An adaptive approach to selecting a flow-partition exponent for a multiple-flow-direction algorithm

Most multiple-flow-direction algorithms (MFDs) use a flow-partition coefficient (exponent) to determine the fractions draining to all downslope neighbours. The commonly used MFD often employs a fixed exponent over an entire watershed. The fixed coefficient strategy cannot effectively model the impact of local terrain conditions on the dispersion of local flow. This paper addresses this problem based on the idea that dispersion of local flow varies over space due to the spatial variation of local terrain conditions. Thus, the flow-partition exponent of an MFD should also vary over space. We present an adaptive approach for determining the flow-partition exponent based on local topographic attribute which controls local flow partitioning. In our approach, the influence of local terrain on flow partition is modelled by a flow-partition function which is based on local maximum downslope gradient (we refer to this approach as MFD based on maximum downslope gradient, MFD-md for short). With this new approach, a steep terrain which induces a convergent flow condition can be modelled using a large value for the flow-partition exponent. Similarly, a gentle terrain can be modelled using a small value for the flow-partition exponent. MFD-md is quantitatively evaluated using four types of mathematical surfaces and their theoretical 'true' value of Specific Catchment Area (SCA). The Root Mean Square Error (RMSE) shows that the error of SCA computed by MFD-md is lower than that of SCA computed by the widely used SFD and MFD algorithms. Application of the new approach using a real DEM of a watershed in Northeast China shows that the flow accumulation computed by MFD-md is better adapted to terrain conditions based on visual judgement.