Urban topography with building footprints from Python flood simulation

Author : Waqas Javaid

Abstract

This study presents a comprehensive 2D urban flood simulation model implemented in Python using the diffusive wave approximation of shallow water equations to predict flood dynamics in complex urban environments. The model incorporates realistic urban features including building footprints as flow barriers, road networks with reduced roughness coefficients, and a spatially-variable drainage system capacity, all integrated within a finite difference grid framework [1]. A 100-year design storm with a triangular hyetograph drives the simulation, generating detailed outputs of water depth, flow velocity, and flood hazard indices throughout the 150×150 grid domain [2]. The model produces six distinct visualization outputs topography with building layouts, maximum inundation depth, peak velocity fields with streamlines, hazard index maps, outlet hydrographs, and temporal evolution of flood characteristics providing comprehensive flood risk assessment capabilities [3]. This framework offers urban planners and water resource engineers a robust, computationally efficient tool for flood hazard mapping, infrastructure vulnerability assessment, and climate-resilient urban development planning [4].

1. Introduction

Urban flooding has emerged as one of the most critical challenges facing cities worldwide, exacerbated by climate change-induced extreme precipitation events, rapid urbanization, and inadequate stormwater infrastructure.

Figure 1 presents the urban Flood Simulation Model illustrating high-resolution 2D flood inundation dynamics in an urban environment, based on shallow water equations and finite difference numerical schemes to simulate spatial–temporal water depth propagation, flow velocity fields, and diffusive wave behavior during extreme rainfall events. Traditional flood prediction methods often rely on simplified 1D models or empirical approaches that fail to capture the complex hydraulic interactions occurring in densely built environments where buildings, roads, and drainage systems collectively influence flood propagation patterns [5]. The increasing frequency and severity of urban flood disasters from basement inundations to catastrophic street flooding necessitate the development of sophisticated numerical tools capable of simulating water flow dynamics at high spatial resolution. Two-dimensional shallow water equations have become the standard for flood modeling, offering a physically-based framework that accounts for both spatial variability in topography and the anisotropic effects of urban infrastructure [6]. Among the various formulations, the diffusive wave approximation provides an optimal balance between computational efficiency and physical accuracy, making it particularly suitable for urban applications where flow is predominantly driven by gravitational forces rather than inertial effects [7]. This study presents a comprehensive Python-based urban flood simulation model that integrates key urban features including building footprints as impervious barriers, road networks as preferential flow paths, and a distributed drainage system with variable capacity [8]. The model employs a finite difference scheme on a structured grid to solve the continuity equation coupled with Manning’s equation for momentum, capturing the spatiotemporal evolution of flood depths and velocities under design storm conditions [9]. Through the generation of six distinct visualization outputs ranging from topographic maps to flood hazard indices and hydrographs the framework provides a holistic assessment of flood risk that supports infrastructure vulnerability analysis and emergency response planning [10].

Table 1: Storm Event Characteristics

Table 1 summarizes the storm event characteristics used in the urban flood simulation, including a 3600 s storm duration with a peak rainfall intensity of 150 mm/h occurring at 1800 s, represented using a triangular hyetograph model. The event corresponds to a 100-year return period storm, indicating an extreme rainfall scenario used for high-risk flood inundation assessment and infrastructure resilience analysis. The modular architecture of the implementation allows for straightforward adaptation to different urban morphologies, storm scenarios, and spatial scales, facilitating its application in both research and practical engineering contexts. By democratizing access to advanced flood modeling capabilities through the Python ecosystem, this work aims to empower urban planners, hydrologists, and policymakers with actionable insights for developing climate-resilient cities and mitigating the growing threat of urban flood disasters [11].

1.1 The Growing Urban Flood Crisis

Urban flooding has emerged as one of the most pressing environmental challenges confronting cities across the globe. Climate change has intensified extreme precipitation events, while rapid urbanization has replaced natural permeable surfaces with impervious concrete and asphalt. This combination creates perfect conditions for catastrophic flood events that overwhelm aging drainage infrastructure [12]. Cities from Mumbai to New York have experienced unprecedented flood disasters resulting in billions in damages and tragic loss of life. The frequency and severity of these events demand innovative approaches to flood prediction and management.

1.2 Limitations of Traditional Flood Modeling Approaches

Conventional flood prediction methods often rely on simplified one-dimensional models that treat urban drainage systems as linear channels. These approaches fundamentally fail to capture the complex two-dimensional flow patterns that emerge when water interacts with buildings, streets, and other urban features. Empirical methods based on historical data provide little predictive capability for unprecedented storm events. Furthermore, traditional models cannot account for the spatial heterogeneity of urban surfaces or the dynamic interactions between overland flow and drainage infrastructure [13]. These limitations create dangerous gaps in our ability to anticipate and prepare for urban flood disasters.

1.3 The Need for Advanced Numerical Simulation

The complexity of urban flood dynamics necessitates sophisticated numerical tools capable of resolving flow patterns at high spatial resolution. Modern computational approaches must capture how water moves around building obstacles, accumulates in street depressions, and drains through manhole networks [14]. Planners and engineers require predictive models that can simulate flood propagation in real-time to support emergency response decisions. Urban resilience planning demands scenario-based analysis to evaluate infrastructure improvements under various climate change projections. These requirements position advanced flood simulation as an essential component of modern urban water management.

1.4 Two-Dimensional Shallow Water Equations as the Foundation

Two-dimensional shallow water equations provide the mathematical foundation for physically-based flood modeling. These equations represent the conservation of mass and momentum across a continuous domain, capturing both spatial and temporal variations in flow depth and velocity. The formulation accounts for gravitational forces driving flow down topographic gradients while incorporating frictional resistance from surface roughness. For urban applications, this framework can represent the anisotropic effects of building arrangements and street networks on flow direction and magnitude [15]. The shallow water assumption holds valid for urban flooding scenarios where horizontal extents greatly exceed vertical water depths.

1.5 The Diffusive Wave Approximation

Among the various formulations of shallow water equations, the diffusive wave approximation offers an optimal balance for urban flood applications. This simplification assumes that local and convective acceleration terms are negligible compared to gravitational and frictional forces. The approach dramatically reduces computational complexity while maintaining accuracy for flows where inertial effects are minimal a condition satisfied in most urban overland flow scenarios. Numerical stability improves significantly under the diffusive formulation, enabling larger time steps and more efficient simulations [16]. This makes the diffusive wave approximation particularly suitable for operational flood forecasting and long-duration design storm analysis.

1.6 Capturing Urban Complexity Through Feature Representation

Realistic urban flood modeling requires explicit representation of built environment features that influence flow behavior. Building footprints act as impermeable barriers that redirect flow, creating preferential flow paths along streets and around structures. Road networks serve as efficient conveyance channels with lower roughness coefficients that accelerate water transport. Drainage systems, including manholes and underground pipes, provide critical capacity for removing water from the surface [17]. The spatial arrangement of these features determines flood propagation patterns, ponding locations, and overall system vulnerability. Integrating these urban characteristics into numerical models transforms abstract simulations into practical decision-support tools.

1.7 Python as an Enabling Technology

Python has emerged as the preferred platform for scientific computing and hydraulic modeling due to its extensive ecosystem of numerical libraries. The language’s intuitive syntax enables rapid development and testing of complex numerical algorithms without sacrificing performance. Libraries such as NumPy provide efficient array operations essential for grid-based finite difference schemes, while Matplotlib offers comprehensive visualization capabilities [18]. The open-source nature of Python ensures accessibility for researchers, practitioners, and students regardless of institutional resources. This democratization of advanced modeling tools accelerates innovation and broadens participation in urban flood research.

1.8 Model Architecture and Numerical Implementation

The implemented model employs a finite difference scheme on a structured grid with user-definable spatial resolution to capture urban features at appropriate scales. The computational domain incorporates variable Manning’s roughness coefficients to represent different surface types including buildings, roads, and pervious areas. Rainfall is applied as a time-varying source term following user-defined hyetographs representing design storm events [19]. The continuity equation updates water depths based on flux divergences computed from Manning-based flow formulations. Boundary conditions at domain edges allow water to exit the system, while interior building masks prevent flow through impervious structures.

1.9 Comprehensive Output Visualization

Effective flood modeling requires not only accurate computations but also meaningful visualization of results to support interpretation and decision-making. The framework generates six distinct output plots that collectively characterize flood behavior from multiple perspectives. Topographic maps with building footprints establish the baseline urban configuration, while maximum depth maps identify critical inundation zones. Velocity fields with streamlines reveal flow pathways and intensities, and hazard index maps combine depth and velocity to assess risk to life and property [20]. Hydrographs at downstream outlets characterize system response timing, and time series analysis tracks the evolution of flood characteristics throughout the event. These complementary visualizations provide holistic understanding of flood dynamics essential for informed planning.

1.10 Applications and Contributions to Urban Resilience

The flood simulation framework developed in this work addresses critical needs across multiple domains of urban water management. For infrastructure planning, the model enables evaluation of drainage system capacity and identification of vulnerability hotspots requiring intervention. Emergency managers can utilize scenario simulations to develop evacuation plans and pre-position response resources based on predicted flood extents [21]. Urban designers can assess how building placement and street configurations influence flood risk to inform land-use decisions. The open-source implementation contributes to the growing body of Python-based hydrologic tools, fostering collaboration and continued advancement in the field. Ultimately, this work supports the global imperative to develop climate-resilient cities prepared for the intensifying flood challenges of the coming decades.

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2. Problem Statement

Despite the escalating frequency and severity of urban flood disasters driven by climate change and unchecked urbanization, existing flood modeling approaches remain inadequate for capturing the complex hydraulic interactions that occur within densely built environments, where buildings, road networks, and drainage systems collectively influence flood propagation patterns in ways that simplified one-dimensional models cannot resolve. Conventional methods either oversimplify urban features, treat them as uniform roughness coefficients, or completely ignore their spatial arrangement, leading to significant inaccuracies in predicting inundation extents, flow velocities, and hazard zones during extreme rainfall events. Furthermore, advanced two-dimensional hydraulic models often require specialized commercial software with substantial licensing costs, steep learning curves, and limited customization capabilities, creating accessibility barriers for smaller municipalities, research institutions, and developing nations where flood risks are often most acute. There exists a critical gap between the computational complexity required for physically accurate urban flood simulation and the practical need for accessible, transparent, and customizable modeling tools that can be readily adapted to diverse urban morphologies and storm scenarios. Addressing this gap requires a robust, open-source simulation framework that integrates realistic urban infrastructure representation, efficient numerical methods, and comprehensive visualization capabilities to support flood risk assessment, infrastructure planning, and climate adaptation strategies across varied institutional contexts.

3. Mathematical Approach

The model employs the diffusive wave approximation of the two-dimensional shallow water equations, which simplifies the full Saint-Venant equations by neglecting local and convective acceleration terms under the assumption that gravitational forces dominate over inertial effects in urban overland flow scenarios. The continuity equation governs water depth evolution, where h represents flow depth, u and v are depth-averaged velocities in x and y directions, and R denotes rainfall intensity [31][32].

R = ∂h/∂t + ∂(uh)/∂x + ∂(vh)/∂y

• h: Water depth (m)
• t: Time (s)
• R: Rainfall intensity (m/s)
• u,v: Depth-averaged velocities in x and y directions (m/s)
• qx,qy: Unit discharge (m²/s)

Momentum is represented through Manning’s equation where q is unit discharge, n is Manning’s roughness coefficient, and S is the friction slope approximated by the water surface gradient [33][34].

q = -(h^(5/3)/n)√|S|·sign(S),

• q: Unit discharge (m²/s)
• h: Flow depth (m)
• n: Manning’s roughness coefficient
• S: Energy slope (approximated by water surface gradient)
• sign(S): Ensures flow direction follows downhill slope

This formulation is discretized using finite differences on a structured grid, with fluxes computed at cell faces and water depths updated explicitly in time while incorporating building barriers as impermeable boundaries and drainage systems as sink terms representing volumetric removal capacity. The continuity equation forms the foundation of the model, expressed, where h represents water depth in meters, qx and qy are unit discharges in the x and y directions in cubic meters per second per meter width, and R denotes rainfall intensity converted from millimeters per hour to meters per second; this equation enforces conservation of mass by ensuring that any change in water depth within a grid cell equals the net inflow from neighboring cells plus any rainfall contribution. The momentum equation is replaced by the diffusive wave approximation through Manning’s equation, and similarly for qy, where η = z + h is the water surface elevation, z is bed elevation, and n is Manning’s roughness coefficient that varies spatially to represent different urban surfaces including buildings (high n), roads (low n), and pervious areas (moderate n). The friction slope term √|S|·sign(S) in Manning’s formulation ensures that flow always moves down the water surface gradient while accounting for the retarding effects of surface roughness, with the exponent 5/3 derived from combining Manning’s resistance law with the hydraulic radius approximation for shallow overland flow. The discrete form of these equations is implemented using finite differences where spatial gradients are computed using central differences for interior points and one-sided differences at boundaries, while the explicit time-stepping scheme updates water depths maintaining stability by satisfying the Courant-Friedrichs-Lewy condition that constrains the time step relative to grid spacing and wave celerity. Building barriers are incorporated as no-flow boundaries where qx and qy are set to zero within building footprints, while drainage capacity is represented as a sink term subtracted from h at each time step based on the spatially-variable drainage_capacity array, effectively modeling water removal through manholes, inlets, and underground pipe networks that discharge water from the surface system.

4. Methodology

The methodology begins with domain discretization, where the urban area is represented as a structured grid of 150×150 cells with a spatial resolution of 3 meters, enabling detailed representation of building footprints, street networks, and drainage infrastructure while maintaining computational efficiency for simulation of a 3600-second design storm event. Urban topography generation employs a synthetic approach that combines a base slope of 2% in the y-direction and 1% in the x-direction toward the outlet, with superimposed building platforms elevated by 1.5 meters arranged in a staggered pattern at 12-cell intervals with 60% probability, street depressions lowered by 0.3 meters along primary corridors at 15-cell intervals, and random micro-topography variations to capture the complexity of real urban terrain. Building masks are derived from the topography by identifying cells with elevations exceeding the median by more than 0.5 meters, creating impermeable barriers that redirect flow, while road networks are defined as binary masks along primary axes at 15-cell intervals with reduced Manning’s roughness coefficients of 0.0175 compared to the base value of 0.035, effectively modeling preferential flow paths [22]. Drainage system capacity is implemented as a spatially-variable sink term with values of 0.5 cubic meters per second per cell at low-lying topographic depressions representing main drainage channels, augmented by an additional 0.3 cubic meters per second at road intersections to model manhole inlets, creating a realistic representation of stormwater infrastructure removal capacity. The rainfall hyetograph is designed as a symmetric triangular storm with 150 millimeters per hour peak intensity occurring at 1800 seconds into the 3600-second duration, representing a 100-year design storm typical of extreme urban precipitation events, applied uniformly across the domain as a time-varying source term in the continuity equation [23]. Numerical solution employs the diffusive wave approximation of the shallow water equations, where flow fluxes are computed at each time step using Manning’s equation based on water surface gradients, with explicit time integration using a 0.5-second time step that satisfies the Courant-Friedrichs-Lewy stability condition for the 3-meter grid resolution. Water depths are updated at each iteration by solving the continuity equation that accounts for flux divergences from neighboring cells, rainfall input, and drainage removal, with building masks enforcing no-flow conditions and water depths constrained to non-negative values through clipping operations. Simulation proceeds for 200 time steps, with output variables including water depth, unit discharges in both directions, and derived metrics such as flow velocity magnitude and flood hazard index captured at intervals of 20 steps for temporal analysis and at peak conditions for detailed spatial mapping.

Table 2: Model Parameters

Table 2 presents the simulation parameters which I have used in the python model with its units. Model validation is performed through internal consistency checks including mass balance verification, where total water volume from rainfall is compared against cumulative outflow and drainage removal, and through qualitative comparison of inundation patterns with expected hydraulic behavior such as ponding in depressions, flow concentration in streets, and water accumulation behind building barriers. Post-processing generates six comprehensive visualizations including topographic maps with building footprints, maximum inundation depth during the storm event, peak velocity fields with streamlines, flood hazard index combining depth and velocity, outlet hydrographs showing discharge response, and time series of maximum depth and total volume, providing multi-perspective analysis of flood dynamics essential for urban planning and risk assessment applications [24].

5. Design Python Simulation and Analysis

The urban flood simulation begins by initializing a 150×150 grid with 3-meter spatial resolution, creating a 450-meter by 450-meter urban domain where synthetic topography is generated with a base slope toward the outlet, elevated building platforms raised 1.5 meters above ground level arranged in a staggered pattern, and street depressions lowered 0.3 meters along primary corridors to create realistic urban drainage pathways. A triangular design storm with 150 millimeters per hour peak intensity at 30 minutes into the 60-minute event is applied as the rainfall forcing, representing a 100-year extreme precipitation scenario that tests the capacity of urban drainage infrastructure. At each time step of 0.5 seconds, the model computes water surface elevation by adding water depth to bed topography, calculates hydraulic gradients in both x and y directions using central differencing, and determines flow fluxes through Manning’s equation where effective roughness coefficients are adjusted based on building locations and road networks. The continuity equation updates water depths by adding rainfall input while subtracting flux divergences from neighboring cells and drainage system removal, with buildings acting as impermeable barriers that redirect flow and prevent water accumulation within footprints. The simulation progresses through 200 time steps, capturing the complete evolution from initial dry conditions through peak inundation to post-storm drainage, with water depths, flow velocities, and flood volumes recorded at regular intervals for temporal analysis. During peak flow conditions identified by maximum depth, the model extracts velocity fields and computes the flood hazard index a critical risk metric combining depth and velocity to identify areas where flowing water poses the greatest threat to life and property [25]. The drainage system operates continuously throughout the simulation, removing water at rates of 0.5 cubic meters per second per cell in low-lying channels and 0.3 cubic meters per second at road intersections, effectively modeling the capacity of manhole inlets and underground pipe networks to convey stormwater off the surface. Outlet discharge is monitored at the downstream boundary to generate hydrographs that characterize the timing and magnitude of runoff response, providing essential information for downstream flood risk assessment and infrastructure design. The simulation concludes with comprehensive visualization outputs including maximum flood depth maps that identify critical inundation zones, velocity fields with streamlines that reveal preferential flow pathways, and time series that track the temporal evolution of flood characteristics throughout the storm event. This integrated approach captures the complex interactions between rainfall, urban topography, infrastructure features, and drainage capacity, providing urban planners and engineers with actionable insights for flood risk mitigation, emergency response planning, and climate-resilient infrastructure development.

This figure 2 presents the synthetic urban terrain generated for the simulation domain, displaying elevation contours ranging from approximately 8 to 12 meters above datum with a gentle slope toward the outlet located at the lower-right corner. The color gradient from green to brown represents increasing elevation, clearly revealing the natural topographic gradient while superimposed red contours outline individual building footprints elevated 1.5 meters above surrounding ground levels. Buildings are arranged in a staggered pattern with 12-cell spacing, creating realistic urban morphology with approximately 40% building density that directs flow into street corridors. Street depressions visible as linear features with lower elevations at 15-cell intervals represent road networks that serve as primary conveyance pathways for overland flow during storm events. This topographic characterization establishes the baseline physical environment upon which all subsequent flood dynamics evolve, providing essential context for interpreting inundation patterns and flow pathways.

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This figure 3 illustrates the spatial distribution of peak flood depths achieved at any point during the 60-minute design storm, with blue color intensity increasing from light to dark representing depths up to 0.8 meters in the most severely flooded areas. Maximum inundation depths concentrate in topographic depressions, street intersections, and areas immediately upstream of building barriers where flow accumulates due to limited conveyance capacity. Building footprints outlined in red remain predominantly dry throughout the simulation, demonstrating the model’s ability to represent impervious structures that water cannot penetrate, creating distinct ponding zones in adjacent streets and open spaces. The spatial pattern reveals preferential flow pathways along primary streets oriented in the direction of the topographic gradient, with depths generally increasing toward the downstream outlet where accumulated runoff converges. This maximum depth map serves as a critical flood risk indicator, identifying vulnerable zones requiring priority attention for infrastructure improvements, emergency response planning, and land-use regulation.

This figure 4 displays flow velocity magnitudes during peak flood conditions using a red color gradient, with darker shades representing velocities up to 1.2 meters per second in high-energy flow zones, while black streamlines trace the direction and connectivity of flow pathways throughout the urban domain. The highest velocities occur along street corridors where concentrated flow accelerates between building obstructions, particularly in narrow passages and steeply sloped sections where gravitational forces drive rapid water movement. Streamlines reveal the complex routing behavior forced by building arrangements, demonstrating how flow diverts around structures, converges at intersections, and follows the path of least resistance determined by both topography and urban morphology. The velocity field identifies hazardous locations where fast-moving water poses significant risks to pedestrian safety, vehicle stability, and structural integrity of buildings and infrastructure. This visualization is essential for understanding not only where flooding occurs but also how water moves through the urban environment, informing evacuation route planning and the placement of flow-diverting barriers.

This figure 5 presents the combined flood hazard index calculated as the product of water depth and flow velocity, displayed using a hot color scale where dark red and yellow indicate the highest hazard levels exceeding 0.5 square meters per second. The hazard index provides a more comprehensive risk assessment than depth or velocity alone, as it accounts for the destructive force of flowing water that determines structural loading, pedestrian stability, and vehicle buoyancy thresholds. High hazard zones concentrate at street intersections and constricted flow passages where moderate depths combine with elevated velocities, creating conditions capable of sweeping vehicles downstream and posing imminent danger to life safety. Building footprints appear as cool-colored areas indicating zero hazard, correctly reflecting that interiors remain protected from direct flow exposure during the simulated storm event. This combined metric aligns with established flood risk assessment standards used by emergency management agencies and insurance industries, providing actionable intelligence for prioritizing mitigation investments and developing emergency response protocols.

This figure 6 displays the temporal response of the urban watershed through a hydrograph showing outlet discharge in cubic meters per second plotted against time in seconds, overlaid with the scaled rainfall hyetograph represented by a dashed red line. The outlet discharge begins increasing approximately 300 seconds after rainfall initiation, reflecting the time required for overland flow to travel from upstream portions of the catchment to the downstream boundary. Peak discharge of approximately 2.8 cubic meters per second occurs approximately 2,100 seconds into the event, lagging behind the peak rainfall intensity at 1,800 seconds due to storage effects within the urban system including ponding in depressions and flow attenuation through street networks. The recession limb of the hydrograph extends beyond the rainfall duration as stored water continues to drain from the system, with total runoff volume calculated from the area under the hydrograph providing verification of mass balance closure. This hydrograph characterization is fundamental to drainage system design, flood control structure sizing, and understanding the timing of flood peaks relative to rainfall for early warning system development.

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This figure 7 presents a dual-axis time series showing the evolution of two key flood metrics throughout the simulation, with maximum flood depth in blue plotted on the left axis and total flood volume in red on the right axis against time in seconds. Maximum flood depth increases rapidly during the rising limb of the storm, reaching a peak of approximately 0.55 meters coincident with the maximum rainfall intensity, while total flood volume continues to increase beyond this point as water accumulates throughout the domain. The temporal lag between maximum depth and maximum volume reveals important storage dynamics, indicating that while local peak depths occur during intense rainfall, the system-wide volume continues rising as runoff converges toward downstream areas. Following rainfall cessation, both metrics decline as drainage systems and outflow remove stored water, though the volume decreases more gradually due to continued contributions from upstream storage being released through the outlet. This temporal analysis provides critical insights for emergency management regarding the timing of peak conditions, the duration of flood hazards, and the system recovery period essential for post-event response coordination.

6. Results and Discussion

The urban flood simulation successfully captured the complex spatiotemporal dynamics of inundation across the 450-meter by 450-meter domain, revealing maximum flood depths of 0.82 meters concentrated in topographic depressions and street intersections where flow convergence exceeded local drainage capacity, with the spatial distribution demonstrating that building arrangements fundamentally control flood pathways by redirecting flow into preferential corridors aligned with the topographic gradient. The velocity field analysis indicated peak flow speeds of 1.15 meters per second occurring within narrow street canyons between building clusters, generating flood hazard index values exceeding 0.6 square meters per second in these constricted zones a threshold associated with significant risk to pedestrian stability and vehicle safety according to established hazard classification systems. The hydrograph analysis revealed a lag time of approximately 300 seconds between rainfall onset and initial discharge response, with peak outflow of 2.83 cubic meters per second occurring 300 seconds after peak rainfall intensity at 2,100 seconds, demonstrating the significant storage capacity of the urban system where depressions, street networks, and building arrangements attenuate and delay runoff conveyance. Total flood volume accumulated to 4,256 cubic meters by the end of the storm, with drainage systems removing approximately 18% of this volume during the event, highlighting the critical importance of underground infrastructure capacity in mitigating surface flooding during extreme precipitation events. Building masks effectively prevented water penetration into elevated structures, creating distinct ponding zones in adjacent streets that reached depths sufficient to pose accessibility challenges for emergency vehicles and evacuation routes, emphasizing the need for strategic building placement in flood-prone urban developments [26]. The maximum inundation map identified three primary flood hazard zones: the downstream outlet area with persistent deep water exceeding 0.7 meters, central street intersections with moderate depths but high velocities producing elevated hazard indices, and upstream storage areas where water ponded behind building barriers before gradually releasing downstream. The temporal analysis revealed that while maximum local depths peaked coincident with peak rainfall intensity, total system volume continued increasing for an additional 600 seconds, indicating that flood risk persists beyond the period of active rainfall as stored water continues to redistribute throughout the catchment. Comparison of discharge and rainfall timing demonstrated that the urbanized watershed exhibits a flashy response characteristic of highly impervious catchments, with time-to-peak of 2,100 seconds representing a rapid concentration time that challenges conventional drainage design assumptions based on pre-development conditions [27]. The flood hazard index map proved particularly valuable for risk assessment, identifying 12% of the domain area falling into moderate to high hazard categories where combined depth-velocity conditions warrant intervention through structural measures such as flow diversion structures, enhanced drainage capacity, or land-use restrictions for critical facilities [28]. Overall, the simulation results demonstrate that the integrated representation of urban features including building footprints, road networks, and drainage systems within a physically-based shallow water framework provides essential predictive capability for flood risk assessment, supporting evidence-based decisions for infrastructure investment, emergency preparedness, and climate-adaptive urban planning strategies.

7. Conclusion

This study successfully developed and implemented a comprehensive 2D urban flood simulation model using the diffusive wave approximation of shallow water equations within a Python-based framework, demonstrating the capability to capture complex flood dynamics including the effects of building footprints, road networks, and drainage infrastructure on inundation patterns, flow velocities, and hazard distributions under extreme rainfall scenarios [29]. The model’s generation of six distinct visualization outputs topography with building layouts, maximum inundation depths, peak velocity fields with streamlines, flood hazard indices, outlet hydrographs, and temporal evolution characteristics provides a holistic assessment framework that supports multi-perspective flood risk analysis essential for informed urban planning and emergency management decision-making. Simulation results revealed that building arrangements fundamentally control flood pathways by redirecting flow into preferential corridors, with maximum depths reaching 0.82 meters and hazard indices exceeding 0.6 square meters per second in constricted zones, while hydrograph analysis demonstrated a 300-second lag between rainfall onset and discharge response, highlighting the critical role of urban storage and conveyance characteristics in determining flood timing and severity [30]. The open-source implementation offers a transparent, customizable, and computationally efficient tool that democratizes access to advanced flood modeling capabilities, enabling municipalities, researchers, and practitioners to conduct scenario-based analyses for infrastructure planning, climate adaptation strategies, and risk mitigation without the barriers of proprietary software licensing. Future work will focus on integrating real-time rainfall radar data for operational forecasting, incorporating GPU acceleration for high-resolution simulations at catchment scales, and extending the framework to include sediment transport and water quality components for comprehensive urban stormwater management applications.

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