中文摘要：

流域地貌形态的科学准确量化是建立具有广泛适用性的流域尺度土壤侵蚀预报模型的关键科学问题之一，分形理论的提出为流域地貌形态特征的定量描述开辟了新的思路。本文基于分形理论，利用GIS技术和多元回归统计方法，以黄土高原丘陵沟壑区第一副区的岔巴沟流域为例，对该流域以分形信息维数为量化指标的流域地貌形态与降雨侵蚀产沙耦合关系进行了初步探讨。研究表明，引入地貌形态分形信息维数的岔巴沟流域降雨侵蚀产沙与地貌形态耦合关系模型可将岔巴沟各支流域差异明显的水沙关系简化为统一的数学表达，消除了由于地貌形态等下垫面因素导致的空间变异性；基于该耦合关系模型的西庄和蛇家沟流域次降雨输沙模数预测值和观测值相对误差较小、总体吻合较好；将地貌形态分形信息维数作为流域土壤侵蚀预报模型中地貌形态因子量化指标不仅可行，而且可靠。

英文摘要：

Scientific accurate quantification of topographic feature of watershed is one of the key issues in establishing an extensively applicable model for prediction of soil erosion on a watershed scale on loess Plateau. Based on the fractal theory and with the aid of the GIS technology and muhianalysis method, coupling relationship between sediment yield from rainfall erosion and topographic features was studied in the Chabagou watershed, which lies on loess Plateau. Results show that the coupling relationship model, into which fractal information dimension of topographic feature of watershed is introduced, can simplify the relationship between runoff and sediment yield that varies from branch to branch of the Chabagou watershed to a uniform mathematic expression. As a whole, the relative error of the prediction of sediment transport modulus of the Xizhuang and Shejiagou watersheds using the model is low. It is feasible and reliable to use fractal information dimension of topographic features of watershed as an index to quantify topographic features of watershed, which is one of the important influencing factors in establishing models for soil erosion prediction on a watershed scale.