An Algorithm‐Independent Definition of Effective Contour Length and Its Impacts on Pixel‐Scale Specific Catchment Area

Abstract

AbstractSpecific catchment area (SCA) is crucial terrain attribute extensively‐adopted in topographically‐driven modelings, which is function of total contributing area (TCA) and effective contour length (EL). Despite of numerous studies about SCA and TCA, none has focused on the investigation of existing EL definitions and adaption of point‐scale SCA concept to two‐dimensional pixel of digital elevation model (DEM). This work conducts a systematic research on rationality of existing EL definitions, proposal of new EL definition and concept of pixel‐scale SCA on gridded DEM. To overcome the defects of existing EL definitions, a new EL definition based on Triangular Discretization and Spatial Geometry (TDSG) is proposed in this work. SCA concept is extended from point scale to pixel scale for adapting to context of gridded DEM. The solutions of true pixel‐scale SCA, TCA, and EL in integral forms are deduced based on the solutions of point‐scale SCAs obtained by method of Zhou and Liu (2002, https://doi.org/10.1080/13658810210149425) or Gallant and Hutchinson (2011, https://doi.org/10.1029/2009WR008540). Besides, true pixel‐scale SCA, TCA, and EL are solved analytically for several synthetic surfaces. Numerical experiments indicate that (a) TDSG definition is superior to all existing EL definitions in physical mechanism, spatial characteristics, and computational precisions on synthetic surfaces and a real‐world DEM. (b) Spatial characteristics of SCA are controlled mainly by TCA and tuned slightly by EL, while overall precision of SCA is affected seriously by both TCA and EL. (c) TDSG definition is the only EL definition of responding accurately and sensitively to convergent and dispersive characteristics of local terrains.