2017). Assessing
surface water flood risk and management strategies under
future climate change: Insights from an agent-based model. Sci-
ence of the Total Environment,595, 159–168.
Jiang, Y., Chen, B., Li, X., & Ding, Z. (2020). Dynamic navigation
field in the social force model for pedestrian evacuation.
Applied Mathematical Modelling,80, 815–826.
Karmakharm, T., Richmond, P., & Romano, D. M. (2010). Agent-
based large scale simulation of pedestrians with adaptive realis-
tic navigation vector fields. TPCG,10,67
–74.
Kreibich, H., Bubeck, P., van Vliet, M., & de Moel, H. (2015). A
review of damage-reducing measures to manage fluvial flood
risks in a changing climate. Mitigation and Adaptation Strate-
gies for Global Change,20(6), 967–989.
Kreibich, H., Seifert, I., Merz, B., & Thieken, A. H. (2010). Develop-
ment of FLEMOcs—A new model for the estimation of flood
losses in the commercial sector. Hydrological Sciences Journal–
Journal des Sciences Hydrologiques,55(8), 1302–1314.
Kvocˇka, D., Falconer, R. A., & Bray, M. (2016). Flood hazard assess-
ment for extreme flood events. Natural Hazards,84(3),
1569–1599.
Lankenau, L., Massolle, C., Koppe, B., & Krull, V. (2020). Sandbag
replacement systems—A nonsensical and costly alternative to
sandbagging? Natural Hazards & Earth System Sciences,20(1),
197–220.
Lee, H. K., Hong, W. H., & Lee, Y. H. (2019). Experimental study
on the influence of water depth on the evacuation speed of
elderly people in flood conditions. International Journal of
Disaster Risk Reduction,39, 101198.
Li, C., & Coates, G. (2016). Design and development of an agent-
based model for business operations faced with flood disrup-
tion. Complex Systems: Fundamentals & Applications,90, 275.
Li, M., Wei, Y., & Xu, Y. (2019). A route navigation algorithm for
pedestrian simulation based on grid potential field. Advances in
Mechanical Engineering,11(12), 1–13.
Liu, X., & Lim, S. (2016). Integration of spatial analysis and an
agent-based model into evacuation management for shelter
assignment and routing. Journal of Spatial Science,61(2),
283–298.
Liu, Y., Okada, N., Shen, D., & Li, S. (2009). Agent-based flood
evacuation simulation of life-threatening conditions using vitae
system model. Journal of Natural Disaster Science,31(2), 69–77.
Lumbroso, D., & Davison, M. (2018). Use of an agent-based model
and Monte Carlo analysis to estimate the effectiveness of emer-
gency management interventions to reduce loss of life during
extreme floods. Journal of Flood Risk Management,11,
S419–S433.
Lumbroso, D., & di Mauro, M. (2008). Recent developments in loss
of life and evacuation modelling for flood event management
in the UK. WIT Transactions on Ecology and the Environment,
118, 263–272.
Lumbroso, D., Gaume, E., Logtmeijer, C., Mens, M., & van der
Vat, M. (2008). Evacuation and traffic management, integrated
flood risk analysis and management methodologies. Floodsite
Consortium Task 17 report number T17-07-02.
Lumbroso, D., Sakamoto, D., Johnstone, W., Tagg, A., &
Lence, B. L. (2011). The development of a life safety model to
estimate the risk posed to people by dam failures and floods.
Dams and Reservoirs, HRPP473.
Lumbroso, D., & Vinet, F. (2012). Tools to improve the production
of emergency plans for floods: Are they being used by the peo-
ple that need them? Journal of Contingencies and Crisis Man-
agement,20(3), 149–165.
Lumbroso, D. M., Simm, J. D., Davison, M., White, K. D., &
Durden, S. (2015). Use of agent-based modelling to validate
hurricane evacuation planning. In Coastal structures and solu-
tions to coastal disasters joint conference (COPRI), pp. 321–329.
9–11 September 2015, Boston, MA.
Mas, E., Koshimura, S., Imamura, F., Suppasri, A., Muhari, A., &
Adriano, B. (2015). Recent advances in agent-based tsunami evac-
uation simulations: Case studies in Indonesia, Thailand, Japan
and Peru. Pure and Applied Geophysics,172(12), 3409–3424.
14 of 17 SHIRVANI ET AL.

McClymont, K., Morrison, D., Beevers, L., & Carmen, E. (2019).
Flood resilience: A systematic review. Journal of Environmental
Planning and Management,63,1–26.
Mohler, B. J., Thompson, W. B., Creem-Regehr, S. H., Pick, H. L., &
Warren, W. H. (2007). Visual flow influences gait transition
speed and preferred walking speed. Experimental Brain
Research,181(2), 221–228.
Néelz, S., & Pender, G. (2009). Desktop review of 2D hydraulic
modelling packages, Science Report SC080035, Joint UK
Defra/Environment Agency fFlood and Coastal Erosion. Risk
Management R&D Program.
Padgham, L., Horne, R., Singh, D., & Moore, T. (2014). Planning for
sandbagging as a response to flooding: A tool and case study.
Australian Journal of Emergency Management (AJEM),29,26–31.
Richmond, P., Coakley, S., & Romano, D. M. (2009). A high perfor-
mance agent based modelling framework on graphics card
hardware with CUDA. In Proceedings of the 8th International
Conference on Autonomous Agents and Multiagent Systems,
pp. 1125–1126. 10–15 May 2009, Budapest, Hungary.
Sen Nag, O. (2018). The largest shopping malls in the United King-
dom [online]. WorldAtlas. Retrieved from https://www.
worldatlas.com/articles/the-largest-shopping-malls-in-the-unit
ed-kingdom.html.
Shirvani, M., Kesserwani, G., & Richmond, P. (2020). Agent-based
modelling of pedestrian responses during flood emergency:
Mobility behavioural rules and implications for flood risk anal-
ysis. Journal of Hydroinformatics,22(5), 1078–1092. doi.org/10.
2166/hydro.2020.031
Tonn, G. L., & Guikema, S. D. (2018). An agent-based model of
evolving community flood risk. Risk Analysis,38(6), 1258–1278.
Toro, E. F. (2001). Shock-capturing methods for free-surface shallow
flows. New York, NY: Wiley.
Tugba, S. (2018). Leading twenty shopping centers in the United King-
dom (UK) as of June 2018, by size (in square meters) [online].
Statista. Retrieved from https://www.statista.com/statistics/
319446/top-shopping-centres-by-size-united-kingdom-uk.
United States Department of Agriculture. (2018). Module
207-hydrograph development. [online]. Natural Resources Con-
servation Service. Retrieved from https://www.nrcs.usda.gov/
Internet/FSE_DOCUMENTS/stelprdb1083020.pdf.
Wang, Y., Liang, Q., Kesserwani, G., & Hall, J. W. (2011). A 2D
shallow flow model for practical dam-break simulations. Jour-
nal of Hydraulic Research,49(3), 307–316.
Wedawatta, G., & Ingirige, B. (2012). Resilience and adaptation of
small and medium-sized enterprises to flood risk. Disaster Pre-
vention and Management: An International Journal,21(4),
474–488.
Williamson, K. (2010). How sandbags work [online].
Howstuffworks. Retrieved from https://science.howstuffworks.
com/nature/natural-disasters/sandbag.htm.
Willis, T., Wright, N., & Sleigh, A. (2019). Systematic analysis of
uncertainty in 2D flood inundation models. Environmental
Modelling & Software,122, 104520.
Wirtz, P., & Ries, G. (1992). The pace of life-reanalysed: Why does
walking speed of pedestrians correlate with city size? Behav-
iour,123(1–2), 77–83.
Zischg, A. (2018). Floodplains and complex adaptive systems—
Perspectives on connecting the dots in flood risk assessment
with coupled component models. Systems,6(2), 9.
How to cite this article: Shirvani M,
Kesserwani G, Richmond P. Agent-based simulator
of dynamic flood-people interactions. J Flood Risk
Management. 2021;14:e12695. https://doi.org/10.
1111/jfr3.12695
SHIRVANI ET AL.15 of 17

APPENDIX
Validation of the non-sequential hydrodynamic
model on FLAMEGPU
Two academic dam-break flow tests were used to verify
the FLAMEGPU implementation of Equation (2) in
updating the state of floodwater stored in the grid of flood
agents. The first test considered symmetric 2D water
propagation over a flat, frictionless, and initially wet area,
and the second involved a wave propagation over a
rough, initially dry area including three mounds.
FLAMEGPU simulations were run on a grid of 128 ×128
flood agents. The results were compared to those of a
sequential counterpart implementation on MATLAB and
with reference predictions reported in the literature.
Radial dam-break flow
This test is often used to verify the implementation of
newly developed shock-capturing flood models
(Toro, 2001; Wang et al., 2011). The wave propagation
happens after instantaneous removal of an imaginary
cylinder-shaped dam located in the centre of a
40 m ×40 m square area, causing a circular wave moving
outwards from the centre. The thin 2.5 m radius circular
wall of this dam retained an initial column of water
2.5 m deep. The rest of the area outside the dam is cov-
ered with 0.5 m of still water. A reference solution was
produced by solving the shallow water equation along
the radial direction r=ffiffiffiffiffiffiffiffiffiffiffiffiffiffi
x2+y2
p(Toro, 2001) by a
second-order accurate scheme over a fine mesh made of
1,001 ×1,001 rectangular elements (Wang et al., 2011).
Figure A1 compares the outputs produced by the non-
sequential hydrodynamic model on FLAMEGPU to those
produced by the sequential counterpart on MATLAB and
the reference solution, in terms of water depth (h) and
unit-width discharge (q=hu) cross sections along the
radial direction at times t= 1.4 s and t= 4.7 s (following
Toro, 2001 and Wang et al., 2011). The predicted water
depth and discharge preserve the radial symmetry at both
output times t= 1.4 s and t= 4.7 s, and the outputs of the
non-sequential hydrodynamic model were identical to
those the sequential counterpart, both agreeing well with
the reference solution. The discrepancies relative to the
reference solution are expected as the latter was com-
puted on a mesh resolution that is eight times finer and
using a higher-order accurate solver.
Dam-break flow over terrain with wetting-and-
drying
The non-sequential hydrodynamic model on FLAMEGPU
was then applied to reproduce dam-break flows over a
rough terrain with uneven ground elevation. This test was
used to verify the robustness of its implementation for
handling wetting-and-drying and step-terrain slopes. It
FIGURE A1 Profiles of
water depth and unit-width
discharge simulated by the non-
sequential hydrodynamic model
on FLAMEGPU (red line)
against those simulated by the
sequential model counterpart on
MATLAB (blue circle-marked
line) and the reference solution
(solid black line)
16 of 17 SHIRVANI ET AL.

assumes a dam-break wave propagating over a
75 m ×30 m closed area with an initially dry floodplain
including three mounds. The imaginary dam was located
along x= 16 m locking an initial body of water with a
height of 1.875 m. The roughness is represented by Man-
ning coefficient n
M
= 0.018 s m
−1/3
. Figure A2 (left) shows
the simulated water surface elevation produced at the
same output times as the results in Huang et al. (2013),
also shown in Figure A2 (right). As shown in Figure A2,
the outputs delivered by the non-sequential hydrody-
namic model on FLAMEGPU were similar to those of
Huang et al. (2013), both demonstrating capability to cap-
ture wave reflections, wetting-and-drying fronts, and to
conserve mass as the dam-break flood ultimately settles
decelerated by friction effects.
FIGURE A2 Dam-break
flow over terrain with wetting-
and-drying. Free-surface
elevation maps simulated by the
non-sequential hydrodynamic
model on FLAMEGPU (left)
compared to the simulated
results reported in Huang
et al., 2013 (right)
SHIRVANI ET AL.17 of 17