基于可变模糊聚类的山丘区小流域洪峰经验公式推求

山丘区小流域暴雨洪水汇流计算是山洪精准预报预警的关键之一。针对山丘区小流域暴雨洪水历时短、成灾快和小流域普遍缺乏实测资料、产汇流非线性特征明显等特点，基于考虑雨强和流域异质性的分布式地貌单位线，开展山丘区小流域单位线峰值经验公式推求的研究。选取甘肃省山丘区26 774个小流域作为研究对象，采用可变模糊聚类方法对小流域单位线进行分类，分类别建立小流域特征因子与单位线峰值之间的经验公式，并进一步探讨所推求经验公式的合理性。结果表明：可变模糊聚类算法能较好地应用于分布式单位线分类，该算法的分类效果非常突出，分类后的单位线经验公式计算效果有显著提升；山丘区小流域汇流过程峰值主要受流域面积、最长汇流路径长度及其坡降的影响，分布式单位线峰值经验公式在山丘区小流域汇流计算具有广阔的应用前景。

Empirical Formulas of Flood Peak Discharge Based on Variable Fuzzy Clustering in Small Mountainous Watersheds

Flash floods in mountainous watersheds are often caused by the rainstorm. They are different from regular floods by having a smaller timescale and a faster flowing front of water and debris. The storm flood in mountainous watersheds presents strong nonlinearity, and the related hydrological calculation remains one of the critical challenges for accurate flash flood forecasting, which is further constrained by the availability of local datasets. In this paper, we present the empirical formulas derived from the distributed unit hydrographs which are subtracted from the rainfall intensity and the spatial variation of terrain, land use and soil type within each watershed. By selecting 26 774 small mountainous watersheds in Gansu province as study sites, we utilize variable fuzzy clustering method to capture the variation of unit hydrographs, and the empirical formulas between the watershed characteristics and the peak discharge of unit hydrographs are obtained in each cluster. The results show that variable fuzzy clustering method performs well in the classification of the distributed unit hydrographs, the derived empirical formulas can produce reliable results on the calculation of flood peak discharge in small mountainous watersheds. Meanwhile, flood peak discharge is mainly affected by drainage area, main channel network length and corresponding longitudinal gradient, and the derived empirical formulas show wide application potential in the hydrological calculation of rainstorm in small mountainous watersheds, especially in ungauged basins.