## 1 Introduction
There are some studies that focus specifically on reducing the overall number of pollutants. By comparing the total reduction of runoff pollutants before and after the construction of the facility, the effect of the facility in controlling runoff pollution is measured [18]. However, further research on the relationship between pollution reduction and facility size (runoff volume control) is needed. Traditional runoff pollution control impact evaluations cannot account for the interaction between facility type, design size, rainfall intensity, rainfall duration, and rainfall return period on runoff pollution reduction. One of the sponge city construction core indexes mentioned in _Sponge City Construction Technical Guide-Low Impact Development Rainwater System (Trial)_ is the annual runoff volume control rate. The design rainfall (H) can be determined through the total runoff control rate, and then the design scale of low-impact development facilities for sponge city construction can be determined through the design rainfall (H). Therefore, the determination of the total annual runoff control rate is directly related to the determination of the size of the source facilities of the sponge city construction, which in turn affects the removal effect of runoff pollutants. The above analysis shows that the control of runoff pollution is mainly achieved through volume control in the construction of sponge cities, and the calculation of runoff pollution is based on the total amount of runoff pollution and the response connection between particular runoff volume and runoff pollutant reduction is yet unknown. The implementation of the total runoff control target includes the reduction and utilization of rainwater, and the main technical measures include infiltration technology and storage technology, and relevant facilities include permeable pavement, grass planting ditch, bioretention pond, rainwater tank, wet pond, rainwater wetland and large (multifunctional) storage facilities [19]. Existing studies mainly focus on the runoff control effect and pollutant reduction effect of a single facility or catchment zone [20; 21]. There is a dearth of analysis and study on the reduction effect of rainwater runoff pollution under various facilities and scenarios, with total annual runoff control as the main indication in the development of sponge city. The total annual runoff control rate is calculated using the year as the time unit, and the runoff volume is mostly regulated by the facility's scale and size. The runoff pollution induced by small and medium-sized rainfall, particularly the early rainfall with the initial scouring impact, is substantially more problematic since the pollutants do not correlate to the rainfall uniformly [22]. The total control mode only controls the total runoff volume and cannot reflect the control proportion of pollution. This leads to ambiguous answers to a number of concerns, including the control effect of source facilities on runoff pollution under various land use features and the scope of initial runoff volume capture rate application. This work offers a novel dimensionless constant (Dc) for the control impact of runoff pollution in order to explore the response connection between the initial runoff volume capture of sponge city construction and the control of runoff pollution. The following quantitative analyses were performed using the SWMM model: (1) the relationship between the scale of sponge city construction facilities (the control rate of total annual runoff) and the volume control of runoff; (2) the response relationship between the design size of typical source volume control facilities (bioretention, permeable pavement, rain barrels) and the reduction of pollutants in urban stormwater runoff; (3) effects of different facility combinations, underlying surface types and other factors on the control effect of stormwater runoff pollution.