基于藤Copula的黄河宁蒙河段冰凌概率预报模型研究

The damage of ice flood in the Ning-Mong Section of the Yellow River is most serious in China. The sudden congestion of a river channel with ice can result in dramatic and rapid water level increases in the spring ice melting period because of ice dam which is usually formed as a result of an accumulation of ice assembling where the slope of a river changes from steeper to milder or where moving ice meets an intact ice cover, and the sudden discharge of water frozen and stored in the freeze-up period. Ice flood forecast is of great importance in reducing the damage, but there are a lot of uncertainties in the ice flood forecast since the ice flood is a product of multiple factor action, therefore the probability forecast which is a quite promising tool to deal with uncertainties will be studied in this research. The maximum discharge and maximum water level in the ice melting period that are concerned variable in the ice flood forecast is taken as predictand variables. The series of the predictand variables and their potential predictor variables will be firstly testified whether they are stationary process, and dependence analysis between the predictand variable and its potential predictor variables will be made to identify the predictor variables. The joint probability distribution of the predictand variable and the predictor variables will be constructed by Vine Copula, and conditional probability of the predictand variable will be estimated on the base of the joint probability distribution, then probability forecast of the predictand variable can be implemented in terms of conditional probability, uncertainty analysis and sensitivity analysis are further carried out to improve the efficiency of probability forecast. This proposal will provide an effective and reliable method for probability forecast, which will be very helpful for the ice flood forecast in the Ning-Mong Section.

黄河上游宁蒙河段是我国凌汛灾害最为严重的地区之一，开河期局部河段常因流冰受阻形成冰坝，加之封冻期增加的槽蓄水量在短时间内集中释放，往往形成高水位的洪峰，致使凌汛灾害频发。冰凌预报可以为凌汛防控提供依据，但是在冰、水、泥沙以及河道形态等多种因素的综合作用下，开河期常规冰凌预报的准确性受到了极大的影响。本研究以凌汛防控的关键参数开河期最大流量和最高水位为研究变量，针对冰凌影响因素的多元性和随机性，在一致性分析基础上解析冰凌预报变量及其潜在影响因素的相关性结构，辨识冰凌预报变量的影响因子；引入藤Copula理论构建冰凌预报变量及其影响因子的高维联合概率分布，建立能够全面考虑冰凌影响因素的、具有较强的灵活性和适用性的冰凌概率预报模型；对预报结果不确定性分析及其影响因素敏感性分析，探索提升冰凌预报精度的途径；推动多元随机变量概率预报模型的发展，为黄河宁蒙河段凌汛灾害防治提供有力的科学工具。

黄河上游宁蒙河段是我国凌汛灾害最为严重的地区之一，开河期局部河段常因流冰受阻形成冰坝，加之封冻期增加的槽蓄水量在短时间内集中释放，往往形成高水位的洪峰，致使凌汛灾害频发。冰凌预报可以为凌汛防控提供依据，但是在冰、水、泥沙以及河道形态等多种因素的综合作用下，开河期常规冰凌预报的准确性受到了极大的影响。本研究以凌汛防控的关键参数开河期最大流量和最高水位为研究变量，建立能够全面考虑冰凌影响因素的、具有较强的灵活性和适用性的冰凌概率预报模型。取得的主要结论如下：（1）受气候变化和工程枢纽的综合影响，近年来宁蒙河段凌情特征呈现显著的非一致性变化趋势，特别是受水利工程枢纽影响较大的石嘴山和巴彦高勒断面。（2）凌汛影响因素分析表明内蒙河段封河期特征水位是影响开河最高水位的主要直接影响因素，封冻期来水量和冰厚对开河最高水位也有显著的影响。内蒙河段开河凌峰一般发生在开河最高水位下落的过程中，开河最高水位是影响开河凌峰的主要直接影响因素，除此之外上游段开河凌峰、开河当日流量也是开河凌峰的影响因素。（3）基于Copula函数的概率预报模型中边缘分布函数对概率预测的影响小于Copula函数，Copula函数是概率预测的决定性因素，Copula函数的尾部特性决定了概率预测曲线的形状。（4）基于藤Copula函数的概率预报模型表现稳健，验证期模型精度与率定期相当，超过80%的实测点距均可以落到概率预报模型给出的90%不确定性区间中；与传统的多元线性回归相比，基于藤Copula函数的概率预报模型不确定区间宽度显著减少，且对非一致性变量模拟更优；此外概率预报模型的条件概率函数还可以用于情景模拟，给出不同情景条件下影响因子的概率组合空间，因此可以广泛用于其他水文变量预报中。