基于分数瞬时单位线的流域汇流模型研究  

Research on watershed routing model based on fractional instantaneous unit hydrograph

作　　者：闫宝伟[1] 段美壮 江慧宁 李正坤 杨文发 张俊 YAN Baowei;DUAN Meizhuang;JIANG Huining;LI Zhengkun;YANG Wenfa;ZHANG Jun(School of Hydropower and Information Engineering,Huazhong University of Science and Technology,Wuhan 430074,China;PowerChina Huadong Engineering Corporation Limited,Hangzhou 311122,China;Bureau of Hydrology,Changjiang Water Resources Commission,Wuhan 430010,China)

机构地区：[1]华中科技大学水电与数字化工程学院,湖北武汉430074 [2]中国电建集团,华东勘测设计研究院有限公司,浙江杭州311122 [3]长江水利委员会水文局,湖北武汉430010

出　　处：《人民长江》2020年第8期84-88,共5页Yangtze River

基　　金：国家重点研发计划项目(2016YFC0402708);中央高校基本科研业务资助项目(2017KFYXJJ195)。

摘　　要：Nash瞬时单位线反映了流域汇流的短程记忆特性,水流的运动过程往往具有历史依赖性和路径依赖性,表现为长记忆性,而分数阶微积分非常适合刻画具有记忆和遗传性质的过程。将Nash汇流系统中微分方程的阶次由整数阶扩展为分数阶,借助拉普拉斯变换得出了分数瞬时单位线,用于描述流域汇流的长程记忆性;并选取可以忽略产流误差影响的试验数据对分数瞬时单位线进行验证后,进一步将分数瞬时单位线应用于新安江模型的地表产流计算。结果表明:该模型可以在一定程度上提高高水部分的模拟效果,从而提高整体的模拟精度,但可能受产流误差的影响,洪峰和径流总量的模拟效果并没有得到明显改善。The Nash instantaneous unit hydrograph reflects the short-term memory of the flow routing,while the hydrological responses of natural river systems are characterized as historical dependence and route dependence with long memory feature.Fractional calculus is a non-local operator expressed in differential-integral form,which is very suitable for describing processes with memory and genetic properties.This paper extended the order of differential equations in the routing system from integer order to fractional order,used the Laplace transform to derive the fractional instantaneous unit hydrograph(FIUH),and applied it to describing the long-term memory of the flow routing.A series of experimental data that were not influenced by the runoff yield error were selected to verify the FIUH.Further,the FIUH was applied to the surface runoff routing of the Xin'anjiang model.The results show that the simulation of the high discharges can be improved to a certain extent,thereby improving the overall simulation accuracy,however it may be affected by the runoff yield error,so the simulated effects for flood peaks and total runoff are not improved significantly.

关 键 词：Nash瞬时单位线 分数瞬时单位线 新安江模型 地表汇流 长程记忆性 

分 类 号：TV121[水利工程—水文学及水资源]