中文摘要：

径流过程具有随机和灰色特征。基于此,将Markov预测与灰色GM（1,2）预测相结合,提出了GM（1,2）-Markov中长期河流年径流量预测模型。通过对黑河正义峡、莺落峡水文站65 a（1949-2014年）的年径流量资料分析,将莺落峡年径流量作为GM（1,2）预测的相关因素数据列,以1990-2009年的数据建立正义峡年径流量GM（1,2）-Markov模型,以2010-2014年的年径流量进行模型验证。结果表明：莺落峡、正义峡年径流量具有较强的相关性;建立的正义峡年径流量预测模型精度为83.65%;预测未来5 a的径流量,预测精度达到了97.12%;GM（1,2）-Markov、GM（1,1）和GM（1,2）模型的模型精度都符合建模的要求,但GM（1,2）-Markov模型的预测精度明显高于GM（1,1）模型和GM（1,2）模型。GM（1,2）-Markov模型为河流径流量的中长期预测提供了一种新方法。

英文摘要：

In arid areas,mid-long term runoff forecasting is very important for water resources planning and management. Because river runoff series has both randomness and gray characteristics,in China,the gray theory was used for forecasting runoff firstly in the late 1980 s,and Markov prediction was used for forecasting runoff beginning this century. For long time series and large random fluctuations series,the prediction effect of gray model was poor and had lower accuracy. Meanwhile,Markov prediction model need data of random and long time series.Both forecasting methods are highly complementary. Therefore,in order to predict the mid-long term annual runoff,some studies had constructed GM（1,1）-Markov prediction model by combining the gray system theory with Markov prediction. Compared with GM（1,1）model,GM（1,2）model introduced a reference series,which have a strong association with the main series. So GM（1,2）model can improve the prediction accuracy of volatility series. In this paper,a GM（1,2）-Markov prediction model was proposed. The paper constructed a GM（1,2）-Markov prediction model for Zhengyixia Station based on data of the Heihe River,Gansu Province,China. Firstly,the annual runoff correlation between Zhengyixia Station and Yingluoxia Station of the Heihe River during the period1949-2014 was analyzed. The annual runoff between Zhengyixia Station and Yingluoxia Station has a strong correlation. So the data of Yingluoxia Station acted as relevant factor data columns,and the data of Zhengyixia Station acted as controlling factors data columns to construct GM（1,2）prediction model. Afterwards,the GM（1,2）-Markov prediction model was established based on the annual runoff data from 1990 to 2009,and this model was verified with the annual runoff data from 2010 to 2014. In order to verify the merits of the GM（1,2）-Markov model,using the same data to establish Zhengyixia＇s annual runoff both GM（1,1）prediction model,and GM（1,2）prediction model. The GM（1,2）-Markov model was t