Optimization of detention ponds for urban stormwater runoff and pollution control in multiple catchments system with analytical probabilistic models and particle swarm Open Access

Urban stormwater has been identified as the second most priority pollutant and a major source of impairment to rivers, lakes, and estuaries (Masoner et al. 2019; Fuchte et al. 2022; Spence et al. 2023; Guo et al. 2024). Detention ponds are stormwater management systems that treat and control urban stormwater (Oxley & Mays 2014; Banihabib et al. 2015; Cavadini et al. 2024; Pirone et al. 2024). Carpenter et al. (2014) evaluated the performance of retrofitted detention ponds and found removal efficiencies of 90, 84, and 42% for total suspended solids (TSSs), ammonia-nitrogen, and zinc respectively. Baird et al. (2020) monitored two ponds concerning their ability for stormwater volume reduction, peak flow mitigation, and improvement in water quality. Results indicated a volume reduction of 60 and 51% for the two ponds and peak flow reductions of 99%. Furthermore, more than 30% reduction in the concentrations of TSS, total phosphorus, and dissolved nitrogen species was observed. Guo (2009) retrofitted a flood control detention pond to also serve as a stormwater quality control pond. Three-level outlets including water quality release in 12–48 h were proposed. With the help of runoff capture curves, the water design water quality control volume was determined from a pre-selected runoff capture percentage. Yang et al. (2023) presented a model to optimize the pond volume taking the cost, TSS, and catchment peak outflow (CPO) as the objectives. Martijn et al. (2024) used a hybrid Markov decision process to model a stormwater detention pond and urban catchment in order to maximize retention time for pollutant sedimentation while minimizing the duration of emergency overflow in the detention pond. Abduljaleel et al. (2023) proposed a methodology to improve detention ponds runoff and water quality controls to cater for climate change impacts. Many researches have been carried out to determine the effectiveness of detention ponds for flood and water pollution control (Liew et al. 2012; Krajewski et al. 2017; Krivtsov et al. 2020; Suripin et al. 2020; Hosseinzadeh et al. 2023).

Analytical probabilistic models (APMs) are closed-form analytical expressions for system output performance derived from the probability distribution of the systems' input variables. The approach was originally proposed by Benjamin and Conell in 1970 and later refined by many researchers. In the APM, rainfall data are discretized into individual events using a pre-defined minimum storm separation time (MSST). The probability distributions of the input variables (rainfall depth, duration, intensity, and inter-event time) are transformed into the probability distribution of output performance using derived probability theory (Adams & Papa 2000). Guo (2001) assessed the suitability of APM in the design of urban flood control detention ponds alongside the design storm and continuous simulation approaches, results show that the three approaches generated similar results in the prediction of peak flow of various durations from small urban catchments. APM has been extensively used by researchers in urban stormwater management (Dan'azumi et al. 2013a, b; Aldrees & Dan'azumi 2023).

Due to the scarcity of funds and the various competing demands, there is a need to use models capable of not only design, but optimization. Such models could be used for sensitivity analysis to screen the best combinations of designs. APMs of urban stormwater management are amenable to optimization (Aldrees & Dan'azumi 2023). Optimization of detention ponds design as urban stormwater management system could be to maximize the benefits of runoff quantity and/or quality control or minimize the cost. It can also be based on the uncertainty as deterministic or stochastic or based on the control approach as either static or dynamic (Shishegar et al. 2018). Particle swarm optimization (PSO) is a technique that can be applied to optimize flood control systems, including detention facilities (Qi et al. 2021). It is a stochastic optimization algorithm based on social simulation models. The most significant advantage of the PSO algorithm is its relatively simple coding and hence low computational cost (Parsopoulos & Vrahatis 2010).

Despite numerous publications on optimizations of various systems using PSO, few publications in stormwater management use PSO. Linear programming, dynamic programming, and nonlinear programming are some commonly used optimization methods in water resources (Reddy & Kumar 2020) and few research applications could be found in stormwater management. Nasrin (2014) developed an incremental dynamic programming forward recursive algorithm to minimize the pumping requirement and maximize the utilization of the detention storage for the closed-gate period subject to the external river water level of the Hatirjheel Detention Basin in Bangladesh. Limbrunner et al. (2013) applied linear and dynamic programming to optimize the placement and sediment-trapping capabilities of infiltration-based stormwater BMPs (including detention ponds) at the watershed scale. Compared to the genetic algorithm, the result shows that dynamic programming effectively solves the sediment-management optimization problem. Rathnam et al. (2002) applied the dynamic programming to a catchment in Hyderabad, India optimize the design of detention ponds system. Result indicated that the cost of the system can be minimized using the model.

Studies that applied PSO to detention pond design are rare. Kumar & Reddy (2007) derived reservoir operation policies using an elitist mutated PSO algorithm. Similarly, Reddy & Kumar (2009) also used an elitist mutated PSO model that integrates the dynamics associated with the water released from a reservoir to the water utilized by crops at the farm level. The model was applied to Malaprabha Reservoir, India, and decisions on reservoir releases and crop water allocations for 10-day periods for each crop, over a year, could be estimated. Ngo et al. (2016) coupled EPA-SWMM with an improved version of PSO called extraordinary PSO (EPSO) for the optimal design of a detention pond system in Seoul, Korea. The result under the optimized scheme was that the peak water level in the pond and downstream area was much smaller than what used to be obtainable before the scheme.

APM and PSO have been employed in the optimization of pollution control performance of wet detention pond in a tropical urban catchment and results indicated that the PSO model out-performs the APM in terms of computational time. It was also found that the optimum detention time in tropical catchments is shorter than what obtains in temperate regions of the world (Dan'azumi et al. 2013a, b). Also, Shamsudin et al. (2014) developed a PSO model to select the best combination of detention pond's volume and outlet size that gives the minimum cost subject to meeting a certain average annual number of spills. The result showed that the PSO simulation is computationally faster, more accurate, and does not need discretization of outlet size when compared to APM. PSO stands out as one of the best evolutionary multi-objective optimization techniques by many researchers due to its speed and ease in implementation (Gad 2022). Despite the numerous literatures on PSO applications in various fields, literatures in water resources applications are very few and specifically very scarce applications to detention pond design. The advantages of APM + PSO, over other conventional methods, include computational flexibility, ease, speed and ability to conduct sensitivity analysis to screen out best alternative combinations of design. The results predicted by the APM + PSO are more precise as compared to those obtained by exhaustive enumeration using APM alone.

Detention ponds are built in urban areas and therefore occupy valuable lands. In addition to land costs, there are costs associated with the construction, operation, and maintenance of the system. The ponds are expected to treat the urban stormwater to meet environmental regulations before discharge into the receiving water. In a typical urban watershed consisting of multiple sub-catchments, the environmental regulations are normally imposed at the watershed's outfall where the stormwater from the watershed enters into the receiving water body. The objective of the estate developer is to minimize the costs associated with the ponds while satisfying the environmental regulations. Optimization involving a system of detention ponds in a regional watershed, which collectively discharges into a common point, is a multi-objective problem commonly encountered (Behera et al. 1999; Travis & Mays 2008; Lim et al. 2014; Bellu et al. 2016). Due to the nature of the problem and the infinite number of combinations of designs required to get the optimum result, a ‘search technique’ is required. This paper presents the optimization of a detention pond system in a regional watershed, consisting of multiple catchments, which discharge to a common point, using PSO. This paper aims to design individual ponds at the sub-catchments such that the pollution control target at the overall watershed's outlet is met. The major advantage derived from the PSO model is that the model can accommodate many smaller ponds in the system and the optimization can be performed with relative ease compared to other methods. For brevity, three sub-catchments, each with a stormwater detention pond, were employed in this research.

Long-term hourly rainfall data were collected from a rain gauge location station in Larkin, Johor Bahru, on the west coast of Peninsula Malaysia (Station ID 1437116). As different criteria are being used in choosing the MSST (Dunkerley 2008); the data were discretized into individual events using a storm separation time of 6 h based on studies by Guo & Urbonas (2002) and Guo (2002). Rainfall characteristics: (i.e. average rainfall duration, average rainfall depth, average rainfall intensity, and average storm separation time) were derived from the rainfall data. APMs of urban stormwater management developed by Adams & Papa 2000 and Chen & Adams (2005, 2006a) were employed in this study. In order to use the APM; the rainfall characteristics must fit the exponential distribution. Therefore, a goodness-of-fit test was conducted with various probability distributions at a 5% level of significance. The null and the alternative hypotheses are:

• H₀: the data follow exponential distribution;

• H_A: the data do not follow exponential distribution.

The APM parameters: (i.e. inverse of average duration of rainfall event λ (h⁻¹), inverse of average depth of rainfall event ζ (mm⁻¹), inverse of average inter-event time ψ (h⁻¹), and average annual number of rainfall events (θ)) were developed from the rainfall characteristics. These parameters, along with the case study catchment characteristics, were used to determine the runoff and pollution control performances using the PSO.

PSO was employed to design the onsite detention ponds at the sub-catchments such that the overall pollution control target (CP) is met at the minimum cost. The simulation was started by calibrating the PSO parameters (inertia, correction factor, and swarm size). Median values for the inertia, correction factor, and swarm size of 0.4, 1.2, and 45 were selected after the calibration and these values are in line with optimum values quoted in PSO literature where maximum exploration and exploitation capability of the swarm are obtained (Parsopoulos & Vrahatis 2010).

The average annual number of spills in Ponds 1, 2, and 3 were arbitrarily set to be 2, 1, and 3 spills per annum, respectively (Table 2). By this, more stringent runoff control is set in Pond 2 (1 spill per annum) compared to Ponds 1 and 3 (2 and 3 spills per annum, respectively). A situation like this arises when one sub-catchment is considered more important in terms of runoff control than the others due to the presence of strategic properties that need to be protected against flood (Rathnam et al. 2002).

The design variables are the pond's storage volume (S_A), release rate (Ω), and pond depth (h_A). Since the cost of a pond is directly proportional to the pond's storage volume, it is evident that any search procedure that locates the minimum volume also locates the minimum cost and vice-versa. The PSO search was conducted; the release rate was varied while keeping the pond's depth and the average annual number of spills constant. The pond's depth was then varied between a minimum value of 1.0 m and a maximum value of 2.0 m (i.e. 1.0, 1.5, and 2.0 m) (Table 2). The PSO simulation was conducted to obtain the least volume and the corresponding release rate that gives the minimum cost.

The pollution control performance is the product of runoff quantity control and the TSS dynamic settling efficiency (Equation (4)). The runoff quantity control (which is the inverse of the overflow rate) and the TSS dynamic settling efficiency were both related to the detention time. As detention time increases, the runoff quantity control decreases due to the risk of overflow. Conversely, as the detention time increases, the pollution control efficiency increases. A trade-off exists between the runoff quantity control and the TSS dynamic settling efficiency. If the design parameters of storage capacity and release rate are kept constant, the overflow probability will be higher for detention ponds designed for catchments in tropical climates (with heavy and frequent rainfall) compared to detention ponds designed for catchments in arid climates (with little and scarce rainfall). Alternatively, keeping the overflow probability constant, will result in frequent release rates from ponds designed in tropical climates compared to ponds designed in arid climates. The optimum pollution control performance of the detention ponds as a function of both the two parameters was presented in Dan'azumi et al. (2013a, b) and Shamsudin et al. (2014).

Rainfall statistics is necessary for developing APM and PSO models because rainfall is the main input to the detention ponds. Table 3 presents the descriptive statistics of the hourly rainfall depth, duration, intensity, and inter-event time. The station has an average annual number of 169 rainfall events. The highest recorded rainfall depth was 526 mm, the highest duration was 200 h and the highest intensity was 45 mm/h. Even though the values are high, the east coast of the peninsular receives much higher rainfall due to the occurrence of the northeast monsoon. Stations on the west coast are blocked by the main range of Banjaran Titiwangsa, thus affecting the quantity of rainfall they receive (Suhaila & Jemain 2007). These values affect the sizing of the pond as areas having higher rainfall need a larger pond volume.

The APM used herein is based on the exponential distribution of rainfall and its application is only valid if the rainfall data follows the distribution. This is true for catchments in Canada, the USA, and Malaysia (Asia). However, Raimondi et al. (2023), Bacchi et al. (2008) and Becciu & Raimondi (2015) tested other probability distributions for many Italian catchments and found that the Weibull and Weibull distributions better fit the frequency distribution of the rainfall characteristics from the observed data. However, they noted that the benefits of their use in the APM are not justifiable since it would make the integration longer and more complex. In addition, its use only brings little improvement in the accuracy of results. This makes the APM amenable to use in various urban stormwater management systems by many researchers (Raimondi et al. 2023).

The result of the APM parameters is presented in Table 4. The parameters are calculated as the inverse of rainfall characteristics, thus the parameters are higher with lower values of rainfall characteristics and vice-versa.

As mentioned earlier, the PSO model was calibrated and the simulation converged before 100 iterations. Median values for the inertia, correction factor, and swarm size of 0.4, 1.2, and 45 were selected which is in line with Parsopoulos & Vrahatis (2010). The inertia (W) was calibrated using 45 swarms and a correction factor (C) = 1.2. The correction factor (C) was calibrated using 45 swarms and inertia (W) = 0.4. Finally, the number of swarm (N) was calibrated using inertia (W) = 0.4 and C = 1.5. The results of the calibrations are presented in Supplementary material (Tables S1, S2, and S3).

The problem has been formulated in Equation (2). This type of problem is commonly encountered in detention pond systems' design (Adams & Papa 2000; Rathnam et al. 2004). Due to the multi-objective nature of this problem, and the infinite number of combinations of ponds' design parameters required to get the optimum result, a ‘search technique’ is required and the PSO model performed very well. A PSO simulation was conducted using the calibrated PSO parameters described in the previous section.

A situation may arise when there are many sub-catchments and the land costs change from one sub-catchment to another. In such cases, the least-cost design for the ponds and the ponds combination can only be obtained through a search technique of this kind and PSO stands tall amongst others (Poli 2008). Moreover, the combination of APM and PSO model out-performs the APM alone in terms of computational time. It is therefore suggested that in tackling optimization problems of this kind, all pond configurations have to be exhausted and the unit costs have to be properly known in order to obtain the optimum (least) cost.

In this research, the PSO algorithm was used to obtain the least-cost design of detention ponds in small sub-catchments such that the pollution control target at the larger watershed is met. The decision variables are the storage volume, release rate, and pond depth. Results indicate that, at a land cost of RM45/m² and construction/maintenance cost of RM30/m², the least-cost combination was that of deep ponds in all the sub-catchments and this corresponds to a combination that occupies the least land area. However, when the land cost was decreased to RM15/m² while maintaining the construction/maintenance cost, the least-cost combination is that of the shallower ponds in all the catchments. This indicates that the least/optimum cost depends on the two costs relative to one another. In all two cases, the runoff and pollution control performances of the onsite ponds and the area-weighted pollution control at the overall watershed were determined from the PSO simulation. It was observed that the PSO can search for the optimum combinations of the design variables that satisfied both the runoff control at individual sub-catchments and the overall downstream pollution control target at the least cost. Although the present example limits the number of sub-catchments to three for clarity, the model can be applied to any number of sub-catchments within a larger watershed and the various combinations of designs can be obtained with relative ease. The APM is based on the assumption of exponential distribution which is true for Canada, USA (North America), and Malaysia (Southeast Asia). Researchers in Italy (Europe) have also used the exponential distribution and their results were found to be very reliable when compared with results from the continuous simulation. Therefore, the APM/PSO model can be applied to other regions of the world with different climates provided the assumption of exponential distribution is used to describe the rainfall characteristics which was found to be reasonable for many climates of the world. The PSO/APM combination for multiple catchment system is novel. It is recommended that a decision support system that will incorporate meteorological, catchment, and pond characteristics altogether be developed, which eventually can be used for the design of detention ponds. Further research on the use APM/PSO model for real time control of detention pond system is also recommended.

The authors extend their appreciation to Prince Sattam bin Abdulaziz University for funding this research work through the project number (PSAU/2024/01/29617).

This study was funded under Prince Sattam bin Abdulaziz project number (PSAU/2024/01/29617).

S.D., A.A., and S.I.A. conceptualized the study. S.D. carried the analysis, A.A., S.D., and S.I.A. wrote, reviewed, and edited the article.

The study did not involve any human participant .

The study did not involve any animal testing.

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

The authors declare there is no conflict.