Floods cause significant damage in cities due to their intensity, frequency, and vulnerability, which are driven by complex internal and external factors. Dynamic behavior of urban response during a flood event is difficult to measure due to urban systems’ complexity and non-linear behavior. This study simulates the flood response dynamics of people, inundated waters, and financial expenditure during a flood event to visualize the dynamics of urban flood events using Colombo City, Sri Lanka, as a case study. Sensitivity analysis was conducted for pumping infrastructure and flood relief expenditure to view the variation of flood damage using Monte Carlo simulation. Results revealed that pumping units and the initial flood relief budget significantly impact the flood recovery of inundated areas. The results were validated using flood water pumping statistics and hydrology models conducted for historical flood events. The system dynamics framework is useful for combining multiple parameters in the flood modeling process to understand the complex relationships between population, flood inundation, and financial relief programs. This framework can be expanded to quantify the effects of mitigation and adaptation strategies in flood-vulnerable cities to optimize the decision-making process.

  • Flood recovery is measured through population interactions, flood water, and funding.

  • Link multiple unit measures and scale variables to assess flood response patterns.

  • Coordination of multiple stakeholders is essential for smooth disaster recovery.

  • Planners can simulate feature variations of natural and social subsystems to flood recovery in cities.

  • System dynamics model incorporated multiple unit measures and scale variables to assess response patterns during a simulated flood event.

  • Rainfall monitoring and automated flood removal are critical for a timely response from the beginning to the end of a flooding event.

Cities are more susceptible to disaster risk than rural settings due to the high concentration of population in a smaller spatial area, an expensive infrastructure network, and the agglomeration of economic activities within urban areas (Gencer 2013; Gu 2019). Moreover, competition for limited space caused an uneven distribution of resources, resulting in a population shift toward environmentally sensitive areas. The impact of natural hazards can be severe on cities in developing countries due to settlements in high-risk zones, poor preparation, and limited information flow between vulnerable communities and institutions (Gu 2019; Nkwunonwo et al. 2020). Floods are one of the most catastrophic disasters cities face, affecting millions of people and damaging economies in an irreversible way (Re 2021). Since 1980, floods have accounted for over 40% of the global loss from natural disasters (catnat.net 2021), prompting city governments to spend billions of dollars on recovery while searching for resilient strategies to keep cities safe from flood-induced losses. However, it is challenging to predict the impacts of flood disasters due to their stochastic nature (Avila-Aceves et al. 2023) and the complexity of urban system interactions. Moreover, cities adopt multiple mitigation and adaptation measures to manage flood impacts and cut across various disciplines at multiple scales, making it challenging to optimally plan response and recovery efforts.

Systems thinking considers cities to be complex, adaptive, and emergent urban systems with evolving interactions among their subsystems to stay in a dynamic equilibrium (Forrester 1973; Dicken 2011). Moreover, human activities and behavioral patterns are essential for measuring the divergent behavior of equilibrium in cities, which cannot be captured using traditional spatial urban models due to the non-synchronized behavior of the physical structure and flows within cities (Ammara et al. 2022). Batty (2017) stated that the complexity of urban interactions on temporal and spatial scales using systems, flows, and networks is vital to assess cities' disequilibrium when facing shocks like natural hazards. Therefore, it is evident that urban flood response measures need a holistic view of all the subsystems within cities and a dynamic focus on physical, social, and environmental interactions to understand the variation in response to disaster situations. Seminal work in disaster management is highly discipline-oriented and focused on multiple disaster impacts using flood models, land-use models, population dynamics, and opinion surveys to assess flood response outcomes in isolation. Engineering principles used for flood mitigation were exclusively studied, whereas population dynamics are often studied by social science fields on flood adaptation. However, the interactions on natural, physical, and social factors are complex during a flood event, demanding an interdisciplinary focus to understand the response behavior of impacted communities. Moreover, the lack of comprehensive frameworks to model urban interactions and limited research on urban systems' responses at multiple spatial and temporal scales are noted in the urban planning discipline. Also, significant gaps in resilience literature are visible in measuring the system response before, during, and after natural hazards such as floods.

This study is expected to bridge the existing research gaps among urban response studies by incorporating multiple variables with different unit measures and empirical interactions. The population and flood water interactions were simulated along with the financial cost of flood relief, which is often ignored in existing modeling frameworks yet crucial for cities to manage their limited resources during flood events. First, this paper uses a comprehensive review of the literature on systems thinking and dynamic modeling. Second, the modeling framework is introduced along with the selected case study. Third, the system dynamics (SD) model results are explained along with the sensitivity assessment. Fourth, a discussion is provided with key insights and future research potential in disaster management and the application of SD models. Finally, the author gives insights into improving this framework to simulate flood response in future studies by minimizing the limitations of existing frameworks.

System dynamics and flood management

The SD concept was introduced to urban analysis by Forrester (1961) by incorporating industrial systems' organizational structure and feedback characteristics. This concept was later used to explain the causal relationships and interdependencies in cities to answer the problems faced by urban systems (Forrester 1973). Eventually, the SD approach was commonly applied in various fields in cities to explain the complex relationships between variables and the non-linearity of existing urban setups by decision-making bodies in urban areas (Tan et al. 2018). A system has interconnected features integrated to achieve a common purpose (Meadows 2008). The urban system, therefore, is comprised of a combination of multiple physical, socio-economic, and environmental variables with interdependent relationships to achieve a common development goal. However, the shocks and stresses in various forms constrain the goal, and multiple factors influence the response of an urban system to achieve such equilibrium. From the socio-ecological perspective, the equilibrium can be a new transformation from the pre-shock status and can be explained using multiple interactions and complex relationships among socio-ecological and technical aspects in cities (Davoudi et al. 2012; Bai et al. 2016; Masnavi et al. 2019). Natural disasters are commonly faced with constraints by cities, where the SD approach is commonly used to explain the response of cities using physical, social, economic, and ecological interactions. Urban flood response studies in the recent past shifted from an engineering basis toward a socio-ecological basis mainly due to the unpredictability of impacts, the continuous transition of equilibrium status in cities, and the influence of socio-economic factors in the urban environment (Grinberger & Felsenstein 2014; Masnavi et al. 2019). Cities are complex systems involving multiple stakeholders and multiple layers of interdependencies. Conventionally, impacts on tangible physical assets and spatial vulnerabilities are addressed by urban planning decision-makers (Sharma 2022). However, the interdependency of urban functions, feedback within the urban structure, and ecosystem services are difficult to assess only in spatial terms and interpret with temporal changes. Moreover, the consideration of cities as complex systems poses challenges to measuring resilience to disasters as dynamic systems with non-linear feedback factors on response strategies.

Incorporating the SD perspective into flood response studies has multiple advantages from the urban planning perspective. First, it helps understand the non-linear dynamics involved in disaster risk and vulnerability factors of socio-economic activities. Conventional vulnerability assessments identify the spatial elements at risk to explain the vulnerability, where it is known that spatial factors alone cannot define the vulnerability of urban areas (Cutter et al. 2003; Balica & Wright 2010; Bigi et al. 2021). Existing socio-political trends, institutional capacity, long-term economic policy changes, and exogenous factors are not always tangible or interpreted physically. Moreover, financial resources may not compensate for the ecosystem services, which can be critical for the non-linear dynamics of the resilience assessment. Second, the co-evolving nature of systems cannot be studied on a fixed spatial or temporal scale. Urban system boundaries can reach local to regional scales from functional perspectives, while the magnitude of disasters can be influenced by indirect relationships at ecosystem scales, which may not align with urban boundaries per se. SD frameworks tackle the dynamic nature of interactions across multiple spatial and temporal scales using stock-flow diagrams. They are flexible enough to work with multiple spatial scales to suit the objectives. This flexibility in SD models is a reason for increasing popularity within flood response and resilience research. Third, response measures using data-driven models are subject to endogeneity, where unaccounted parameters can cause the target variable to fluctuate. Meadows (2008) explained this using the idea of ‘rich become richer, and poor become poorer in the economy’. Conventional modeling frameworks are prone to endogeneity due to errors in assumptions, selection bias, and simultaneity (Waddell 2005; Muñiz & Rojas 2019; Guerrero et al. 2021). SD models can incorporate external measures that cannot be measured using spatial parameters such as climate change and transboundary factors, population attitude, and socio-political stresses into resilience measures. Fourth, natural disaster risks can be sensitive to the initial conditions before a disaster to form different outcomes in the assessment and reveal the unpredictable nature of disaster impacts. Therefore, framing a specific disaster event without temporal variations before and after cannot signify the level of resilience in urban areas. SD models can incorporate multiple impacts with temporal effects, which are necessary to determine the adaptive capacity of the urban environment to face natural hazards. Finally, feedback loops are essential elements to be considered in resilience studies. In urban environments, disaster effects and causal factors can reinforce the perceived damages during disasters (Bempah & Øyhus 2017; Peiris et al. 2024). For example, property values can be reduced in flood-prone areas, and it can attract vulnerable communities into risky regions and thereby increase damage during future disasters. Growth, income, and development policies can influence such reinforcing loops, which resilience assessments must address. Moreover, stakeholder involvement from multiple strata (local to central governments) has to be addressed from policy level to grassroot level implementable strategies, which can be evaluated and simulated using SD models. Therefore, the SD framework offers multiple benefits to address urban resilience in the context of natural disasters like floods to design effective response strategies.

Integration of multiple models in disaster management

One of the key challenges in disaster management models is to capture the multiple impacts in multiple layers of society. For example, natural phenomena of extreme rainfall can trigger a pluvial flood event by exceeding the infiltration capacity of land (Houston et al. 2011). However, the flood will become a nuisance once it disrupts the community's livelihood or city functions by impacting the physical and socio-economic space. Researchers in various disciplines have identified this effect (Davoudi et al. 2012; McClymont et al. 2020; Peiris 2024). However, when cities cannot avoid floods due to their geographic location, mitigation and adaptation strategies are often used to minimize the damage and reduce the economic costs of disasters. It is difficult to simulate multiple factors together due to limited access to data and information or complexities involved in urban systems within cities. Moreover, dynamic models become extremely challenging when uncertainties emerge with variables (Martinez-Moyano & Richardson 2013). However, it is necessary to incorporate community perception, financial cost, and political decision-making into disaster management since those factors directly influence the response of cities to floods. This is evident for cities in developing countries where financial constraints often constrain disaster management budgetary allocations (Allaire 2018; Parida 2020). According to the ‘Observatoire Permanent Des Catastrophes Naturelles’ database (2021), annual flood damage exceeds one billion in United States Dollars globally. Therefore, understanding the damage costs and recovery expenses when planning flood management strategies is challenging yet essential. This study is one of the attempts to incorporate financial factors into flood simulation models, which can be useful for disaster managers and policymakers in the field.

Compartment models in epidemiology are commonly used to understand population movements within a confined space and diagnose disease vulnerability among populations (Brauer 2008). Susceptible-infectious-recovered models, commonly known as SIR models, are effective in epidemiology to model diseases among populations, including the COVID-19 pandemic (Fan et al. 2020; Peiris 2021). SIR models have been used to model population movement, pathogens, and infrastructure planning (Coalson et al. 2021; Lee et al. 2021). Resident populations in flood-risk zones are an important factor in managing flood response during a flood event, and therefore, SD models can combine with the SIR model to simulate the temporal variation of risks from the beginning to the end of a flood event. The key feature common to both models is the ability to capture discrete variations of temporal variables. So, in disaster management studies, simulation of the population movement from the initial stage of flood inundation to the complete dissipation is useful to understand the risk behavior and effects of mitigation strategies. This has been conducted using mobile phone movement data during hurricane events in the past (Hong et al. 2021). Similarly, floodwater removal and related financial and population changes have been less studied in temporal simulations. Moreover, SD models are extensively used in flood management (Gotangco et al. 2016; Links et al. 2018) and business management (Meadows 2008; Martinez-Moyano & Richardson 2013) separately, which have the potential to be expanded in related interdisciplinary work to improve resilience and optimize strategies. The SD modeling framework is useful for decision-makers to test the effectiveness of policies and programs. In many cities, disaster-related agencies are fragmented or work in isolation to develop multiple strategies that may have negative consequences or ignore some key stakeholders in flood situations. Moreover, due to the stochastic nature of floods, structural mitigation measures cannot manage flood threats as factors like rainfall and upstream water flows are difficult to predict in a flood disaster (Avila-Aceves et al. 2023). In addition, the fund allocations for mitigation and adaptation strategies are highly unequal, so decision-makers need to test multiple scenarios with different levels of resources to handle vulnerable communities during flood events. SD models can incorporate multiple variables from different levels to assess the effectiveness of policy actions and strategies. This is an added advantage for ground-level handling of resources in disasters.

Modeling framework

This study uses dynamic modeling of key variables, namely, population at risk, flood water concentration, and disaster relief funding allocation during a flood disaster, to simulate the effects over a period of 100 h of a flood event. The simulation process was applied in Colombo City, Sri Lanka, to showcase the temporal variation of resource use and to benchmark the existing mitigation measures by the decision-making authorities using flood events that occurred in May 2016. The modeling structure, objectives, reference modes, and insights are given to manage future flood disasters and develop effective preparedness strategies from an urban planning perspective. The SD modeling process involves eight steps, as explained in Figure 1. These steps are developed from a problem-oriented approach focused on complex real-world scenarios (Martinez-Moyano & Richardson 2013). SD models use differential equations to explain the changes of a stock variation in discrete time variations (Equation (1)).
Figure 1

Key steps involved in SD modeling.

Figure 1

Key steps involved in SD modeling.

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Equation (1): Stock variation with the time in a system component.

In this study, the dynamics during a flood event are used to simulate the SD model. The scope of the study used the dynamic interactions among heterogeneous factors during a flood event – from the start of flooding to the complete recovery of floods – based on the cities' physical response for 100 h (approximately 4 days).

The problem statement gives the depth of the existing dynamics of a problem along with the expected solutions in the real world. The goal setting and the identification of gaps in the existing dynamic situation are useful for applying the SD framework (Martinez-Moyano & Richardson 2013). Key stakeholders involved in flood management and literature review are used to identify dynamic processes and develop interactions among such processes during floods. Once all the variables that influence flood damage have been identified, these were prioritized, and the behavior was followed over time to identify the impact of such variables on the problem. The interactions of multiple variables causing flood impact in cities were drawn using Vensim PLE Plus 9.3.5 software. The interactions are indicated in Figure 2.
Figure 2

Interactions among variables in the urban environment are identified through the problem definition stage.

Figure 2

Interactions among variables in the urban environment are identified through the problem definition stage.

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The study's goal was to recover the city's key functions during the flood event and restore the daily activities as soon as possible. In this context, damage to physical infrastructure and utilities (road network, water supply, and energy plants) poses a significant threat to the functions of the city, and operational services such as food, healthcare, energy, and mobility were considered measurement levels in the model structure. Discussion outcomes of planning agencies concluded that road inundation is the critical factor for mobilizing goods and services during a flood event, so floodwater removal from the road network is the most sensitive factor in the recovery process. Accordingly, road inundation for more than 3 days (72 h) was the threshold for service disruption. The objective has been set to reduce the inundation time to 12–24 h (1 day) for access to relief services and material flow in the city. Existing action plans to achieve this objective range from installing floodwater pumping stations around streams, temporarily relocating people in flood-risk zones, and stocking essentials such as food and medicine before a flood event (preparation).

Reference modes were generated for the critical variables identified in the discussions on population, financial expenditure, and road inundation length. The reference modes are detailed in Figure 3.
Figure 3

Reference modes were generated for the variables affected by flood events.

Figure 3

Reference modes were generated for the variables affected by flood events.

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Based on the reference mode and the conceptual model for dynamic interactions in the city, momentum solutions identified were the conservation of the floodplain by eliminating undesired buildings, the relocation of encroached communities from the flood-risk zone, increasing the flood relief budget for timely recovery, and the relocation of critical infrastructure (i.e. grid substations for power transmission, potable water storage systems, and public transport terminals) from high-risk zones. The temporal variation was taken for 10 years from 2020 to 2030, with annual extreme flood impacts as the assumed scenario. For simulation, the variation of reference modes during a past flood event (May 2016) in the city of Colombo, Sri Lanka, has been selected to demonstrate the dynamic interactions.

Case study

Colombo City is the commercial capital of Sri Lanka, located on the Western coast of the island, with a significant concentration of population and industries. Kelani River, one of the largest rivers in terms of stream outflow, flows across the city and frequently floods Colombo City during Southwest monsoon rains (Figure 4). Heavy rains, followed by increased upstream flow, caused a major flood event in May 2016, disrupting livelihood and activities for a few weeks. During the floods in 2016, the inundation of roads for days posed challenges to move goods and services to the affected communities and restore critical infrastructure and utilities. City administration and planners have identified several actions to be prepared for future flood events and coordinated efforts to minimize the damage and restore critical functions to manage the impact of floods.
Figure 4

Location of Colombo City and flooded areas during May 2016.

Figure 4

Location of Colombo City and flooded areas during May 2016.

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The system boundary used for the flood analysis in the case study is Colombo City, and its suburbs were directly affected by the extreme flood events in 2016. The temporal boundary is selected as the days required for the city to return to its normal situation from the day of the first rainfall. Therefore, 100 days from the first day of rainfall is selected for the SD model application. The view of floods was taken from an urban decision-maker's perspective, where the actual information was obtained from disaster management agencies. This was followed by a focus group discussion with officials involved in flood relief activities.

According to official figures and discussions, flood water retention in streets was the main problem identified in the problem framing exercise. In addition, constraints to supply chains, epidemics, and waterborne diseases after floods, as well as disruption to the livelihoods of lower-income groups, were identified as secondary issues caused by the floods. The study aims to return to daily functions by removing flood waters from the streets since the Indian Ocean is accessible to the city from the west direction. During the discussion, the stakeholders' top priorities were restoring road transport, water supply, and energy supply. Given the uncertainty of rainfall, they agreed to continue with historical rainfall and inundation data for modeling purposes. The model information used for fixing pumps was collected from government agencies (MCUDP 2022). Rainfall information recorded during the 2016 flood event is detailed in Table 1.

Table 1

Rainfall data recorded daily during extreme rainfall events from 13th to 20th May 2016

StationRainfall in mm during days of the month (13–20 May 2016)
Total (mm)
13th May14th May15th May16th May17th May18th May19th May20th May
Castlereigha 6.20 15.60 137.50 116.30 72.00 15.80 68.20 11.60 443.20 
Nortona 20.90 11.70 201.50 200.50 109.40 12.10 77.00 47.00 680.10 
Moussakellea 6.00 14.50 155.00 82.00 84.50 19.50 62.30 7.00 430.80 
Canyona 30.50 13.00 179.20 187.50 87.10 22.90 64.00 12.10 596.30 
Laxapanaa 20.60 12.00 158.50 167.90 129.10 12.70 78.50 20.20 599.50 
Norwoodb 11.80 37.70 86.00 35.40 68.60 17.10 45.00 2.70 304.30 
Kitulgalab 23.10 32.90 336.90 70.00 66.90 51.60 138.70 21.90 742.00 
Deraniyagalab 142.60 22.80 355.50 91.70 69.40 58.20 144.30 14.30 898.80 
Holombuwab 37.80 16.60 201.60 88.70 101.30 10.30 40.30 11.10 507.70 
Glencourseb 60.40 16.10 225.80 78.00 73.70 26.60 108.90 1.40 590.90 
Hanwellab 7.00 11.60 160.70 17.90 48.70 9.30 108.30 1.30 364.80 
Nagalagam Streetb 2.60 82.60 217.40 7.60 13.40 1.70 10.10 0.00 335.40 
Colomboc 2.80 76.40 256.90 26.00 19.50 0.90 9.80 0.80 393.10 
StationRainfall in mm during days of the month (13–20 May 2016)
Total (mm)
13th May14th May15th May16th May17th May18th May19th May20th May
Castlereigha 6.20 15.60 137.50 116.30 72.00 15.80 68.20 11.60 443.20 
Nortona 20.90 11.70 201.50 200.50 109.40 12.10 77.00 47.00 680.10 
Moussakellea 6.00 14.50 155.00 82.00 84.50 19.50 62.30 7.00 430.80 
Canyona 30.50 13.00 179.20 187.50 87.10 22.90 64.00 12.10 596.30 
Laxapanaa 20.60 12.00 158.50 167.90 129.10 12.70 78.50 20.20 599.50 
Norwoodb 11.80 37.70 86.00 35.40 68.60 17.10 45.00 2.70 304.30 
Kitulgalab 23.10 32.90 336.90 70.00 66.90 51.60 138.70 21.90 742.00 
Deraniyagalab 142.60 22.80 355.50 91.70 69.40 58.20 144.30 14.30 898.80 
Holombuwab 37.80 16.60 201.60 88.70 101.30 10.30 40.30 11.10 507.70 
Glencourseb 60.40 16.10 225.80 78.00 73.70 26.60 108.90 1.40 590.90 
Hanwellab 7.00 11.60 160.70 17.90 48.70 9.30 108.30 1.30 364.80 
Nagalagam Streetb 2.60 82.60 217.40 7.60 13.40 1.70 10.10 0.00 335.40 
Colomboc 2.80 76.40 256.90 26.00 19.50 0.90 9.80 0.80 393.10 

Note: The highest daily rainfall at each gauging station is marked in bold.

aOperated by the Ceylon Electricity Board (hydropower reservoir-based stations).

bOperated by the Irrigation Department of Sri Lanka (Kelani River-based stations).

cOperated by the Meteorological Department of Sri Lanka (weather monitoring station).

The locations of each gauging station are shown in Figure 5. For this study, stream gauging stations located along the Kelani River (stream gauging stations) are considered for the flood analysis. The comparison of the maximum water level recorded at the Nagalagam Street Water Gauging Station – the closest water level recording station to Colombo City Center and the outfall of the Kelani River – with the records is shown in Figure 6. Key stakeholders involved in flood management in Colombo city are detailed in Table 2.
Table 2

Key stakeholders involved in the flood management during the 2016 flood event and stakeholder discussion of this study

AgencyRoleFocus areas on flood response
District Secretariat and Divisional Secretary Divisions (DS) Financial allocation for flood relief services Population recovery, financial mobilization 
Disaster Management Center (DMC) Flood impact assessment and recovery services Population recovery 
Sri Lanka Land Development Corporation (SLLDC) Floodwater removal and wetland management Flood water management 
Urban Development Authority (UDA) Land-use planning and flood-risk assessment Flood water management 
Road Development Authority (RDA) Road construction and infrastructure management Flood water impact on infrastructure 
Ceylon Electricity Board (CEB) Power generation and transmission Flood water impact on energy infrastructure 
National Water Supply and Drainage Board (NWSDB) Potable water treatment and distribution Flood water impact on water infrastructure 
Community-based Organizations (CBOs) Impact assessment of the population during floods Population recovery and resource management 
AgencyRoleFocus areas on flood response
District Secretariat and Divisional Secretary Divisions (DS) Financial allocation for flood relief services Population recovery, financial mobilization 
Disaster Management Center (DMC) Flood impact assessment and recovery services Population recovery 
Sri Lanka Land Development Corporation (SLLDC) Floodwater removal and wetland management Flood water management 
Urban Development Authority (UDA) Land-use planning and flood-risk assessment Flood water management 
Road Development Authority (RDA) Road construction and infrastructure management Flood water impact on infrastructure 
Ceylon Electricity Board (CEB) Power generation and transmission Flood water impact on energy infrastructure 
National Water Supply and Drainage Board (NWSDB) Potable water treatment and distribution Flood water impact on water infrastructure 
Community-based Organizations (CBOs) Impact assessment of the population during floods Population recovery and resource management 
Figure 5

Locations of hydro-gauging stations to monitor rainfall and flood water levels (Source: Irrigation Department of Sri Lanka).

Figure 5

Locations of hydro-gauging stations to monitor rainfall and flood water levels (Source: Irrigation Department of Sri Lanka).

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Figure 6

Maximum water levels recorded at the Colombo (Nagalagam Street) Water Gauging Station for historical flood events.

Figure 6

Maximum water levels recorded at the Colombo (Nagalagam Street) Water Gauging Station for historical flood events.

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Once the simulation was completed, the model was validated using the Urban Flood Risk Mitigation Model (UFRM) developed for flood runoff retention (InVEST 2017). Moreover, the flood mitigation pumps installed near the St. Sebastian North Lock Pumping Station (SSNLPS) were used for the physical validation of the simulation. The smallest administration unit (Grama Niladhari Divisions (GND)) was used for model testing and results interpretation. Sedawatta GND, with about 64 hectares of land area, was selected for the testing. The location of SSNLPS within Sedawatta GND is shown in Figure 7.
Figure 7

St. Sebastian North Lock Pumping Station is located within Sedawatta GND. Source: Author, Google Earth Pro Satellite Imagery.

Figure 7

St. Sebastian North Lock Pumping Station is located within Sedawatta GND. Source: Author, Google Earth Pro Satellite Imagery.

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SD model results

The analytical framework emphasized the variation of key selected parameters during a flood event to simulate resource flow and response behavior of cities. Results from SD frameworks tackle the dynamic nature of interactions across multiple spatial and temporal scales using stock-flow diagrams and are flexible enough to work with multiple spatial scales to suit the objectives. This flexibility in SD models is a reason for increasing popularity within urban resilience research. For this study, the population living in the risk zones, funding allocation for relief services, and flood water removal were taken as stocks for the simulations. Key variables used to simulate are shown in Table 3. Due to the unavailability of reliable data sources, some of the information was used as reference values for model explanation.

Table 3

Parameters used for the simulation of multiple variables during flood events

Variable typeUnitInitial values
Total population at the risk zone People 9,000 
Flood-vulnerable population People 1,000 
Initial government budget for relief Sri Lankan Rupees (LKR) 1,000,000 
Social expenditure length Hours 32 (distributed for flood water removal) 
Flood water concentration Cubic meters (m3
Rainfall intensity (depth) Millimeters 200 (every 6 h until 20:00 h) 
Flood water pumping units Pumps 3 (operational for 8 h) 
Flooded area Hectares 64.3683 
Variable typeUnitInitial values
Total population at the risk zone People 9,000 
Flood-vulnerable population People 1,000 
Initial government budget for relief Sri Lankan Rupees (LKR) 1,000,000 
Social expenditure length Hours 32 (distributed for flood water removal) 
Flood water concentration Cubic meters (m3
Rainfall intensity (depth) Millimeters 200 (every 6 h until 20:00 h) 
Flood water pumping units Pumps 3 (operational for 8 h) 
Flooded area Hectares 64.3683 

Note: Initial values are generated based on Sedawatta GND flood-risk population data and pumping design data from agencies.

Stock and flow diagrams were developed for each stock variable indicating the variation a period of over 100 h. Populations affected by floods are modeled using the SIR-type model to simulate the state of the population changing from risk to vulnerability and from vulnerability to recovery within the flood plain. A proportion of people removed from vulnerable stock considering the deaths and permanent migration of people from the flood plain. Moreover, recovered populations are repositioned as risk stocks because they will keep staying in the flood-risk zone continuously.

Similarly, flood inflow is initiated by the extreme rainfall event, which is unevenly distributed for 20 h. The flood outflow is calculated using two variables, natural discharge from the basin and pumping outflow. Three pumps will continuously work for 8 h to remove the excess water from streets to regain the road network before the flood event, and pumping rates were calculated based on the numerical objective of the study. Moreover, the initial budget of LKR 1,000,000.00 will be spent on flood relief (social recovery) of people and the pumping of flood water. The interlinked stock and flow diagram is shown in Figure 8.
Figure 8

Stock and flow diagram of variable interaction during the flood event.

Figure 8

Stock and flow diagram of variable interaction during the flood event.

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The simulation of stocks and flows and their causal effects on the population within flood-vulnerable zones, flood water discharge from the neighborhood, and capital expenditure management during flood relief work provide insights into the dynamics of the distribution of people, flood water, and money. Figures 911 illustrate the variation of each stock with the time during a simulated flood event.
Figure 9

Dynamics of the population living in the flood-risk zone.

Figure 9

Dynamics of the population living in the flood-risk zone.

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Figure 10

Dynamics of flood water variation within the urban watershed during the flood event.

Figure 10

Dynamics of flood water variation within the urban watershed during the flood event.

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Figure 11

Dynamics of capital expenditure variation during the simulated flood event.

Figure 11

Dynamics of capital expenditure variation during the simulated flood event.

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According to Figure 9, the population at risk becomes vulnerable with the initiation of the flood scenario. However, with the flood removal initiated within the first 10 h, the vulnerable population recovered and reached back to the initial levels before the flood. The total population will not reach the same levels before the flood event due to deaths and permanent migration from the vulnerable proportion.

Floodwater concentration is initiated by extreme rainfall in a short period (2 m at 6-h intervals), and floodwater outflow to the ocean is a combination of gravity flow and the pumping process (Figure 10). Due to the efficiency of flood outflow, the flood waters will be eliminated within 24 h. Recovery practices for population and infrastructure can be initiated soon after flood water removal.

Expenditure on community relief services and the pumping process will be initiated from the initial period to carry out essential activities during flood concentration (Figure 11). The capital expenditure for social recovery will continue beyond the pumping cost to manage post-flood recovery activities. However, the expenses can vary largely depending on the context and the significance of the damage by land-use types (residential, commercial, or industrial property damage). Therefore, the expenses provided here can be used with contextual parameters to justify the possible costs incurred in a future disaster scenario.

Sensitivity analysis

Sensitivity analysis in SD modeling is used to measure the output variables for a given set of assumptions in the model. Multivariate sensitivity simulation or Monte Carlo simulation is used to measure the variability of outputs based on controllable changes from the decision-maker's perspective. However, sensitivity analysis is not only a tool to define the optimum changes of a social system like population behavior but also a useful process to identify the feasibility of changing the inputs in a flood situation. Monte Carlo simulation is generally applied in uncertain input variables or significant risks involving actions. In this study, expenditure allocated for flood relief services and the performance of flood water pumps are identified as critical variables with high uncertainty due to the priorities of government budgetary allocations and the maintenance cost of pumping operations. This study used sensitivity graphs by percentiles using Vensim PLE Plus 9.3.5 software.

As shown in the stock and flow model, population movement and rainfall quantities are not easy to predict or influential in the disaster event. The capital expenditure on the disaster recovery services and flood water pumping capacity are within the controllable scope of the decision-making bodies. The multivariate simulation of variables with 200 simulation runs with 1,234 noise seeds is used as default in this study. The parameters used for the sensitivity analysis are shown in Table 4.

Table 4

Parameters used in the simulation of sensitivity analysis

ParameterDistributionMinimum valueMaximum value
Government budget Uniform LKR 800,000.00a LKR 1,200,000.00a 
No. of pumps Uniform 
ParameterDistributionMinimum valueMaximum value
Government budget Uniform LKR 800,000.00a LKR 1,200,000.00a 
No. of pumps Uniform 

aLKR denoted Sri Lankan Rupees as the currency of Sri Lanka.

According to Table 4, the uniform distribution of variables was selected. The default values for the government budget were LKR 1,000,000.00 and three pumps. The repeated simulation with the given range will provide the impact of the variables on the flood relief process. Figures 12 and 13 show the Monte Carlo simulation of hourly government expenditure (outflow for floods) and the variation of flood water in the selected area (flood outflow), respectively.
Figure 12

Variation of expenditure during the flood event based on sensitivity simulation for funding allocation.

Figure 12

Variation of expenditure during the flood event based on sensitivity simulation for funding allocation.

Close modal
Figure 13

Variation of pumping of flood water from the area based on sensitivity simulation for the number of pumps.

Figure 13

Variation of pumping of flood water from the area based on sensitivity simulation for the number of pumps.

Close modal
Time graphs are generated for pumping cost and expenses for flooding (flood outflow) to assess the variation during changing parameters in the simulation. Figure 14 shows the variation of flood outflow and pump cost variables for changes to pumping units from one to five (horizontal axis), and Figure 15 shows the variation of the same variables for a government budget of LKR 800,000.00 to 1,200,000.00. The vertical axis shows the number of runs assigned for each parameter and values obtained at each specified section.
Figure 14

Time graph of sensitivity output for pumping units.

Figure 14

Time graph of sensitivity output for pumping units.

Close modal
Figure 15

Time graph of sensitivity output for initial government budget.

Figure 15

Time graph of sensitivity output for initial government budget.

Close modal

According to Figure 14, the most frequent runs for flood outflow were initiated from 2.62 to 2.96 pumps, while pumping costs varied throughout the sensitivity simulation. However, the lowest pumping cost simulations occurred in the lowest range (0.92–1.26), while the highest simulation frequency was obtained for pump cost from the 3.3–3.64 range. The base run or original values for the pumping units were three, and iterations peaked around the base run in this situation.

Figure 15 shows the frequency histogram of iterations when the initial government budget ranges around the base value of LKR 1,000,000.00. In this case, the most iterations are visible for pumping cost and flood expenditure when it is less than the base value. Flood outflow expenses show the highest iterations (approximately 25 simulations) around expenses ranging from LKR 860,000.00 to 894,000.00, while pumping costs peaked around LKR 996,000.00 to 1,030,000.00. At the same time, the lowest simulations for flood outflow expenses were generated around LKR 900,000.00, while the lowest pumping cost iterations were generated around LKR 1,100,000.00.

Based on the histogram, the decision-makers can compare the sensitivity of controllable parameters to the objectives of flood removal in the city, and the number of iterations can be increased for more computational capacity, while parameters can be changed to view the population variation from risk zones to vulnerability. However, the sensitivity analysis must be used carefully to determine the changes in capital expenditure and resource allocation to different areas during the flood events. The uncertainty of rainfall patterns and social mobility during flood events can significantly vary the empirical results with simulation values.

Validation of results

The SD framework used population flow, funding, and flood water removal from Sedawatta GND as a case study to simulate the dynamic interactions during a flood event. The funding information is changing rapidly, and the city or country's overall economic performance and multiple budget-related factors could affect the expense allocation. Therefore, the funding component is highly volatile and needs to be applied on a case-by-case basis. However, hydrology models are available to validate flood inundation and distribution over the watershed. Therefore, the UFRM model (InVEST 2017) was used for watersheds of the Kelani River and assessed for runoff reduction at the SSNL pumping station located at Sedawatta GND. The UFRM model was applied for the maximum rainfall recorded at the Nagalagam Street Gauging Station (NSGS) in May 2016, as shown in Table 1. The other inputs used for the UFRM model are land-use data, sub-watersheds, soil hydrology information, and curve numbers for each land-use category (Kadaverugu et al. 2021; Quagliolo et al. 2021). The model applied in InVEST Model workbench 3.14.0 and the runoff reduction results for the Kelani River are shown in Figure 16.
Figure 16

The runoff retention index for the Kelani River Basin shows that runoff is the highest among coastal urban areas.

Figure 16

The runoff retention index for the Kelani River Basin shows that runoff is the highest among coastal urban areas.

Close modal

According to Figure 16, the coastal urban areas toward the west of the Kelani River Basin (KLB) show significantly lower runoff retention, which means that those areas are susceptible to flooding with high runoff. The water level data from the NSGS were used for river discharge quantity calculations during the May 2016 flood event and validated using the pump discharge variation of the SD model. The discharge information at the NSGS is shown in Table 5.

Table 5

Flood information records at Nagalagam Street based on the May 2016 flood event and the UFRM model

1. UFRM model data
2. 2016 Flood records (NSGS)
3. Pumping station (SSNLPS)a
Subbasins08Return period20 yearsDesign capacity30 m3/s
Maximum rainfall 250 mm Maximum rainfall 217.4 mm Simulation rainfall 255 mm 
Total area 1.4589 km2 Maximum discharge 1,550 m3 /s Pump capacity 5 m3/s 
Runoff Retention 27,835 m3   Number of pumps 
Flood volume 317,539.85 m3   Operation water level (condition) 1.5 m + Mean Sea Level 
1. UFRM model data
2. 2016 Flood records (NSGS)
3. Pumping station (SSNLPS)a
Subbasins08Return period20 yearsDesign capacity30 m3/s
Maximum rainfall 250 mm Maximum rainfall 217.4 mm Simulation rainfall 255 mm 
Total area 1.4589 km2 Maximum discharge 1,550 m3 /s Pump capacity 5 m3/s 
Runoff Retention 27,835 m3   Number of pumps 
Flood volume 317,539.85 m3   Operation water level (condition) 1.5 m + Mean Sea Level 

Sources: 1. Author, 2. Irrigation Department, 3. Sri Lanka Land Development Corporation (MCUDP 2022).

According to Table 5, the pumping stations can discharge a total of 432,000 m3 in an 8-h duration at 50% capacity. Based on Kelani River's actual flood data, the existing pumping capacity is sufficient for the 2016 flood event. This is proved since the design capacity of pumps is for a 100-year return period. The full discharge of SSNLPS over an 8-h period is 864,000 m3 (30 m3 /s capacity). At the same time, the SD model has a maximum flood water reach of 987,799 m3 (at 10 h), with an average concentration of 84,628.75 m3 over a 100-h period. Accordingly, the actual pumps can reach 87.5% of the modeled output at the KLB. However, this accounts only for the pumps alone, where supporting reservoir improvements and mitigation measures to reduce flood water concentration are implemented in the KLB (MCUDP 2022). Therefore, the real flood discharge data support the SD modeling results with over 85% accuracy.

This study used an SD modeling framework to simulate the performance of critical variables during a flood event. Using Colombo, Sri Lanka, as a case study, the framework is tested with available data to model empirical scenarios during floods caused by extreme rainfall in May 2016. As per the stakeholder discussion outcomes, flood water pumping was the priority of the agencies as the preferred option to minimize flood damage. However, it is a challenging decision in the context of Colombo, Sri Lanka, as the financial and human resources are in limited capacity. Cities in developing countries often face challenges in implementing mitigation strategies due to a lack of financial commitments (Svetlana et al. 2015; Peiris et al. 2024). Adaptation strategies are often used in cities due to limited resources and the complexity of community interactions during flood events (Askman et al. 2018). Upon the flood disaster in 2016, the Government of Sri Lanka established a series of mitigation measures within Colombo City and its suburbs to reduce flood damage at a cost of over LKR 25 billion (approximately USD 125 million in 2021) over 5 years from 2017 to 2022 (MCUDP 2022). One of the reasons for this study is to evaluate the investment from a different viewpoint, as population mobility is often ignored in the flood modeling process. However, the results show that simulation of the population in the flood-risk region, mitigation measures, and flood relief expenses can support disaster managers and policymakers in understanding the technical and socio-economic dimensions of the disaster management process. Moreover, the SD framework is useful to amend existing processes by adding or removing variables that can optimize the flood management process. For example, the pumping stations and infrastructure improvement have reduced an area of 3 km from flooding in a 50-year return period and sectoral economic benefits of LKR 2,190 million (MCUDP 2022). This may not be sufficient for policymakers without understanding the overall impact on society and affected people in future flood events. Therefore, this study provides crucial input to understand the effects at the grassroot level by implementing long-term flood mitigation projects.

The results show that the operation of pumps is an expensive method yet effective in removing flood water from streets in the short term. However, long-term strategies to manage the vulnerable population from the flood impact zone are still useful. This simulation framework assisted in identifying the key variables and their relationships with flood removal. In past studies, one or more variables (population movement or infrastructure damage) were used for response measurements with the constraint of using multiple variables with different units or scalability. The SD framework provides a useful bridge to bring multiple parameters into a single analytical model and simulate changes of one factor to visualize the causal relationship among other factors. This study simulated the relationship between vulnerable populations during a flood event, flood water concentration, and government expenses on relief activities to view the dynamic response behavior during a flood event. This framework can be scaled up to a city or a region with multiple factors and scales to see the interactions of complex urban systems during flood events. Moreover, the decision-makers can understand the interdisciplinary nature of problems associated with floods and generate common solutions to recover from the impacts of floods. For example, funding agencies can decide the resource allocation along with rescue service operators to decide evacuation routes and flood water removal process efficiently to manage the disaster risk. Also, SD offer a common platform to stakeholders ranging from hydrology experts, urban planners, and economists to simulate multiple disaster scenarios with different input parameters (rainfall intensity, urbanization rate, and damage to properties). This framework can be used to manage future disaster risk through planning and preparation to face uncertainties posed by climate change and related scenarios.

All relevant data are included in the paper or its Supplementary Information.

The authors declare there is no conflict.

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