The Runoff Prediction Models Based On Markov Chains

River is an important source of human survival and development.Runoff prediction is one of the important preconditions for flood control and water resources development.Especially for some short-term hydraulic activities,such as river clearance,dam maintenance,flood forecasting,etc.,runoff prediction is usually carried out on a weekly time scale.Although the prediction accuracy of runoff prediction model has been greatly improved after years of research and development,there is still need to investigate of the traditional runoff prediction models.A non-homogeneous Markov chain runoff prediction model(NHMC-RPM)and a second-order Markov chain runoff prediction model(SOMC-RPM)are constructed respectively based on Markov chain theory,and the models are applied to the Huayuankou hydrological station and Toudaoguai hydrological station in the Yellow River Basin to verify the validity of the above models.The main contents are as follows.(1)A NHMC-RPM is established based on the average weekly runoff data.Firstly,the mean square error method is used to determine the state space.Secondly,the overlapping forward method is proposed to establish the transition probability matrices corresponding to the predicted period.Finally,the predicted intervals of runoff are obtained by calculating the expectation based on the prediction distribution.(2)A SOMC-RPM is modified based on the above runoff data.Firstly,memory state is introduced to transform the second-order Markov chain into an equivalent first-order homogeneous Markov chain which is used to describe the runoff series.Then the block matrix method is used to simplify the calculation of the one-step transition probability matrix.In addition,the state distribution of the second-order Markov chain at the predicted time is obtained by summing the same transition state.Finally,the predicted intervals of runoff are obtained by calculating the prediction distribution.(3)NHMC-RPM and SOMC-RPM are both applied to the runoff prediction of Huayuankou hydrological station and Toudaoguai hydrological station in the Yellow River Basin.The prediction results are compared with the prediction accuracy of the first-order homogeneous Markov chain at the above two hydrological stations,respectively.The results show that the prediction performance of NHMC-RPM is the best at Huayuankou,while that of SOMC-RPM at Toudaoguai is the best.These results indicate that NHMC-RPM is more suitable for rivers with large short-term runoff variation,while SOMC-RPM is more suitable for rivers with strong temporal correlation of runoff.The research will further enrich the runoff prediction method,broaden the application range of non-homogeneous Markov chain and second-order Markov chain.Based on the comparison of NHMC-RPM and SOMC-RPM,the theoretical basis and decision-making basis are provided for river managers to formulate strategies for flood control and water resources development.