基于谐波分析的黄土高原小流域沟谷分布规律研究

研究黄土高原侵蚀沟分布规律对于土壤侵蚀评估和植被恢复模式设计具有重要意义。该文以 陕北黄土高原吴起县铁边城镇四面窑沟流域为研究区，使用1∶10 000数字高程模型（DEM） ，利用谐波分析和周期图分析方法，研究了黄土高原侵蚀沟的分布规律。结果表明，利用谐波分析和周期图分析均可得到侵蚀沟的分布周期。相比较而言，周期图分析可以更加直观地得到满足显著性检验的分布周期，但谐波分析还可以根据周期检验结果，得到对应的谐波模型。通过计算四面窑沟流域东面支沟沟谷分布周期，共得到23个满足检验要求的周期，在500～1 000 m之间显著周期最多，占总周期数的35%；在300～500 m显著周期数量次多，占26%。当谐波数为9和10时，周期显著性水平最高，对应的周期分别为1 017.35和915.60 m；在DEM上，每间隔105 m提取一个高程数据并进行谐波分析，最终得到由3个谐波组成的地形起伏谐波模型。 

Quantifying valley topographic distribution using harmonics analysis in the Loess Plateau

Relief variation and gully distribution in the Loess Plateau region are important consideration in soil erosion control and vegetation recovery. Simianyaogou Watershed in Tiebiancheng Towership of Wuqi County，Shaanxi Province was used in this study. Variation of relief and its reoccurrence were analyzed with 1∶10 000 DEM by harmonics analysis method and periodogram. Results show that dominant periods of relief variation can be derived by periodogram more obviously and easily than by harmonics analysis，while harmonics analysis can obtain relief variation simulation models as well as its periods. There were 23 significant periods of relief variation on eastern slope of the study area，35% of them ranged from 5 00 to 1 000 m and 26% ranged from 300 to 500 m. The most significant variation periods were 1 01735 and 91560 m corresponding to harmonic numbers of 9 and 10. Based on the elevation series obtained from DEM at an 105 m interval，a model with three harmonics was built for describing relief variations.