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Title: Addressing numerical challenges in introducing a reactive transport code into a land surface model: a biogeochemical modeling proof-of-concept with CLM–PFLOTRAN 1.0

Abstract

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 computationalmore » 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 function provides a smooth transition between a zero-order rate when the reactant is abundant and first-order rate when the reactant becomes limiting. When the half saturation is small, marching through the transition may require small time step sizes to resolve the sharp change within a small range of concentration values. Our results from simple tests and CLM-PFLOTRAN simulations caution against use of SU and indicate that accurate, stable, and relatively efficient solutions can be achieved with LT and downregulation with Monod substrate limiting function and residual concentration.« less

Authors:
ORCiD logo; ; ORCiD logo; ; ; ; ; ORCiD logo; ; ORCiD logo; ;
Publication Date:
Research Org.:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Sandia National Lab. (SNL-CA), Livermore, CA (United States); Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Sponsoring Org.:
USDOE Office of Science (SC); Work for Others (WFO)
OSTI Identifier:
1240298
Alternate Identifier(s):
OSTI ID: 1240537; OSTI ID: 1261540; OSTI ID: 1266840; OSTI ID: 1327768
Grant/Contract Number:  
AC05-00OR22725; NGEE-Arctic; AC04-94AL85000
Resource Type:
Journal Article: Published Article
Journal Name:
Geoscientific Model Development (Online)
Additional Journal Information:
Journal Name: Geoscientific Model Development (Online) Journal Volume: 9 Journal Issue: 3; Journal ID: ISSN 1991-9603
Publisher:
Copernicus Publications, EGU
Country of Publication:
Germany
Language:
English
Subject:
58 GEOSCIENCES

Citation Formats

Tang, Guoping, Yuan, Fengming, Bisht, Gautam, Hammond, Glenn E., Lichtner, Peter C., Kumar, Jitendra, Mills, Richard T., Xu, Xiaofeng, Andre, Ben, Hoffman, Forrest M., Painter, Scott L., and Thornton, Peter E.. Addressing numerical challenges in introducing a reactive transport code into a land surface model: a biogeochemical modeling proof-of-concept with CLM–PFLOTRAN 1.0. Germany: N. p., 2016. Web. doi:10.5194/gmd-9-927-2016.
Tang, Guoping, Yuan, Fengming, Bisht, Gautam, Hammond, Glenn E., Lichtner, Peter C., Kumar, Jitendra, Mills, Richard T., Xu, Xiaofeng, Andre, Ben, Hoffman, Forrest M., Painter, Scott L., & Thornton, Peter E.. Addressing numerical challenges in introducing a reactive transport code into a land surface model: a biogeochemical modeling proof-of-concept with CLM–PFLOTRAN 1.0. Germany. https://doi.org/10.5194/gmd-9-927-2016
Tang, Guoping, Yuan, Fengming, Bisht, Gautam, Hammond, Glenn E., Lichtner, Peter C., Kumar, Jitendra, Mills, Richard T., Xu, Xiaofeng, Andre, Ben, Hoffman, Forrest M., Painter, Scott L., and Thornton, Peter E.. 2016. "Addressing numerical challenges in introducing a reactive transport code into a land surface model: a biogeochemical modeling proof-of-concept with CLM–PFLOTRAN 1.0". Germany. https://doi.org/10.5194/gmd-9-927-2016.
@article{osti_1240298,
title = {Addressing numerical challenges in introducing a reactive transport code into a land surface model: a biogeochemical modeling proof-of-concept with CLM–PFLOTRAN 1.0},
author = {Tang, Guoping and Yuan, Fengming and Bisht, Gautam and Hammond, Glenn E. and Lichtner, Peter C. and Kumar, Jitendra and Mills, Richard T. and Xu, Xiaofeng and Andre, Ben and Hoffman, Forrest M. and Painter, Scott L. and Thornton, Peter E.},
abstractNote = {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 function provides a smooth transition between a zero-order rate when the reactant is abundant and first-order rate when the reactant becomes limiting. When the half saturation is small, marching through the transition may require small time step sizes to resolve the sharp change within a small range of concentration values. Our results from simple tests and CLM-PFLOTRAN simulations caution against use of SU and indicate that accurate, stable, and relatively efficient solutions can be achieved with LT and downregulation with Monod substrate limiting function and residual concentration.},
doi = {10.5194/gmd-9-927-2016},
url = {https://www.osti.gov/biblio/1240298}, journal = {Geoscientific Model Development (Online)},
issn = {1991-9603},
number = 3,
volume = 9,
place = {Germany},
year = {2016},
month = {3}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record at https://doi.org/10.5194/gmd-9-927-2016

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Cited by: 4 works
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