A Generalized Multistep Dynamic (GMD) TOPMODEL

Abstract

IntroductionTOPMODEL (Beven & Kirkby, 1979) continues to be one of the most widely applied hydrological models in both research and practice (Beven et al., 2021). It assumes that, independent of their specific spatial locations, some parts of the catchment will manifest similar tendencies to become, and remain, saturated during a storm. Based on a catchment-specific Topographic Index (TI) of similarity, these areas are grouped together to form Hydrologically Similar Units (HSUs), for which the numerical computations are performed when estimating a catchment's runoff response to rainfall. This grouping has enabled the dramatic reduction in runtimes associated with TOPMODEL, compared to fully spatially distributed models such as those of Freeze and Harlan (1969), Loague (2010), and Gao et al. (2015.Though fast, TOPMODEL is a lumped model in that only a single value of catchment average subsurface storage is updated in each timestep, from which individual HSU subsurface storage values are back-calculated according to the deviation of their TI value from the catchment average TI value (Beven, 2011, p. 211); hence, it can be construed as a quasi single-store (equally a pseudo multi-store) model. Implicit in such application of a time-invariant TI is the assumption (a) that the transients of water-table between HSUs across the catchment are fast enough, that in each timestep water table can be approximated by a steady-state configuration. At the same time the (quasi) single-store representation leads to assumption (b) that during rainfall there is always downslope flow at each and every point in the catchment, equal to the recharge rate from all of the upslope areas draining to that point (i.e., there is always downslope connectivity everywhere, all the way to the stream network) (Beven et al., 2021). Both assumptions (a) and (b) are clearly approximations.Dynamic-TOPMODEL of Beven and Freer (2001) relaxed both of the above assumptions by allowing subsurface storage of individual HSUs to vary locally and independently of both the catchment average storage and TI, by incorporating a time-dependent kinematic wave solution to the subsurface flow. However, since its introduction 20 years ago, and despite significantly improving catchment representation, the original steady-state version has remained the preferred choice (albeit sometimes with modifications/improvements) (