Which type of slope gradient should be used to determine flow-partition proportion in multiple-flow-direction algorithms – tangent or sine?

Abstract. This paper revisits the tangent expression for the slope gradient (tan β) used in the general flow-partition function in multiple-flow-direction (MFD) algorithms. The deduction of the flow-partition function performed here based on hydrological theory shows that sin β, instead of tan β as used currently, provides a clear theoretical basis for determining the flow-partition proportions in MFD algorithms.