基于贝叶斯模型平均理论的水文模型合成预报研究

Study on forecast combination of different hydrological models by Bayesian model averaging

通过亚高斯模型分别对实测和水文模型预报的洪水序列进行正态分位数变换,并建立变换后的实测与预报时间序列的线性关系;然后根据贝叶斯模型平均理论,以实测序列条件下某一水文模型为最优模型的概率为权重,对各模型预报变量的条件概率密度函数进行加权,得到预报变量的概率密度函数,即高斯混合模型,从而实现了不同水文模型预报的合成及概率预报;最后,采用期望最大化算法估计高斯混合模型的参数。以密赛流域为实例,对本文的方法进行了验证。结果表明,基于贝叶斯模型平均的水文模型的合成预报不仅可以提供精度较高的均值预报,而且可以通过置信区间估计,定量评价模型预报的不确定性。

The time series of the observed flood and forecasted flood by hydrological model are transformed into normally-distributed variables by the meta-Gaussian approach,a linear relationship between the two types of variables is established. Then a Gaussian mixture model for the probability density function of forecast variables is obtained by taking a weighted average of the conditional probability distribution of different hydrological models according to the Bayesian model averaging theory,with the probability of individual hydrological models being the optimal alternatives under the observed data used as the weights. Thus,a forecast combination of different hydrological models is obtained in the form of probabilistic forecast. Parameters of the mixture model are estimated by the expectation maximum algorithm. Application to a test case of Misai basin, Zhejiang Province indicates that the proposed model is of better accuracy in forecasting expected values. This model provides an estimation of confidence interval of the forecast,so that the uncertainty of forecast can also be quantitatively assessed.