马斯京根模型基于水量平衡原理和线性槽蓄假定而建立，模型自提出以来不断得到改进。归纳起来，模型改进思路主要体现在水量平衡微分方程、槽蓄方程以及参数取值三方面。在已有模型改进思路基础上，通过引入组合流量系数，尝试构建新的马斯京根演进模型。模型以同一断面历史多时刻流量线性组合代替槽蓄方程中当前单时刻流量，并采用微分进化算法进行模型参数率定。以滦河大黑汀水库以下至滦县河段为例，分别选取不同量级的10次代表性水流过程进行模拟。结果表明，模型模拟精度较未改进得到了提高。

Based on the principle of water balance and the hypothesis of linear channel storage, the Muskingum routing model has been in the modifying all the time. In general, the modifying are mainly focused on the differential equation of water balance, the equation of channel storage, and the parameter calibration. On the basis of previous studies, this paper established a modified Muskingum model. In the modified model, the current single period flow was substituted for the combination of historical flows at the same cross section with the combination coefficient of flow. Then, the parameters were calibrated with the Differential Evolution Algorithms. The reach Daheiting Reservoir to Luanxian in Luanhe River was used as a case study. And 10 different flows were selected for simulating and demonstrating the validity of the proposed model and the results suggested the potential improvement in flow simulation.

国家973计划课题 (2013CB036406)；国家科技重大专项项目 (2012ZX07205)；环保公益性行业科研专项经费项目 (2013467042)