Evaluation of hydraulic adequacy of runoff disposal in urban watersheds of rapidly expanding towns

Flooding in city centers has become a major concern all over the world (Edamo et al. 2022a, 2022b, 2022c, 2022d). The towns are rapidly expanding, and as a result, enormous volumes of impermeable surfaces have replaced the natural landscape. The process of urbanization can modify urban hydrological response and negatively affect surface and downstream streams because of the presence of impermeable surfaces (Ukumo et al. 2022a, 2022b, 2022c). In addition, global climate change and the rapid progress of urbanization, the frequent occurrence of flooding disasters and non-point source pollution seriously threaten the sustainable development of modern cities (Yin et al. 2021).

Recent urban flooding incidents have highlighted the challenges related to hydraulic adequacy in several cities around the world. For instance, in 2020, Zhengzhou, China experienced severe flooding after intense rainfall, resulting in significant casualties and infrastructure damage (Edamo et al. 2022a, 2022b, 2022c, 2022d). The city's drainage system was overwhelmed, leading to widespread inundation in the urban center. Another example is Jakarta, Indonesia, which has been grappling with recurrent flooding due to rapid urbanization, inadequate drainage infrastructure, and land subsidence. In 2021, heavy rainfall caused extensive flooding, displacing thousands of residents and disrupting daily life (Ukumo et al. 2022a, 2022b, 2022c). Similarly, in 2022, London, United Kingdom, faced significant flooding as a result of heavy rains, leading to property damage, transportation disruptions, and power outages. These recent events underscore the urgent need for improved hydraulic infrastructure and effective flood management strategies to mitigate the impacts of urban flooding on communities worldwide (Edamo et al. 2022a, 2022b, 2022c, 2022d).

Deep-rooted vegetation removal and changes to the natural drainage network can result in decreased infiltration, greater surface runoff, and maximize massive floods (Seka & Mohammed 2016). In order to reduce urban floods, stormwater drain networks in cities are typically built to effectively collect and transmit surplus surface runoff (Gregersen et al. 2013). However, most of them experience decreased functionality and capacity for transferring runoff flow, and their level of service decreases as a result of degradation in time, improper maintenance, inappropriate design, aging, sedimentation, increase in material roughness, and structural deterioration. Although urbanization and climate change increase runoff volume and peak flow rates, even when a drainage system is functioning, the design capacity of the system is insufficient for extreme events and flood occurrences (Chen et al. 2011).

Metropolitan drainage is an important piece of municipal infrastructure for transferring water away from cities. The goal of minimizing flood consequences is to transfer water as quickly and completely as possible away from urbanized areas (Buta et al. 2020). Every storm drainage system design necessitates the gathering of basic data, knowledge of the project site, and a fundamental grasp of the hydrologic and hydraulic principles and drainage regulations at work. With a combination of insufficient integration of road and urban stormwater drainage infrastructure development and poor management, quite a bit of the area is prone to flooding. According to Burgan (2022) proper runoff estimation and modeling are necessary for urban drainage system management. So evaluating the existing drainage system and runoff response of the urban watershed must reveal the solutions to such challenges in the world, particularly Ethiopia. Due to the various challenges faced during the rainy season, numerous areas in Arba Minch town of Ethiopia experienced flooding, necessitating the implementation of effective solutions. Poor existing drains, as well as their incorrect operation and management, may cause severe floods, resulting in road surface damage and difficulties, as well as stormwater invading some inhabitants' homes. The master plan of Arba Minch Town from 1963 to 1995 shows that the town is highly expanding. Edamo et al. (2022a, 2022b, 2022c, 2022d) indicated that Arba Minch town is growing fast, and it is expected to expand up to the end of Shara Kebele (the small administration unit far from the existing town). According to the municipality office drainage design documents in Arba Minch town, some of the existing drainage structures dated back more than a decade. Furthermore, the capacity is usually reduced by clogging materials (solid wastes dumped from nearby residences) and sediments carried from upstream lands. It needs to check the performance of channels to accommodate and safely pass peak floods. It is common to observe significant depth of flood spreading over the road surfaces of the town.

In a given landscape or location, increased impervious surface can result in lower infiltration and increased runoff (Zhang et al. 2019). Due to development and the consequent increase in runoff, drainage networks that were previously capable of handling significant storm events may no longer be capable of accommodating the runoff, resulting in severe floods, destruction of stormwater structures, and stream bank erosion.

Most researchers in Ethiopia who evaluated the performance of existing drainage systems were rarely concerned with the hydraulic adequacy of drainage systems to dispose runoff in quickly expanding towns (Seka & Mohammed 2016; Jothimani et al. 2020). Despite the rapid expansion of the Arba Minch urban watershed, there exists a critical lack of understanding regarding the hydraulic adequacy of its runoff disposal systems. No prior studies have investigated the existing infrastructure's capacity to handle increased peak flows and runoff volumes generated by ongoing development.

Several researchers have explored the hydraulic adequacy of urban watersheds to dispose of runoff, shedding light on different aspects of the problem. For example, Bibi et al. (2023) conducted a study in a metropolitan area, utilizing a hydrological model to assess the impact of land use changes on the hydraulic capacity of stormwater management systems. Their work focused on evaluating the effectiveness of different drainage infrastructure configurations in mitigating flooding risks. In a similar vein, Jothimani et al. (2020) investigated the performance of low-impact development practices in urban watersheds using a combination of hydrological and hydraulic models. Their research aimed to evaluate the effectiveness of green infrastructure elements, such as bio-retention basins and permeable pavements, in reducing peak flows and enhancing the hydraulic adequacy of runoff disposal systems.

While these studies contribute valuable insights, there are still some shortcomings in the existing literature. Firstly, there is a need for more comprehensive investigations that consider the combined effects of hourly peak rainfall and urbanization on the hydraulic adequacy of urban watersheds. Additionally, the majority of previous studies have focused on case studies, limiting the generalizability of their findings.

This paper aims to address these gaps by providing a comprehensive evaluation of the hydraulic adequacy of urban watersheds to dispose of runoff, considering the influence of hourly peak rainfall and urbanization expansion. We utilize an integrated modeling approach that combines hydrological and hydraulic simulations, taking into account the specific characteristics of the study area. By doing so, we aim to provide novel insights into the performance of stormwater management systems and identify strategies for improving the hydraulic adequacy of urban watersheds in a more holistic and generalized manner.

The Storm Water Management Model (SWMM) was carefully chosen to simulate urban flooding in this study since it is a dynamic hydrologic-hydraulic model that can simulate peak runoff and flooding volume. The dynamic flood routing method was best for large drainage networks and accounts for the theory of unsteady flow in an open channel and the Green-Ampt equation suitable to predict the infiltration rate because it is based on Darcy's Law and requires homogeneous characteristics soil types (Bibi & Kara 2023). Hence dynamic flood routing and Green-Ampt equation are chosen for this study.

Calibration and validation, based on measured flow, are essential steps to improve the accuracy of the results. Hence, this research incorporates flow measurement at specific locations to calibrate and validate the model parameters, ensuring accurate output from the model. Additionally, hourly rainfall data was used to enhance the precision of the estimation as it is recommended by developers (Rossman & Huber 2016). Therefore, this study plays a significant role to manage urban drainage systems of rapidly expanding towns.

Mean (M), Standard Error (SE), Coefficient of Variation (CV), Median (MD), Standard Deviation (SD), Skewness (SK), Minimum (Min.), Maximum (Max.), and Confidence Level (95.0%) (CL) value of rainfall used is shown Table 1.

The geologic units in the rift valley region are mostly the product of tertiary volcanic activity. The entire rift valleys are defined as genesis grading in metamorphic granites, ignimbrites (consolidated hot-ash flows), and granodiorites with ancient basement rocks underpinning them. The western and northwestern Rift Valley escarpments and highlands all contributed to the many cycles of sediments of silts, sands, gravels, pebbles, cobbles, and subsurface formations (Ukumo et al. 2022a, 2022b, 2022c).

Different materials were used in this study. ArcGIS 10.1 was obtained from Agricultural and Natural Resource Sciences Water Irrigation and Energy Development Bureau (ANRS WIEDB) and it was used for catchment delineation and parameter extraction. ERDAS Imagine is used to determine LULC through satellite image classification.

SWMM was downloaded from the website ftp://ftp.epa.gov/epa_ceam/wwwhtml/ceamhome.htm and used for rainfall-runoff simulation. The PCSWMM rainfall-runoff model was used for preparing data for SWMM and for calibration and validation of parameters. Also, it was used for rainfall-runoff simulation and the difference is that PCSWMM uses GIS data directly without converting files into .inp file format. A standard table of experimental values was used to get runoff coefficient values, Manning roughness ‘n’ values for overland flow, open and closed conduits, table of depression storage values, and table of soil characteristics (Morita 2014). This is found in the SWMM reference table (Rossman & Huber 2016).

Notch is a device used for flow measurement on conduits. V-notch with 60-degree inclination was selected for flow measurement. It was made depending on the dimension of selected channel and used for flow measurement.

For this investigation, information and data collection were obtained via two sources, which include primary and secondary sources. DEM 12.5 m by 12.5 m was found from Alaska Satellite Facility (ASF) and used for sub-catchment delineation, flow direction, and slope of each sub-catchment. Satellite Image was found from Landsat.usgs.gov and supervised image classification applied for extracting LULC data.

Hourly rainfall data was found from Arba Minch farm station and used for rainfall-runoff simulation. Coordinates data was found from field survey and used as a pour point in watersheds delineation and to determine node invert elevation.

Map was found from Arba Minch Town Municipality office and used to identify outlet drainages and dividing areas. Channel geometry and dimensions was found through field survey and from Arba Minch municipality office, then it can be used for SWMM drainage parameters. All drainage channel geometry determined from municipality office is rectangular.

Observed flow data was found through direct measurement by using notch, from only two selected drainage channels. Only two channels were selected because measurement on many outlets needs special automatic measuring device and also there were restrictions related to time and finance for this investigation. It was used for calibration and validation of primary simulated runoff result. Channels are selected depending on ease of access for measurement and similarity of channels by geometry, construction material and lining (all are concrete lined). Measurement is taken for 15 events and rainfall intensity on each event is determined from Arba Minch farm station.

Notch is suitable for measuring flow on drainage channels because flow on drainage channel is very small. Notch is a structure used to measure flow in open channels and it is similar to weir in purpose but the only difference is the material used to construct the structures. Weir is a concrete or masonry structure while notch is generally made of metallic plate, and notch is smaller in size than weir (Niyonkuru et al. 2018). There are different types of notches including rectangular, triangular, and trapezoidal. Triangular notch is used in cases of small discharge and is best to measure discharge in an open channel with highest accuracy when measuring flowrate (usually ±2%), (Rossman & Huber 2016). A coefficient of discharge for a triangular weir or notch is fairly constant for all the heads. On the other hand, for a rectangular weir or notch the shape of the nappe is affected by the head and therefore the coefficient of discharge varies with the head.

Additionally, ventilation of V-notch is not necessary because the crest length of V-notch is equal to zero, so the occurrence of negative pressure was negligible. Hence triangular notch with angle of 60 degrees is chosen for flow measurement in the selected drainage system.

Hence it is good to take minimum value for determining the height of weir from the bottom of the channel to the crest, to get advantage for measuring discharge during low flow in the channel.

The dimensions of the designed weir plate such as width of channel (b), depth of the channel (D), height of the channel (H), and the perimeter (P) of the channel are described in Table 2.

The Stormwater Management Model (SWMM) by the Environmental Protection Agency (EPA) is a dynamic rainfall-runoff simulation model used for a single event or long-term (continuous) simulation of runoff quantity and quality from most metropolitan regions (Rossman & Huber 2016). It is one of the distributed, conceptual, event parameter models created in the 1970s by the United States EPA. SWMM can model yearly or time series runoff as well as single event runoff and may accommodate geographic variability in rainfall distribution, catchment parameters such as LULC, soil character, and topographic factors like slope.

It provides an integrated environment for modifying data and viewing simulation results in various formats. Because it is in the public domain, it is freely available. The SWMM approach is widely adaptable, making it the most popular of all accessible urban runoff models (Piazza & Ursino 2023). SWMM was validated in our country for several investigators, as described in the literature; the EPA stormwater management model was chosen among various semi-distributed models.

Bibi et al. (2023) employed a comprehensive approach to assess the town's drainage system's ability to handle runoff. They combined Geographic Information Systems (GIS) analysis for LULC and infrastructure mapping, hydrological modeling to simulate runoff generation, and hydraulic modeling to evaluate the capacity of the drainage network. Data on land cover, topography, rainfall patterns, and existing drainage infrastructure were incorporated to build a detailed model of the urban watershed. The model's accuracy and reliability were ensured through calibration and testing using historical rainfall and runoff data. This multi-faceted approach provides valuable insights into the town's preparedness for managing stormwater runoff, especially considering the challenges posed by rapid expansion.

SWMM's runoff component is based on a network of sub-catchment regions that receive precipitation and create runoff and pollutant loads (Rossman & Huber 2016). SWMM's routing section transfers runoff through a network of pipelines, channels, storage/treatment devices, pumps, and regulators. During a simulation period comprised of numerous time steps, SWMM tracks the quantity and quality of runoff generated within each sub-catchment, as well as the flow velocity, flow depth, and water quality in each pipe and channel.

Rain gauges and sub-catchments are the primary items used to model the rainfall/runoff process. A network of nodes and links is used to model the conveyance element of the drainage system. Nodes are basic junctions, flow dividers, storage units, or outfalls represented by points. Conduits (pipes and channels), pumps, or flow regulators (orifices, weirs, or outlets) connect nodes via links. Finally, curves, time series, time patterns, and control rules are utilized to characterize the inflows and operating behavior of the many physical objects in a SWMM model. SWMM objects include rain gauges, sub-catchments, junctions, dividers, conduits, weirs, outfalls, orifices, storage units, and pumps.

Equations (4) and (6) (continuity and Manning's) are basic equations which SWMM uses to compute surface runoff (Rossman & Huber 2016). Equations (5) and (6) are dealing with the watershed and not with the drainage channel.

This method solves the continuity equation along with a simplified form of momentum equation in each conduit. It allows flow area to vary both spatially and temporally within a conduit. However this form of routing cannot account for backwater effects, entrance/exit losses, flow reversal, or pressurized flow, and is also restricted dendritic network layouts (Rossman & Huber 2016).

It takes channel storage, backwater, entrance/exit losses, flow reversal, and pressurized flow into account. It may be used for any general network configuration, even those with multiple downstream diversion loops, because it ties together the solution for both water levels at nodes and flow in conduits. Different investigators choose dynamic wave routing for investigation and prove most suitable (Recanatesi et al. 2017; Bibi & Kara 2023). Hence the dynamic wave routing approach has been chosen for this inquiry.

All sub-catchment physical properties are intimately related to its geometrical shape and topographical condition. Physical parameters contain size, width, and slope, which are all directly related to the geometric shape and topographic aspects of each sub-catchment, and are crucial inputs for rainfall-runoff simulation in SWMM.

The geometry of each sub-catchment is calculated using GIS or using SWMM utilizing automatic lengthening. The area of a drainage channel is defined by its depth and width. The depth and width established by the municipality office range between 0.6 and 1.5 m and 0.7 and 2 m, respectively. Furthermore, the length of the drainage channel from node to node established by field survey ranges from 3 to 1,700 m, and the total length of the drainage channel across the town is 78.8 km as of the beginning of 2020.

The slope raster was created in ArcGIS using the DEM. The average slope for individual sub-catchments was added as an attribute to the sub-catchments shape file using ArcGIS's ‘Zonal Statistics’ tool. The drainage channel slope is governed by node elevation and ranges from 0.000035 to 2.7%. Table 4 shows the slope of several drainage channels.

The SWMM handbook was used to identify the experimental values of hydrological parameters. These include the impervious fraction percentage, soil characteristics, Manning's roughness (n), and depression storage. All experimental values in these tables were generated based on the land cover types in the urban region, which were retrieved from the catchment's remote sensing pictures. The categorized raster image was converted into a polygon shape using ArcGIS. This polygon contains LULC subareas of various sorts. Weighting the average runoff coefficients of all LULC by the entire area yields the impervious fraction of each polygon. The soil parameters are determined by the selected loss method, Green-Ampt or Hortons. The selection of loss model depends on the available data.

Different approaches are used in SWMM to simulate the runoff processes for pervious and impermeable surfaces. In addition, several model parameters are estimated based on the imperviousness of sub-catchments (Piazza & Ursino 2023). As a result, imperviousness evaluation results are very important in hydrological parameter estimating work. The imperviousness of the urban surface is strongly connected to the type of land cover.

Classification is the process of grouping pixels from remotely sensed images into groups with similar properties (Dero et al. 2021). This could be accomplished using either supervised or unsupervised methods. Supervised Classification (SC) occurs when pixel classes are specified by the user by identifying known classification sites (i.e., training sites). The software performs Unsupervised Classification (UC) by categorizing pixels into a predetermined number of statistical clusters. It is frequently done when the researcher has minimal expertise of the subject under examination. When compared to SC pictures, UC produces a ‘noisy’ image. SC, on the other hand, can be problematic in circumstances of human error and unfamiliarity with the studied area. In theory, the SC approach is the best classifier (Ayele et al. 2022). Hence supervised image classification is selected for this investigation.

Supervised categorization generates spectral signatures from user-specified locations. One way is to assign a pixel to the class with the highest likelihood of resemblance, i.e., Maximum Likelihood (ML). Sentinel-2 photos were originally recommended for use. Sentinel-2 photos obtained from Earth Explorer (http://earthexplorer.usgs.gov) in 2019 G.C. ERDAS IMAGINE 2014 software was used to pre-process the image. The preprocessing of satellite images included layer stacking and the creation of a composite band before classification (Andualem & Gebremariam 2015). Because it can be maintained by the user based on the real LULC information of the area, a supervised picture classification approach was utilized.

Supervised categorization entails assigning colors to indicate different types of land use and land cover depending on the raster choice (band compositions) chosen and the coordinates collected on the real land uses. Coordinates taken from actual areas of various land uses can also be supplied to identify the land use type of that spot. Many samples were collected (the technique is known as sampling) by circling the points and colors denoting land usage. These were given names like roof, asphalt, and bare dirt, and were colored with the signature editor tool in ERDAS Imagine. In general, the process consisted of: training sites based on color interpretation and coordinate points representing land use types, training samples and editing signature (assigning names and colors) to the identified LULC categories, ordering ERDAS imagine to classify the image with supervised image classification method based on land use/land cover representation of samples, and finally converting the classified raster image to polygon on Arc-GIS window. Additional polygons with similar LULC classes are merged into a single polygon representing the given land use and LULC. This categorized map (shape file) was created and separated into research area sub-sections.

It is compulsory to aggregate lands in different land uses into major categories based on the existing LULC character of the area. The existing land uses were aggregated into five main categories. The aggregation was mainly based on their impervious character or runoff coefficient values of LULC categories.

Asphalts are road pavement-covered areas used for roads, walkways, town centers, and markets. Cobble refers to any locations in town that are covered by cobble roads, as well as rocky areas or areas covered with gravel. In the town, vegetation comprises regions covered with trees, grass, and gardens. All regions covered with bare earth and roads not covered with cobble or asphalt are considered bare soil. Roof encompasses all regions covered by any form of roof, whether residential, commercial, or public.

Surface roughness values were allocated to each sub-catchment based on the types of surface condition (from LULC categories) to surface roughness values from the SWMM table of reference values for n-impervious and n-pervious, respectively.

The main driving force in rainfall-runoff-quality modeling is precipitation (Edamo et al. 2022a, 2022b, 2022c, 2022d). The quality of stormwater runoff and nonpoint source runoff is intimately related to the precipitation time series. These time series can span from a few seconds for a single event to hundreds of seconds for a multi-year simulation. The rain gauge object in SWMM is used to represent a source of precipitation data. Any number of rain gauges may be used to depict spatial variability in precipitation patterns.

Precipitation data for a specific rain gauge is provided in the form of a user-defined time series or an external data file. It should be noted that precipitation is sometimes used interchangeably with rainfall, but precipitation statistics may also include snowfall. The SWMM program distinguishes between rainfall and snowfall by a user-supplied dividing temperature because both are simply presented as incremental intensities or depths (Rossman & Huber 2016).

In SWMM, employing the Green-Ampt method to estimate average capillary suction, saturated hydraulic conductivity (K), and initial moisture deficit involves considering the soil's characteristics and infiltration properties. The average capillary suction is determined by assessing the soil's capillary rise potential. Saturated hydraulic conductivity (K) is calculated using the Green-Ampt formula, which incorporates soil parameters such as porosity and storativity (Table 5). The initial moisture deficit, expressed as the volume of air to the volume of voids fraction, is derived from the difference between the soil's initial and field capacities. These parameters are integral to modeling water movement and infiltration in urban watersheds within SWMM, aiding in the simulation of stormwater runoff and drainage processes.

Models might be used to aid in urban drainage design for protection against flooding for a certain return period (e.g., five or ten years), or to protect against pollution of receiving waters at a certain frequency (e.g., only one combined sewer overflow per year). SWMM is capable of simulating both single rainfall events as well as long-term time histories (e.g. several years or more) of a continuous precipitation record. In fact, the only distinctions between the two as far as SWMM is concerned is the simulation duration requested by the user and the need to supply meaningful initial conditions when only a single event is simulated (Edamo et al. 2022a, 2022b, 2022c, 2022d).

Continuous simulation offers an excellent result but not the only method for obtaining the frequency of events of interest to quantify or qualify. It has disadvantages of a higher run time and the need for a continuous rainfall record. This has led to the use of a ‘design storm’ or ‘design rainfall’ or ‘design event’ in a single event simulation instead. Of course, this idea long preceded continuous simulation, before the advent of modern computers.

Calibration is the process of adjusting model input parameters to make the modeled hydrograph rationally match the observed hydrographs by using model calibration criteria (Ðukić & Erić 2021). Sensitivity analysis, model calibration, and rainfall_runoff simulation was done for Arba Minch Town. Sensitive parameters used for Arba Minch Town were: slopes, percentage impervious, n-pervious, n-impervious, suction head, hydraulic conductivity, and initial deficit. A superior model PCSWMM with Parameter Estimation (PEST) tool calibration feature or calibration using R programming is used for the calibration of parameters. The most sensitive parameters were given by the model tool which is Sensitivity-based Radio Tuning Calibration (SRTC). The sensitive parameters given by SRTC on sub-catchments are shown on Table 6.

However, the study mostly used the available parameters based on the Green-Ampt infiltration model and data gathering; these were % slope, % impervious, n-impervious, n-pervious, suction head, conductivity, and initial deficit.

To support the SWMM model calibration and validation, monitored rainfall through the basin and recorded stream flow at drainage system was needed. But no flow gauges were installed on Arba Minch Town, therefore two points were selected for measuring with notch. Depth was recorded for 15 events to calibrate sensitive parameters and validate the SWMM model for the study area. Also hourly rainfall data of 15 events parallel to the day that the depth was recorded were determined from Arba Minch farm station and used for model calibration and validation. The observed flow is generated from 11.02 ha and 12.87 ha from site 1 and site 2, respectively. Also the length of drainage channel carying the runoff was 926.08 m and 1,989.33 m from site 1 and site 2, respectively. Now the total coverage of sub-catchments for runoff generation is 1.73% and the total drainage channel coverage is 3.7%, those available in the town.

Now the consistency of the flow monitoring data is assessed as part of the model calibration and validation process. Also, model simulation errors were quantified by measuring the difference between observed and simulated hydrographs. Results of all comparative studies were analyzed with five error functions such as Root Mean Square Error (RMSE), coefficient of determination (R²), the Integral Square Error (ISE), Standard Error of Estimate (SEE), and Simple Least Square Error (SLE) to verify the accuracy of the model.

Now according to Edamo et al. (2022a, 2022b, 2022c, 2022d), if observed and modeled values have a strong optimistic linear correlation, R is close to 1. If R value is exactly 1, this shows a perfect positive fit. The coefficient of determination is useful since it gives the proportion of the variance (fluctuation) of one variable that is predictable from the other variable.

Additionally dividing RMSE by the mean of observed values results in a Root Mean Square Error Dimensionless (RMSED). The RMSE and RMSED were between 0 and infinity. A smaller value (closer to zero) indicates a better model.

Now dividing LSE by squared observed values results in a dimensionless measure of relationship between the observed and measured values. This is Least Squares Error Dimensionless (LSED). The value for both LSE and LSED near to zero implies excellent calibration rating.

Continuity and routing errors are measurements used to assess the balance of computed inflows, outflows, and storage values. The goal is to minimize these errors, aiming for values as close to zero as possible. Continuity error is calculated by dividing the sum of all outflows from the network by the sum of all inflows to the network. This metric provides insights into the amount of water lost or gained during the routing process. A higher continuity error suggests significant water loss or gain during routing, highlighting areas where improvements are needed to ensure accurate water flow management. Routing error, on the other hand, is determined by subtracting the computed outflow from the desired or expected outflow at each node or segment of the network, allowing for the identification and quantification of deviations between the actual and intended water flow paths, helping to pinpoint areas where adjustments or corrections are necessary for effective water flow management.

We examined the hydraulic capacity of runoff disposal systems in an urban watershed of a rapidly expanding town in this study. Our findings provide important insights into the current state of stormwater management infrastructure and suggest potential areas for improvement. In this section, we present and discuss our study's important findings, such as the hydraulic adequacy of existing runoff disposal systems, the identification of possible bottlenecks, and the implications for future development and stormwater management measures.

The area covered by each LULC type and the percentage coverage was presented in Table 7. The information will play a significant role in determining flood risk in Arba Minch Town.

The main goal of image classification was to create a land use/land cover map for determining percentage impervious. Hence percentage impervious is determined for each sub-catchment, and it varies from 0.7 to 91.9%. Some of the percentage impervious for sub-catchments is shown on Table 8.

Model calibration involved the evaluation and adjustment of sensitive parameters in the PCSWMM and SWMM5 models. Ensuring the accurate assessment of input data for a spatially distributed physically based catchment modeling system required significant effort to establish reliability. The Sensitivity-based Radio Tuning Calibration (SRTC) tool provided the latest sensitive parameters. Three specific events, summarized in Table 8, were selected for calibration and validation based on the peak flow observed during those times.

The calibration duration took 2.5 hr for an event in Nov 05 2019 and 5.25 hr for Nov 06, 2019. The validation process acquired 3.75 hr for an event in Nov 07, 2019. This indicates that as the data length increases, the time it takes for calibration also increases. The selected parameters were improved during calibration. The parameters before and after calibration were shown for some of sub-catchments in Tables 9 and 10, respectively.

As indicated in Tables 9 and 10, the percent of impervious is a sensitive parameter in SWMM. Suction head and slope are also sensitive while calibrating the model.

The hydrograph shows the calibration and validation results, the blue graph shows before calibration, red shows observed hydrograph, green shows calibrated hydrograph, and the black shows validated hydrograph.

Short term simulation was considered in this study to obtain a full understanding of the system performance on current conditions. By running the hydrological model with the intensity data, the runoff generation within the area was obtained for 373 sub-catchments. Total runoff volume of 9,494.15*10³ m³ was generated from 373 sub-catchments and peak runoff determined varies from 0.01 to 4.48 m³s⁻¹. Runoff results for some of the sub-catchments are shown in Table 11.

Simulation result for sub-catchments for three-year rainfall data show that total infiltration varies from 950.85 mm to 2,141.3 mm, and total runoff volume varies from 230 m³ to 1,300,760 m³.

The link simulation shows the depth of flow in conduits, in nodes, flooded nodes or links, and water profile of the flow. The simulation results for some of the links are shown in Table 12.

The simulation result for link shows that the time of occurrence varies from 0 to 1,053 days, maximum flow varies from 0.00 to 1.113 m³s⁻¹, maximum full flow varies from 0 to 4.42 m³s⁻¹, maximum velocity varies from 0 to 3.42 m³s⁻¹ and maximum full depth varies from 0 to 1 m. The maximum permissible velocity for concert lined channel is >5 ms⁻¹ [United States Agency for International Development (USAERD)]. Hence, this investigation has maximum velocity lower than the permissible velocity which is safe against erosion.

Node flooding output is an important aspect of assessing the performance and reliability of stormwater management systems. Node flooding happens when a drainage system's capacity is surpassed, causing water to back up and flood in specific spots. It is critical for successful stormwater management and infrastructure planning to understand and accurately predict node floods. The outputs for flooded node are shown in Table 13.

Table 13 shows that some of the nodes in the town were flooded. This is an indication of the existence of poor performance or inadequate drainage system. The simulation status report shows that sections between flooded junctions are surcharged (flooded). Some of the surcharged conduits are shown in Table 14.

In the context of evaluating the hydraulic adequacy of runoff disposal in urban watersheds of rapidly expanding towns, the literature underscores the importance of accurate runoff estimation. Runoff, generated by precipitation events in urban areas, poses a significant challenge in terms of managing stormwater and preventing flooding (Ukumo et al. 2022a, 2022b, 2022c). Various methodologies for runoff estimation, such as the Rational Method, SCS Curve Number method, and distributed hydrological models, have been explored in the literature to assess the capacity of drainage systems in accommodating increasing urbanization (Yin et al. 2021; Bibi et al. 2023). These studies emphasize the need for a comprehensive understanding of local hydrological characteristics, land use patterns, and infrastructure design to ensure the effective and sustainable disposal of runoff in the face of urban expansion.

The evaluation of hydraulic adequacy is pivotal for urban planners and engineers to develop resilient stormwater management strategies in rapidly growing towns, mitigating potential risks associated with inadequate drainage systems (Recanatesi et al. 2017; Yin et al. 2021; Bibi & Kara 2023). Yin et al. (2021) provided a comprehensive review of the construction, assessment, operational, and maintenance aspects of sponge city practices in China, which aim to mitigate urban flooding through sustainable stormwater management. Recanatesi et al. (2017) conducted a case study in a peri-urban watershed in the metropolitan area of Rome, Italy, to assess the effectiveness of stormwater runoff management practices and best management practices (BMPs) in the context of soil sealing. These studies collectively shed light on the challenges and potential solutions for managing urban flooding and ensuring the hydraulic adequacy of runoff disposal in urban areas.

The classification of land use and cover types aids in defining surface qualities such as imperviousness, vegetation cover, and soil infiltration capacity, all of which have a direct influence on stormwater runoff generation and routing (Li et al. 2019). Reliable estimates of runoff volumes, peak flows, and pollutant loads need accurate characterization of these features.

Several studies have looked into how land use and cover classification affect the accuracy of SWMM runoff predictions. For example, Zhang et al. (2019) investigated the impact of several land use and cover classification techniques on SWMM simulations in an urban catchment. SWMM's performance was evaluated using three categorization schemes: the United States Geological Survey (USGS) National Land Cover Database (NLCD), the Soil Conservation Service (SCS) curve number approach, and a high-resolution land use map obtained from remote sensing data. The high-resolution land use map produced the most accurate projections, followed by the NLCD, while the SCS approach produced the least accurate predictions.

Another study by Li et al. (2019) evaluated the impact of land use and cover classification on SWMM simulations in a mixed urban and agricultural catchment. The researchers compared the performance of SWMM using three different land use and cover datasets: the NLCD, a land use map derived from Landsat imagery, and a land use map derived from high-resolution aerial imagery. They found that the high-resolution aerial imagery-based land use map produced the most accurate runoff predictions, followed by the Landsat-based map, while the NLCD resulted in the least accurate results.

These studies emphasize the significance of using reliable and high-resolution land use and cover categorization datasets for SWMM simulations in order to increase runoff prediction accuracy. When compared to coarser datasets like the NLCD, high-resolution datasets obtained from remote sensing technologies, such as aerial imaging and satellite data, provide more specific information about land use and cover types. This greater degree of detail enables a more detailed depiction of surface attributes and, as a result, more accurate runoff predictions.

Using high-resolution land use and cover datasets produced from remote sensing technology increases the accuracy of SWMM simulations when compared to coarser datasets, according to studies. As a result, precise land use and cover classification is critical for dependable stormwater management and planning (Niyonkuru et al. 2018).

It is obvious that percentage impervious is a sub-catchment parameter in SWMM. Investigations indicated that percentage impervious and some other SWMM parameters can be estimated depending on imperviousness of sub-catchments (Adugna et al. 2019; Afrin et al. 2021; Bibi et al. 2023).

The study's findings emphasize the need for assessing the hydraulic adequacy of runoff disposal systems in rapidly developing metropolitan regions. The findings suggest that existing infrastructure may be unable to cope with increased runoff volumes and velocities, potentially resulting in flooding. This highlights the importance of proactive stormwater management system planning and design to handle future urban growth (Ren & Khayatnezhad 2021).

Recent research has shown the need for calibrating SWMM models using observed data and the need to modify model parameters to attain the best fit (Idrissou et al. 2022). Validation with independent data validates the calibrated model's correctness even further. These procedures improve the accuracy of SWMM predictions and aid in stormwater management.

Bibi et al. (2023) conducted a new study on the examination of node flooding in an urban catchment using SWMM. The researchers used SWMM to simulate several rainfall scenarios and then assessed the node flooding output. They investigated the link between rainfall intensity, duration, and node flooding. The study discovered that SWMM successfully anticipated node flooding episodes, and the findings provided useful insights into the drainage system's vulnerability to flooding. This study emphasizes the usefulness of SWMM highlights in assessing and predicting node flooding in metropolitan environments.

The analysis discovered that the town's existing drainage system was unable to handle the increased runoff caused by urbanization. The model simulations demonstrated that the system experienced significant surcharging during high rainfall events, resulting in localized flooding in numerous regions. The researchers pinpointed specific places where hydraulic capacity had been exceeded and offered viable mitigation methods to address the issue (Bibi et al. 2023).

SWMM model software performance must be reviewed in order to decrease the degree of error, extent of correctness, consistency, and adaptability (Niyonkuru et al. 2018). To evaluate the model's performance, a forecast efficiency criterion is required. Because SWMM software is used for both hydrological and hydraulic modeling, evaluating its performance requires subjective and/or objective judgments of the model's simulated behavior's closeness to observed or estimated value.

Bibi et al. (2023) used SWMM to explore the impact of climate change on node flooding. Based on the climate estimates and node flooding output, the researchers simulated future rainfall scenarios. Climate change, they discovered, could greatly increase the frequency and severity of node flooding episodes. To prevent the possible implications of greater node flooding, the study underlined the significance of including climate change considerations into stormwater management planning. Incorporating SWMM in stormwater management planning allows for effective mitigation of flood risks and ensures the reliability of drainage systems. Bibi et al. (2023) focused on the impact of climate change, urbanization, and low-impact development practices on urban flooding.

The presence of flooded nodes can cause poor performance of drainage systems flooded or inadequacy of those drainage systems within those nodes (Oli Emama et al. 2022). Statistical summary reports were available from the model simulation summary report of SWMM.

According to the simulation result, some existing drainage systems show poor performance or inadequacy, hence it is obvious that for historical data (long term simulation) depending on different return period the number of surcharged conduits will exactly increase. This will happen due to increased urbanization results in higher imperviousness and that is responsible for generation of high runoff.

As settlements continue to grow in size, stormwater runoff management becomes increasingly critical (Adugna et al. 2019; Afrin et al. 2021; Bibi et al. 2023). The natural hydrological cycle is altered by urbanization, resulting in increased impervious surfaces and decreased infiltration capacity (Edamo et al. 2022a, 2022b, 2022c, 2022d). This causes increased runoff volume and velocities, which can overwhelm current drainage systems and create flooding. Consequently, determining the hydraulic sufficiency of runoff disposal in urban watersheds is critical for long-term urban development and successful stormwater management.

Moreover, the study reveals the efficacy of advanced modeling tools in determining the hydraulic sufficiency of runoff disposal systems. The researchers were able to accurately replicate the behavior of the urban watershed and pinpoint areas of concern by combining GIS analysis, hydrological modeling, and hydraulic modeling (Edamo et al. 2022a, 2022b, 2022c, 2022d). This method can be used in other fast-growing developing towns to assess drainage systems and guide decision-making processes.

Using SWMM, this investigation assessed the adequacy of drainage structures in Arba Minch town. Primary and secondary data were collected during the assessment. The model was calibrated and validated using 15 occurrences with recorded flow depth on two outlet locations and rainfall data from those events on the same day as the flow depth collected. On PCSWMM, event-based calibration was performed, with two events for calibration and one for validation of the model, with the flow estimated using the parallel recorded depth. LULC maps were identified from Sentinel-2 image and LULC maps of the year 2019 were produced. LULC classification recognized five land use/land cover categories, namely: asphalt, cobble, vegetation, bare soil, and roof. Now, the result shows that 33.49% of the area is covered with highly impervious land cover and among different land uses, bare soil takes the largest percent in the town. Depending on identified LULC data, percentage impervious of the area was calculated for each sub-catchment and varies from 0.7 to 91.9%.

For model calibration, sensitive parameter evaluation and adjusting was done on PCSWMM and for the SWMM5 model. The last sensitive parameters were given by the model tool which is Sensitivity-based Radio Tuning Calibration (SRTC). The overall calibration and validation result on two selected points. Three events were taken into consideration for calibration and validation. The calibration duration took 2.5 h for an event in Nov 05, 2019 and 5.25 h for Nov 06, 2019. The validation process acquired 3.75 h for an event in Nov 07, 2019. Overall, the calibration resulted in a good fit with observed daily flows for the simulation period, according to RMSE, R², ISE, SEE and SLE.

The performance of SWMM model for the area was carried out using Root Mean Square Error (RMSE), and Nash-Sutcliffe or coefficient of determination (R²), the Integral Square Error (ISE), Standard Error of Estimate (SEE), and Simple Least square Error (SLE) value and the results are in limitations RMSE = 0.00102, R² = 0.98, ISE = 5.94, SEE = 0.00072, SLE = 0.00000259 on site one and RMSE = 0.00124, R² = 0.98, ISE = 5.61, SEE = 0.00093, SLE = 0.00000438 on site two which is very good. So, the SWMM is a powerful tool for analyzing the effective urban flood water control and management for the study area and other related towns in the world.

The drainage structures study using SWMM results suggests that some areas of the junction and connections (conduit) were flooded as a result of insufficient hydrological (runoff volume) and hydraulic (size of drainage structures) study. The drainage system is not affected by the slope. Because the velocity within the drainage system was less than 5 m/s, the concrete-lined channel is safe from erosion and siltation; nonetheless, siltation may occur in the drainage system owing to solid waste dumping. 7.46% of the town was flooded due to the inadequate drainage infrastructure. Based on three-year rainfall data, the Arba Minch town catchment generates a total runoff volume of 9,494.15*10³ m³. Peak discharge from 373 sub-catchments ranges from 0.01 to 4.5 m³s⁻¹. According to the Arba Minch town's future development master plan, the town will expand significantly, which will be responsible for the creation of increasing impervious surface. As a result, a huge number of existing drainage channels were predicted to be insufficient in the future to accommodate the runoff generated by the town area. Thorough hydrological and hydraulic study should be performed prior to the building of drainage infrastructure in order to safeguard the environment from the impact of flooding. Furthermore, additional research should be conducted by merging future climate and water quality data with long-term historical data for different return periods.

We would like to thank all institutions and individuals for providing necessary data for this study.

No fund was provided from any source.

Data cannot be made publicly available; readers should contact the corresponding author for details.

The authors declare there is no conflict.