The sustainable development of urbanized areas [1
] should be understood as growth based on the proper usage of natural resources, including water [3
], which is commonly endangered by urbanization itself [6
], population growth, and climate change [4
]. Climate change may be mainly related to floods, droughts, heatwaves, and other threats to human comfort and urban environments caused by increased numbers of rapid and extreme weather events [9
The volume of available water resources may be significantly reduced by anthropogenic pressure caused by water usage by residents, services, and industry. The improper handling of sanitary sewage, combined with increased urbanization, may also affect the availability of water. Thus, the protection and sustainable management of water resources to prevent water shortages are crucial to the sustainable development of urbanized regions.
The increase in the degree of urbanized catchments, related to the construction of living and public buildings, services, roads, pavements, and parking lots, clearly affects the natural water balance of catchment [10
Urbanization changes catchment hydrology and leads to the generation of high-peak runoff flows in a relatively short time. On the other hand, in a natural catchment, a significant part of rainwater infiltrates the soil, recharges the groundwater, and is absorbed or transpired by plants [7
]. In the case of an urbanized catchment with a range of 70–100% of the surface area being sealed, the surface runoff may reach 55% of rainfall depth, while evapotranspiration and infiltration may reach 30% and 15% of the surface water, respectively [13
]. By contrast, in natural catchments evapotranspiration reaches 40%, while infiltration supplies the groundwater to approx. 50% of the rainfall depth. Surface runoff in natural catchments is significantly lower and reaches a level of only 10% of the precipitation [9
However, the development or construction of new or existing centralized stormwater systems for urbanized areas, as a typical and standard reaction to urban development should no longer be treated as feasible [11
]. Thus, an effective source control solution is required to significantly reduce runoff, urban flooding risks, and pollutant discharge to surface water [16
]. The development of urbanized areas is being increasingly supported by low-impact development (LID) urbanistic planning techniques [17
], whose main purpose is urban flooding management through the control of stormwater outflow and weakening of peak runoff flows [22
]. These additional advantages are possible due to the use of numerical modeling applications in LID optimization. Studies have shown that the application of the storm water management model (SWMM) model combined with the genetic algorithm (GA) allows for an increase in LID efficiency and a reduction of application costs [25
]. Sustainable stormwater management systems [12
], the alternative to the traditional stormwater removal, reduce surface runoff and limit flow peaks and flooding by increasing interception, evapotranspiration, and infiltration [15
]. These gains are possible by using plants (green architecture, green roofs [26
]), the retention capabilities of porous materials (green roof fillings), permeable passageway surfaces [27
], or over-ground and underground water reservoirs [29
]. The methods of stormwater management oriented towards increased infiltration of stormwater into the soil utilize classic pavement materials with gaps or materials pervious to water, allowing for a reduction of the runoff volume and an increase in the infiltration ratio [15
]. Additionally, LID applications bring environmental benefits, including improvements in water quality, a decrease in air pollution [33
], and an increase in biodiversity. Green infrastructure is capable of significantly reducing the volume of surface runoff from 50% to 100%, in relation to the catchment characteristics and local precipitation [9
]. The model studied by the LID module confirmed the influence of LID (infiltration ditches, permeable surfaces, and green roofs) on surface runoff reduction [37
]. The presented methods of stormwater management also result in an improvement of the water quality due to the usage of biogens by plants and pollutant adsorption on the surface of the solid phase particles of porous media [9
]. The reduction in the total phosphorus (TP) and total suspended solids(TSS) volumes by green infrastructure was reported to be at a range of 65–100% [9
]. There are also reported social and economic advantages to LID [39
]. The application of damming baffles in stormwater systems is an exemplary implementation of LID to urban water management. Studies by Starzec and Dziopak [42
] showed an increase in retention capacity and a decrease in determined peak flow by 60%, in comparison to traditional stormwater removal systems. In order to determine the efficiency of various LID systems, the control of the volumetric outflow of water is required, i.e., by the application of a flow meter with a wide flow velocity range [43
The reduction of the drinking water demand in residential areas and the decrease in anthropogenic pressure exerted on surface waters by untreated stormwater is possible due to the application of various rainwater harvesting (RWH) systems [44
]. RWH, as a method of interception and storage of rainwater, allows us to obtain non-potable water for domestic purposes, including toilets, laundry, and gardening, reducing the drinking water demand by 60–80% [44
]. Harvested water can be stored in different types of tanks. Studies based on tanks introduced to existing stormwater systems combined with their real-time operational monitoring indicated that in relation to the location and volume of the tank, a reduction of runoff volume by 18–40% was possible [55
]. The application of optimization techniques results in more effective reuse of acquired rainwater and a decrease in the surface runoff volume, which is important for smart city planning and development [56
]. Real-time control techniques can also help in decreasing the flows discharged from quality-oriented combined sewer overflow devices [58
Retention tanks represent important objects in municipal sewerage networks [59
]. The distinct shape of the retention chamber enables us to employ any configuration of outlet devices, which allows us to achieve a constant outflow rate from the tank. Thus far, a similar effect has been achieved in multi-chamber tanks, with a rectangular cross-section of the retention chamber. Despite similar hydraulic efficiency, the placement and manufacturing of a pipe tank are much easier than in the case of a classic rectangular tank, since it can be located more easily, and its interference with the existing network of the underground infrastructure is lower. The currently employed methods of tank dimensioning are largely based on hydrodynamic modeling. Due to the complexity of the modeled phenomena, issues with the continuity of the calculation algorithm can occur. Examples involving the application of hydrodynamic models for the dimensioning of pipe tanks were presented by Kisiel et al. [64
] and Mrowiec [60
]. Graphical methods connected with the numerical solving of differential equations are quite popular, since they permit relatively quick calculation of the tank volume, while also being highly precise. However, other methods were also developed, in which a hydrograph of the tank outflow was schematized using a triangle, rectangle, or trapezium shape [59
]. In turn, a simplified model with a graphical–analytical method was proposed by Szeląg and Kiczko [69
]. However, the obtained results exhibited the limited applicability of the proposed calculation method.
The aim of this paper is to present an advanced graphical–analytical method for pipe tank design, integrated with a comprehensive sensitivity and error dependency analysis. Such a dimensioning method can be used as a complement and support tool in combination with the currently used hydrodynamic models. The assessment of the influence of the inflow hydrograph parameters and the outlet device characteristics on the designed tank volume is important from the point of view of selecting the input parameters for its dimensioning, in order to meet the required overflow and flooding criteria (e.g., overflow and flooding occurrence/periodicity, number of storm overflows per year, and flooding return time). The application of an artificial intelligence method enables us to investigate the influence of the interactions between the hydrograph parameters and the characteristics of outlet devices on the results of the volume calculations, and thus allows us to propose a methodology for reducing these interactions, which is the main novelty of this paper. This objective fits within the issue of sustainable urban stormwater management systems by enhancing the possibility of local retention, enabling the use of the accumulated stormwater (in case of separate storm sewer systems without the presence of sanitary wastewater, which is a common situation in Poland) as well as mitigating local flood occurrences due to the hydraulic surcharge and decrease of the CSOs (combined sewer overflows) of the sewerage system.
The results of the performed analysis confirm that the proposed integrated pipe tank design methodology can be used in engineering practice for the initial estimation of tank volume without the use of the correction module. Using the graphical and analytical methods, it is possible to pre-define the length of the tank chamber and to design the overflow devices. The additional implementation of data-mining methods allows us to detail the simulation results so that they are consistent with the results of the calculations of the length of the reservoir chamber obtained by means of differential equations. However, when designing the tank, special attention should be paid to the exact identification of the inflow hydrograph parameters to the tank, because they have a key impact on its dimensions.
The use of data mining methods in the calculation procedure led to improved error prediction results using the proposed pipe tank design method, as compared to the data obtained by the hydrodynamic model (SWMM).
The conducted analyses indicated that the flow reduction coefficient was an important factor affecting prediction errors related to the retention chamber length. It was indicated that the error increased with the coefficient value.
Reducing the tank length prediction error is significant from the viewpoint of optimizing the solutions applied to stormwater sewerage systems and runoff control, as well as the creation of hybrid systems consisting of sewer system retention and surface retention. This is significant in terms of obtaining the hydraulic retention effect, which is also important for improving the operational conditions of stormwater sewerage systems. This is essential in terms of making decisions on the modernization, reconstruction, or adoption of optimal variants of the stormwater sewerage system being designed.
Taking into account the usefulness to the engineering practice of the obtained results, the development of the proposed pipe tank dimensioning methodology and the possibility of its use for different hydrograph shapes are justified, despite the fact that the hydrograph shapes may differ from synthetic ones on real catchment runoff.