地形湿度指数(TWI)能够定量指示地形对土壤湿度空间分布的控制，是一种应用广泛的地形属性。目前基于栅格DEM的TWI 计算方法结果各异，因此有必要对TWI 算法进行定量评价。对TWI 算法通常是应用实际DEM数据进行评价，但实际DEM中存在的数据源误差会干扰对算法误差的评价。针对该问题，本文介绍了一种用不含数据源误差的人造DEM定量评价TWI算法误差的方法。本文选择4 种代表性TWI算法：基于经典单流向算法的TWI算法、基于经典多流向算法的TWI算法、基于局域地形自适应多流向算法的TWI算法，以及自适应多流向算法与最大下坡相结合的TWI算法，应用该评价方法构建了一组模拟4 种典型复合地形条件的人造表面，并分别离散成具有不同空间分辨率(1 m、10 m和30 m)的人造DEM数据，对TWI算法进行定量评价。评价结果显示：在中心凸、凹坡和马鞍面地形条件下，基于多流向算法计算的TWI优于基于单流向算法的TWI结果；在山脊地形条件下，基于单流向算法的结果仅次于MFD-md结合最大下坡度算法计算的结果。随着分辨率降低，基于多流向算法计算结果的误差逐渐增加，而基于D8 算法的计算结果随着地形条件的不同而呈现出不同的变化趋势。本文所推荐的TWI算法定量评价方法通过简单扩展也同样适用于其他复合地形属性算法误差定量评价。
Topographic Wetness Index (TWI) is a widely-used topographic attribute which can predict the control of terrain on spatial distribution of soil moisture. Diverse TWI algorithms might get very different results; therefore, it is necessary to assess the algorithms. Traditional error assessment method applies TWI algorithms to 'real-world' DEM, but the error from DEM quality might interfuse the error from algorithms and thus influence the accuracy of evaluation. To solve the problem, this paper proposes an assessment method of error from TWI algorithm with artificial DEMs which can avoid data source error. Four typical TWI algorithms, i.e. TWI algorithm based on a typical single flow direction algorithm (D8), TWI algorithm based on a typical multiple flow direction algorithm (FD8), TWI algorithm based on an adaptive multiple flow direction algorithm (MFD-md), and TWI algorithm using MFD-md in which the maximum downslope, instead of traditional slope gradient, is used to estimate the tanβ in equation of TWI, are evaluated by the proposed assessment method. First, four artificial surfaces are constructed to simulate typical compound terrain conditions, i.e. convex-centred slope, concave-centred slope, saddle-centred slope, and ridge-centred slope, respectively. Secondly, the artificial surfaces are converted to three sets of artificial DEM data with different cell size (1 m, 10 m, and 30 m) to apply TWI algorithms to compute TWI. Third, the theoretical TWIs for every artificial surface are calculated to quantitatively assess the error from TWI algorithms based on RMSE. Assessment result shows that TWI algorithms based on multiple flow direction algorithm (MFD) perform better than TWI algorithm based on single flow direction algorithm (SFD), i.e. D8, under terrain conditions of convex-centred slope, concave-centred slope and saddle-centred slope. Under ridge-centred slope terrain condition, the result of TWI algorithm based on SFD is just inferior to the result of TWI algorithm which combines MFD-md with maximum downslope algorithm. As the resolution becomes coarser, errors of TWI algorithms based on MFD become larger on the whole, while the trends of results of TWI algorithm based on SFD vary with different terrain conditions. The proposed quantitative assessment method for TWI algorithm can be similarly used to assess algorithms of other compound topographic attributes, such as specific catchment area, stream power index, and so on.
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