Multiple equidistant belt technique for width function estimation through a two-segmented-distance strategy

Abstract

In order to estimate flow distance and width function more accurately, the triangulation with linear interpolation (TLI) method to approximate the missing flow distance values within a cell except for the cell center. Then a new flow distance algorithm (D∞-TLI) is proposed to estimate the flow distance using a two-segment-distance strategy, while two segmented-distances in and outside a local 3 × 3 window are severally modelled with D∞ and TLI. Then, using the continuous flow distance field approximated over a cell region, this cell can be divided into multiple equidistant belts (MEB) to estimate the width function. Assessments using four numerical and two real-world terrains demonstrate that D∞-TLI outperforms nine existing flow distance algorithms and has a mean absolute relative error (MARE) lower than 5%. Moreover, the combination of D∞-TLI and MEB extracts width function which is less affected by unreasonable artificial fluctuation and has a MARE lower than 3%.