• 论文 •

### An Improved Markov Chain Model Based on Autocorrelation and Entropy Techniques and Its Application to State Prediction of Water Resources

ZHOU Ping1, 3, ZHOU Yuliang2, JIN Juliang2, LIU Li2, WANG Zongzhi3, CHENG Liang2, ZHANG Libing2

1. (1. College of Hydrology and Water Resources, Hohai University, Nanjing 210098, China;
2. College of Civil Engineering, Hefei University of Technology, Hefei 230009, China;
3. State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Nanjing Hydraulic Research Institute, Nanjing 210029, China)
• 出版日期:2011-03-24 发布日期:2011-04-06

### An Improved Markov Chain Model Based on Autocorrelation and Entropy Techniques and Its Application to State Prediction of Water Resources

ZHOU Ping1, 3, ZHOU Yuliang2, JIN Juliang2, LIU Li2, WANG Zongzhi3, CHENG Liang2, ZHANG Libing2

1. (1. College of Hydrology and Water Resources, Hohai University, Nanjing 210098, China;
2. College of Civil Engineering, Hefei University of Technology, Hefei 230009, China;
3. State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Nanjing Hydraulic Research Institute, Nanjing 210029, China)
• Online:2011-03-24 Published:2011-04-06

According to the relationships among state transition probability matrixes with different step lengths, an improved Markov chain model based on autocorrelation and entropy techniques was introduced. In the improved Markov chain model, the state transition probability matrixes can be adjusted. The steps of the historical state of the event, which was significantly related to the future state of the event, were determined by the autocorrelation technique, and the impact weights of the event historical state on the event future state were determined by the entropy technique. The presented model was applied to predicting annual precipitation and annual runoff states, showing that the improved model is of higher precision than those existing Markov chain models, and the determination of the state transition probability matrixes and the weights is more reasonable. The physical concepts of the improved model are distinct, and its computation process is simple and direct, thus, the presented model is sufficiently general to be applicable to the prediction problems in hydrology and water resources.

Abstract:

According to the relationships among state transition probability matrixes with different step lengths, an improved Markov chain model based on autocorrelation and entropy techniques was introduced. In the improved Markov chain model, the state transition probability matrixes can be adjusted. The steps of the historical state of the event, which was significantly related to the future state of the event, were determined by the autocorrelation technique, and the impact weights of the event historical state on the event future state were determined by the entropy technique. The presented model was applied to predicting annual precipitation and annual runoff states, showing that the improved model is of higher precision than those existing Markov chain models, and the determination of the state transition probability matrixes and the weights is more reasonable. The physical concepts of the improved model are distinct, and its computation process is simple and direct, thus, the presented model is sufficiently general to be applicable to the prediction problems in hydrology and water resources.