A Fully Coupled Numerical Solution of Water, Vapor, Heat, and Water Stable Isotope Transport in Soil

Abstract

Modeling water stable isotope transport in soil is crucial to sharpen our understanding of water cycles in terrestrial ecosystems. Although several models for soil water isotope transport have been developed, many rely on a semi-coupled numerical approach, solving isotope transport only after obtaining solutions from water and heat transport equations. However, this approach may increase instability and errors of model. Here, we developed an algorithm that solves one-dimensional water, heat, and isotope transport equations with a fully coupled method (MOIST). Our results showed that MOIST is more stable under various spatial and temporal discretization than semi-coupled method and has good agreement with semi-analytical solutions of isotope transport. We also validated MOIST with long-term measurements from a lysimeter study under three scenarios with soil hydraulic parameters calibrated by HYDRUS-1D in the first two scenarios and by MOIST in the last scenario. In scenario 1, MOIST showed an overall NSE, KGE, and MAE of simulated δ¹⁸O of 0.47, 0.58, and 0.92‰, respectively, compared to the 0.31, 0.60, and 1.00‰ from HYDRUS-1D; In scenario 2, these indices of MOIST were 0.33, 0.52, and 1.04‰, respectively, compared to the 0.19, 0.58, and 1.15‰ from HYDRUS-1D; In scenario 3, calibrated MOIST exhibited the highest NSE (0.48) and KGE (0.76), the smallest MAE (0.90) among all scenarios. These findings indicate MOIST has better performance in simulating water flow and isotope transport in simplified ecosystems than HYDRUS-1D, suggesting the great potential of MOIST in furthering our understandings of ecohydrological processes in terrestrial ecosystems.