城市地表径流污染物浓度数学模型的建立及验证

针对目前描述城市地表径流污染物排放过程的数学模型不能完全适用于不同降雨过程的情况,本研究建立了一个全新的P/r模型.P/r模型以地表沉积物量(P)与降雨强度(r)的比值为主要参数,描述了降雨过程产生的地表径流中污染物的排放规律.基于对发生在陕西省西安市的3场降雨事件的实测数据的模拟,本研究建立的P/r模型的预测值与实测值的归一化目标函数、相关系数和相关指数均优于Sartor-Boyd冲刷模型.根据对P/r模型进行的不确定性分析,当Nash-Sutcliffe效率系数为0.46时,采用P/r模型对陕西省西安市地表径流中的污染物浓度进行模拟时应采用的最大比浓度常数(Km)和径流冲刷能力半饱和常数(KS)的取值范围分别为0.65~1.35 kg·min·L-1和0.16~0.22kg·min·mm-1·L-1.P/r模型的预测带平均相对宽度(ARIL)为1.21,预测带对实测值的覆盖度为67%.Sartor-Boyd冲刷模型对具有地表径流初期冲刷效应且降雨强度波动较小的降雨事件的模拟结果较好,但对于不具有地表径流初期冲刷效应的降雨事件、间歇性降雨事件及降雨强度波动较大的降雨事件并不适用.本研究建立的P/r模型的适用范围广泛,对于上述Sartor-Boyd冲刷模型不能适用的降雨事件均可适用.与Sartor-Boyd冲刷模型相比,P/r模型能够更好的描述城市地表径流的污染物排放规律.P/r模型的提出能够进一步推动地表径流排污过程数学模型的发展.

Establishment and verification of a novel mathematical model for pollutant concentrations in urban rainfall runoff

The present mathematical models for describing pollutant emission process of urban runoff are not fully applicable for different rainfall processes. In this study, a novel P/r model was proposed. The ratio of sediment yields on urban surface to rainfall intensity was taken as the main parameter in the P/r model for elucidating the pollutant emission of runoff caused by rainfall events. Through simulating three rainfall events happened in Xi'an, Shaanxi province, China, it was concluded that normalized objective function, correlation coefficient and correlation index between the simulations and the observations obtained from the P/r model were better than those from the most frequently used Sartor-Boyd wash-off model. The results from the uncertainty analysis of the P/r model showed that when Nash-Sutcliffe efficiency coefficient was 0.46, the ranges of the maximum specific concentration constant (K_m) and the half-saturation coefficient of the runoff wash-off capacity (K_S) were 0.65~1.35 kg·min·L^-1 and 0.16~0.22 kg·min·mm^-1·L^-1 respectively by using the P/r model. The average relative interval length (ARIL) of the prediction band of the P/r model was 1.21, and the coverage of observations by the probability bands was 67%. Normally, Sartor-Boyd wash-off model is suitable to rainfall events with first flush phenomena of surface runoff and a narrower fluctuation range of rainfall intensity. It is however not suitable and P/r model is in turn applicable for rainfall events without first flush phenomena of surface runoff, intermittent rainfall events and rainfall events with a broader fluctuation range of rainfall intensity. Therefore, the P/r model shows a wider range of application than the Sartor-Boyd wash-off model. Compared with the Sartor-Boyd wash-off model, the P/r model had better performances in describing the variation of pollutant concentration in the urban runoff process. The P/r model could promote the development of the mathematical model in simulating the runoff pollutant emission process.