Journal Article

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

Li, Huijie, Fu, Han, Neil, Eric John, Si, Bingcheng

2025

Overview

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. Plain Language Summary To accurately trace how water navigates through ecosystems, we depend on numerical models that replicate the behavior of water stable isotopes within the soil. Traditional approaches to these models typically solve the equations related to water flow and temperature first, then addressing the equations for isotopes. This sequential approach can inadvertently amplify inaccuracies in the isotope data. Our novel method MOIST, concurrently resolves the equations for water, heat, and isotopes. We validated MOIST by comparing it with both analytical predictions and real‐world observations. The findings demonstrate that MOIST aligned closely with both theoretical expectations and actual measurements, establishing its credibility as an effective tool for simulating the transport of stable water isotopes within the soil‐plant‐atmosphere continuum. Key Points A fully coupled soil water, heat, and isotope transport model, named MOIST, was developed The fully coupled method is less sensitive to spatial and temporal discretization and more accurate than the semi‐coupled method MOIST is a powerful and open‐source tool for simulating one‐dimensional water stable isotope transport within soil

• Publisher: John Wiley & Sons, Inc,Wiley
• Subject: Algorithms / Ecohydrology / Ecosystems / Exact solutions / fully coupled / Heat / heat transfer / Heat transport / Hydrologic cycle / Hydrological cycle / isotope transport simulation / Isotopes / lysimeters / Mathematical analysis / Mathematical models / Moisture content / Numerical models / Soil / Soil analysis / Soil moisture / Soil temperature / Soil water / Stable isotopes / Terrestrial ecosystems / Transport equations / vapors / Water / Water flow / water stable isotopes