Calculation method for the topographic index in TOPMODEL

The topographic index, ln(α/tanβ), is an important parameter of many physically based hydrological models.The TOPMODEL is based on the calculation of ln(α/tanβ) index and its distribution.In terms of a digital elevation model (DEM), α is the cumulative upslope area draining through per contour length to a pixel, which reflects the tendency of water to accumulate at any point in the catchment, tanβ is the local slope angle of the cell, which reflects the tendency for gravitational forces to move that water downslide.The calculation method for ln (α/tanβ) index widely used is the multiple flow direction algorithm developed by Quinn et al (1991).It follows that, in the algorithm, the contour length normal to the direction of flow flowing out the current cell is used to determine both α and tanβ, and that the calculated total cumulative contributing area of downslide grid cell does not include the area of the current cell.These are unreasonable.It is found that the contour length used to determine α should be that normal to the direction of flow entering into the current cell, rather than that flow out the current cell.The improved algorithm calculating the ln(α/tanβ) index is presented, in which the area of the current cell is included in the calculated total cumulative contributing area of downslide grid cell.The different between the results of the two algorithms is described.