中文摘要：

基于栅格DEM的流向算法是数字地形分析的重要研究内容之一。在分布式水文模型、土壤侵蚀等领域中，当需要获取与流向直接相关的水文参数（如汇流面积、地形指数等）的详细空间分布时，多流向算法（MFD）明显优于单流向算法（SFD）。根据所采用的水流分配策略，将现有MFD分为四类：（1）固定水流分配权重的MFD；（2）水流分配权重随汇流面积变化的MFD；（3）水流分配权重随局域地形特征变化的MFD；（4）基于局域形态单元的MFD。从模型合理性、算法复杂度和易用性、对DEM误差的敏感性等方面进行的分析表明，水流分配权重随局域地形特征变化的MFD优于其他三类MFD。目前对MFD采用人造DEM数据集的直接定量评价研究还十分不足，文章以一个例子来体现直接定量评价MFD的可行性及有效性，同时也定量反映出水流分配权重随局域地形特征变化的MFD具有更低的计算误差。目前通用的针对流向算法的DEM洼地平区预处理算法多针对SFD而设计，不适合MFD的实际应用，本文对适用于MFD的DEM预处理算法所应具有的特征也进行了讨论。

英文摘要：

The flow direction algorithm based on gridded DEM is an important component of digital terrain analysis. The multiple flow direction algorithm （MFD） is obviously better than the single flow direction algorithm （SFD） when the spatial pattern of hydrological parameters （such as flow accumulation and topographic index） are needed in many research areas （e. g. distributed hydrologic model, soil erosion）. Based on the flow partitioning strategy adopted, this paper classifies MFD algorithms as of four types： （1） MFD with a fixed flow partitioning exponent; （2） MFD with the flow partitioning exponent varying with pre-computed flow accumulation; （3） MFD with the flow partitioning exponent varying with local topographic attribute; and （4） MFD based on local topographic form. The discussion according to the rationality of model, complexity and practicality of algorithm, and sensitivity with the errors of DEM shows that the MFD with the flow partitioning exponent varying with local topographic attribute excels the other three types of MFD. There is a shortage of research on the quantitative assessment of MFD by artificial DEM. This paper uses an example to illustrate the quantitative assessment of MFD, and also shows that the MFD, with the flow partitioning exponent varying with local topographic attribute, produces a lower error than other algorithms. In the applications of flow direction algorithms, current pre-processing methods for depressions and flat areas in DEM are designed mainly for SFD. Most of them are not appropriate for the application of MFD. This paper also discusses the characteristics of the pre-processing method of DEM which is appropriate for MFD.