A hybrid framework for the spin-up and initialization of distributed coupled ecohydrological-biogeochemical models

Accurate initialization is a critical step in fully distributed ecohydrological and soil biogeochemical modeling applications, yet is often hindered by the computational cost of achieving steady-state conditions across large spatial domains. This study presents a novel initialization framework that combines a flux-tracking 1D spin-up with a random forest (RF) algorithm to efficiently generate spatially heterogeneous and topography-informed initial conditions accounting for lateral fluxes of water, carbon, and nutrients. The framework first performs a limited number of 1D simulations to obtain steady-state conditions in a subset of representative cells, then uses RF to extrapolate these results across the catchment. Applied to T&C-BG-2D, a fully coupled distributed ecohydrological-soil biogeochemical model, the scheme reconstructs over 90 % of the spatial variability in soil carbon and nutrient patterns in terms of probability distribution similarity while reducing computational demands by up to 90 % compared to a fully distributed spinup procedure. A sensitivity analysis across multiple simulation scenarios reveals that the number of tracked cells required, varying from 20 % to 40 % of total domain grid cells, depends on the catchment's spatial complexity and the environmental covariates embedded in the RF predictors. The framework developed here can be applied to other spatially distributed models that explicitly account for lateral transfer fluxes, enabling large-scale distributed ecohydrologicalbiogeochemical model initialization under constrained computational budgets.