A Generalized Multistep Dynamic (GMD) TOPMODEL

There 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.

Automated summary

This paper discusses the lack of Ordinary Differential Equation (ODE) models in numerical hydrology and the problems with fixed timestep techniques. By reformulating Dynamic-TOPMODEL into a constraint-handling ODE form and developing the Generalized Multistep Dynamic TOPMODEL, the authors improve the applicability and performance of the models. The results show that adaptive timestepping can significantly improve model runtime, and the iso-basin spatial discretization and improved TI classification method also enhance model performance.