Modelling the high-resolution dynamic exposure to flood in city-region

Urban flooding exposure is generally investigated with the assumption of stationary disasters and disaster-bearing bodies during an event and thus cannot satisfy the increasingly elaborate modeling and management of urban floods. In this 10 study, a comprehensive method was developed to simulate dynamic exposure to urban flooding considering residents’ travel behavior. First, a flood simulation was conducted using the LISFLOOD-FP model to predict the spatiotemporal distribution of flooding. Second, an agent-based model was used to simulate residents’ movements during the urban flooding period. Finally, to study the evolution and patterns of urban flooding exposure, the exposure of the population, roads, and buildings to urban flooding was simulated using Lishui, China, as a case study. The results indicated evident spatiotemporal variations in 15 urban flooding and population distribution. The exposure increased with increasing rainfall and flooding severity. The urban area near the Oujiang River was the most severely flooded and indicated the highest exposure of the population, roads, and buildings. Furthermore, the impacts of flooding on roads were greater than those on the population and buildings. This study presents the first fully formulated method for dynamic urban flood exposure simulation with high spatiotemporal resolution. The quantitative results of this study can provide fundamental information for determining urban flood disaster vulnerability, 20 assessing socioeconomic losses, managing urban disaster risk, and establishing emergency response plans.


Introduction
Storm flooding has become increasingly frequent and severe with the intensification of climate change and the rising frequency of extreme weather events (Dankers and Feyen, 2008;Hammond et al., 2015).Urban floods are major natural disasters in many cities around the world and seriously threaten human life and social and economic activities (Gain et al., 2015).
Effectively coping with floods and their adverse effects is an important part of disaster prevention, mitigation, and risk management (Atta-Ur-Rahman, 2014).Non-engineering measures, such as exposure assessment, are currently the main way of managing urban flooding risk (Chen et al., 2015).Exposure refers to the presence of people, livelihoods, environmental services and resources, infrastructure, or economic, social, or cultural assets in areas that could be adversely affected by natural disasters (IPCC, 2012).Urban flood disasters involve the adverse effects of heavy rain and other factors on city systems in data, it cannot identify the purpose of human activities, and human disaster response behavior cannot be simulated.The ABM can simulate not only the population distribution but also the interaction among the population (as disaster victims), hazard factors, and disaster-prone environments (Yin, et al., 2016b).Previous studies have used the ABM to simulate human responses to disasters, which, in turn, have been used in natural disaster risk research (Johnstone, 2012;Huang et al., 2015).Nevertheless, the simulation results do not reflect the exposure characteristics of the disaster-bearing bodies and their dynamic changes (Dawson et al., 2011).
Therefore, the objectives of this study were to develop a novel method using the LISFLOOD-FP model and an ABM to simulate the exposure of urban populations, roads, and buildings to flooding under varying conditions and to implement the method as a case study in a real city.Several scenarios, including diverse flooding types and various responses of residents to flooding, were considered in this regard.Additionally, dynamic features of the real world were incorporated to improve the micro exposure analysis.Exposure simulation is a useful tool for estimating disaster vulnerability and assessing losses, and the quantitative results under different scenarios of this study are likely to benefit relevant government agencies in assessing risk, issuing warnings, and planning emergency responses to urban natural disasters.In particular, considering the dynamic distribution of the population during a flood disaster, a more reasonable migration measure can be taken to minimize casualties.

Study area and data sources
Lishui City, Zhejiang Province, China, was used as the study area because of the availability of the required data and flooding history.The urban district of Lishui is a largely hilly and mountainous area, and the Oujiang River traverses its southern and eastern parts.The study area is located in the central district of Lishui, covers an area of 43.4 km 2 , and has a population of approximately 71,673 (Fig. 1).The frequency of heavy rainstorms and persistent concentrated rainfall events rises sharply in May and June during the Meiyu flood period, which often results in flood disasters.On August 20, 2014, a heavy rainfall event lasting a few days produced a 50-year flood in Lishui and caused considerable loss of property.
The datasets used in this study included a digital elevation model and river, road, building, population, and observation data consisting of river discharge and water level.Travel survey data were used to determine daily routines.Additionally, traffic flow and water accumulation data were used for validation.Table 1 describes the sources and uses of the datasets.
We randomly selected 500 residents in the study area to participate in a questionnaire survey on daily activities.We collected data on their social characteristics to distinguish population types.There were 100 people under 18 years of age, 300 middleaged people (18-60 years), and 100 elderly people (>60 years).Employed people and males accounted for 55% and 50%, respectively.Lastly, 14% of the population had received higher education.The distribution of the above social characteristics was close to the actual population distribution in the study area.

Methods
This study comprised three aspects: disaster simulation, human activity simulation, and dynamic exposure assessment (Fig. 2).
The first step included fluvial and pluvial flooding simulation based on the LISFLOOD-FP model.The simulation of human activity subsequently used ABM to obtain the spatiotemporal distribution of the population under different scenarios.Finally, the developed model was combined with the results of the previous two steps to assess the dynamic exposure of the population, roads, and buildings to urban flooding.

Flood models
There is a wide variety of existing hydrological or hydrodynamic models that are capable of simulating fluvial or pluvial flooding, including the Storm Water Management Model (SWMM) (Rossman, 2015), LISFLOOD (Bates and De Roo, 2000), MIKE-SHE (DHI, 2000), MIKE-11 (Havnø et al., 1995), MOUSE (Lindberg et al., 1989), HEC-RAS (Brunner, 2008), and HEC-HMS (Charley et al., 1995).LISFLOOD-FP (Bates et al., 2013) is a coupled 1D/2D hydraulic model based on a raster grid and was designed for research purposes at the University of Bristol, United Kingdom.LISFLOOD-FP uses a square grid as the computational grid to simulate 1D river and 2D floodplain hydraulic changes.The applicability of the model has been verified by several studies (Horritt and Bates, 2002;Bates and De Roo, 2000).Therefore, the LISFLOOD-FP model was chosen for the simulation of fluvial and pluvial flooding in this study.
Floodplain flows were described in terms of continuity and momentum equations discretized over a grid of square cells, which allowed the model to represent 2D dynamic flow fields for the floodplain.It assumed that the flow between two cells was simply a function of the free surface height difference between these cells: where ℎ , is the free surface height of water at node (i,j), ∆ and ∆ are the cell dimensions, n is the effective grid scale Manning's friction coefficient for the floodplain, and   and   describe the volumetric flow rates between the floodplain cells in the  and  directions, respectively.The flow depth, ℎ  , represents the depth through which water can flow between two cells, and d is the difference between the highest free surface height of water in the two cells and the highest bed elevation.
The types of flooding simulated in this study included pluvial and fluvial floods.Due to the lack of hourly rainfall observation data, we used designed rainfall data for pluvial flood simulation.Synthetic rainfall data for a return period of 50 years were simulated using the Chicago hyetograph method (CHM) (Cen et al., 1998).The rainfall data were determined using the rainstorm intensity formula (Eq.(3)), rainfall duration time (T), and peak position (r).
where  is the rainfall intensity (mm min -1 ),  is the return period, and t is the time.The parameters , ,  and  are related to the characteristics of the local rainstorm and need solutions. is the rainfall parameter, i.e., the design rainfall (mm) for 1 minute at a 10-year return period,  is the rainfall variation parameter (dimensionless),  is the rainfall duration correction parameter, i.e., the time constant (minutes) that can be added to convert the curve into a straight line after logarithmic calculation of the two sides of the rainstorm intensity formula, and  is the rainstorm attenuation index, which is related to the return period.The "r" value refers to the relative rainfall peak time, i.e., a value from 0 to 1, where 0 means the maximum rainfall at the beginning of the rainfall event, and 1 means the maximum rainfall at the end of the rainfall event.To simulate the 2014 flood, we fixed r at 0.2 based on the assumption that the peak is located at the one-fifth point of the design hyetograph.
Additionally, the rainfall duration was 6 hours (6 am to 12 pm), and the accumulated rainfall was nearly 148 mm.The parameters , ,  and  were estimated from the rainstorm intensity formula for Lishui City obtained from the "Zhejiang City Rainstorm Intensity Formula Table " published by the Hangzhou Municipal Planning Bureau (Table 2).The rainfall simulation results are shown in Fig. 3(a).The river discharge and water level input data for fluvial flood simulation used observational data from Lishui's 50-year flood in 2014, provided by the Liandu Hydrological Station (Fig. 3(b)).The river discharge data for the Daxi and Haoxi rivers on August 20, 2014 were obtained from the Xiaobaiyan and Huangdu stations, respectively, and the observational data for water levels at the outlets were those for the Kaitan Dam.

ABM
Several modeling techniques, often collectively referred to as social simulation, have been successfully used to represent the behaviors of humans and organizations.These include event and fault trees, Bayesian networks, microsimulation, cellular automata, system dynamics, and ABMs.Research methods based on ABMs have been gradually introduced into the field of natural disaster risk assessment.ABM is considered most suitable for addressing challenges associated with simulating the complexity and dynamic variability of population exposure to flooding because of its capacity to capture interactions and dynamic responses in a spatial environment (Dawson et al., 2011).
An ABM is a computational method for simulating the actions and interactions of autonomous decision-making entities in a network or system to subsequently assess their effects on the system as a whole.Individuals and organizations represent agents.
Each agent individually assesses its situation and makes decisions based on a set of rules.Agents may execute various behaviors appropriate for the system component they represent e.g., production or consumption.Therefore, an ABM consists of a system of agents and the relationships between them.Even a simple ABM can exhibit complex behavior patterns, because a series of simple interactions between individuals may result in more complex system-scale outcomes that could not have been predicted just by aggregating individual agent behaviors.
The ABM was developed as a concept in the late 1940s, and substantial applications were realized with the emergence of highpowered computing.Such applications include those in political sciences (Axelrod, 1997), management and organizational effectiveness, and social network behavior (Sallach and Macal, 2001;Gilbert and Troitzsch, 2005).In recent years, it has been introduced to the geosciences and other fields to provide novel ideas for the study of modern geography, including land use simulation and planning as well as residential choice and space differentiation (Benenson et al., 2002).The urban flood disaster system is a typical complex "natural and social" system.The use of ABM to simulate space-time distributions of populations is expected to quantify the dynamic exposure of populations to urban flood disasters.For example, Dawson et al. (2011) proposed a dynamic ABM for flood event management to evaluate population vulnerability under different storm surge conditions, dam break scenarios, flood warning times, and evacuation strategies.

Spatiotemporal simulation of population distribution
Individual travels were simulated using ABM by defining the activity patterns of different types of residents to subsequently obtain the distribution of the population at each moment.The ABM of residents' travels established in this study included two core elements of agents and activities, and two basic elements of blocks and networks.
Residents were independent individuals with subjectivity.This study abstracted them as agents.Only a limited number of agent classifications were used to reduce the number of agent types.The types of agents were classified according to the social characteristics of the residents.Age and gender characteristics mainly affect the ability of people to respond to disasters.The self-help abilities of minors under 18 years of age and residents older than 60 years are generally poor.In the event of natural disasters, they are generally categorized as the objects of help.The middle-aged group (18-60 years old) generally has greater physical strength with a better ability to cope with disasters.Unemployed people are more vulnerable to natural disasters.On one hand, their living environments and resistance to disasters are poor; on the other hand, their economic conditions are limited, which impedes recovery after the disaster and seriously affects their daily life in the short term.Education level is related to the possibility of an individual receiving early warning information.Individuals with higher education levels are more likely to respond to early warning information and are more aware of disasters than those with low education levels are (Terti et al., 2015;Shabou et al., 2017).Additionally, different travel modes have different effects on the activity patterns of people and on exposure levels when disasters occur.Therefore, the agent types were divided according to age, gender, employment status, education level, and travel mode.
Activities were classified as work, study, recreation, shopping, at-home, and travel.An activity pattern consisted of a series of activities to describe the spatiotemporal distribution of the agent.The location and scope of an agent were restricted to blocks and networks.Different types of agents had different activity patterns, and the same agent type could also have different activity patterns in different scenarios.The travel survey data were used according to the demographic properties of the agent to generate synthetic daily routines.To capture the variability in the travel survey and the uncertainties in behavior, synthetic daily routines were described in probabilistic terms.Figure 4 presents an example of the synthetic daily routine of an agent with the following demographic characteristics: male agent, aged 18-60 years, and employed.In this example, the agent started the day at 8 am on a weekday and had a 0.8 probability of going straight to work, going home, and so on.
The study area was discretized into several blocks to improve the spatial resolution of the exposure results.The major factors that affect the flood exposure included rivers, roads, land use, and buildings.The discretization procedure was conducted with GIS tools (intersection and editing tools of the ArcGIS software) (Lü et al., 2018).Blocks were activity places for agents and represented the smallest unit of exposure.This study divided blocks into five categories: residential area, school, company, recreational area, and others.Additionally, residential areas were subdivided into classes I, II, III, and IV according to the type of building.
In this study, the network referred to roads and restricted the spatial travel scope of an intelligent agent.Rural roads, highways, and urban roads (including main roads, sub-trunk roads, and their branches) were included in the network.The route selection criteria were defined once the different activities from each individual's schedule were located, and road section attributes were specified.Although various factors are involved in the route choice process, several studies have indicated that minimizing travel time is the principal criterion for selecting routes (Papinski et al., 2009;Ramming, 2001;Bekhor et al., 2006).Here, a simple but effective shortest path method was used.The classical Dijkstra algorithm is a single-source shortest path algorithm that provides trees of minimal total length and time in a connected set of nodes (Dijkstra, 1959).The activity pattern attributions concerned only the starting times and durations of the activity sequences, thus indicating that the travel duration for each individual was computed based on the distance between the different activity locations.Therefore, the implemented schedules may be distorted compared to the assigned schedules in terms of travel duration (Terti et al., 2015).
We obtained the departure and destination block of each stage according to the activity patterns, and then calculated the shortest path consisting of a series of road sections.At each moment, the block in which the agent was located was calculated, e.g., if an agent was on the road, according to the variation in speed of its walking or riding on a bus or in a car, the road section where it was located was calculated.The same was done during flooding, except that the activity patterns were different.

Impacts of disasters on resident activities
This study accounted for the adaptability or adjustment behavior of residents to a disaster during the disaster event.The type of activity and its sensitivity to disaster affected the residents' disaster response behavior.Recreation and shopping activities were easier to cancel and postpone than work and study were (Cools et al., 2010).The sensitivities of residents to disasters depended on their socioeconomic characteristics and risk factors such as disaster-related (i.e., flood-related) knowledge and experience.People with higher education levels are more knowledgeable about disasters and are more likely to receive early warning information and take effective measures (Terti et al., 2015).Additionally, it is easier for workers to ignore the risks of a disaster (Ruin et al., 2007;Drobot et al., 2007).Therefore, this study accounted for the impacts of education level on the response behavior of residents to disaster events.
The impacts of a disaster on population distribution were determined by defining different activity patterns and their changing probabilities.Figure 5 indicates activity patterns during different disaster scenarios for employed adult men who had received higher education.The "bad weather" scenario was similar to the "daily activity" pattern.For instance, changes in travel probability during "bad weather" due to a rainstorm reflected the adaptive behavior of residents.The "warning" scenario assumed that the government had issued early warning information at 8 a.m., the schools had suspended classes on weekdays, and the resident responses were stronger than those to the "bad weather" scenario, resulting in greater differences in activity patterns.

Dynamic exposure assessment
Dynamic exposure was calculated based on the simulations of spatiotemporal distributions of the population and flooding.
Therefore, the exposure at each moment was calculated according to the population distribution and flood data at that time.
Based on the data availability, this study focused only on three types of disaster-bearing bodies, namely population, roads, and buildings.
Population exposure generally refers to the population exposed to the impacts of disaster events and is characterized by regional population size or population density.This study selected the exposed population and accounted for vulnerable groups and road users.Among these, age was the primary factor impacting vulnerability.Specifically, the young (people under the age of 18 years) and the elderly (people over the age of 60 years) were the vulnerable groups.
As the basic skeleton of a city, roads are not only the media for daily travel of passengers and freight transportation but also disaster-bearing bodies (Yin, et al., 2016a), as they are vulnerable to flood disasters.This study selected the number and lengths of exposed roads to reflect road exposure.
Finally, the aggravation of urban flooding has made flooded buildings more common in urban areas, resulting in loss of internal property and construction structure.The dynamic state of building exposure is related to the safety of both the building and the nearby population.In this study, the area of the exposed building and depth of accumulated water in the building were considered building exposure.

Scenario design
The daily behaviors of people are characterized by certain patterns with regard to daily, weekly, monthly, and annual cycles.
Rainstorm ("bad weather") and disaster response measures adopted by an organization ("warning") are likely to affect people's daily behaviors.Therefore, 12 scenarios, representing different flooding types and human activities, were designed in this study (Table 3).S1, S2, S7, and S8 were control groups that indicated human activity with no rain and no warning, while the rest of the scenarios were experimental groups.

Model implementation and parameter setting
As an important spatial data management and analysis technology, GIS plays a crucial role in the dynamic exposure analysis

Block generation
Blocks are irregular vector units whose size represents spatial resolution.Therefore, the spatial resolution of the results is related to the study area and data.In this study, the study area was divided into 237 blocks based on the method introduced in Sect.3.3, with a minimum area of 2731.64 m 2 .The block types and their spatial distributions are shown in Figs. 6 and 7, respectively.Most of the blocks in the study area were categorized as residential areas, whereas blocks of recreational areas and others (which indicated rivers) were few and concentrated.

Parameter setting
To reduce the number of agent types, only a limited number of agent classes were used.The distribution of population characteristics for Liandu District is shown in Table 4.The agents were divided into 18 types for daily (non-disaster) scenarios (S1, S2, S7, and S8) and 24 types for disaster scenarios (all other scenarios) based on the influence of education level on individual disaster response behavior (Fig. 8).
The census did not identify individuals according to address, and at the start of each simulation, an agent population with the same distribution of age, gender, employment, education level, and travel mode was therefore randomly located within the residential area for the case study.The synthetic daily routines were described in probabilistic terms to capture the variability in the travel survey and uncertainties in behavior.The probabilities of agents' daily activities were generated based on the travel survey.We estimated the probabilities of all the activities of the population groups under investigation.

Exposure threshold
Although flood fatalities have a number of causes, such as physical trauma, heart attack, or electrocution, drowning accounts for two-thirds of such fatalities (Jonkman and Kelman, 2005).Previous research has established that the probability of death or serious injury as a result of exposure to flooding is dominated by floodwater depth and velocity (Abt et al., 1989;Karvonen et al., 2000;Lind et al., 2004;Jonkman and Penning-Rowsell, 2008).Additionally, the rate of water level rise can play an important role in this regard.However, other factors, such as age, fitness level, height, and weight of the individual, are important for determining their vulnerability to disasters.A comprehensive review of the flood-related casualty data and methods for assessing the risk of death or serious harm to people caused by flooding is provided by the Department for Environment Food and Rural Affairs and Environment Agency (2003) and Jonkman and Penning-Rowsell (2008).In this study, rather than predicting mortality (which is subject to random factors in addition to those mentioned previously), exposure to floodwater depths of 25 cm or greater under relatively fast flowing (2.5 m s -1 or greater) conditions was established as the threshold for the most vulnerable people (DEFRA and Environment Agency, 2003).This provided a conservative estimate of individuals vulnerable to floodwater rather than an estimate of mortality (Dawson et al., 2011).
Since building steps (thresholds) exert a blocking effect on shallow flooding, they are likely to reduce the degree of flooding by restricting flood water to the outside of the building, thereby reducing the exposure of the building.Therefore, this study assigned the height of building steps to corresponding block types according to the Chinese architectural design standards and actual conditions of the study area (Table 5).It should be noted that the block type "Other" constituted rivers and did not contain buildings.Therefore, the exposure of buildings was determined according to the depth of the flood and the height of building steps.The depth of the water entering the building was the difference between the depth of the flood and the height of steps.

Flood simulation
The temporal resolution of the flood simulation results was unified with other output results for 30 minutes.included roads in the center of the city and was larger than the actual flooding area.This difference could be attributed to different definitions of "water accumulation."The simulation results presented in Fig. 11 included all areas where the accumulated water depth during the flooding period was greater than 15 cm.The actual water accumulation point was defined as one experiencing rainfall of greater than 50 mm over a 24-hour period.Additionally, it was characterized by the water accumulation depth of the road reaching 15 cm (the meteorological department issued a blue rainstorm warning at this level), the water withdrawal time reaching 1 hour, and the water accumulation scope value being greater than 50 m 2 .Certain gaps existed between the observational data and the actual river discharge since the observation station was far from the study area.
Hence, the results indicated that the simulated water accumulation area during the fluvial flood (Fig. 11(b)) was smaller than that of the actual situation.

Simulation of the spatiotemporal population distribution
The spatial and temporal resolutions of the modeling results could be adapted to the study area.The area of the minimum block was 2731.64 m 2 .The temporal resolution of the results was 30 minutes, which could be set to 10 minutes or even 1 minute according to need.Additionally, no accurate traffic model was used to simulate agents' movements on roads.On one hand, it was for improving efficiency.On the other hand, we did not pay attention to high temporal resolution human movements (e.g., with precision to 1 minute or 1 second).We only focused on the population distribution for a specific period of time, and the temporal resolution requirement of human activities was therefore low.
The spatiotemporal distribution of the population was simulated based on six scenarios: (1) daily, weekday (S1, S7), (2) daily, weekend (S2, S8), (3) bad weather, weekday (S3, S9), ( 4) bad weather, weekend (S4, S10), ( 5) warning, weekday (S5, S11), and ( 6) warning, weekend (S6, S12). Figure 12 indicates the population variation for blocks and roads for the six scenarios.In theory, the simulated value should be much larger than the measured value since the former indicates the number of people, whereas the latter represents the number of cars and buses.However, as indicated in Fig. 14, the simulated value was close to the measured value.This could be attributed to the assumption that the study area was closed and the simulated population was the number of permanent residents, excluding the migrant population.In reality, the number of migrants in the urban area during the daytime is large owing to its geographical location.This study simplified human activities when simulating the spatiotemporal distribution of the population, resulting in a small number of pedestrians on the road.However, both the simulated and measured values were essentially similar with regard to changes in their trends.Therefore, the simulation method for the spatiotemporal distribution of the population is feasible, and the results are reliable.

Dynamic exposure assessment
Figure 15 presents the population exposure variation for two selected areas.The difference between pluvial and fluvial flood scenarios could be attributed to differences in the changes and degrees of water accumulation.Figure 15(a) indicates that population exposure was the highest for the daily scenario, followed by the bad weather and minimum warning scenarios.
However, as indicated in Fig. 15(b), the population was most exposed to both weekend and weekday warning scenarios.This is attributed to the assumption that the disaster response behavior adopted by residents was to reduce travel, i.e., the refuge of residents was the residential area.The response was not based on the exposure of the residential area.Therefore, when residential areas, such as Block 6, were exposed to floods, the residents chose to reduce travel, resulting in an increase in the population in residential areas and consequently increasing the population exposure.According to the analysis of the 12 scenarios, the government departments can carry out disaster prevention and mitigation measures for areas with high population exposure, such as evacuation prior to the disaster and initiation of key rescue operations during the disaster.The method proposed in this study can help to determine vulnerable populations and road users in the exposed blocks.Because we considered vulnerable people and road users when we constructed the population groups (agents), we could obtain similar information from the results of vulnerable populations and road users in the exposed blocks, such as the exposed population.
Such information is of great practical significance.
Figure 16 presents variations in the road and building exposures of two selected areas with serious flooding.The road and building exposures for the study area are presented in Fig. 17.It can be concluded that road and building exposures during pluvial and fluvial floods also varied with flood depth.The exposed road length of the block fluctuated, whereas the building was either entirely exposed or not exposed.Furthermore, the area of the road affected by pluvial and fluvial floods was greater than that of the buildings.As indicated in Fig. 17, exposed buildings were present in only a few areas (blocks), whereas roads were affected in several areas.Buildings were least exposed due to high thresholds or the number of building steps designed and built in recent years, whereas roads and population were severely affected by floods.

Conclusions
Urban flooding considerably impacts the daily lives of residents and not only affects commuting but also causes casualties and traffic congestion.This study proposed a method for determining high-resolution dynamic exposure to urban flooding.First, the spatiotemporal distributions of pluvial and fluvial floods were simulated by the LISFLOOD-FP model.Second, the responses of residents to bad weather and government measures (warnings) were incorporated to develop an ABM to simulate residents' activities during flooding.Finally, urban exposure during different flood scenarios was comprehensively simulated and was based on the population and hydrological simulation results, road and building data, and the case study of the Lishui urban district.
The method proposed can provide the government with high resolution dynamic exposure of the population, roads and buildings to flooding as well as information for urban vulnerability and loss assessment, and can support government disaster risk management.It could further provide effective reference information for residents' travels.This study comprised four main elements.First, different spatiotemporal distributions of water depth and velocity predictions were obtained using the LISFLOOD-FP model.Second, an ABM was used to simulate the spatiotemporal distributions of the population.Third, the impacts of pluvial and fluvial floods on buildings were found to be small, whereas those on roads and the population were greater.Finally, if residents reduced their travels (i.e., stayed at home), the exposure of the population in exposed residential areas increased.
It should be noted that there is no comprehensive way of verifying the proposed method.This is because parameters of human behavior and psychological processes are difficult (or, to some extent, impossible) to obtain.In this study, the proposed method was verified indirectly.Actual traffic data for each road intersection were collected and compared with the simulated population results.Data for actual water accumulation points were also compared with the simulated water accumulation results.Nonetheless, the study had some limitations, e.g., considerable uncertainties regarding the use and design of the ABM.
These included differences in the responses of residents of the same type to disasters in the same scenario.Therefore, this study simply attempted to reflect reality.Based on the survey data, we designed simplified activity patterns, which were consistent with the actual situation of the study area.Simplification of the behavior patterns and disaster responses of residents was inevitable, resulting in differences between the simulation results and reality.Our study focused on an explorative method, whereas the results were an application case.Due to the limitation of the study area and data, the current results were general and preliminary.The proposed method has many areas in need of improvement, such as the ABM design.Therefore, future studies should focus on optimizing the proposed method and practical case studies, which may produce more informative results.

Tables
Table 1 Data used in this study.
Table 2. Parameter values for the rainstorm intensity formula.
Table 3. Parameter variations used in the simulation scenarios.

5
Table 4. Sociodemographic characteristics of the population in the case study area.
of urban floods.Because of the simplicity, readability, and extensibility of the Python programming language, an increasing number of research institutes are adopting it for development.Therefore, the model was developed using the Visual Studio Code software (Visual studio code, 2018) and Python programming language(Python, 2018).The development of the graphical user interface (GUI), GIS module, and drawing module was realized by Qt(Qt, 2018), Geopandas (Geopandas,   2018), and Matplotlib (Matplotlib, 2018), respectively.
Figure 9 indicates the accumulated water depths and velocities of pluvial and fluvial floods in the study area.The pluvial and fluvial floods exerted significant impacts, and the urban area near the Oujiang River was the most severely flooded.Water also accumulated in the inner areas of the city, mainly on roads, in the case of pluvial flood disasters.The variations in water depth and velocity for eight severely flooded areas (including blocks and roads) are presented in Fig. 10.Spatiotemporal variations in flooding were observed.Figures 9 and 10 show that water depth was the main factor that caused life and property losses, whereas water velocity had little or no effect.The flood simulation results were indirectly validated by actual water accumulation points.During the 50-year flood in 2014, the city had 10 flooded roads and 18 water accumulation points.The actual hydrological points selected according to the study area and urban flooding results simulated by the prototype system are indicated in Fig. 11.To avoid overlap with the simulated water accumulation results for roads, the actual flooding points in the figure only included road junctions, and the entirety of Gucheng road (the Lutang to Dayou Street section) and Liyang Street (which connected the senior middle school to the Sanyan temple section) was represented by corresponding intersection points.Figure 11 indicates that both the simulation results and actual water accumulation points were mainly distributed along the river.The simulated water accumulation area (Fig. 11(a))

Figure 12 (
Figure12(a) shows that, among the three weekend scenarios, the population in the playground (Block 77) changed more than that in the company(Block 113).Figure 12(b)  indicates that the population on the roads was volatile, and the morning peak hour over the weekend was delayed by 1 hour in comparison to that on weekdays.The population distribution in the study area is shown in Fig.13.The population was unevenly distributed and concentrated in recreational and residential areas over the weekend.However, the population distribution on weekdays was relatively uniform.The concurrent population distribution for the six scenarios changed significantly over the weekend, whereas the distribution on weekdays changed little.Figures12 and 13indicate that the population change patterns were different for different blocks types.The daily routines of several people started from the residential area (home) in the morning, was followed by school or company blocks on weekdays and recreational areas over weekends, and concluded with a return to the residential area at night.During the occurrence of rainstorms or the reception of warning messages, different types of people reacted differently (continuing, postponing, or cancelling routine activities).Vulnerable people, such as the elderly and children, and sensitive people, such as the homeless, were more likely to cancel travel plans.Additionally, recreational activities were more likely to be canceled than were study and work activities.The reliability of the simulation of the spatiotemporal population distribution was indirectly verified by using traffic flow data.Due to the lack of data for 2014, we used traffic flow data from June 24 to July 7, 2017.The simulated total number of residents passing the four intersections (such as the junction of the Liqing and Huayuan roads) and the actual measured traffic flow at the intersections during the morning and evening peak hours on weekdays and weekends are shown in Fig.14.The traffic flow data in Fig.14are multi-day average results.

Figure captions Figure 1 .
Figure captions Figure 1.Location of the study area in Lishui City (left) and a digital elevation model (DEM) indicating details of the study area (right).

Figure 2 .
Figure 2. Overview of the dynamic exposure simulation of urban flooding.

Figure 3 .
Figure 3. Rainfall simulation results based on the Chicago hyetograph method, and observational data used for fluvial flood simulation.

Figure 4 .
Figure 4. Synthetic daily routine generated from the travel survey and census data for an employed male agent aged 18-60 years.

Figure 5 .
Figure 5. Activity patterns for a highly educated, employed male agent aged 18-60 years during disaster scenarios.

Figure 6 .
Figure 6.Number of different block types.

Figure 7 .
Figure 7. Spatial distribution of blocks in the study area.

Figure 8 .
Figure 8. Agent types for daily and disaster scenarios.Daily scenarios refer to S1, S2, S7, and S8 and the rest are disaster scenarios.

Figure 9 .
Figure 9. Maps of accumulated water depths and velocities."T" indicates time.

Figure 10 .Figure 11 .
Figure 10.Changes in the surface water depth (dep) and velocity (vel) for eight severely flooded areas.Figure 11.Map of the flooded area indicating the flooding simulation and real flood in 2014.Data for the flooded area were provided by Lishui City Housing and Urban-Rural Construction Bureau.Figure 12. Population changes in blocks and roads for the six scenarios.

Figure 13 .
Figure 13.Population distribution for the six scenarios."T" indicates time.

Figure 14 .
Figure 14.Traffic flow and population simulation results during peak hours on weekdays and weekends.Traffic flow data were provided by the Lishui City Traffic Bureau.Real means measured value.LQ is Liqing Road, KF is Kaifa Road, HY is Huayuan Road, ZJ is Zijin Road, and LT is Lutang Street.

Figure 15 .
Figure 15.Changes in population exposure of two blocks for the 12 scenarios.Block 168 was a recreational area, and Block 6 was a residential area.

Figure 16 .Figure 17 .
Figure 16.Changes in road and building exposure in severely flooded blocks.Exposed road length and building area represent road and building exposure, respectively.Figure 17.Map of road and building exposures."T" indicates time.

Figure 1 .Figure 3 .Figure 4 .
Figure 1.Location of the study area in Lishui City (left) and a digital elevation model (DEM) indicating details of the study area (right).