skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Technical Note: A generic law-of-the-minimum flux limiter for simulating substrate limitation in biogeochemical models

Abstract

We present a generic flux limiter to account for mass limitations from an arbitrary number of substrates in a biogeochemical reaction network. The flux limiter is based on the observation that substrate (e.g., nitrogen, phosphorus) limitation in biogeochemical models can be represented as to ensure mass conservative and non-negative numerical solutions to the governing ordinary differential equations. Application of the flux limiter includes two steps: (1) formulation of the biogeochemical processes with a matrix of stoichiometric coefficients and (2) application of Liebig's law of the minimum using the dynamic stoichiometric relationship of the reactants. This approach contrasts with the ad hoc down-regulation approaches that are implemented in many existing models (such as CLM4.5 and the ACME (Accelerated Climate Modeling for Energy) Land Model (ALM)) of carbon and nutrient interactions, which are error prone when adding new processes, even for experienced modelers. Through an example implementation with a CENTURY-like decomposition model that includes carbon, nitrogen, and phosphorus, we show that our approach (1) produced almost identical results to that from the ad hoc down-regulation approaches under non-limiting nutrient conditions, (2) properly resolved the negative solutions under substrate-limited conditions where the simple clipping approach failed, (3) successfully avoided the potential conceptual ambiguities that are implied by thosemore » ad hoc down-regulation approaches. We expect our approach will make future biogeochemical models easier to improve and more robust.« less

Authors:
 [1];  [1]
  1. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Dept. of Climate and Carbon Sciences
Publication Date:
Research Org.:
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Biological and Environmental Research (BER) (SC-23)
OSTI Identifier:
1377412
Grant/Contract Number:  
AC02-05CH11231
Resource Type:
Accepted Manuscript
Journal Name:
Biogeosciences (Online)
Additional Journal Information:
Journal Name: Biogeosciences (Online); Journal Volume: 13; Journal Issue: 3; Journal ID: ISSN 1726-4189
Publisher:
European Geosciences Union
Country of Publication:
United States
Language:
English
Subject:
58 GEOSCIENCES

Citation Formats

Tang, J. Y., and Riley, W. J. Technical Note: A generic law-of-the-minimum flux limiter for simulating substrate limitation in biogeochemical models. United States: N. p., 2016. Web. doi:10.5194/bg-13-723-2016.
Tang, J. Y., & Riley, W. J. Technical Note: A generic law-of-the-minimum flux limiter for simulating substrate limitation in biogeochemical models. United States. doi:10.5194/bg-13-723-2016.
Tang, J. Y., and Riley, W. J. Fri . "Technical Note: A generic law-of-the-minimum flux limiter for simulating substrate limitation in biogeochemical models". United States. doi:10.5194/bg-13-723-2016. https://www.osti.gov/servlets/purl/1377412.
@article{osti_1377412,
title = {Technical Note: A generic law-of-the-minimum flux limiter for simulating substrate limitation in biogeochemical models},
author = {Tang, J. Y. and Riley, W. J.},
abstractNote = {We present a generic flux limiter to account for mass limitations from an arbitrary number of substrates in a biogeochemical reaction network. The flux limiter is based on the observation that substrate (e.g., nitrogen, phosphorus) limitation in biogeochemical models can be represented as to ensure mass conservative and non-negative numerical solutions to the governing ordinary differential equations. Application of the flux limiter includes two steps: (1) formulation of the biogeochemical processes with a matrix of stoichiometric coefficients and (2) application of Liebig's law of the minimum using the dynamic stoichiometric relationship of the reactants. This approach contrasts with the ad hoc down-regulation approaches that are implemented in many existing models (such as CLM4.5 and the ACME (Accelerated Climate Modeling for Energy) Land Model (ALM)) of carbon and nutrient interactions, which are error prone when adding new processes, even for experienced modelers. Through an example implementation with a CENTURY-like decomposition model that includes carbon, nitrogen, and phosphorus, we show that our approach (1) produced almost identical results to that from the ad hoc down-regulation approaches under non-limiting nutrient conditions, (2) properly resolved the negative solutions under substrate-limited conditions where the simple clipping approach failed, (3) successfully avoided the potential conceptual ambiguities that are implied by those ad hoc down-regulation approaches. We expect our approach will make future biogeochemical models easier to improve and more robust.},
doi = {10.5194/bg-13-723-2016},
journal = {Biogeosciences (Online)},
number = 3,
volume = 13,
place = {United States},
year = {2016},
month = {2}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 2 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

The Community Earth System Model: A Framework for Collaborative Research
journal, September 2013

  • Hurrell, James W.; Holland, M. M.; Gent, P. R.
  • Bulletin of the American Meteorological Society, Vol. 94, Issue 9
  • DOI: 10.1175/BAMS-D-12-00121.1

Trait-Based Representation of Biological Nitrification: Model Development, Testing, and Predicted Community Composition
journal, January 2012

  • Bouskill, Nicholas J.; Tang, Jinyun; Riley, William J.
  • Frontiers in Microbiology, Vol. 3
  • DOI: 10.3389/fmicb.2012.00364

Nitrogen limitation on land and in the sea: How can it occur?
journal, January 1991

  • Vitousek, PeterM.; Howarth, RobertW.
  • Biogeochemistry, Vol. 13, Issue 2
  • DOI: 10.1007/BF00002772

Preferential use of organic nitrogen for growth by a non-mycorrhizal arctic sedge
journal, January 1993

  • Chapin, F. Stuart; Moilanen, Lori; Kielland, Knut
  • Nature, Vol. 361, Issue 6408
  • DOI: 10.1038/361150a0

Terrestrial phosphorus limitation: mechanisms, implications, and nitrogen–phosphorus interactions
journal, January 2010

  • Vitousek, Peter M.; Porder, Stephen; Houlton, Benjamin Z.
  • Ecological Applications, Vol. 20, Issue 1
  • DOI: 10.1890/08-0127.1

A global model of carbon, nitrogen and phosphorus cycles for the terrestrial biosphere
journal, January 2010


CLM4-BeTR, a generic biogeochemical transport and reaction module for CLM4: model development, evaluation, and application
journal, January 2013

  • Tang, J. Y.; Riley, W. J.; Koven, C. D.
  • Geoscientific Model Development, Vol. 6, Issue 1
  • DOI: 10.5194/gmd-6-127-2013

Carbon–Concentration and Carbon–Climate Feedbacks in CMIP5 Earth System Models
journal, August 2013

  • Arora, Vivek K.; Boer, George J.; Friedlingstein, Pierre
  • Journal of Climate, Vol. 26, Issue 15
  • DOI: 10.1175/JCLI-D-12-00494.1

Sulfur limitation increases nitrate and amino acid pools in tropical forages
journal, January 2013

  • Schmidt, Fabiana; De Bona, Fabiano D.; Monteiro, Francisco A.
  • Crop and Pasture Science, Vol. 64, Issue 1
  • DOI: 10.1071/CP12336

Meta-analysis of high-latitude nitrogen-addition and warming studies implies ecological mechanisms overlooked by land models
journal, January 2014


An improved and generalized second order, unconditionally positive, mass conserving integration scheme for biochemical systems
journal, March 2008


Soil heterogeneity in lumped mineralization–immobilization models
journal, May 2008


Positive Numerical Integration Methods for Chemical Kinetic Systems
journal, July 2001


The role of phosphorus dynamics in tropical forests – a modeling study using CLM-CNP
journal, January 2014


A generic biogeochemical module for Earth system models: Next Generation BioGeoChemical Module (NGBGC), version 1.0
journal, January 2013


Future productivity and carbon storage limited by terrestrial nutrient availability
journal, April 2015

  • Wieder, William R.; Cleveland, Cory C.; Smith, W. Kolby
  • Nature Geoscience, Vol. 8, Issue 6
  • DOI: 10.1038/ngeo2413

Dynamics of C, N, P and S in grassland soils: a model
journal, February 1988

  • Parton, W. J.; Stewart, J. W. B.; Cole, C. V.
  • Biogeochemistry, Vol. 5, Issue 1
  • DOI: 10.1007/BF02180320

Nitrogen limitation on land: how can it occur in Earth system models?
journal, February 2015

  • Thomas, R. Quinn; Brookshire, E. N. Jack; Gerber, Stefan
  • Global Change Biology, Vol. 21, Issue 5
  • DOI: 10.1111/gcb.12813

Nitrogen cycling and feedbacks in a global dynamic land model: MODELING THE LAND NITROGEN CYCLE
journal, January 2010

  • Gerber, Stefan; Hedin, Lars O.; Oppenheimer, Michael
  • Global Biogeochemical Cycles, Vol. 24, Issue 1
  • DOI: 10.1029/2008GB003336

The Community Earth System Model: A Framework for Collaborative Research
journal, February 2013

  • Hurrell, James W.; Holland, M. M.; Gent, P. R.
  • Bulletin of the American Meteorological Society
  • DOI: 10.1175/BAMS-D-12-00121

Influence of carbon-nitrogen cycle coupling on land model response to CO 2 fertilization and climate variability : INFLUENCE OF CARBON-NITROGEN COUPLING
journal, December 2007

  • Thornton, Peter E.; Lamarque, Jean-François; Rosenbloom, Nan A.
  • Global Biogeochemical Cycles, Vol. 21, Issue 4
  • DOI: 10.1029/2006GB002868