https://orcid.org/0000-0001-8160-8875
Abstract
In urban flood modeling, the accuracy of surface and subsurface flow calculations greatly depends on the parameterization of the drainage system. Incorporating the influence of the sewer pipe system is, therefore, integral to accurately simulating urban inundation during short-duration rainfall events. However, obtaining comprehensive data on sewer systems in developing countries is currently challenging. To mitigate this situation, we propose a method for developing a synthetic sewer network to supplement the representation of the sewer system in urban flood models, particularly in data-scarce domains. The model implements the concept of shallow water equation for surface flow and a 1D slot model for pipe flows with an interaction equation between them. We compare case studies with and without discharge interaction between the surface and hypothetical sewer system for the 2020 flood event in an urban subcatchment within the Marikina Basin, Philippines. Results show that the synthetic sewer pipe integration can capture the urban flood propagation more appropriately. Information such as flood depth and pipe flow discharge can aid in identifying flood-prone areas where sewer system parameters may require modifications. The proposed method can be used as an alternative to performing high-resolution urban flood simulations with limited availability of sewer network data.
HIGHLIGHTS
Developed GIS methodology to incorporate a synthetic sewer pipe network into urban flood modeling.
Possibility of simulating urban inundation without detailed sewer pipe network data for data-scarce domains.
Storm water pipes that are susceptible to overflow (bottleneck and choke point regions) can be identified through the simulations.
INTRODUCTION
For torrential rainfall events, extreme inundation results from the overflow of river water due to excessive runoff from the mountains triggered from prolonged monsoon rains or rapid melting of snow and ice. For short-duration storm events, however, urban inundation can be largely attributed to the accumulated effect of pluvial and fluvial flooding, which is exacerbated when the drainage system is overwhelmed and is no longer capable of conveying subsurface water flow to discharge outlets (Hsu et al. 2000). In addition, the impervious properties of surfaces in urban areas, unlike in open soil areas, reduce the capability of the surface to absorb flood water, accelerating runoff concentration into the downstream area that results in inundation (Xu et al. 2021). As a result, there has been a growing interest on research of the effect of urbanization, land use change, and the corresponding impacts of connected and disconnected impervious surfaces in the drainage systems in recent years (i.e., Zhao et al. 2023; Wang et al. 2019; Li et al. 2023). The ability to model the flow dynamics within a pipe system not only has an important role in urban flood control and mitigation but also in traffic advisories and long-term flood solutions.
Integrated sewer pipe modeling in urban flood simulation has been developed and implemented for many years. These numerical flood models utilize parameters that are simplified using a geographic information system (GIS) (Djordjević et al. 1999). Some of the commercial sewer pipe models in applications include the Illinois Urban Drainage Area Simulator (ILLUDAS) (Terstriep & Stall, 1974), the Model for Urban Sewers (MOUSE) (Lindberg et al. 1989; Mark et al. 1998; DHI 1999), the Storm Water Management Model (SWMM) (Huber & Dickinson 1998; Hsu et al. 2000; Rossman & Simon 2022), LISFLOOD (Neal et al. 2011), MIKE FLOOD (DHI 2021), and Infoworks (Bouteligier et al. 2001; Babovic & Mijic 2019). In recent years, overland flow and sewer flow have been simultaneously simulated through a dual drainage concept, where the surface flow is computed by considering the natural paths and retention basins as draining systems, while sewer pipes and inlets are considered in conveying the subsurface flow. These models use manholes as interaction points that connect the flow from the surface to the sewer system and vice versa (Lee et al. 2016). However, the integration of storm drains into a pipe network provides a more realistic representation of urban systems. Storm drains have the potential to cause lag times for flood peaks and could reduce the sewer pipe inundation time (Noh et al. 2016).
In practical applications, actual storm drain network data are needed to simulate urban flooding with the integration of sewer pipes. This concept has been utilized in studies such as those of Hsu et al. (2000), Mark et al. (1998), Chen et al. (2007), Lee et al. (2016), and Lee & An (2019). The sewer network data should be fully determined so that the model accurately resembles a schematic view of the actual system. Because of the extensive input data required to parameterize these storm drain flood models, these techniques are only applicable for small-scale domains. Simulations of large-scale urban inundation remain an ongoing challenge for recent urban flood models (Guo et al. 2021). For smaller catchments in large cities, sewer network data are often easily accessible. If these data are not available, storm drain networks are delineated with GPS (global positioning system) surveys (Andimuthu et al. 2019). However, without detailed field surveys, these data are not generally available for a lot of cities in developing countries. The implementation of sustainable urban drainage systems in developing countries is particularly complex (Nobrega dos Santos et al. 2021). For example, in urban China, administrative agencies that have custody of storm drain system construction and maintenance are uncoordinated. In addition, the applicable laws and regulations are incomplete (Huang et al. 2018). Tucci (2000) stated that the urban drainage problem in these regions is mainly due to the low investment in urban drainage facilities, resulting in inadequate drainage management and design. Consequently, maintaining a detailed sewer network record can be a challenging task and is often sidetracked in favor of other, more pressing sustainability problems.
Therefore, to address this problem, this research aims to supplement the limited sewer pipe data in an urban system. This allows the possibility of simulating urban flooding without detailed pipe network data. To accomplish such simulation, a synthetic representation of the storm drain network was developed using GIS containing the actual properties of manholes, sewer pipes, and storm drains in the study domain. To test the effectiveness of the proposed method, two simulations (with and without sewer pipe integration) were performed for the 2020 urban flood event in Marikina Basin, Philippines. An analysis of the interaction between surface and sewer flow and its influence on the reduction of flooding is presented. In theory, the inclusion of flow interaction in the calculation should improve the accuracy of flood simulation (Chang et al. 2018).
For this research, the synthetic sewer system created using GIS software was generated based on the dendritic drainage pattern and order method. These were based on stream channels and tributaries determined by elevation data. The delineation of the pipe system in urban flood models based on the order method was performed by selecting the major stream pipeline as the principal tributary pipeline. This method has already been well established in sewer pipe modeling by several researchers (Agarwal 1998; Romshoo et al. 2012; Lee et al. 2018). However, only a handful of studies have focused on the development of hypothetical sewer networks to represent storm drain systems in application for urban flood modeling. Research similar to that of Jeffers & Montalto (2018) performed an abstract conceptual flood modeling incorporating fractal scaling geometries to characterize natural basins. Bertsch et al. (2017) generated a synthetic pipe system to supplement missing drain inlet data from an existing pipe network to simulate urban flooding. Both simulations were performed using domains with areas of approximately 1 km2. Previous studies have not reported the subcatchment-scale generation of a hypothetical sewer network system. Hence, this research is aimed to supplement the research limitations that are often encountered in representing the inclusion of sewer pipe interaction in urban flood modeling, particularly in data-scarce domains, allowing the provision of a more accurate urban flood inundation that is critical for flood preparation and mitigation. The arbitrary properties of the synthetic sewer pipe system in the proposed methodology would also facilitate parameter adjustments that can be utilized in providing solutions for optimizing the sewer pipe connection in reducing overwhelming of sewer pipes and minimizing the urban flooding.
DATA AND METHODS
Surface and sewer pipe interaction through storm drain inlets.
The urban flood model consists of a two-dimensional surface flow model and a one-dimensional drainage pipe model. The flow interaction between the surface and subsurface drainage flows occurred through drain boxes. The exchange discharge through storm drain inlets was calculated based on the discrepancies in the pressure head on the surface, drainbox, and sewer pipe using the weir and orifice equations (Lee et al. 2013). For this research, storm drain shall be referred to as the infrastructure designed to drain flood water (storm/rainwater) from the surface to the sewer system, while the term drainbox shall be used to describe the interior of the storm drain inlet with a rectangular cross-section.
SURFACE INUNDATION MODEL
represents the conservative variable in vector form; 
and 
represent the x- and y-direction fluxes, respectively; while 
is the source term. The variables are expressed as follows:
is the rainfall intensity; 
and 
are the bed slopes in x- and y-direction, respectively; 
and 
are the friction slope slopes in x and y directions, respectively, and 
is the discharge rate between surface and subsurface system, represented by the dividend of 
(See Equations (9) and (10)) and the area of the computational cell 
(Lee & An 2019).SEWER PIPE MODEL
, 
, and 
represent the vector forms of the flow variables, fluxes, and source terms, respectively.
is the average pressure over the area, 
is the floodwater density, 
is the discharge rate between drainbox and pipe system, represented by the dividend of 
(See Equations (13) and (14)) and the length of the computational length of pipe cell 
, g is the gravitational acceleration, 
is the pipe slope, and 
is the friction slope, expressed in Manning's formula as:
is Manning's coefficient. Equation (3) is discretized into a finite volume using the Euler method (An et al. 2018a, 2018b):
th computational cell, respectively, 
is the timestep, 
is the length of the side of the cell, and 
is the numerical flux between i and 
. For a more detailed discussion of the sewer pipe model concept used in this study, the reader may refer to Lee et al. (2013).SURFACE–DRAINBOX AND DRAINBOX–PIPE INTERACTION
is the water depth inside the drainbox, 
is the bottom area of the drainbox, and 
and 
are the surface-to-drainbox and drainbox-to-pipe discharge, respectively. The surface-to-drainbox discharge can be determined by the difference between the water depth at the surface, 
, and the piezometric head inside the drainbox, 
:
, the water inflow (+Q) or surcharge (−Q) is defined by the following weir equation:
, inflow or surcharge is defined by the orifice equation:
and 
are the storm drain cover area and perimeter, respectively, g is the acceleration due to gravity, and 
is the smallest storm drain cover width. Weir and orifice coefficients 
and 
derived from urban flood experimental results (Lee et al. 2013) are defined as 0.48 and 0.57, respectively. The negative notation for Q in 
is assigned when the piezometric head exceeds the surface water level and inundation begins to occur; hence, overflow occurs.
and the piezometric head inside the sewer pipe 
:
, water inflow (+Q) or surcharge (−Q) is defined by the following equation:
, inflow or surcharge is defined by orifice equation:
, 
, and 
are the cross-sectional area, perimeter, and diameter of the hypothetical slot connecting the drain box and sewer pipe, respectively.CONSTRUCTING SYNTHETIC SEWER PIPE SYSTEM
Surveyed measurements of sewer pipe, manhole, and storm drains in the study area.
Surveyed measurements of sewer pipe, manhole, and storm drains in the study area.
Schematic diagram of creating a synthetic sewer pipe system using GIS.
The GIS development of the sewer pipe, manhole, and drainbox can be categorized into four parts: (1) creating point/polyline shapefiles, (2) creating connecting sewer pipe system parameters, (3) adding corresponding elevation data, and (4) supplementing surveyed information in the attributes, listed in Table 1. The constructed shapefiles are then exported as textfiles to be used as the input data for the urban flood model.
Properties of the synthetic sewer system
| Parameter abbreviation | Description | Units/constant values | |
|---|---|---|---|
| Sewer pipe | ID | Pipe ID | – |
| L | Segment length | m | |
| slope | Slope | Dimensionless (>0.02) | |
| man_n | Manning coefficient | Dimensionless (0.012) | |
| ID_up_mh | ID of connecting upstream manhole | – | |
| umh_z0 | Upstream manhole bottom elevation | m | |
| ID_ds_mh | ID of connecting downstream manhole | – | |
| dmh_z0 | Downstream manhole bottom elevation | m | |
| Manhole | ID | Manhole ID | – |
| x | Location in x-coordinate | – | |
| y | Location in y-coordinate | – | |
| z0 | Manhole bottom elevation | m | |
| shape | Manhole shape | (circular/rectangular) | |
| D | Diameter (circular) or width (rectangular) | m | |
| Drainbox | ID | Drainbox ID | – |
| w | Width | m | |
| L | Length | m | |
| A | Area | m2 | |
| P | Face perimeter | m | |
| D | Depth | m | |
| z | Surface elevation | m | |
| z0 | Drainbox bottom elevation | m | |
| x | Location in x-coordinate | – | |
| y | Location in y-coordinate | – | |
| b0 | Smallest width of the storm drain cover | m | |
| d_t | Diameter of the connecting tube | m |
| Parameter abbreviation | Description | Units/constant values | |
|---|---|---|---|
| Sewer pipe | ID | Pipe ID | – |
| L | Segment length | m | |
| slope | Slope | Dimensionless (>0.02) | |
| man_n | Manning coefficient | Dimensionless (0.012) | |
| ID_up_mh | ID of connecting upstream manhole | – | |
| umh_z0 | Upstream manhole bottom elevation | m | |
| ID_ds_mh | ID of connecting downstream manhole | – | |
| dmh_z0 | Downstream manhole bottom elevation | m | |
| Manhole | ID | Manhole ID | – |
| x | Location in x-coordinate | – | |
| y | Location in y-coordinate | – | |
| z0 | Manhole bottom elevation | m | |
| shape | Manhole shape | (circular/rectangular) | |
| D | Diameter (circular) or width (rectangular) | m | |
| Drainbox | ID | Drainbox ID | – |
| w | Width | m | |
| L | Length | m | |
| A | Area | m2 | |
| P | Face perimeter | m | |
| D | Depth | m | |
| z | Surface elevation | m | |
| z0 | Drainbox bottom elevation | m | |
| x | Location in x-coordinate | – | |
| y | Location in y-coordinate | – | |
| b0 | Smallest width of the storm drain cover | m | |
| d_t | Diameter of the connecting tube | m |
In this research, manhole is assumed to be a closed pit that acts as a junction for sewer pipes and does not contribute to the surface and subsurface flow interaction. The pipe roughness coefficient was assumed to be 
(Lee et al. 2013). The elevation of each point was obtained from the elevation data. The concept of the creation of the synthetic pipe system follows the Revised National Plumbing Code of the Philippines (NANPAP 2000), where the maximum distance between manholes is 91 m, and the uniform slope between manholes should be greater than 0.02 sloping downwards to the point of disposal.
The sewer system was constructed within the subcatchment, following a combination of dendritic and rectangular drainage patterns (Mejia & Niemann 2008), tracing the stream channel identified from elevation data. The delineation of the pipe system in the urban flood model based on the order method (Lee et al. 2018) was performed by selecting the major stream pipeline as the principal tributary pipeline. The objective of the method is to simplify the extensive pipe network data based on subjective judgement of individual researchers, with the aim of easing the computational load, as performed in Lee et al. (2018). A dendritic pattern was used as a baseline for the network construction due to it being one of the most common drainage patterns and the earliest morphology in the development of drainage systems (Yu et al. 2022). The branching of the network is performed from the original pipeline with consequent orders. Synthetic sewer pipe system construction within the subcatchment considers the following conditions: (1) the order of the upstream and downstream manholes follows the stream flow toward the river and (2) upstream and downstream manholes were assigned with higher and lower elevations, respectively. If the second condition is not satisfied, the manhole bottom elevations are modified to satisfy both conditions.
STUDY AREA AND DATA
Observed rainfall data during Typhoon Vamco 2020 in the Marikina-Pasig watershed.
Observed rainfall data during Typhoon Vamco 2020 in the Marikina-Pasig watershed.
Location of the urban subcatchment and the rain gauge stations in the watershed. The red rectangles in the left figure indicate the corresponding locations of the flooding in Figure 6(a)–(c).
Location of the urban subcatchment and the rain gauge stations in the watershed. The red rectangles in the left figure indicate the corresponding locations of the flooding in Figure 6(a)–(c).
According to the rainfall data (Figure 4), increased precipitation was observed in the mountains (data from Tanay station) from 11 November 2020 18:00 h to 12 November 2020 00:00 h, resulting in rising river water levels prior to intense rainfall being observed in the urban domain. Because of this, even though Science Garden station is the nearest station to the study domain, incorporating the rainfall input data from neighboring sources is important.
) of the surrounding subcatchments within the watershed into the hydraulic cells of the urban domain (
). The adaptive mesh refinement scheme applied in this simulation allowed the division of grid sizes from the initial parent cell (
) to subsequent children cells (
) to (
) and so forth, until the model encountered a numerical error, finally settling for the finest cell size of 6.25 m × 6.25 m. Previous studies emphasized that greater uncertainties on boundaries and streamlines occur when generating larger-scale cells (Zhou et al. 2021). The resolution of the flood cells was assigned to be in this resolution, with a working theory that the grid size should be smaller than the average width of the smallest roads, which was approximately 10 m, to avoid stalled flow in the calculations. In this simulation, the upstream discharge and downstream water level were automatically computed during the integration, eliminating the need to establish the initial boundary conditions. Based on the field survey, the water levels started to rise around 12 November 2020 4:00 h in the upper section of the subcatchment, peaked at 10:00–14:00 h, and subsided at 15:00–16:00 h. The simulation was then performed for a 24 h period from 12 November 2020 00:00 h to 12 November 2020 23:00 h, to simulate the increasing and decreasing flood depth. The rainfall event resulted in different flood levels in different parts of the urban domain, as shown in Figure 6. 
2020 rainfall event observed inundation (∼0.5, ∼1.0, and >2.0 m) in the urban areas surrounding the Marikina River.
2020 rainfall event observed inundation (∼0.5, ∼1.0, and >2.0 m) in the urban areas surrounding the Marikina River.
RESULTS AND DISCUSSIONS
Simplified synthetic drainage network created using a Dendritic pattern and Order method.
Simplified synthetic drainage network created using a Dendritic pattern and Order method.
CASE COMPARISON
Two flood simulation cases were conducted: one without sewer pipe integration (Case 1) and the other with sewer pipe integration (Case 2). Case comparisons are presented to illustrate the influence of the pipe integration in the flood inundation extent, flood depth, downstream water levels, and flow rates of the pipe system. Additionally, flood validations were performed to assess the effectiveness of these case simulations.
FLOOD INUNDATION AND DEPTH
Flood inundation comparison for Case 1 and Case 2 at t = 12 to t = 24 h highlighting areas A–D.
Flood inundation comparison for Case 1 and Case 2 at t = 12 to t = 24 h highlighting areas A–D.
Flood depth timeseries comparison (m) of areas a–d for Case 1 (red line) and Case 2 (blue line).
Flood depth timeseries comparison (m) of areas a–d for Case 1 (red line) and Case 2 (blue line).
Figure 9 shows the reduction in flood depth for Case 2 compared to Case 1, demonstrating the effectiveness of sewer pipe integration in reducing inundation. Inundation depth reductions of up to 1.75–3.0 m are observed in Areas B–D. Notably at Area A, an increase in flood depth was observed in Case 2 at t = 9 and 11 h. This increase is attributed to a bottleneck phenomenon within the pipe at Area A, where reduced flow discharge is observed due to the overwhelming flood flow within the pipe junction.
DOWNSTREAM WATER LEVEL
Observed and simulated water level (Case 1 and Case 2) at Tumana station.
Figure 7 illustrates the maximum peaks of the observed and simulated (Case 1 and Case 2) water level, ranging from 23.5 to 23.6 m, 22.9 to 23.4 m, and 23.6 to 23.9 m, respectively. Although the simulated water level peaks exhibit minimal differences compared to the observed values, a noticeable time gap between the occurrences of the maximum peaks can be observed. The observed maximum peaks were recorded between 20 November 07:00 and 11:00 h, whereas the simulated Case 1 and Case 2 water levels peaked from 14:00 h to 21:00 h. This delay in the timing of the water level increase can be attributed to the exclusion of the overall influence of all the upstream sewer networks. These networks contribute to the abrupt flood flow from upstream catchments to the study area. This effect is evident in the difference in the start of water level increase for Case 1 and Case 2, which occurred at around 7:00 and 5:00 h, respectively. Notably, Case 2 closely aligns with the observed start time of water level increase, which is November 12th at 0:00 h.
PIPE FLOW RATES
Simulated pipe flow discharge Q (m3/s) at t = 6 to t = 24 h.
In addition to the pipe flow Q calculations, the developed model can also simulate the current water depth h (m) and wetted area A (m2) within the pipe. This capability enables the identification of recurring pressurized pipes and subsequent surcharge points during urban flood events. As a result, this study can provide valuable information to improve pipe construction practices, ultimately reducing the risk of urban flooding.
FLOOD VALIDATION
Simulated maximum flood depth and extent imbedded for Case 1, with flood depth validation data (colored square points).
Simulated maximum flood depth and extent imbedded for Case 1, with flood depth validation data (colored square points).
Simulated maximum flood depth and extent for Case 2, imbedded with flood depth validation data (colored square points).
Simulated maximum flood depth and extent for Case 2, imbedded with flood depth validation data (colored square points).
and 
correspond to the observed and model-simulated flood depths at the surface, while N corresponds to the total number of flood observation points. Given a total of 31 flood points, RMSEs for the flood depth (m) for Case 1 and Case 2 are calculated to be 18.6 and 5.6, respectively. This aligns with the analysis of the change in the downstream water level (Figure 10), where Case 2 simulations can generate deeper and more expanded flooded areas in the downstream and river tributaries as compared to Case 1. This outcome results from the additional volume of water flowing from upstream to the downstream subcatchments through the influence of the integration of the sewer network in Case 2 simulations. 
Vamco 2020 flood event observed and simulated flood depths (Case 1 and Case 2).
While the simulation results integrating sewer pipes (Case 2) are closer to the observations than simulations without pipe integration (Case 1) (Figures 8–14), with RMSE improvements from 18.6 to 5.6, a more meticulous integration of pipe parameters is recommended for a more accurate replication of the observed inundation. To reproduce the reduction in flood depth on a wider scale within the domain, creating a higher-order synthetic sewer network must be considered. This would allow the model to better simulate the recession of floods in pseudo-catchments, resulting in more precise simulations. However, generating a higher-order synthetic sewer system poses difficulties in locating elevation errors and addressing simulation instabilities. Additionally, given the synthetic nature of the sewer system, which was constructed with substantial assumptions on the location, dimensions, and characteristics of the sewer parameters, some uncertainties are to be expected. Due to difficulties in obtaining detailed pipe data for an urban domain of this scale, achieving a precise replication of the urban flooding may not be feasible. Therefore, the method can be applied as a supplementary process in representing missing data, with a strong recommendation for quality checking during the construction of the synthetic system.
CONCLUSIONS
This study presents an approach for simulating short-term urban flooding by integrating surface and sewer pipe modeling. In areas lacking comprehensive storm drain data, a synthetic representation of the sewer network using GIS has been proposed. The model was tested for a recent flood event in an urban subcatchment within the Marikina River, Philippines, and was found to be effective in recreating the urban inundations.
The results highlight the feasibility of simulating urban flooding with a synthetic pipe system using the urban flood model, and the details of the procedures are presented in this paper. The model's capacity to calculate spatial variations in pipe flows and water depth within the pipe provides an opportunity to identify areas where proactive measures can be taken to reduce urban flooding. For instance, increasing pipe diameter in bottleneck regions and adjusting connected pipe orientations can reduce surcharge events. Such measures not only improve sewer construction but also reduce the risk of urban flooding.
However, it is important to acknowledge that the model's accuracy may be limited by numerical modeling constraints and assumptions made during the construction of the synthetic sewer network. Due to computational restrictions, only a second-order synthetic sewer network (principal pipeline + secondary tributary pipeline) was performed for this research. Future studies will be focused on the improvement of the model's capability to handle data-intensive simulations, enabling a more detailed and accurate urban flood simulation. Furthermore, incorporating daily stream flow for combined sewer network needed to be considered for future simulations. Uncertainties are also expected due to the considerable assumptions involved in the construction of the synthetic representation of the sewer network. To address this, sensitivity analyses of model input parameters are recommended to identify the most optimized sewer network set up in minimizing urban flood risk. Nevertheless, the model offers critical insights that can contribute to solving long-term issues in urban flooding, particularly in terms of drainage system construction and modification. The ability to incorporate a synthetic representation of the pipe system allows the possibility of including the influence of the drainage system in flood simulations, even in the absence of comprehensive sewer pipe data. The challenge of lacking comprehensive sewer pipe data has been an ongoing issue in urban flood research, pivotal for flood mitigation in developing countries. The findings of this research can serve as a valuable reference for flood management strategies aimed at reducing the impact of rainfall-induced floods. These strategies may involve measures such as expanding pipe diameters in narrow areas and constructing controllable orifice flood outlets and pumping stations. This information is vital in enhancing the quality of sewer construction and minimizing the risk of urban floods.
FUNDING
This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2021R1A2C200553012). In addition, the authorship of the following research work, ‘A Study on the Improvement of Urban Inundation Management Policy to Response to Climate Crisis’ (RE2022-15), was funded by the Korea Environment Institute (KEI).
DATA AVAILABILITY STATEMENT
All relevant data are included in the paper or its Supplementary Information.
CONFLICT OF INTEREST
The authors declare there is no conflict.
