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基于重标极差（R/S）和小波分析的黄土坡耕地产流产沙变化研究 
张慧荟, 章 慧, 董 艳, 张青峰

西北农林科技大学资源环境学院


摘要: 
为探明降雨条件下黄土坡耕地微地形径流和泥沙变化规律，通过 5°、10°、15°、20°、25°坡和直线坡、人工锄耕、人工掏挖、等高耕作4种耕作方式组合条件下的室内模拟降雨试验，应用基于分形理论的重标极差（R/S）分析法对径流和泥沙时间序列的变化趋势进行预测，同时使用小波（Morlet）分析对各径流和产沙序列的变化主周期进行识别。结果表明：径流序列的赫斯特指数变化区间为[0.567，0.798]，产沙量时间序列的赫斯特指数变化区间为[0.632,0.861]，两者均大于0.5，呈现长程正相关。因此，坡耕地下一时段的径流量和产沙量时间序列与过去时段变化趋势相同；4种耕作措施的径流量最大峰值均出现在28~29 min，部分耕作措施的产沙量序列可能存在30 min以上的长周期，需要更长的时间序列验证。用R/S分析法结合小波分析，预测未来的产流产沙趋势，结果具有可靠性。该研究丰富了径流和泥沙输移理论，对农业生产和水土保持等方面研究具有指导意义。 
关键词: 径流 产沙 R/S分析 Morlet小波分析 Hurst指数 
DOI：10.11766/trxb201704190031 
分类号: 
基金项目:国家自然科学基金项目（41371273） 

Characterization of Runoff and Sediment Yield in Farmlands on Loess Slopes Based on R/S and Wavelet Analysis 
ZHANG Huihui, ZHANG Hui, DONG Yan, ZHANG Qingfeng

College of Resources and Environment, Northwest A&F University

Abstract: 
【Objective】On the Loess Plateau of China, water erosion in slope farmlands is the major type of soil erosion. Knowledge about changes in runoff and sediment yield therein will sure contribute to understanding nature of the erosion on a microscopic scale. The objective of this study was to investigate temporal variation of runoff and sediment yield on microrelief like farmland on loess slope under rainfall. An inlab experiment was designed to have slopes, 5°, 10°, 15°, 20°, and 25° in gradient, and four commonly adopted tillage patterns (flat slope, artificial digging plowing, artificial backhoe plowing, contour tillage) paired in combination. 【Method】For the inlaboratory experiment, a steel trough (2.0 m long, 1.0 m wide and 1.0 m deep ) filled with soil was set up with slope gradient adjustable in the range of 0～30°. Rainfall was simulated with downward sprinklers, 18 m high above the ground, which allows all the artificial raindrops to reach targeted terminal velocity and size of raindrops in natural rainfall and to distribute like a natural rainfall. Each artificial rainfall event lasted 90 minutes. Samples of runoff were collected every two minutes after the initiation of runoff for. fractaltheorybased rescaled range analysis (R/S) to predict trend of the variation of temporal sequence of runoff and sediment and for Morlet wavelet analysis to identify principal cycles of the variation of each runoff and sediment yield sequence.【Result】Results show that Hurst index of the runoff sequence lies in the section between 0.567 and 0.798, while that of the sediment sequence in the section between 0.632 and 0.861, both being higher than 0.5, displaying a longrange positive correlation between the two. Hence the temporal sequence of runoff and sediment yield on loess slope farmlands in future will remain the same as that in the past. In addition, the volume of runoff and sediment yield displayed a positive and negative logarithmic relationship, respectively, with duration of rainfall, expressed by the equation of S=a+ bln t (R2>0.5, a and b are constants). Generally, runoff peaked in volume 28 to 29 minutes after its initiation on the slope farmlands regardless of tillage pattern, while, sediment yield might have a long cycle of over 30 minutes in sequence on slope farmlands under certain tillage, indicating that the sediment yield on these slope farmlands might vary periodically every 30 minutes, which, however, needs to be validated by more detailed data of a longer time sequence.【Conclusion】All the findings in the study demonstrate that it is reliable to use R/S analysis combined with Morlet wavelet analysis in predicting temporal variation of runoff and sediment yield. This study also enriches the theory of runoff and sediment transfer, and lays a foundation for indepth understanding of the runoff and sediment, which is of great significance to further researches on relationship between soil erosion and time sequence on a microtopographic scale. 
Key words: Runoff Sediment R/S analysis Morlet wavelet method Hurst index 





