Studying rainfall characteristics affecting low-impact development runoff control measures via numerical simulation

With the acceleration of urbanization, the hydrological cycle has been significantly affected in the form of reduced groundwater recharge, increased runoff and peak, and so on. These changes increase the risk of urban flooding (Leopold 1968; Walsh et al. 2005). Frequent extreme rainfall events in recent years, such as the catastrophic floods in Beijing and Zhengzhou, have highlighted the vulnerability of urban drainage systems (Wu et al. 2017; Zhang et al. 2021). To address this challenge, China has actively promoted the concept of a ‘sponge city’ and established a corresponding evaluation system, in which the runoff control rate is a key indicator. However, the current research on the relationship between runoff control rate and different rainfall characteristics is not in-depth, which limits the accuracy and effectiveness of sponge city planning (Wang et al. 2013; Leng et al. 2020).

Rainfall is the main catalyst of urban flood, and its rainfall intensity, distribution pattern, accumulation and duration play a crucial role in characterizing urban flood dynamics. The temporal distribution of rainfall affects inundation degree, area and peak value, and is crucial for understanding flood process (McRobie et al. 2013). Therefore, the effects of rainfall duration, intensity and type on runoff control rate must be carefully studied. However, current studies have focused on a single type of rainfall, typically using 2 - or 24-h design rainfall as input data to assess the effectiveness of runoff control. This one-size-fits-all approach lacks granularity to account for different rainfall patterns. The effect of rainfall pattern on runoff control has not been fully explored. The rainfall pattern is a key determinant of rainfall characteristics and has great influence on the calculation of runoff control results.

Despite its pivotal role, the impact of rainfall pattern on runoff control effect remains underexplored, as indicated by the limited existing literature. Rainfall pattern, a key determinant of rainfall characteristics, significantly influences runoff control outcome calculations. Scholars have touched on this subject (Parsons & Stone 2006; Luo et al. 2018; Mu et al. 2021). Tama et al. (2023) constructed a model based on W_flow to predict the runoff volume from rainfall and applied it to the estimation of water inflow from Gajah Mungkur reservoir (Wonogiri) in Indonesia; Kencanawati & Maulana (2023) modified a simple hydrological formulation (rational method) based on fieldwork and compared a numerical rainfall model to the relationship model by using the simulation parameters, namely rainfall, infiltration, land use, and stream for hydrological conditions. Thus, the relationship between rainfall and reservoir inflow is predicted and compared to The Hydrologic Engineering Center's-Hydrologic Modeling System (HEC-HMS) calculations; Cacal et al. (2023) utilizes ArcGIS and QGIS, which perform the geospatial analysis and provide the HEC-HMS model's hydrologic modeling inputs, construct a rainfall–runoff simulation model, was simulated to determine the peak flow and amount of water. The above studies address the simulation of runoff from watersheds or reservoirs. For urban runoff control, the current Storm Water Management Model (SWMM) is mainly relied on for simulation and calculation (Luan et al. 2017; Bai et al. 2018), but the model is simplified for the surface, under the condition of large return period, when the pipe network overflow, the pipe network catchment can only simulate the overflow volume of the pipe network nodes, but not simulate the flooding of water from the nodes in the surface after the overflow, and cannot accurately calculate the amount of water that will be accumulated on the surface of the surface to enter the pipe network after the drainage capacity of the pipe network has been restored. Also, the physical mechanism of hydrological model is not clear, and there are more microtopographies in the city. Thus, the hydrological model response to the surface microtopography is not obvious. On account of this, some scholars use the hydrodynamic model to simulate the law of rainfall–runoff. Hou et al. (2017) who examined urban flooding severity under varied peak coefficient scenarios using a two-dimensional hydrodynamic model. Wu et al. (2018) coupled hydrodynamic inundation models to assess low-impact development (LID) efficacy across diverse scenarios, showing distinct control effects based on varying rainfall scenarios. Yang et al. (2020) investigated the response of LID runoff control effect to the design storm return period based on a two-dimensional hydrodynamic model of a coupled pipe network system in 2020, and concluded that the difference of runoff control rate gradually decreases with the increase of return period, and the trend of the decrease of runoff control rate is gradually flattened, but when conducting the study, only the factor of rainfall return period is considered, and the model is in the primary version. The authors consider more rainfall scenarios by using more optimized models and more rainfall parameters in the computational part of the pipe network and LID facilities, with the aim of further quantifying the response law of LID to rainfall. At the same time, the construction of sponge cities will cause land use changes, and such changes will have an impact on the response law of rainfall and runoff processes (Verma et al. 2023; Waikhom et al. 2023), and Chadee et al. (2023) proposed to study the law of runoff characteristics based on localized climate characteristics. While research on the interaction between runoff processes and rainfall patterns exists, there's a dearth of comprehensive understanding, warranting a deeper investigation.

In light of this, a two-dimensional urban rainfall model is utilized to investigate the nuanced relationship between runoff control rates and various rainfall factors. The study concentrates on the coupled pipe network within a community-scale context. By simulating the response patterns of runoff control rates to distinct rainfall factors, the research seeks to enhance our comprehension of runoff control laws. Our research contributes to the vital knowledge base underpinning sponge city planning, particularly the runoff control rate – a cornerstone in designing flood-resilient urban spaces. This research adopts a multifaceted approach, encompassing simulations of rainfall–runoff routing for different return periods and rainfall characteristics. The ensuing sections detail our numerical modeling, study area, parameter calibration, and comprehensive results and discussions.

In conclusion, this study seeks to enhance the understanding of the intricate interplay between rainfall characteristics and the efficacy of runoff control measures. By delving into the multifarious factors influencing runoff control rates, the study aims to provide valuable insights for the ongoing evolution of sponge city initiatives and the concomitant challenges in assessing runoff control efficiency. The runoff control rate is one of the basic data types necessary for government designers to formulate special plans for a sponge city. Sponge city construction is still in the pilot stage, and all units are in the period of continuous learning and exploration. Accurately assessing the runoff control rate under rainfall with different characteristics for the special planning and evaluation of sponge cities is a difficult issue. In this research, therefore, the author used a model to simulate rainfall–runoff routing conditions with storms for return periods of 1a, 2a, 5a, 20a, and 50a under the same rainfall return period (Bayat et al. 2019). The peak coefficients were 0.1, 0.2, 0.4, 0.5, 0.6, 0.8, 0.9, and the rainfall durations are 2, 6, 12, and 24 h.

This section outlines the modeling approach employed for the three LID measures in the study area: permeable pavement, vegetative swale, and rain garden (Qin et al. 2013; Bonneau et al. 2017).

The runoff evolution process of permeable pavement shares similarities with that of conventional road surfaces. However, key parameters such as infiltration rate and Manning coefficient diverge from those of roads. To accurately model permeable pavement, underlying surface parameters are derived from measured data. Runoff processes on the pavement surface are simulated using a two-dimensional SWE, akin to road surfaces.

For vegetative swales and rain gardens, considerations extend beyond Manning and infiltration rate differences relative to green land. These LID measures possess distinct storage depths and overflow ports at their storage termini. The modeling strategy encompasses the use of a finite volume model to address the two-dimensional SWE, capturing runoff dynamics both within and beyond the facility boundaries. Overflow flow is evaluated through the application of the weir flow formula, with the excess runoff routed into the pipe network.

The GAST model, integrating the G–A model, facilitates an in-depth exploration of the interplay between LID measures and rainfall characteristics, unraveling the mechanisms underpinning runoff control effects.

The ensuing sections delve into the specifics of model implementation and parameterization, shedding light on the nuanced interactions between LID measures, runoff dynamics, and infiltration behaviors. This meticulous modeling approach is integral to comprehending the intricate relationships dictating runoff control rates and their sensitivity to various rainfall scenarios.

The model runoff process follows the principle of water balance. For numerical simulation calculations, urban stormwater surface water flows were calculated using dynamic wave methods. Two-dimensional shallow water equations are solved using the Godunov format finite volume method, and the second-order MUSCL method performs spatial interpolation on variable values to improve calculations precision (Simons et al. 2014; Hou et al. 2015). In the control unit, the HLLC approximation Riemann solver is used to calculate the matter and momentum flux on the interface. The bottom slope flux method is used to deal with the problem of non-conservation of momentum caused by complex terrain, that is, the slope source term in a calculation unit is converted into a flux located on the unit boundary (Hou et al. 2013a; b). This method can be well coordinated with the interface flux, which is convenient to reach the full stability condition. Friction is calculated using the semi-implicit method. When solving the problem of wet and dry alternation often encountered in flooding process, based on the proposed hydrostatic reconstruction (Hou et al. 2014; 2019), an accuracy format adaptive method was introduced, that is, under the condition that the water depth at the wet and dry boundaries changes drastically, the second-order format of the algorithm is automatically reduced to the first order to ensure the stability of the calculation, and the two-step Runge–Kutta method is used for time advancement. In order to improve the computational efficiency of high-resolution DEM, the model uses GPU parallel computing technology to achieve high-speed computing. The explicit volume method of Godunov scheme is very suitable for GPU parallel calculation. When solving the pipe network module, the finite difference method is used to discrete the equation and calculate the flow in the drainage-pipe as unsteady flow. The diffusion wave equation can accurately and truly reflect the operation state of the drainage system by calculating the flow in the drainage-pipe and correcting the negative water depth of the rainwater well.

Using the computed results, the NSE is computed as 0.93, and NSE of the other condition is computed as 0.96, as shown in Table 3. This rigorous calibration-validation cycle underscores the precision and reliability of the hydrodynamic model in capturing the interplay between LID measures and rainfall characteristics. The model's adeptness in simulating complex rainfall patterns strengthens its capacity to analyze runoff control effects across diverse scenarios, facilitating a comprehensive understanding of urban flood management within the context of sponge cities.

The simulation conducted in this study featured a model boundary constrained by wall boundaries, with no inflow from surrounding areas. A Courant number of 0.5 was employed to ensure stability. The investigation encompassed the effects of varying rain peak coefficients, return periods, and durations on the runoff control efficacy, leading to the following findings.

In our quest to accurately quantify the influence of varying rainfall peak coefficients on runoff control effectiveness across distinct return period scenarios, we embarked on an investigation into the pipe network system's responsiveness to these peak coefficients. Employing a coupled two-dimensional urban flooding model with a pipe network system, we simulated the runoff control effect across diverse storm scenarios. The outcomes are summarized in Table 4.

Figure 12 highlights that, for each return period, augmenting the peak coefficient led to a gradual increase in the flow through the outlet pipe. This pattern signifies greater water ingress into the pipe network, subsequently raising drainage pressures within the network. This phenomenon can be attributed to the positioning of the rainfall peak toward the conclusion of the rainfall event, where the soil is already saturated, facilitating heightened water entry into the pipe network during the peak phase. Consequently, flow increases, and the peak duration experiences an elongation.

The comprehensive interplay between rainfall peak coefficients, runoff dynamics, and the intricate mechanics of LID measures are further underscored in subsequent sections, advancing our comprehension of urban flood management nuances within the context of sponge city initiatives.

Among the influential factors, rainfall intensity stands as a pivotal determinant in runoff control efficacy, holding particular importance under constant underlying surface conditions and uniform rainfall durations. An examination of the intricate relationship between rainfall intensity and runoff control effectiveness, through the lens of our established model, offers profound insights into the multifaceted facets shaping runoff control outcomes. This exploration holds immense significance in unraveling the nuances of the factors steering runoff control efficacy.

Figures 14 and 15 collectively illustrate that, irrespective of the varied limiting conditions, an inverse relationship prevails between runoff control rates and increasing rainfall intensity. Figure 14, for instance, depicts a gradual reduction in the runoff control rate as rainfall intensity escalates under diverse rain peak coefficient scenarios for distinct return periods. As an example, when considering a 1-year return period, the runoff control rate stands at 92.18%, which declines to 46.13% when the rainfall corresponds to a 50-year return period, with a rain peak coefficient of 0.1. Analogously, at a peak coefficient of 0.5, the corresponding runoff control rates drop from 92.36 to 44.97%.

Furthermore, comparing Figure 15(a) and 15(b) showcases that as rainfall amounts increase with the same duration, the corresponding rainfall intensity heightens, leading to reduced runoff control rates. For instance, when rainfall is uniformly distributed and the duration is 2 h, a rainfall amount of 19.2 mm yields a runoff control rate of 88.32%, whereas an amount of 87.22 mm corresponds to a rate of 55.47%. The trend persists even when considering designed rainfall scenarios. When the rainfall amount is 19.2 mm and the duration is 2 h, the runoff control rate is 86.17%, dropping to 53.12% with a rainfall amount of 87.22 mm. Longer durations yield higher runoff control rates due to the increased period for water infiltration and storage.

Rainfall intensity directly signifies the amount of rainfall per unit of time. Under equivalent underlying surface conditions, heightened intensity results in greater rainfall magnitude during each interval, leading to amplified surface runoff and consequently diminished runoff control rates. It's intriguing to note that comparing data in Figure 15(a) and 15(b) reveals a divergence: when the rainfall duration matches the rainfall event, the runoff control rate for designed rainfall surpasses that of uniformly distributed rainfall. This discrepancy arises due to the pronounced rainfall intensity peak within the designed rainfall, driving higher surface runoff and a subsequently elevated runoff control rate.

In summary, the intricate relationship between rainfall intensity, duration, distribution, and runoff control efficacy shapes the landscape of urban flood management. Understanding these nuances enhances our capacity to design effective strategies for runoff control, especially in the context of planning resilient sponge cities.

Undoubtedly, rainfall duration holds a position of prominence as a determining factor in runoff control rates, even under identical rainfall conditions. An investigation into the ramifications of rainfall duration on runoff control effectiveness holds considerable importance, as it offers valuable insights into the complex interplay between these parameters and their cumulative impact on regional runoff control outcomes. To this end, our study employed the model to simulate runoff control outcomes for diverse rainfall durations under consistent rainfall conditions.

As rainfall duration increases, the outlet volume of the pipe network diminishes, leading to a proportional increase in the runoff control rate under equivalent rainfall conditions, as showcased in Table 5 and Figure 17. Shorter distribution times yield amplified rainfall intensity, which in turn produces more surface runoff. This runoff traverses the pipe network, amplifying discharge volumes and subsequently lowering the runoff control rate. Remarkably, under identical durations, the runoff control rate diminishes with increased rainfall. Within the same return period, a shift from a 2-h to a 24-h duration can trigger a change in the runoff control rate ranging from 11.17 to 39.16%. Evidently, rainfall duration's impact on runoff control rates is substantial, underscoring its pivotal role in influencing these outcomes.

The ensuing sections delve further into the intricate dynamics of runoff control efficacy, elucidating the interplay of multiple factors and refining our comprehension of urban flood management strategies in the context of sponge cities.

As observed in Figure 18(c), uniform trends characterize rainfall flow processes across distinct durations under identical rainfall amounts. Specifically, as rainfall duration increases, peak discharge diminishes. This trend can be attributed to the unimodal nature of the designed rainfall pattern, which boasts a robust peak intensity, albeit within a relatively shorter duration. This combination leads to a truncated peak discharge duration, accompanied by a heightened peak discharge. For instance, for a rainfall condition featuring a 6-h duration and 65.7554 mm amount, peak discharge is 0.0038 m³/s under uniform rainfall intensity, while utilizing the designed rainfall yields a peak discharge of 0.2274 m³/s.

Under designed rainfall conditions, the runoff control rate dwindles as rainfall amounts increase within identical durations. Referring to Table 4, a 2-h duration at 19.2 mm rainfall corresponds to a runoff control rate of 86.17%, which decreases to 53.12% at 87.22 mm. Similarly, at 12-h duration and 38.79 mm rainfall, runoff control rates dip from 96.43 to 75.34% as the rainfall amount ascends. Interestingly, under consistent rainfall amounts, increasing rainfall duration is met with escalating runoff control rates. For instance, at 38.79 mm, the runoff control rate rises from 81.39% for a 2-h duration to 92.32% for a 24-h duration. Likewise, at 67.76 mm, corresponding rates for 2-h and 24-h durations are 68.39 and 81.62%, respectively.

This multifaceted analysis unveils the intricate interplay of factors influencing runoff control efficacy, shedding light on the dynamic relationship between rainfall duration, intensity, and their collective impact on urban flood management within the context of sponge cities.

This study delves into the intricate dynamic interplay between rainfall characteristics and their efficacy in runoff control, leveraging sophisticated two-dimensional urban flood modeling and pipeline network simulations. The results underscore a minimal influence of the peak factor on runoff control rates, with adjustments from 0.1 to 0.9 eliciting mere 0.79–2.55% variations across different return periods. This suggests that alterations in peak rainfall intensity distribution do not significantly alter runoff mitigation outcomes. Furthermore, the study highlights the profound implications of rainfall duration and intensity, as prolonged and intense storms lead to reduced runoff control rates. Both uniform and design rainfall scenarios exhibit similar response patterns, albeit with a more pronounced influence of rainfall intensity under design conditions and a stronger impact of duration under uniform rainfall.

Collectively, these findings contribute to a refined comprehension of how rainfall attributes interact and shape the effectiveness of urban runoff control. The study's insights carry substantial implications into urban flood management, particularly within the ambit of sponge city initiatives. As urbanization intensifies and extreme weather events become more frequent, the conclusions drawn from this research can serve as a pivotal foundation for crafting sustainable and effective flood control strategies. Moving forward, the author intends to develop a rapid assessment model for rainfall–runoff control rates, integrating this work with machine learning algorithms, to furnish a more potent tool for urban planners and runoff management practitioners.

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

The authors declare there is no conflict.