基于模糊集修正加权马尔可夫模型在新疆降水预测中的应用

The Modified Model of Weighted Markov Chain Based on Fuzzy Sets and Its Application in Precipitation Prediction of Xinjiang

【目的】为提高降水预报精度，准确预测一个地区未来的降水丰枯状况和降水量，为该地区工农业生产生活提供决策参考。【方法】以年降水时间序列为研究对象，利用模糊集理论和加权马尔可夫模型建立一种基于模糊集的修正加权马尔可夫预测模型。该模型改进加权马尔可夫模型中初始状态向量的确定方法，即通过引入模糊集理论，基于距离测度建立隶属度函数，计算出随机变量序列各时段序列值隶属于所有状态的隶属度，并将隶属度向量作为该时段的初始状态向量。【结果】根据新疆1957—2010年的年降水数据，利用该模型预测新疆2011～2012年的降水丰枯状况及降水量预报值。2011—2012年丰枯状态的预测结果与实际完全一致，降水量预测值的误差分别为0．99％，0．54％。进一步利用该模型动态预报了2013—2017年的降水丰枯状况及降水量。【结论】基于模糊集的修正加权马尔可夫模型具有更高的预测效果，可用于新疆降水丰枯状况预报和降水量预测。

[ Objective ] The project aim at improving the prediction accuracy of precipitation forecast and making an accurate precipitation state and precipitation forecast for the future can provide a better decision - making reference for industrial and agricultural production as well as daily life. [ Method ] By taking time seties of annual precipitation as the research object, using fuzzy sets theory and weighted Markov Chain Model to construct a modified model of weighted Markov Chain based on fuzzy sets. The model mainly improves the method to determine the initial state vector of weighted Markov Model. That was done by introducing the fuzzy set theory, establishing the membership function based on the distance measure, we calculated the membership of every time sequence value of random variables sequence, and took the membership vector as the initial state vector for the time period. [ Result] According to the annual precipitation data of Xinjiang during 1957 - 2010, the model was applied in the prediction of the precipitation state and annual precipitation forecast in Xinjiang during 2011 -2012. The results showed that the prediction of the precipitation state was consistent with the actual state, and the prediction errors of precipitation were 0.99% and 0. 54%, respectively. Furthermore, it was used to dynamically forecast the precipitation state and annual precipitation form 2013 to 2017 by using the model. [ Conclusion ] The modified model of weighted Markov Chain based on fuzzy sets had higher prediction accuracy, which could be applied in the precipitation state forecast and precipitation prediction in Xinjiang.