Design and optimization of urban open drainage systems under compound flooding: a rank based sequential SWMM simulation optimization framework

1 Introduction

Global climate change and increasing anthropogenic activities are altering the hydrological cycle worldwide, resulting in more frequent flooding in both riverine and urban catchments (Banihashemi and Zarepour Sohi, 2022). The increasing frequency and intensity of extreme precipitation events enhance river discharge, thereby increasing the risk of fluvial flooding, while also generating higher surface runoff in rapidly urbanizing and often unplanned catchments, leading to pluvial flooding (Alifu et al., 2022; Guo et al., 2021; IPCC., 2021; Yin et al., 2018; Zhang et al., 2022). In addition, urban expansion transforms permeable land surfaces into impervious areas, reducing infiltration and natural storage capacity and increasing peak runoff (Arnold et al., 1996; Chen et al., 2017; Jacobson, 2011; Shuster et al., 2005; Yin et al., 2018). These changes place considerable stress on existing urban drainage infrastructure, which is often not designed to accommodate the combined effects of rapid urbanization, altered rainfall patterns, and increasing flood magnitude (Arnbjerg-Nielsen et al., 2013; Zhou et al., 2013). This situation becomes particularly critical when an urban area is located near a river or coastal zone, where elevated downstream water levels can restrict or even block gravity driven storm water drainage. In such a scenario, flooding is not governed by rainfall runoff alone, but by the combined interaction of intense local precipitation, high river water levels or coastal tides, and backflow through the drainage network (Bevacqua et al., 2019; Wahl et al., 2015; Zscheischler et al., 2020). This interaction creates a compound flooding scenario, in which pluvial runoff accumulates within the urban drainage system while fluvial or coastal water levels restrict efficient outfall discharge of the urban drains (Ganguli and Merz, 2019; Liu et al., 2024; Santiago-Collazo et al., 2019; Zscheischler et al., 2020). However, many existing drainage design and optimization methods overlook such compound flood mechanisms, leading to underperformance of drainage infrastructure and repeated flood damages (Apel et al., 2016; Arnbjerg-Nielsen et al., 2013; Zhou et al., 2013).

Most existing optimization-based drainage design studies primarily focus on closed conduit systems, detention storage, LID placement, and operational control, with comparatively limited attention given to open channel drainage systems and their interaction with terrain, road levels, and practical hydraulic constraints (Eckart et al., 2018; Fletcher et al., 2013; Guo et al., 2021; Ngamalieu-Nengoue et al., 2019; Parkinson and Mark, 2005). However, in many developing urban regions, stormwater is predominantly conveyed through open channels and roadside drains, where channel geometry, ground elevation, road elevation, flow depth, and velocity play a critical role in determining drainage performance (FHWA, 2009; Parkinson and Mark, 2005). Optimization frameworks that neglect these factors and focus only on pipe sizing or storage placement may therefore fail to capture realistic design constraints, particularly in rapidly urbanizing areas. In addition, many existing approaches assume simplified or fixed downstream boundary conditions and do not explicitly incorporate river induced backflow effects (Ngamalieu-Nengoue et al., 2019; Nicklow et al., 2010; Seyedashraf et al., 2021), which is a critical limitation for river adjacent urban catchments. During high river stages, drains can become submerged upto certain level, reducing discharge capacity or causing reverse flow into the drainage network, thereby leading to system failure even when internal capacity is sufficient (Huong and Pathirana, 2013; Li et al., 2025; Santiago-Collazo et al., 2021). Ignoring such compound pluvial–fluvial interactions can result in unrealistic design solutions and underestimation of flood risk (Bevacqua et al., 2019; Santiago-Collazo et al., 2019; Zscheischler et al., 2020).

Urban drainage system design has progressed from traditional empirical methods to advanced simulation–optimization approaches. Early practices relying on Intensity Duration Frequency (IDF) curves and design storms often assume idealized rainfall patterns, leading to under or over designed systems (Chow et al., 1988; CPHEEO., 2012; Isikwue et al., 2012; McCuen, 1989). Event based hydrologic–hydraulic models such as SWMM are therefore widely used to simulate runoff generation, routing, surcharge, and flooding under realistic storm scenarios (Rossman, 2015; Thrysøe et al., 2021; Torcato, 2016), and have been coupled with optimization to identify cost effective and performance oriented solutions for SuDS, LID, detention storage, and real-time control (Di Matteo, 2017; Eckart et al., 2018; Seyedashraf et al., 2022). However, multi-objective evolutionary algorithms such as NSGA-II, MOEA/D, and Borg-MOEA remain computationally expensive because of the large number of required hydrodynamic simulations and often face scalability and convergence limits on large networks (Deb et al., 2002; Ngamalieu-Nengoue et al., 2019; Nicklow et al., 2010); surrogate assisted methods can reduce simulation effort but introduce training and validation overhead that is case dependent (Dai et al., 2025; Garzón et al., 2022; Razavi et al., 2012). Collectively, these limitations reveal a clear research gap: the absence of a computationally tractable framework that optimizes open channel, road aligned drainage geometry under an explicit compound rainfall river stage (backflow) boundary while honoring practical hierarchical ranking and road level constraints, particularly in data scarce, rapidly urbanizing riverine cities.

To address this gap, the present study develops a rank-sequential SWMM simulation–optimization framework for the design of urban open channel and roadside drainage systems under compound pluvial–fluvial conditions, and its core innovation boundary is defined by four contributions. First, the framework directly optimizes open channel, road aligned drain geometry, namely invert levels, cross sectional dimensions, and flow depths, rather than pipe sizing, detention storage, or LID placement, thereby addressing a class of systems that dominates drainage in developing riverine cities yet remains underrepresented in optimization studies. Second, it embeds an explicit compound rainfall–river stage boundary in which an elevated downstream river level and the resulting backflow are imposed during the optimization itself, so that outfall submergence and reverse flow are treated as design conditions rather than as post hoc checks. Third, it introduces a hierarchical drain ranking constraint that increments rank at every junction, unlike the Strahler scheme, enforcing monotonic downstream capacity growth; this both reflects the structure of road aligned urban networks and prunes the feasible search space, providing a computationally tractable alternative to population based metaheuristics (e.g., NSGA II). Fourth, it links the optimized channel design to a road level (Effective Filling) post optimization step, connecting hydraulic design to the practical road raising requirements needed to keep roads serviceable and, in extreme cases, to act as secondary conveyance. Channel depths are treated as discrete decision variables and widths as continuous variables, with non-linear hydraulics resolved by dynamic wave SWMM simulation; the problem is therefore solved with a constraint based rank-sequential search coupled to SWMM. We also delimit these claims: the contribution lies in the integrated, constraint guided design workflow and its application to compound flood-prone open drain systems, not in proposing a new optimization algorithm; the design is based on a single deterministic compound rainfall–river stage scenario rather than a joint probability formulation; and the optimized configurations are subsequently cross checked using an independent HEC-RAS 2D rain-on-grid model of overland flow and floodplain inundation forced by the same rainfall and river stage boundary.

2 Materials and methods

The methodology for optimizing the design of an open drainage system is illustrated in Figure 1. The proposed methodology consists of four phases: input data preparation, pre optimization, optimization, and post optimization. Initially, spatial and hydrological data are collected. The digital terrain model (DTM) represents terrain elevation and slope. Precipitation data are used to determine design storm intensity, and Land Use Land Cover information is used to identify urban areas, road networks, and natural drainage routes. These inputs form the basis of the SWMM model setup and all subsequent design steps.

2.1 Pre optimization

2.1.1 Layout selection

Identification and layout selection of open drainage channels along the existing urban road network serves as the preliminary step in the proposed methodology. Leveraging these readily accessible alignments not only streamlines construction processes but also facilitates effective long-term maintenance of the drainage infrastructure. Studies show that up to 80% of sewer infrastructure is constructed parallel to the road network (Mair et al., 2017), demonstrating the viability of this layout selection strategy. This approach also optimizes land acquisition and minimizes conflicts with buildings and underground infrastructure by proposing primary, secondary, and tertiary open drains along road layouts. The proposed strategy is consistent with modeling practices in urban hydrology, as reported by Meierdiercks et al. (2017), where terrain informed connectivity is fundamental to achieve efficient network performance. Integrating drainage channels parallel to the existing road network creates a maintainable and hydraulically responsive system well suited to modern urban settings.

2.1.2 Establishing a hierarchical ranking system

In urban drainage design, hierarchical ranking ensures that drains are sized to handle increasing runoff volumes as flow progresses downstream. This approach is inspired by watershed stream ordering methods, particularly the Strahler scheme (Tarboton et al., 1991; Simone, 2023). However, the proposed ranking system differs fundamentally from the Strahler scheme: whereas Strahler ordering increments the rank only when two tributaries of equal rank converge, the proposed scheme increments the drainage rank at every junction, regardless of the ranks of the incoming tributaries. This ensures that hydraulic demand on downstream conduits always increases monotonically, even when tributaries of unequal rank merge-a condition that is common in urban road aligned networks but is not captured by the Strahler approach. This junction-wise increment is particularly appropriate for urban road-aligned drainage networks, which are predominantly dendritic, contain a high density of road intersections, and frequently combine tributaries of unequal scale. Under these conditions, equal-rank confluence rules (as in Strahler ordering) would under-represent the stepwise growth in conveyance demand that occurs at successive junctions along the road network. As shown in Figure 2, when conduits of different ranks meet at a junction, the downstream conduit is assigned a rank one higher than the maximum rank among all upstream conduits. In the SWMM representation, each conduit connects one upstream (From) node to one downstream (To) node. Although multiple upstream conduits may merge at a junction, the network is structured as a directed acyclic graph to prevent closed loops and maintain unambiguous downstream flow routing.

Rankdownstream=max(Rankupstream)+1(1)

This hierarchical ranking methodology serves three important functions in the design process: (i) it ensures correct sizing of downstream drains relative to upstream drains, reducing the likelihood of undersized channels that could cause flooding (Lu et al., 2022); (ii) it systematically identifies higher ranked drains that are larger in size and require more frequent monitoring and maintenance (Parkinson et al., 2007); and (iii) it reduces the feasible search space for the rank-sequential optimization by enforcing non-decreasing downstream capacity as a structural constraint, thereby improving computational tractability.

2.1.3 Sub catchment slope extraction, channel slope correction, and outlet elevation constraints

In urban areas where the drainage outfall discharges into a river, rising river water levels during high flow conditions may induce backflow into the drainage network. If the invert level of the outfall is lower than the river stage, flow reversal can occur, creating a hydraulic wedge that reduces effective conveyance as water depth exceeds the normal flow depth of the channel. Therefore, appropriate setting of outlet elevations is essential to maintain gravity driven flow. To mitigate backflow risk, local terrain slopes derived from the Digital Terrain Model (DTM), historical river stages, and hydraulic boundary conditions at each outfall were analyzed. Based on these datasets, outlet elevation constraints were defined to ensure uninterrupted discharge under both normal and elevated river stage conditions. This approach reduces reliance on mechanical measures such as pumps and flap gates and promotes passive hydraulic stability. In addition, road crest elevations were aligned with the top level of the drainage channels to preserve natural overland flow pathways. Improper elevation differences between road surface and channel invert may cause localized ponding or obstruction of runoff. Therefore, coordinated elevation planning for both drainage and road infrastructure is necessary to achieve a hydraulically stable and practically implementable urban drainage system.

2.1.3.1 Longitudinal slope evaluation and smoothing

During the preliminary phase of the optimization framework, longitudinal slope correction is performed to eliminate unrealistic negative gradients and ensure smooth hydraulic transitions across the drainage network.

Each channel segment k, defined by upstream node A and downstream node B, is initially evaluated using Equation 2

SAB=ZA−ZBLAB(2)

where z_*A* and z_*B* are the invert levels at nodes A and B, respectively, and L_*AB* is the segment length.

To enhance topographic consistency, the slope of segment i is adjusted using its eight nearest hydraulically connected neighbors, denoted as the set Ni. From this set, only the physically meaningful positive slopes are retained:

Ni+={Sj∈Ni:Sj>0(3)

If no valid positive slopes are found within the neighborhood, the search window is progressively expanded. Otherwise, the average of the valid slopes is computed as

S¯i=1|Ni+|∑j∈Ni+Sj(4)

This average value is then used to smooth segments exhibiting negative gradients:

Sicorrected=S¯i if Si≤0(5)

2.1.3.2 Limiting of channel slope based on hydraulic considerations

While smoothing removes negative slopes, excessively steep gradients may lead to high flow velocities and potential erosion. According to Manning's equation:

V =1nR23s12(6)

flow velocity increases with the square root of slope. Therefore, steep longitudinal slopes may produce velocities exceeding the permissible velocity limits recommended for concrete lined urban open drains (typically 0.3–3 m/s; CPHEEO., 2012; Chow, 1959).

To maintain hydraulic stability and constructability, an upper bound on slope is imposed:

Smax=12000(7)

This value is consistent with commonly adopted urban drainage practices in low gradient floodplain environments and provides a conservative limit that controls excessive velocity, prevents erosion of channel lining, ensures gradual longitudinal transitions, and maintains practical excavation depths. All SWMM drain (channel) longitudinal slopes in this study are expressed in percent; the imposed upper bound of 1/2000 (0.05%) reflects the very flat terrain of the study area. Accordingly, the final slope is defined as:

Accordingly, the final slope is defined as:

Sifinal=min(Sicorrected, Smax)(8)

This correction process ensures hydraulically realistic longitudinal profiles while preserving gravity driven flow under the design storm combined with the adopted elevated river stage boundary. Because open channel flow is driven by the water surface gradient, continued rainfall raises the in drain water level so that discharge to the river resumes, at a reduced rate, once this level marginally exceeds the river stage, and a larger channel cross section lowers the head build up required to convey a given runoff. Gravity drainage therefore remains effective provided the river stage stays below the raised road and plinth protection levels.

2.2 Rank-sequential SWMM simulation–optimization framework

2.2.1 Objective function

The decision variables in the proposed optimization method are the channel dimensions, namely width and depth. An open drainage system comprises n channels, represented by the dimension vector V = {(d_*i*, w_*i*)|i = 1, 2, …, n}, where d_*i* and w_*i* are the depth and width of channel i, respectively. In the absence of project specific bill of quantities rates for excavation, lining, spoil disposal, road restoration, and ancillary works, the present optimization does not minimize a complete monetary construction cost. Instead, it minimizes the total geometric channel volume as a first order proxy for excavation and material requirements at the preliminary design stage:

min Z = ∑i=1nLidiwi(9)

where Z is the total geometric channel volume (m³), L_*i* is the length of channel i (m), and d_*i* and w_*i* are its depth and width (m), respectively. This proxy is deliberately simpler than comprehensive open channel cost models, which account separately for depth dependent earthwork, lining, and water loss costs (Swamee et al., 2000). Therefore, Z is not interpreted as the total construction cost or as a complete economic optimum. Lining, road raising or filling, spoil disposal, and other ancillary works are outside the optimization objective and are considered separately during post optimization engineering assessment. Minimizing Z identifies compact channel geometries that satisfy the specified hydraulic and design constraints while avoiding an unsupported monetary cost assumption.

2.2.2 Constraints

The following constraints are imposed on all candidate solutions:

*No flooding at each channel junction:***

Fi=0(10)

where F_*i* is the flood volume along each channel i = 1, 2, 3…, n, within a UDS with ‘n' number of channel junctions.

Relative peak water depth of the channel:

hiDi <1(11)

where h_*i*, i and D_*i* are the channel's water depth, index, and design depth, respectively.

*Velocity range at the channel peak flows:***

Vmin≤Vi ≤ Vmax(12)

Utilization of the channel:

Pi≤95%(13)

P_*i* is the percentage of the utilization of the channels. It is calculated from the output of the SWMM model after simulation.

The channel depth should not be smaller than its corresponding upstream channels:

Di≥Max{Upstream Drainage Depth(Di)}(14)

*Width constraint:***

Di∈Z(15)

Wi ≤αDi(16)

Where, Z is a positive integer, and α is a factor ranging from 2 to 0.5

Ground level constraint:

ILi+Di ≤ GLi(17)

where IL_*i* and GL_*i* are the invert level and ground level of each drain respectively.

*River backflow constraint:***

ILoutfall+ Doutfall≥HFL(18)

Initialization of the optimization model:

Before optimization begins, every conduit in the drainage network is assigned the same initial depth based on the elevation difference between the High Flood Level (HFL) of the receiving river and the invert level (IL) at the outfall node. Mathematically, this initial depth applied to all drains is expressed as

Dinitial = HFL-ILoutfall(19)

where d° is the initial depth assigned to all drains in the network prior to the rank-sequential search, HFL is the adopted river stage used as the fluvial boundary condition, and IL is the invert level of the outfall node.

This initialization places river water inside the drainage system before any channel is resized. Under the imposed river stage boundary, the network therefore starts from a backwater loaded condition in which the downstream water level may exceed the outfall invert and induce flow reversal or reduced conveyance. The rank-sequential optimization then proceeds from upstream to downstream, selecting the minimum feasible geometry for each drain while SWMM evaluates hydraulic performance under the combined design storm and elevated river stage. In this way, upstream sizing decisions are made with river induced backwater already present in the network, rather than under an empty free outfall assumption. After the complete network geometry has been obtained, the final optimized configuration is evaluated as a whole in SWMM under the same rainfall and river stage boundary conditions, and only designs that satisfy the hydraulic constraints for the full network are retained. SWMM outputs such as peak water depth, velocity and flooding volume are checked against the imposed constraints for every candidate and for the final network wide verification. All candidate design variables (d_*i*, w_*i*) are provided as inputs to the SWMM model, which dynamically simulates hydraulic performance for each configuration under the specified design storm and boundary conditions. For every candidate solution, SWMM outputs such as peak water depth, velocity, and flooding volume are evaluated against the imposed constraints. Only solutions that satisfy all hydraulic and geometric constraints are considered feasible and retained within the optimization process. The proposed method enforces a no overflow constraint Equation 10 and limits relative channel water depth to less than one Equation 11, so that retained designs do not exceed hydraulic capacity under the design rainfall and river stage boundary.

V_*min*, V_*max* As per Equation 12, the minimum velocities of the flow in the channel are often limited to avoid sedimentation, and maximum velocities are limited to avoid erosion, which are 0.3 m/s and 3 m/s, respectively, consistent with permissible velocity limits for concrete/cement lined channels (Manning's n = 0.012; CPHEEO., 2012; Chow, 1959). The optimized designs yield peak channel velocities that remain below this 3 m/s limit, because the imposed slope cap constrains longitudinal gradients in this low gradient floodplain setting. The slope of terrain is required to be interpreted into the sub catchment slope in the SWMM model instead of taking the average slope of the watershed.

The proposed methodology focuses on the design of UDS comprising rectangular and trapezoidal open drains, which are commonly adopted in urban environments. The framework can be extended to configurations involving circular conduits with appropriate geometric modifications. The optimization problem is solved using an iterative constraint-based search strategy. For a given set of discrete depth and width combinations, SWMM simulations are executed to evaluate hydraulic feasibility under the specified rainfall and boundary conditions. Candidate solutions that violate any hydraulic or geometric constraint are rejected. Among all feasible configurations, the solution yielding the minimum total geometric channel volume is selected. Depth is treated as a discrete variable and hydraulic responses are obtained through numerical SWMM simulation; solutions are obtained by the iterative constraint based search rather than by a formal algebraic optimization solver. Figure 3 illustrates the workflow of the constraint based optimization framework for urban open drainage design, showing the iterative evaluation of candidate solutions against key hydraulic and spatial constraints before storing the corresponding optimal depth, width, and invert level values. The search is performed after the HFL–IL initialization described above, so that each SWMM evaluation already includes river backwater within the drains.

2.2.3 Post optimization constraints: road elevation adjustment

After optimizing the drainage channel dimensions, the post optimization stage focuses on adjusting road elevations to ensure compatibility with the finalized drainage layout. This step is essential in urban areas where it is necessary to raise the road surface above the drainage channel top level to prevent water ingress and to allow safe vehicular movement during storm events, and in extreme cases, to allow the road itself to function as a secondary conveyance pathway. The FABDEM dataset (Forest and Buildings Removed Copernicus DEM; Hawker et al., 2022) is used as the reference elevation data to estimate the amount of filling required along each roadway. The top elevation of each optimized drainage channel is compared with the corresponding road level derived from the DTM. Where the existing road elevation is lower than the optimized channel crest, additional vertical fill is recommended to maintain sufficient freeboard and reduce flood risk. This elevation difference termed Effective Filling is calculated for each road segment in the drainage network. By incorporating this step, the framework ensures that designed road levels will protect the city from flooding and remain hydraulically efficient and practically feasible in urban environments. It should be noted that FABDEM is a global bare earth elevation model with a reported vertical accuracy of approximately 1.12 m mean absolute error (2.33 m RMSE) in built up areas and about 2.9 m mean absolute error in densely vegetated terrain (Hawker et al., 2022); in this study it was not locally corrected or validated against RTK GPS, total station, or LiDAR survey data. The Effective Filling estimates therefore inherit this DEM uncertainty (of the order of 1 3 m depending on land cover), and the recommended fill heights should be regarded as planning level values to be refined with ground survey during detailed design.

3 Experiment design

To evaluate the efficacy of the optimization cum design framework, two study areas were selected in North Guwahati, Assam, India. These study areas are situated in Kumar Bhaskar Barman Township of North Guwahati, named Ghorajan and Bipinjan and are shown in Figure 4. The two watersheds are adjacent to each other and each represent unique hydrological and infrastructure properties, which can be useful for comparative assessment.

Statistical analysis for the calculation of the design High Flood Level (HFL) was performed to quantify hydrologic risk and support drainage system design within the two watersheds. The Gumbel extreme value distribution (Gumbel, 1954, 1958), was fitted to annual maximum river stage data recorded between 1997 and 2016, obtained from the Water Resources Department, Government of Assam. This method is widely used for modeling extreme hydrological events and provides a robust basis for estimating design flood levels at various return periods. The 1997–2016 annual maximum series was adopted because it constitutes the continuous, internally consistent, and quality controlled stage record maintained at the gauge by the Water Resources Department, Government of Assam, referenced to a single datum. It is acknowledged that more recent Central Water Commission (CWC) observations, including the extreme Assam–Brahmaputra floods of 2020 and 2022, are available; incorporating these more recent and more severe events would very likely raise the upper tail flood frequency estimates, particularly for the longer 15-year and 100-year return periods. Because the river stage enters the present framework only as a boundary condition, updating the HFL from an extended record is a direct extension that does not alter the design methodology.

Figure 5a shows the frequency of water levels exceeding 48 m, 49 m, and 50 m between 1997 and 2016. The Water Resources Department, Government of Assam, has set a danger mark of 49.68 m, which is well below the historical maximum-recorded water level of 51.46 m. Figure 5b shows the estimated flood levels for return periods ranging from one to 100 years. The HFL corresponding to a 15-year return period is 49.50 m, and that corresponding to a 100-year return period is 50.50 m. In this study, 49.50 m is adopted as a fixed elevated river stage boundary for a scenario-based compound flood design rather than as a joint probability design flood.

3.1 Design scenario for compound flooding

Compound flooding arises from the concurrent or sequential occurrence of pluvial runoff and elevated fluvial stage. A rigorous probabilistic treatment would require estimation of the joint exceedance probability of rainfall and river stage, typically through bivariate frequency analysis or copula based modeling. Such a joint probability design is not undertaken in the present study. Instead, the optimization is performed under a single, explicitly defined compound flood design scenario that combines a service level urban design storm with an elevated river stage boundary condition intended to stress outfall hydraulics and induce backwater effects. The adopted scenario pairs a 5-year design storm with a fixed Brahmaputra stage of 49.5 m (approximately the 15-year Gumbel estimate from the 1997–2016 annual maximum stages). The 5 year rainfall return period is consistent with commonly adopted practice for minor urban storm water and roadside open drains in India, which are often sized for relatively frequent events (typically in the 2–5 year range). The 49.5 m river stage is not claimed to share the same return period as the rainfall. Rather, it is imposed as a conservative fluvial stress boundary near the official danger mark (49.68 m) to ensure that channel geometry and outfall settings remain hydraulically feasible when drainage capacity is reduced by river backwater during a design rainfall event. Accordingly, the resulting design should be interpreted as compound flood aware under the stated rainfall–stage pair, not as an optimal design for a prescribed joint return period. It is also acknowledged that 49.5 m lies slightly below the official danger mark (49.68 m) and well below the historical maximum stage of 51.46 m; therefore, the present scenario does not represent the most extreme historically observed river condition. Multi scenario testing and joint rainfall–stage frequency analysis are identified as priorities for future extension of the framework.

3.2 SWMM model setup and parameterization

This study employs a scenario-based design analysis, uses typical SWMM model parameter values appropriate to a data-scarce setting, and has not performed local calibration against measured discharge or water-level records. The model setup and results that follow should therefore be interpreted within these premise boundaries.

The hydrologic–hydraulic simulations used in the optimization were performed in EPA SWMM with dynamic wave flow routing. Table 1 summarizes the principal model settings extracted from the SWMM input files used for the Ghorajan and Bipinjan networks. These parameters are reported to support reproducibility; they are representative modeling assumptions for a data scarce setting and were not calibrated against observed discharge or water level records. No SWMM calibration or validation against gauged flows was performed in this study. In the absence of continuous monitoring data, the present results should be interpreted as scenario-based design outcomes under the stated rainfall and river stage boundary conditions, rather than as a locally calibrated flood forecast. Future work may improve confidence using flood marks and community reported inundation evidence in similarly data scarce urban settings (Hossain et al., 2026). The design rainfall applied at raingage RG1 is the SWMM timeseries “5_yrs”: an intensity hyetograph at 15 min intervals over 2 h (eight pulses; peak intensity 85.82 mm h?¹; approximate storm depth ≈ 79 mm). The simulation window extends for 10 h to capture runoff routing and recession. Open channel Manning's n is 0.012, corresponding to concrete/cement lined channels (with limited segments at 0.01). Infiltration is modeled by the SCS Curve Number method, typically with CN = 80 and a drying time of 7 days. Most sub catchments are assigned 80% imperviousness.

Table 1. Principal EPA SWMM model settings used for the Ghorajan and Bipinjan case studies.

3.3 Independent HEC-RAS 2D rain-on-grid cross check of the optimized design

The optimized drainage network obtained from EPA SWMM is independently cross-checked against a two dimensional HEC-RAS rain-on-grid model that simulates overland flow and floodplain inundation. SWMM is used to represent rainfall–runoff transformation and hydraulic routing within the drainage network, including junction water levels and backwater effects at outfalls. However, SWMM has limited capability to resolve spatially distributed surface flow velocities and water depths once runoff leaves the drainage network.

To address this limitation, HEC-RAS 2D is employed to simulate two-dimensional shallow water flow over the floodplain and road network. The cross check is exemplified at Outfall 1 of Case Study 1, which serves as a representative outfall location for an inter model consistency assessment of the proposed methodology. HEC-RAS 2D solves the depth averaged shallow water equations on an unstructured mesh to represent spatial variations in flow depth and velocity across the floodplain (Brunner, 1995). The HEC-RAS 2D model is driven independently of SWMM using a direct rainfall on grid approach, in which the same design rainfall applied to SWMM is imposed directly over the two dimensional computational mesh; no SWMM derived discharge or hydrograph is transferred to HEC-RAS 2D. The adopted Brahmaputra stage of 49.5 m is applied as a downstream stage boundary so that river backwater is represented within the 2D domain, and the drainage channel geometry is burned into the terrain with local mesh refinement along the channel path and at the outfall. The discharge at Outfall 1 is then extracted across a profile line at the outfall for comparison with the corresponding SWMM outfall hydrograph. The two-dimensional mesh was refined along the burned channel alignment and transitioned to coarser cells approximately 20 m away from the drain; the computational time step was set equal to the SWMM routing step of 20 s; a Manning's roughness of 0.012 was assigned to the lined channels, consistent with the SWMM model; and the diffusion wave form of the shallow water equations was solved.

This independent HEC-RAS 2D rain-on-grid simulation enables evaluation of surface flood propagation and inundation in the study area under the given river stage condition. Because the same design rainfall and the same 49.5 m river stage boundary drive both models while neither supply inputs to the other, the SWMM network model and the HEC-RAS 2D model each represent compound river and rainfall flooding independently, and their comparison provides an independent cross check rather than a self-referential coupling.

4 Results and discussion

4.1 Analysis of solutions from the rank-sequential SWMM simulation–optimization framework

This study integrates engineering constraints directly into the optimization framework to develop a functional open drainage system tailored to the topographic and urban conditions of the study areas. As shown in Figure 6a Most of the channels follow a rectangular cross section and are aligned parallel to existing roads to ensure constructability and access for maintenance (Skrede et al., 2020; Miguez et al., 2012). The drainage networks for Case Study 1 and Case Study 2 include five natural outfall points that discharge into the Brahmaputra River. Simulations were conducted using SWMM, where each watershed was divided into multiple irregularly shaped sub catchments shown in Figure 6b.

This allowed for accurate representation of terrain variations, drainage pathways, land cover, and soil characteristics influencing runoff behavior. Channel slopes were assigned based on terrain derived elevation data and are presented in Figure 7a.

It should be noted that the sub catchment slopes shown in Figure 6b are overland surface slopes expressed as dimensionless gradients (m/m), obtained from DEM derived percent slopes by dividing by 100, whereas the SWMM drain (channel) longitudinal slopes in Figure 7a are reported in percent (%). These are two distinct quantities and are not directly comparable on the same numerical scale. The maximum sub catchment slope of about 36 m/m corresponds to a small number of steep, DEM derived hillslope cells and influences only the overland runoff timing, not the channel design; such isolated high values reflect local terrain steepness in the digital elevation model rather than any inconsistency in the channel slope constraint. The drain slope design bound of Equation 6 (1/2000, i.e. 0.05%) applies only to the channel longitudinal slopes shown in Figure 7a.

Before optimizing channel dimensions, natural and positive slopes were enforced along each conduit segment using the slope correction procedure outlined in Equation 1–Equation 4 and Equation 6–Equation 7. After all key inputs, including invert levels, ground elevations, and slopes had been defined, the drainage dimensions were optimized using the rank-sequential SWMM simulation–optimization approach. The resulting set of optimized conduit sizes is presented in Figure 7b, showing how the design variables adjusted to satisfy both hydraulic and spatial constraints.

The optimized open drainage networks developed for the two study areas (i) Ghorajan (Case Study 1) and (ii) Bipinjan (Case Study 2) exhibit a wide range of cross-sectional sizes, reflecting their adaptation to varying hydrological conditions, terrain characteristics, and design constraints. The corresponding channel geometries obtained from the optimization process are summarized in Table 2.

Table 2. Distribution of optimized cross sectional areas for both study areas.

The results show that a large portion of the total drainage length approximately 49.78 km lies within the smallest cross sectional category (areas less than 5 m²). This pattern reflects the dominance of smaller flows in upstream sections and localized sub catchments. A further substantial length falls within the 5–10 m² and 10–15 m² ranges, together accounting for 55.54 km, indicating the need for greater capacity in downstream sections to handle accumulated runoff. In contrast, larger channels, particularly those with cross sectional areas between 40 and 60 m², occur less frequently but are strategically placed near outfall locations to safely convey peak discharges to the Brahmaputra River.

The design is mathematically consistent with the downstream depth continuity constraint Equation 13 and hydraulically continuous, striking a practical balance between hydraulic reliability and geometric compactness. To verify the hydraulic performance of the optimized design, channel fill percentages were evaluated against the utilization constraint Equation 12. Figure 8 shows that most drainage segments operate within acceptable utilization limits. Table 3 shows the distribution of fill percentages for the optimized drainage network, and most of them are well used across the system. Out of the total drainage length of about 128.33 km, only 14.78 km (approximately 11.5%) operates at lower fill levels (0–40%), suggesting a low hydraulic loading in these sections. However, a large portion of the network, 44.58 km (34.7%), operates within the 61–80% fill range; while 45.55 km (35.5%) operates close to full capacity, with fill levels between 81% 95%.

Table 3. Fill percentage distribution across different sections in both study areas.

This distribution indicates that the majority of drains operate close to their design capacity, reflecting an efficient and well-utilized drainage system. However, during extreme rainfall events beyond the design return period, some sections operating near full capacity may experience stress. This information helps identify vulnerable locations that may require monitoring or additional freeboard provision in future design iterations. The optimization problem comprised 429 channel segments for Case Study 1 (Ghorajan) and 162 channel segments for Case Study 2 (Bipinjan), giving 858 and 324 decision variables respectively, since each segment carries one discrete depth and one continuous width. These two networks span an approximately threefold range in scale, covering catchment areas of about 31.9 km² (Ghorajan) and 10.8 km² (Bipinjan), which demonstrates that the framework scales across networks of markedly different extent. For Case Study 1, a total of 3,156 model evaluations took 11.7 h on a High Performance Server (HPS) with dual Intel^® Xeon^® Silver 4114 processors (2.2 GHz base frequency, up to 3.0 GHz, 40 threads). In Case Study 2, 1,056 evaluations were performed in 1.5 h using the same hardware configuration. SWMM simulations were executed with eight parallel threads (8 CPU Cores), and it supports faster and efficient hydraulic computations. Overall, the optimization framework adds minimal computational burden to the system, increasing run time by a few seconds per iteration.

4.2 Analysis of river backflow effects on the drainage network

To evaluate the hydraulic performance of the optimized drainage system under the adopted compound flood scenario, a set of simulations was carried out using an initial river water level of 49.5 m as the fluvial boundary condition. This water level was applied as a boundary condition at the outfall nodes, and the system was then subjected to the 2-h design rainfall hyetograph (timeseries “5_yrs”) within the 10-h simulation window. Figure 9 displays the flow pattern at all the five outfalls. The results clearly show the interaction between river water level and the response of the drainage system. By incorporating river-induced backflow during the design phase, the optimization framework ensures that drainage channels are sized to accommodate both normal downstream conveyance and temporary flow reversal conditions. This bidirectional consideration helps prevent junction overflow and maintains free surface flow within the designed channels under the adopted compound flooding conditions. The early onset of backflow further indicates that even a small rise in river stage can significantly impair urban drainage system performance, even before the official danger level is reached (Liu et al., 2024). The river stage is held constant at 49.5 m throughout the simulation, which conservatively represents sustained backwater during the design storm. Because open channel flow responds to the water surface gradient rather than the bed slope, continued rainfall raises the in drain water level and, once this level marginally exceeds the river stage, discharge to the river resumes at a reduced rate; a larger channel cross section lowers the head build up needed to convey a given runoff. Gravity drainage thus continues to function, at reduced capacity, as long as the river stage remains below the raised road and plinth protection levels. Active drainage becomes strictly necessary only for the more extreme condition in which the river stage exceeds these protected levels (approaching the historical maximum of 51.46 m), or when sustained runoff exceeds the reduced gravity discharge available at the permissible head.

Ignoring backflow during design can lead to critical gaps in system performance, particularly for channels located near outfalls. The results also show that recovery from flow reversal is influenced not only by channel geometry but also by the rate at which rainfall driven inflow enters the system. This highlights the importance of simulating both river and rainfall flooding simultaneously when designing drainage infrastructure in riverine urban settings.

4.3 Road level design and effective filling

Calculation of filling depth requirements across the Bipinjan and Ghorajan watersheds reveals clear spatial variation driven by local topography, based on a planned road level (RL) of 51.0 m, as illustrated in Figure 10. This recommended road level is below the historical maximum Brahmaputra stage of 51.46 m and should therefore be interpreted as a scenario linked adaptation target rather than protection against the most extreme historically observed river stage. Areas in closer proximity to the Brahmaputra River generally exhibit higher existing ground elevations due to historically raised embankments and natural levee deposits, and consequently require lower filling depths. In contrast, areas located within low-lying wetland zones demand significantly greater filling, with depths exceeding 4 m in several sections, underscoring the need for urban planning approaches that are responsive to local ground conditions and flood exposure.

In Case Study 1 (Ghorajan), the filling requirement is substantial, with the longest road network segment 26.78 km falling within the 4–5 m filling depth category, and an additional 8.68 km requiring fills exceeding 5 m. This reflects the predominantly low lying and wetland influenced terrain of the Ghorajan watershed, where existing road surfaces fall far below the required drainage channel crest and flood protection levels. In Case Study 2 (Bipinjan), the filling requirement is comparatively modest: the majority of the road network falls within the 0–1 m filling category (14.18 km), and only 0.34 km requires fills in the 3–4 m class, with none exceeding 4 m, indicating relatively higher natural ground elevations in that watershed. The complete distribution of filling lengths across depth categories for both study areas is presented in Table 4.

Table 4. Length of filling required for each study area.

Raising road levels and building plinths above the Brahmaputra's High Flood Level (HFL), with an additional margin to account for future climate variability, is central to the long-term resilience strategy proposed in this study. Such elevation-based interventions directly reduce the exposure of buildings to flood inundation and ensure that critical urban infrastructure remains operational during extreme flood events (Liu et al., 2024).

4.4 Hydraulic performance under compound flooding: SWMM–HEC-RAS 2D consistency assessment

The hydraulic performance of the optimized drainage network was evaluated using SWMM together with an independent HEC-RAS 2D rain-on-grid model. SWMM was employed to simulate rainfall–runoff transformation and hydraulic routing within the drainage network, while the HEC-RAS 2D model, forced by the same design rainfall and the same 49.5 m river stage boundary, independently represented overland flow and floodplain inundation as shown in Figure 11. Because no SWMM discharge is transferred to HEC-RAS 2D, the two models are independent, and their comparison provides a cross check of the designed drainage hydraulics against a physically distinct overland flow representation.

Simulation results indicate that the optimized drainage system effectively conveys stormwater and maintains hydraulic stability during the design rainfall event, even when river water levels are at the design HFL of 49.5 m. The spatial patterns of water depth and flow velocity obtained from HEC-RAS 2D show that rain-on-grid overland inundation is concentrated in low-lying areas near the outfalls and does not spread widely across the modeled domain. These results indicate that the optimization framework produces designs that are hydraulically stable and practically feasible under the specified combined fluvial–pluvial design scenario.

Although the SWMM optimization enforces a no overflow constraint at network junctions, reaches operating at high relative water depth still indicate where conveyance is most stressed under the compound scenario. Comparing these near capacity SWMM reaches with the rain-on-grid inundation extents from HEC-RAS 2D shows a consistent spatial flood response across the two independent models: zones of elevated in drain water depth align with greater surface water depth near the outfalls in the two dimensional simulation. This agreement supports the optimized design as an inter model consistency check and underscores that river backwater and overland inundation must be explicitly considered in urban drainage planning for riverine cities.

Figure 12 presents a comparison of discharge hydrographs from SWMM and HEC-RAS 2D at the selected outfall. Both models produce similar peak discharges and follow comparable temporal patterns, demonstrating consistent hydraulic behavior between the 1D drainage network simulation and the 2D floodplain model. Minor differences observed during the recession phase are primarily attributable to floodplain storage effects and overland flow processes that are explicitly represented in the 2D simulation but not in the 1D network model. Quantitatively, at this representative outfall the two hydrographs agree closely in peak magnitude, with SWMM and HEC-RAS 2D peaks of about 184 and 186 m³ s?¹ (a peak relative error of −1.0%) and a peak timing difference of roughly 23 mins, giving a coefficient of determination R² of 0.76. The Nash–Sutcliffe efficiency, computed with the HEC-RAS 2D series as the reference, is 0.59, and the discharge volume over the common window differs by about 35%. This moderate efficiency and volume difference arise mainly from the extended recession and floodplain storage behavior resolved by the 2D model but not by the 1D network model. This indicates that the comparison reflects a genuine inter model assessment rather than a by-product of transferring one model's output into the other, because the two models are driven independently by the same rainfall and river stage forcing. These metrics are summarized in Table 5.

Table 5. Quantitative inter model agreement metrics between the SWMM and HEC-RAS 2D discharge hydrographs at the representative outfall (outfall 1, case study 1).

4.5 Discussion

Urban drainage systems in riverine cities face compound flooding driven by the simultaneous occurrence of intense pluvial runoff and elevated fluvial river stages a hazard fundamentally different from conventional single source flooding. In low gradient floodplain cities such as North Guwahati, seasonal Brahmaputra stage rises reduce hydraulic gradients at drainage outfalls, diminish discharge capacity, and in extreme cases induce reverse flow into the drainage network. This phenomenon affects rapidly urbanizing riverine cities across developing countries, yet conventional drainage design standards and optimization frameworks do not provide explicit mechanisms for incorporating river backflow constraints. The rank-sequential SWMM simulation–optimization framework developed in this study addresses this gap directly. By formulating channel width and depth as decision variables within a constrained optimization problem and solving it through a rank-sequential, SWMM driven constraint evaluation strategy, the framework simultaneously satisfies hydraulic feasibility constraints, hierarchical network capacity requirements, and river backflow safety conditions at outfall nodes. The present framework reports its full computational cost transparently: the Case Study 1 (Ghorajan) network of 429 channel segments (858 decision variables) was optimized in 11.7 h over 3,156 SWMM evaluations, and the Case Study 2 (Bipinjan) network of 162 channel segments (324 decision variables) in 1.5 h over 1,056 evaluations, unlike surrogate assisted methods that often exclude training data generation and validation overhead from their reported runtimes. Reported runtimes for evolutionary algorithms such as NSGA II for example, 15.6 h for 12,000 evaluations on a 19 pipe network (Lin et al., 2020) are cited here only as indicative context from the literature and not as a controlled head to head benchmark, because such studies differ from the present work in network size, computing hardware, software implementation, and optimization objectives. Expressed per channel segment, the rank-sequential search required only about seven SWMM evaluations per conduit in both case studies, compared with several hundred evaluations per pipe implied by population based multi-objective algorithms; this gap is largely structural, since evolutionary methods evolve an entire population toward a Pareto front whereas the present method tests only a small set of feasible depth–width combinations at each segment. A rigorous speed comparison would require executing these algorithms on the same networks and hardware, which is beyond the scope of this study; the runtimes reported here are therefore intended to demonstrate the tractability of the proposed framework on large real world networks rather than to claim superiority over any specific algorithm.

The optimized drainage networks for Ghorajan and Bipinjan watersheds exhibit hydraulically consistent and geometrically compact characteristics. Approximately 82% of the total network length (105.32 km of 128.33 km) uses cross sectional areas smaller than 15 m², with larger sections concentrated near downstream trunk channels and outfalls a pattern directly reflecting flow accumulation and the influence of Brahmaputra backwater near outfall zones. Channel utilization analysis shows that 70.2% of the network operates within the 61–95% fill range, confirming that the design avoids both gross oversizing and dangerous under sizing. The hierarchical ranking system, which increments drain rank at every junction regardless of tributary rank, unlike the Strahler scheme, enforces strict monotonic downstream capacity growth, eliminates hydraulically infeasible candidate solutions early in the search process, and substantially reduces computational overhead. Post optimization, road filling recommendations derived from FABDEM elevation data reveal significant spatial variability: Ghorajan requires 35.46 km of road network to be raised by more than 4 m, reflecting its low lying wetland influenced terrain, while Bipinjan requires no filling exceeding 4 m due to relatively higher natural ground elevations. An independent HEC-RAS 2D rain-on-grid cross check under the same design storm and river stage boundary showed good agreement with the SWMM outfall hydrographs, with localized inundation near outfall zones identifying critical monitoring areas for future adaptive management.

The spatial distribution of the optimized designs can be explained mechanistically by the interplay of terrain, flow convergence, and the imposed constraints. First, terrain exerts the primary control. The low lying, wetland influenced Ghorajan catchment presents shallow natural gradients and allows Brahmaputra backwater to intrude farther inland; consequently, larger downstream cross sections concentrate near outfalls, and road raising is extensive about 26.78 km of road network falls in the 4–5 m fill category and a further 8.68 km requires more than 5 m of fill, giving 35.46 km needing more than 4 m overall (26.78 km in the 4–5 m class plus 8.68 km above 5 m). By contrast, the higher, better-drained ground of Bipinjan produces steeper conveyance gradients: most of its road network lies in the 0–1 m fill band (14.18 km), and no sections require fills exceeding 4 m. The planned road level of 51.0 m used for Effective Filling calculations sits just below the historical maximum Brahmaputra stage (51.46 m), so the fill map is also a statement of the protection envelope adopted for the design scenario. Second, flow convergence characteristics shape the size hierarchy. Because the ranking scheme increments capacity at every junction, cross sectional area grows monotonically along flow accumulation paths: approximately 49.78 km of the network remains in the smallest class (< 5 m²), and approximately 82% of the network length stays below 15 m², while the few large sections cluster on high order trunk reaches near outfalls where discharge converges and backwater is strongest. Third, the constraints determine how each segment meets its demand. The longitudinal slope cap ( ≤ 1/2000, i.e. 0.0005 m/m) prevents the optimizer from steepening channels, so additional capacity is achieved by widening and deepening rather than by increasing slope, keeping peak velocities within the permissible range for concrete lined channels ( ≤ 3 m s?¹) and avoiding scour. The no overflow, freeboard, and fill ratio constraints together yield the observed 61–95% utilization band for about 70% of the network, avoiding both oversizing and unsafe undersizing; and the downstream not smaller than upstream rule enforces compact, monotonic sizing while pruning infeasible candidates early.

From a project feasibility standpoint, these same features make the designs actionable for municipal planning, while also clarifying their limits. Alignment of drains along the existing road network reduces land acquisition and conflicts with buildings; compact cross sections and moderate velocities limit excavation and lining stress; and the Effective Filling maps translate the hydraulic design into concrete road raising works that local agencies can prioritize by depth class. At the same time, feasibility is conditional: FABDEM derived fills are planning level values (± 1–3 m vertical uncertainty) that must be refined with ground survey before construction; the designs remain gravity based within the adopted protection envelope (road/plinth levels above the design river stage of 49.5 m) and would require active measures (pumps, gated or flap outfalls) if river stage exceeds those levels or if sustained rainfall outpaces the reduced gravity discharge; and the volume only objective does not yet include lining, spoil disposal, or full construction cost, so a subsequent detailed costing step is needed before tendering. In short, the framework is intended as a computationally tractable master planning tool for compound flood aware open drain sizing, not as a ready to construct bill of quantities.

To position the proposed framework relative to existing approaches, Table 6 provides an indicative comparison with representative simulation–optimization studies. The comparison is not like for like: most published NSGA II and surrogate assisted applications target closed pipe networks or LID/storage placement without river backflow in the optimization loop, whereas this study optimizes open channel geometry under an explicit elevated river stage boundary. Within that literature context, the most direct quantitative contrast is computational effort per network element: the rank-sequential search required about seven SWMM evaluations per conduit (3,156 runs for 429 Ghorajan segments; 1,056 runs for 162 Bipinjan segments), whereas population based NSGA II applications typically require of the order of 104 evaluations in total (e.g., 12,000 evaluations for a 19 pipe network in Lin et al., 2020, i.e. roughly 630 evaluations per pipe) and frequently depend on search space reduction pre processing that eliminates a large fraction of the decision variables to remain tractable (Ngamalieu-Nengoue et al., 2019). The principal advantage of the present method is therefore tractability on large real networks (591 conduits across the two case studies) together with explicit handling of river backflow during optimization. Its principal limitation, relative to multi-objective evolutionary methods, is that it returns a single constraint feasible, volume efficient design rather than a full Pareto front of cost–performance tradeoffs, and it is not intended to replace metaheuristics where a diverse trade off set is the goal. As noted above, these figures differ in network size, hardware, and objectives and are therefore indicative context rather than a controlled head-to-head benchmark.

Table 6. Indicative comparison of the proposed rank-sequential framework with representative simulation–optimization approaches for urban drainage design.

Quantitative entries are taken from the respective studies and represent indicative literature context rather than a controlled, same hardware benchmark.

Several limitations of this study warrant acknowledgment and point toward important directions for future research. The optimization is based on a single deterministic compound flood design scenario (5 year design storm and fixed river stage of 49.5 m). This scenario-based formulation does not quantify the joint exceedance probability of rainfall and river stage, nor does it explore a full suite of alternative rainfall–stage combinations or spatial rainfall variability. Climate change is projected to intensify both rainfall extremes and Brahmaputra flood magnitudes, meaning that the current design capacities may require upward revision under future scenarios. Furthermore, the flood frequency analysis is based on the 1997–2016 annual maximum stage record and does not include the more recent extreme floods of 2020 and 2022; extending the record with the latest CWC observations would refine the estimated design water levels, especially for the higher return periods. Moreover, the adopted design scenario represents a short duration pluvial event under a fixed elevated river stage. Gravity drainage remains effective as long as the river stage stays below the raised road and plinth protection levels; however, for the more extreme condition in which the river stage exceeds these levels (approaching the historical maximum of 51.46 m), or when sustained rainfall exceeds the reduced gravity discharge available at the permissible head, active measures such as pumping stations, gated or flap outfalls, and raised outfall levels would be required. Their integration into the optimization framework is an important direction for future work. It is also emphasized that the SWMM–HEC-RAS 2D comparison is an inter model consistency assessment carried out at a single representative outfall (Outfall 1, Case Study 1): because both models are driven by the same prescribed design rainfall and river stage forcing rather than by independent observed data (no observed discharge, gauge, or flood mark records were available), the agreement should be interpreted as an independent inter model cross check rather than a real world validation. Extending the assessment to all outfalls and typical waterlogging points, and validating against observed flood marks or community reported inundation (e.g., Hossain et al., 2026), are identified as important directions for future work. Parameter uncertainty including Manning's roughness, infiltration rates, and sub catchment characteristics is not explicitly treated, and stochastic or robust optimization approaches would strengthen design confidence. Furthermore, the road filling requirements are derived from the FABDEM global DEM (~30 m), which was not validated locally against ground survey benchmarks; its vertical error (approximately 1.12 m mean absolute error in built up areas and up to about 2.9 m in vegetated or wetland terrain; Hawker et al., 2022) propagates directly into the Effective Filling estimates, so the recommended fill heights should be confirmed with RTK GPS, total station, or LiDAR survey prior to construction. The HEC-RAS 2D cross check was conducted for representative outfall conditions; moreover, although the designed channel cross sections were burned into the FABDEM derived terrain with local mesh refinement, the 30 m base resolution of FABDEM cannot resolve the fine (1–3 m) channel hydraulics as precisely as the 1D SWMM model, so the 2D simulation is best interpreted as an independent overland flow cross check rather than a substitute for the 1D drainage representation. Fully dynamic two way coupling between the drainage network and the floodplain–for example using the native pipe network Urban Modeling capability introduced in HEC-RAS 6.7/7.0–is identified as a valuable future direction that would better capture feedback effects such as floodplain storage attenuating peak flows or backwater propagating upstream into the network. In addition, the optimization objective minimizes total geometric channel volume as a preliminary proxy for excavation and material requirements and does not represent a full multi component construction cost; lining, road filling, spoil disposal, and ancillary works are therefore assessed outside the objective function. Importantly, the SWMM model was not calibrated or validated against observed discharge or water level data; the reported designs are therefore conditional on the adopted parameterization and boundary scenario. Despite these limitations, the rank-sequential SWMM simulation–optimization framework built entirely on open source tools (SWMM, R) and freely available data (FABDEM, OpenStreetMap) provides a computationally tractable, physically transparent, and practically implementable approach to compound flood aware drainage design under the adopted scenario, and is replicable across rapidly urbanizing riverine cities in data scarce developing regions.

5 Conclusions

This study presents a rank-sequential SWMM simulation–optimization framework for the design of open urban drainage systems under a specified compound rainfall–river stage scenario, demonstrated on the Ghorajan and Bipinjan watersheds of North Guwahati on the Brahmaputra floodplain. Its core contribution is an integrated, constraint guided design workflow rather than a new metaheuristic: open channel, road aligned geometries (invert, width, and depth) are optimized under an explicit elevated river stage boundary so that outfall submergence and reverse flow are design conditions, not post hoc checks; a hierarchical ranking scheme that increments capacity at every junction enforces monotonic downstream growth and keeps the search tractable (~7 SWMM evaluations per conduit); and a post optimization Effective Filling step links the hydraulic design to road raising requirements. The design boundary pairs a 5-year rainfall event with a fixed river stage of 49.5 m and is interpreted as a scenario-based compound flood stress condition, not a joint probability design. The objective minimizes total geometric channel volume as a preliminary excavation proxy rather than a full construction cost.

The optimized networks are hydraulically consistent and geometrically compact. About 82% of the network length stays below 15 m², with larger sections concentrated on trunk reaches near outfalls where flow converges and Brahmaputra backwater is strongest; about 70% of channels operate in the 61–95% fill band, indicating efficient utilization without gross oversizing. Terrain explains the contrast between catchments: low-lying Ghorajan requires 35.46 km of road raising above 4 m, whereas higher ground Bipinjan needs none. An independent HEC-RAS 2D rain-on-grid cross check forced by the same rainfall and river stage boundary showed close peak agreement with the SWMM outfall hydrograph (peak relative error about −1%), supporting inter model consistency rather than claiming real world validation. Within the adopted protection envelope, gravity drainage reduces reliance on pumps and gates; active interventions would be needed only if the river stage exceeds the raised road and plinth levels (approaching the historical maximum of 51.46 m) or if sustained rainfall outpaces the reduced gravity discharge.

Several limits define the innovation boundary and the next steps. The framework returns a single constraint feasible, volume efficient design rather than a Pareto front; FABDEM derived fill heights are planning level values that inherit DEM vertical uncertainty and require ground survey before construction; the SWMM model was not calibrated against observed flows; and the HEC-RAS comparison covers one representative outfall under shared forcing. Future work should extend to multi scenario and joint probability compound events, climate change projections, observation based validation (e.g., flood marks), local DEM correction, full multi component costing, and where needed dynamic two way network floodplain coupling (including native HEC-RAS Urban Modeling). Within these bounds, the open source, data scarce workflow offers a practically implementable master planning tool for compound flood aware open drain design in rapidly urbanizing riverine cities, consistent with the objectives of Sustainable Development Goal 11.

Generative AI statement

The author(s) declared that Generative AI was used in the creation of this manuscript. During the preparation of this work, the authors used Grammarly, QuillBot, and OpenAI's ChatGPT to check grammar and correct sentences. Additionally, the authors employed the Turnitin plagiarism detection service to identify and prevent any instances of plagiarism within the manuscript. Following the use of these tools and services, the authors thoroughly reviewed and edited the content as needed and take full responsibility for the content of the publication.

Any alternative text (alt text) provided alongside figures in this article has been generated by Frontiers with the support of artificial intelligence and reasonable efforts have been made to ensure accuracy, including review by the authors wherever possible. If you identify any issues, please contact us.

Publisher's note

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.

Footnotes

Edited by: Vikram Kumar, Govt. of Bihar, India

Reviewed by: Pan Wu, Sun Yat-sen University, China

Md Shahadat Hossain, Institute of Water Modeling, Bangladesh