复权马尔可夫链及其在怒江水沙预测中的应用

Re-weighted Markov chain for numerical sediment prediction of the Nujiang river in China

针对传统马尔可夫链及其改进的预测方法只能进行状态预测的局限,根据相依随机变量的特点,在以传统马尔可夫链预测方法求得各状态预测概率的基础上,进一步以状态预测概率为权重与状态平均值加权求和,实现了马尔可夫链预测方法从状态预测到数值预测的关键性改进。利用我国西南国际大河怒江干流道街坝水文站1957-2010年径流和1964-2010年悬移质输沙序列为分析期,2011-2015年径流和悬移质输沙为验证期,对所建立的复权马尔可夫链预测方法步骤进行验证表明,复权马尔可夫链预测方法具有较高的数值预测精度,能够满足随机时间序列短期数值预测的需要。

In view of the limitations of traditional Markov chain and its improved prediction methods which can only predict the state, in this paper we realized a critical improvement of the Markov chain forecasting method to being able to conduct numerical prediction. We did so by using weighted summation of the average value of each state multiplied by the corresponding predicted probability, on the basis of obtaining the predicted probability of each state with the traditional Markov chain forecasting method according to the characteristics of dependent stochastic variables. The data of this study were collected from Daojieba hydrological station on the Nujiang river,which is a famous international river in southwest China. We used the runoff series from 1957 to 2010 and the suspended sediment series from 1964 to 2010 for analysis, and used the runoff and suspended sediment series from 2011 to 2015 for validation. Results showed that the re-weighted Markov chain forecasting had a high accuracy in numerical prediction and could meet the demand of short-term numerical prediction in stochastic time series.