A Generalized Multistep Dynamic (GMD) TOPMODEL

Abstract

AbstractThere is a lack of Ordinary Differential Equation (ODE) formulations in numerical hydrology, contributing to the lack of application of canned adaptive timestep solvers; hence the continued dominance of fixed (e.g., Euler) timestep techniques despite their fundamental problems. In this paper, we reformulate Dynamic‐TOPMODEL into a constraint‐handling ODE form and use MATLAB's advanced adaptive ODE‐solvers to solve the resulting system of equations. For wider applicability, but based on existing research and/or first principles, we developed Generalized Multistep Dynamic TOPMODEL which includes: iso‐basin spatial discretization, diffusion wave routing, depth‐dependent overland flow velocity, relaxing the assumption of water‐table parallelism to the ground surface, a power‐law hydraulic conductivity profile, new unsaturated zone flux, and a reference frame adjustment. To demonstrate the model we calibrate it to a peat catchment case study, for which we also test sensitivity to spatial discretization. Our results suggest that (a) a five‐fold improvement in model runtime can result from adaptive timestepping; (b) the additional iso‐basin discretization layer, as a way to further constrain spatial information where needed, also improves performance; and (c) the common‐practice arbitrary Topographic Index (TI) discretization substantially alters calibrated parameters. More objective and physically constrained (e.g., top‐down) approaches to TI classification may be needed.