Coupling a Reactive Transport Code with a Global Land Surface Model for Mechanistic Biogeochemistry Representation: 1. Addressing the Challenge of Nonnegativity

• Published in: Geoscientific Model Development
• Main Authors: Tang, Guoping, Yuan, Fengming, Bisht, Gautam, Hammond, Glenn E., Lichtner, Peter C., Collier, Nathaniel O., Kumar, Jitendra, Mills, Richard T., Xu, Xiaofeng, Andre, Ben, Hoffman, Forrest M., Painter, Scott L., Thornton, Peter E.
• Language: unknown
• Published: 2022
• Subjects: 58 GEOSCIENCES; Arctic
• Online Access: http://www.osti.gov/servlets/purl/1240537; https://www.osti.gov/biblio/1240537; https://doi.org/10.5194/gmd-9-927-2016

Reactive transport codes (e.g., PFLOTRAN) are increasingly used to improve the representation of biogeochemical processes in terrestrial ecosystem models (e.g., the Community Land Model, CLM). As CLM and PFLOTRAN use explicit and implicit time stepping, implementation of CLM biogeochemical reactions in PFLOTRAN can result in negative concentration, which is not physical and can cause numerical instability and errors. The objective of this work is to address the nonnegativity challenge to obtain accurate, efficient, and robust solutions. We illustrate the implementation of a reaction network with the CLM-CN decomposition, nitrification, denitrification, and plant nitrogen uptake reactions and test the implementation at arctic, temperate, and tropical sites. We examine use of scaling back the update during each iteration (SU), log transformation (LT), and downregulating the reaction rate to account for reactant availability limitation to enforce nonnegativity. Both SU and LT guarantee nonnegativity but with implications. When a very small scaling factor occurs due to either consumption or numerical overshoot, and the iterations are deemed converged because of too small an update, SU can introduce excessive numerical error. LT involves multiplication of the Jacobian matrix by the concentration vector, which increases the condition number, decreases the time step size, and increases the computational cost. Neither SU nor SE prevents zero concentration. When the concentration is close to machine precision or 0, a small positive update stops all reactions for SU, and LT can fail due to a singular Jacobian matrix. The consumption rate has to be downregulated such that the solution to the mathematical representation is positive. A first-order rate downregulates consumption and is nonnegative, and adding a residual concentration makes it positive. For zero-order rate or when the reaction rate is not a function of a reactant, representing the availability limitation of each reactant with a Monod substrate limiting ...