基于贝叶斯平均的非点源污染多模型模拟与不确定性分析

Multi-model Simulation and Uncertainty Analysis of Non-point Source Pollution Based on Bayesian Model Averaging

流域非点源污染模型是评价和控制非点源污染的有效工具,但单一模型模拟存在较大的不确定性,使得流域非点源污染的多模型模拟成为必然趋势。选取HSPF、SWAT和GWLF 3个结构不同的非点源污染模型,在单个模型最优模拟序列的基础上,采用最大期望值方法对模型权重计算,基于贝叶斯模型平均(BMA)方法对流域氨氮月负荷和硝态氮月负荷进行多模型模拟并对其90%的不确定性区间进行分析。以伊逊河流域的实测数据为例进行应用,结果表明:BMA多模型模拟方法的模型效率均高于单一模型,单个模型的效率越高,其在BMA多模型模拟中的权重越大,同时BMA的90%置信区间对实测值具有较高覆盖率。这表明,BMA方法不仅可以通过均值模拟得到更好的模拟效果,而且还可以不确定性区间评价多模型模拟结果的不确定性。研究结果为流域非点源污染负荷模拟提供了更多丰富的信息,可以为非点源污染控制提供科学支撑。

Watershed models are cost-effective and powerful tools for evaluating and controlling non-point source pollution,while there is great uncertainty depending on single model simulation which makes multi-model ensemble simulation become inevitable trend. In this study,three nonpoint source pollution models with different structures,named HSPF,SWAT and GWLF,were selected to conduct watershed monthly non-point pollution source ensemble simulation based on Bayesian model averaging (BMA) method,and the expectation maximum algorithm was used to estimate the parameters of the BMA in order to obtain BMA simulation and 90% uncertainty interval. The result using the observed data of the Yixunhe watershed revealed that the Coefficient of Determination and Nash-Sutcliffe Coefficient of the BMA model simulate monthly ammonia nitrogen load and nitrate nitrogen load were higher than that of the single model. The higher the efficiency of a single model is,the greater the weight during the BMA ensemble simulation is. The 90% confidence interval of BMA has a high coverage of measured values in this study. This indicates that the BMA method can not only provide simulation with higher precision through ensemble simulation,but also provide quantitative evaluation of the model structure through confidence interval,which could offer rich information of the non-point source pollution simulation.