基于贝叶斯模型平均的水文模型不确定性及集合模拟

An Analysis of Hydrological Modeling and Ensemble Simulation Uncertainty Using the Bayesian Model Averaging

单一模型在水文过程模拟和预报中存在诸多不确定性,集合模拟是减少不确定性影响的有效方法。在水文模型参数估计的两类方法基础上(分别选用SCE-UA算法和SCEM-UA算法为代表),选用3个基于子流域的半分布式水文模型(新安江模型、混合产流模型和HYMOD模型),综合考虑模型参数和模型输入的不确定性,并采用贝叶斯模型平均(BMA)将3个模型的模拟结果集合进行概率预报。结果表明:SCE-UA算法和SCEM-UA算法优化的参数都能使模型取得较好的模拟效果,但SCEM-UA算法能得到模型参数的后验概率分布,并获取模型的概率预报区间,具有更大的优势;考虑模型输入不确定性,模拟径流的精度没有较大提高,但概率预报区间精度有一定的改善;采用BMA方法集合多模型模拟结果,综合考虑模型参数、模型输入和模型结构的不确定性,其模拟结果要优于单一模型,说明水文集合模拟的优越性;BMA集合后,SCEM-UA算法的模拟结果较SCE-UA算法的模拟结果具有更准确的概率预报区间。

In this study,the hydrological modeling uncertainty analysis and ensemble simulation based on the Bayesian Model Averaging（BMA） method are set up in Mishui Basin,South China.The Xinanjiang model,hybrid rainfall-runoff model,and HYMOD model are first calibrated by two parameter optimization algorithms,namely the Shuffled Complex Evolution（SCE-UA） method and the Shuffled Complex Evolution Metropolis（SCEM-UA） method.Then,the input uncertainty is quantified by utilizing a normal distributed error multiplier.Lastly,the ensemble simulation sets calculated from the three models are combined by using the BMA method.Both the SCE-UA and SCEM-UA result in good and comparable streamflow simulations.Specifically,the SCEM-UA implies parameter uncertainty and provided the posterior distribution of the parameters.In terms of the precipitation input uncertainty,the precision of streamflow simulations has not improved remarkably.Fortunately,the BMA combination has not only improved the precision of streamflow prediction,but also quantified the uncertainty bounds for the simulation sets.The prediction interval calculated by using SCEM-UA based BMA combination appears superior to that calculated by using SCE-UA based BMA combination.In summary,the overall results suggest that the comprehensive uncertainty analysis concerning model parameter uncertainties and multi-model ensembles by using the SCEM-UA algorithm and BMA method are advantageous and very practical for streamflow prediction and flood forecasting.