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Title: Transient dynamics of terrestrial carbon storage: mathematical foundation and its applications

Abstract

Terrestrial ecosystems have absorbed roughly 30 % of anthropogenic CO 2 emissions over the past decades, but it is unclear whether this carbon (C) sink will endure into the future. Despite extensive modeling and experimental and observational studies, what fundamentally determines transient dynamics of terrestrial C storage under global change is still not very clear. Here we develop a new framework for understanding transient dynamics of terrestrial C storage through mathematical analysis and numerical experiments. Our analysis indicates that the ultimate force driving ecosystem C storage change is the C storage capacity, which is jointly determined by ecosystem C input (e.g., net primary production, NPP) and residence time. Since both C input and residence time vary with time, the C storage capacity is time-dependent and acts as a moving attractor that actual C storage chases. The rate of change in C storage is proportional to the C storage potential, which is the difference between the current storage and the storage capacity. The C storage capacity represents instantaneous responses of the land C cycle to external forcing, whereas the C storage potential represents the internal capability of the land C cycle to influence the C change trajectory in the next timemore » step. The influence happens through redistribution of net C pool changes in a network of pools with different residence times. Moreover, this and our other studies have demonstrated that one matrix equation can replicate simulations of most land C cycle models (i.e., physical emulators). As a result, simulation outputs of those models can be placed into a three-dimensional (3-D) parameter space to measure their differences. The latter can be decomposed into traceable components to track the origins of model uncertainty. In addition, the physical emulators make data assimilation computationally feasible so that both C flux- and pool-related datasets can be used to better constrain model predictions of land C sequestration. Overall, this new mathematical framework offers new approaches to understanding, evaluating, diagnosing, and improving land C cycle models.« less

Authors:
; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ORCiD logo;
Publication Date:
Research Org.:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1394454
DOE Contract Number:  
AC05-00OR22725
Resource Type:
Journal Article
Journal Name:
Biogeosciences (Online)
Additional Journal Information:
Journal Volume: 14; Journal Issue: 1; Journal ID: ISSN 1726-4189
Publisher:
European Geosciences Union
Country of Publication:
United States
Language:
English
Subject:
54 ENVIRONMENTAL SCIENCES

Citation Formats

Luo, Yiqi, Shi, Zheng, Lu, Xingjie, Xia, Jianyang, Liang, Junyi, Jiang, Jiang, Wang, Ying, Smith, Matthew J., Jiang, Lifen, Ahlström, Anders, Chen, Benito, Hararuk, Oleksandra, Hastings, Alan, Hoffman, Forrest, Medlyn, Belinda, Niu, Shuli, Rasmussen, Martin, Todd-Brown, Katherine, and Wang, Ying-Ping. Transient dynamics of terrestrial carbon storage: mathematical foundation and its applications. United States: N. p., 2017. Web. doi:10.5194/bg-14-145-2017.
Luo, Yiqi, Shi, Zheng, Lu, Xingjie, Xia, Jianyang, Liang, Junyi, Jiang, Jiang, Wang, Ying, Smith, Matthew J., Jiang, Lifen, Ahlström, Anders, Chen, Benito, Hararuk, Oleksandra, Hastings, Alan, Hoffman, Forrest, Medlyn, Belinda, Niu, Shuli, Rasmussen, Martin, Todd-Brown, Katherine, & Wang, Ying-Ping. Transient dynamics of terrestrial carbon storage: mathematical foundation and its applications. United States. doi:10.5194/bg-14-145-2017.
Luo, Yiqi, Shi, Zheng, Lu, Xingjie, Xia, Jianyang, Liang, Junyi, Jiang, Jiang, Wang, Ying, Smith, Matthew J., Jiang, Lifen, Ahlström, Anders, Chen, Benito, Hararuk, Oleksandra, Hastings, Alan, Hoffman, Forrest, Medlyn, Belinda, Niu, Shuli, Rasmussen, Martin, Todd-Brown, Katherine, and Wang, Ying-Ping. Sun . "Transient dynamics of terrestrial carbon storage: mathematical foundation and its applications". United States. doi:10.5194/bg-14-145-2017.
@article{osti_1394454,
title = {Transient dynamics of terrestrial carbon storage: mathematical foundation and its applications},
author = {Luo, Yiqi and Shi, Zheng and Lu, Xingjie and Xia, Jianyang and Liang, Junyi and Jiang, Jiang and Wang, Ying and Smith, Matthew J. and Jiang, Lifen and Ahlström, Anders and Chen, Benito and Hararuk, Oleksandra and Hastings, Alan and Hoffman, Forrest and Medlyn, Belinda and Niu, Shuli and Rasmussen, Martin and Todd-Brown, Katherine and Wang, Ying-Ping},
abstractNote = {Terrestrial ecosystems have absorbed roughly 30 % of anthropogenic CO2 emissions over the past decades, but it is unclear whether this carbon (C) sink will endure into the future. Despite extensive modeling and experimental and observational studies, what fundamentally determines transient dynamics of terrestrial C storage under global change is still not very clear. Here we develop a new framework for understanding transient dynamics of terrestrial C storage through mathematical analysis and numerical experiments. Our analysis indicates that the ultimate force driving ecosystem C storage change is the C storage capacity, which is jointly determined by ecosystem C input (e.g., net primary production, NPP) and residence time. Since both C input and residence time vary with time, the C storage capacity is time-dependent and acts as a moving attractor that actual C storage chases. The rate of change in C storage is proportional to the C storage potential, which is the difference between the current storage and the storage capacity. The C storage capacity represents instantaneous responses of the land C cycle to external forcing, whereas the C storage potential represents the internal capability of the land C cycle to influence the C change trajectory in the next time step. The influence happens through redistribution of net C pool changes in a network of pools with different residence times. Moreover, this and our other studies have demonstrated that one matrix equation can replicate simulations of most land C cycle models (i.e., physical emulators). As a result, simulation outputs of those models can be placed into a three-dimensional (3-D) parameter space to measure their differences. The latter can be decomposed into traceable components to track the origins of model uncertainty. In addition, the physical emulators make data assimilation computationally feasible so that both C flux- and pool-related datasets can be used to better constrain model predictions of land C sequestration. Overall, this new mathematical framework offers new approaches to understanding, evaluating, diagnosing, and improving land C cycle models.},
doi = {10.5194/bg-14-145-2017},
journal = {Biogeosciences (Online)},
issn = {1726-4189},
number = 1,
volume = 14,
place = {United States},
year = {2017},
month = {1}
}

Works referenced in this record:

Simple three-pool model accurately describes patterns of long-term litter decomposition in diverse climates
journal, August 2008


Quality: A Bridge between Theory and Experiment in Soil Organic Matter Studies
journal, September 1996

  • Ågren, Göran I.; Bosatta, Ernesto; Agren, Goran I.
  • Oikos, Vol. 76, Issue 3
  • DOI: 10.2307/3546345

Importance of vegetation dynamics for future terrestrial carbon cycling
journal, May 2015


Soil-carbon response to warming dependent on microbial physiology
journal, April 2010

  • Allison, Steven D.; Wallenstein, Matthew D.; Bradford, Mark A.
  • Nature Geoscience, Vol. 3, Issue 5
  • DOI: 10.1038/ngeo846

FLUXNET: A New Tool to Study the Temporal and Spatial Variability of Ecosystem–Scale Carbon Dioxide, Water Vapor, and Energy Flux Densities
journal, November 2001


Linear Analysis of soil Decomposition: Insights from the Century Model
journal, May 1998


Finding generality in ecology: a model for globally distributed experiments
journal, December 2013

  • Borer, Elizabeth T.; Harpole, W. Stanley; Adler, Peter B.
  • Methods in Ecology and Evolution, Vol. 5, Issue 1
  • DOI: 10.1111/2041-210X.12125

Dynamics of Carbon and Nitrogen in the Organic Matter of the Soil: A Generic Theory
journal, July 1991

  • Bosatta, Ernesto; Agren, Goran I.
  • The American Naturalist, Vol. 138, Issue 1
  • DOI: 10.1086/285213

Texture, Climate, and Cultivation Effects on Soil Organic Matter Content in U.S. Grassland Soils
journal, January 1989


Contributions to accelerating atmospheric CO2 growth from economic activity, carbon intensity, and efficiency of natural sinks
journal, October 2007

  • Canadell, J. G.; Le Quere, C.; Raupach, M. R.
  • Proceedings of the National Academy of Sciences, Vol. 104, Issue 47
  • DOI: 10.1073/pnas.0702737104

Model Uncertainty, Data Mining and Statistical Inference
journal, January 1995

  • Chatfield, Chris
  • Journal of the Royal Statistical Society. Series A (Statistics in Society), Vol. 158, Issue 3
  • DOI: 10.2307/2983440

The role of residence time in diagnostic models of global carbon storage capacity: model decomposition based on a traceable scheme
journal, November 2015

  • Yizhao, Chen; Jianyang, Xia; Zhengguo, Sun
  • Scientific Reports, Vol. 5, Issue 1
  • DOI: 10.1038/srep16155

Attributing the increase in atmospheric CO2 to emitters and absorbers
journal, July 2013

  • Ciais, P.; Gasser, T.; Paris, J. D.
  • Nature Climate Change, Vol. 3, Issue 10
  • DOI: 10.1038/nclimate1942

Forest water use and water use efficiency at elevated CO 2 : a model-data intercomparison at two contrasting temperate forest FACE sites
journal, March 2013

  • De Kauwe, Martin G.; Medlyn, Belinda E.; Zaehle, Sönke
  • Global Change Biology, Vol. 19, Issue 6
  • DOI: 10.1111/gcb.12164

Ever-fluctuating single enzyme molecules: Michaelis-Menten equation revisited
journal, December 2005

  • English, Brian P.; Min, Wei; van Oijen, Antoine M.
  • Nature Chemical Biology, Vol. 2, Issue 2
  • DOI: 10.1038/nchembio759

Examining soil carbon uncertainty in a global model: response of microbial decomposition to temperature, moisture and nutrient limitation
journal, January 2013


A biochemical model of photosynthetic CO2 assimilation in leaves of C3 species
journal, June 1980

  • Farquhar, G. D.; von Caemmerer, S.; Berry, J. A.
  • Planta, Vol. 149, Issue 1
  • DOI: 10.1007/BF00386231

Assessing uncertainties in a second-generation dynamic vegetation model caused by ecological scale limitations
journal, July 2010


Coordinated distributed experiments: an emerging tool for testing global hypotheses in ecology and environmental science
journal, April 2013

  • Fraser, Lauchlan H.; Henry, Hugh AL; Carlyle, Cameron N.
  • Frontiers in Ecology and the Environment, Vol. 11, Issue 3
  • DOI: 10.1890/110279

Climate–Carbon Cycle Feedback Analysis: Results from the C 4 MIP Model Intercomparison
journal, July 2006

  • Friedlingstein, P.; Cox, P.; Betts, R.
  • Journal of Climate, Vol. 19, Issue 14
  • DOI: 10.1175/JCLI3800.1

Observations and assessment of forest carbon dynamics following disturbance in North America: FOREST CARBON AFTER DISTURBANCE
journal, June 2012

  • Goetz, S. J.; Bond-Lamberty, B.; Law, B. E.
  • Journal of Geophysical Research: Biogeosciences, Vol. 117, Issue G2
  • DOI: 10.1029/2011JG001733

Oscillatory enzyme reactions and Michaelis-Menten kinetics
journal, July 2013


Vulnerability of high-latitude soil organic carbon in North America to disturbance
journal, January 2011

  • Grosse, Guido; Harden, Jennifer; Turetsky, Merritt
  • Journal of Geophysical Research, Vol. 116
  • DOI: 10.1029/2010JG001507

Mapping of CO 2 at high spatiotemporal resolution using satellite observations: Global distributions from OCO-2 : HIGH RESOLUTION MAPPING OF SATELLITE CO
journal, March 2012

  • Hammerling, Dorit M.; Michalak, Anna M.; Kawa, S. Randolph
  • Journal of Geophysical Research: Atmospheres, Vol. 117, Issue D6
  • DOI: 10.1029/2011JD017015

Evaluation and improvement of a global land model against soil carbon data using a Bayesian Markov chain Monte Carlo method: Calibration of a carbon cycle model
journal, March 2014

  • Hararuk, Oleksandra; Xia, Jianyang; Luo, Yiqi
  • Journal of Geophysical Research: Biogeosciences, Vol. 119, Issue 3
  • DOI: 10.1002/2013JG002535

Microbial models with data-driven parameters predict stronger soil carbon responses to climate change
journal, March 2015

  • Hararuk, Oleksandra; Smith, Matthew J.; Luo, Yiqi
  • Global Change Biology, Vol. 21, Issue 6
  • DOI: 10.1111/gcb.12827

Modelling photosynthesis of cotton grown in elevated CO2
journal, April 1992


Effects of biotic disturbances on forest carbon cycling in the United States and Canada
journal, October 2011


Global climate change and soil carbon stocks; predictions from two contrasting models for the turnover of organic carbon in soil
journal, January 2005


Terrestrial biosphere model performance for inter-annual variability of land-atmosphere CO2 exchange
journal, March 2012


Fire dynamics during the 20th century simulated by the Community Land Model
journal, January 2010


Global Carbon Budget 2015
journal, January 2015

  • Le Quéré, C.; Moriarty, R.; Andrew, R. M.
  • Earth System Science Data, Vol. 7, Issue 2
  • DOI: 10.5194/essd-7-349-2015

Modeling permafrost thaw and ecosystem carbon cycle under annual and seasonal warming at an Arctic tundra site in Alaska: MODELING PERMAFROST C CYCLE
journal, June 2014

  • Li, Jianwei; Luo, Yiqi; Natali, Susan
  • Journal of Geophysical Research: Biogeosciences, Vol. 119, Issue 6
  • DOI: 10.1002/2013JG002569

On the Temperature Dependence of Soil Respiration
journal, June 1994

  • Lloyd, J.; Taylor, J. A.
  • Functional Ecology, Vol. 8, Issue 3
  • DOI: 10.2307/2389824

Parameter identifiability, constraint, and equifinality in data assimilation with ecosystem models
journal, April 2009

  • Luo, Yiqi; Weng, Ensheng; Wu, Xiaowen
  • Ecological Applications, Vol. 19, Issue 3
  • DOI: 10.1890/08-0561.1

Toward more realistic projections of soil carbon dynamics by Earth system models: SOIL CARBON MODELING
journal, January 2016

  • Luo, Yiqi; Ahlström, Anders; Allison, Steven D.
  • Global Biogeochemical Cycles, Vol. 30, Issue 1
  • DOI: 10.1002/2015GB005239

Dynamic disequilibrium of the terrestrial carbon cycle under global change
journal, February 2011


ELEVATED CO 2 DIFFERENTIATES ECOSYSTEM CARBON PROCESSES: DECONVOLUTION ANALYSIS OF DUKE FOREST FACE DATA
journal, August 2001


Sustainability of terrestrial carbon sequestration: A case study in Duke Forest with inversion approach: SUSTAINABILITY OF TERRESTRIAL CARBON SEQUESTRATION
journal, March 2003

  • Luo, Yiqi; White, Luther W.; Canadell, Josep G.
  • Global Biogeochemical Cycles, Vol. 17, Issue 1
  • DOI: 10.1029/2002GB001923

Ecological forecasting and data assimilation in a data-rich era
journal, July 2011

  • Luo, Yiqi; Ogle, Kiona; Tucker, Colin
  • Ecological Applications, Vol. 21, Issue 5
  • DOI: 10.1890/09-1275.1

Predictability of the terrestrial carbon cycle
journal, December 2014

  • Luo, Yiqi; Keenan, Trevor F.; Smith, Matthew
  • Global Change Biology, Vol. 21, Issue 5
  • DOI: 10.1111/gcb.12766

Soil carbon and nitrogen mineralization: Theory and models across scales
journal, July 2009


Temporal Changes in c and n Stocks of Restored Prairie: Implications for c Sequestration Strategies
journal, September 2008

  • Matamala, R.; Jastrow, J. D.; Miller, R. M.
  • Ecological Applications, Vol. 18, Issue 6
  • DOI: 10.1890/07-1609.1

Using ecosystem experiments to improve vegetation models
journal, May 2015

  • Medlyn, Belinda E.; Zaehle, Sönke; De Kauwe, Martin G.
  • Nature Climate Change, Vol. 5, Issue 6
  • DOI: 10.1038/nclimate2621

A Method for Scaling Vegetation Dynamics: the Ecosystem Demography Model (ed)
journal, November 2001


Energy Storage and the Balance of Producers and Decomposers in Ecological Systems
journal, April 1963


The Structure, Distribution, and Biomass of the World's Forests
journal, November 2013


Forest soil carbon and nitrogen cycles under biomass harvest: Stability, transient response, and feedback
journal, June 2016


Analysis of Factors Controlling Soil Organic Matter Levels in Great Plains Grasslands1
journal, January 1987


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

Observations and modeling of biomass and soil organic matter dynamics for the grassland biome worldwide
journal, December 1993

  • Parton, W. J.; Scurlock, J. M. O.; Ojima, D. S.
  • Global Biogeochemical Cycles, Vol. 7, Issue 4
  • DOI: 10.1029/93GB02042

Terrestrial ecosystem production: A process model based on global satellite and surface data
journal, December 1993

  • Potter, Christopher S.; Randerson, James T.; Field, Christopher B.
  • Global Biogeochemical Cycles, Vol. 7, Issue 4
  • DOI: 10.1029/93GB02725

Modeling fire and the terrestrial carbon balance: MODELING FIRE AND LAND CARBON BALANCE
journal, July 2011

  • Prentice, I. C.; Kelley, D. I.; Foster, P. N.
  • Global Biogeochemical Cycles, Vol. 25, Issue 3
  • DOI: 10.1029/2010GB003906

Predictive Models of Forest Dynamics
journal, June 2008


Structural analysis of three global land models on carbon cycle simulations using a traceability framework
journal, January 2014


Circumpolar assessment of permafrost C quality and its vulnerability over time using long-term incubation data
journal, October 2013

  • Schädel, Christina; Schuur, Edward A. G.; Bracho, Rosvel
  • Global Change Biology, Vol. 20, Issue 2
  • DOI: 10.1111/gcb.12417

A model-data intercomparison of CO 2 exchange across North America: Results from the North American Carbon Program site synthesis
journal, January 2010

  • Schwalm, Christopher R.; Williams, Christopher A.; Schaefer, Kevin
  • Journal of Geophysical Research, Vol. 115
  • DOI: 10.1029/2009JG001229

Comparison of Radiative and Physiological Effects of Doubled Atmospheric CO2 on Climate
journal, March 1996


Inverse analysis of coupled carbon–nitrogen cycles against multiple datasets at ambient and elevated CO 2
journal, September 2015

  • Shi, Zheng; Yang, Yuanhe; Zhou, Xuhui
  • Journal of Plant Ecology, Vol. 9, Issue 3
  • DOI: 10.1093/jpe/rtv059

A general mathematical framework for representing soil organic matter dynamics
journal, November 2015

  • Sierra, Carlos A.; Müller, Markus
  • Ecological Monographs, Vol. 85, Issue 4
  • DOI: 10.1890/15-0361.1

When is a measured soil organic matter fraction equivalent to a model pool?
journal, September 2002


Biophysical and economic limits to negative CO2 emissions
journal, December 2015

  • Smith, Pete; Davis, Steven J.; Creutzig, Felix
  • Nature Climate Change, Vol. 6, Issue 1
  • DOI: 10.1038/nclimate2870

Soil Carbon Saturation: Linking Concept and Measurable Carbon Pools
journal, January 2008

  • Stewart, Catherine E.; Plante, Alain F.; Paustian, Keith
  • Soil Science Society of America Journal, Vol. 72, Issue 2
  • DOI: 10.2136/sssaj2007.0104

Causes of variation in soil carbon simulations from CMIP5 Earth system models and comparison with observations
journal, January 2013

  • Todd-Brown, K. E. O.; Randerson, J. T.; Post, W. M.
  • Biogeosciences, Vol. 10, Issue 3
  • DOI: 10.5194/bg-10-1717-2013

A two-leaf model for canopy conductance, photosynthesis and partitioning of available energy I:
journal, May 1998


Oscillatory behavior of two nonlinear microbial models of soil carbon decomposition
journal, January 2014


Responses of two nonlinear microbial models to warming and increased carbon input
journal, January 2016


Soil hydrological properties regulate grassland ecosystem responses to multifactor global change: A modeling analysis
journal, January 2008

  • Weng, Ensheng; Luo, Yiqi
  • Journal of Geophysical Research, Vol. 113, Issue G3
  • DOI: 10.1029/2007JG000539

Ecosystem carbon storage capacity as affected by disturbance regimes: A general theoretical model: THE REGIME MODEL
journal, July 2012

  • Weng, Ensheng; Luo, Yiqi; Wang, Weile
  • Journal of Geophysical Research: Biogeosciences, Vol. 117, Issue G3
  • DOI: 10.1029/2012JG002040

Regional uptake and release of crop carbon in the United States
journal, January 2011


Global soil carbon projections are improved by modelling microbial processes
journal, July 2013

  • Wieder, William R.; Bonan, Gordon B.; Allison, Steven D.
  • Nature Climate Change, Vol. 3, Issue 10
  • DOI: 10.1038/nclimate1951

Traceable components of terrestrial carbon storage capacity in biogeochemical models
journal, March 2013

  • Xia, Jianyang; Luo, Yiqi; Wang, Ying-Ping
  • Global Change Biology, Vol. 19, Issue 7
  • DOI: 10.1111/gcb.12172

Enzyme Kinetics, Past and Present
journal, December 2013


Carbon quality and the temperature sensitivity of soil organic carbon decomposition in a tallgrass prairie
journal, July 2012


Carbon and nitrogen dynamics during forest stand development: a global synthesis
journal, February 2011


Rates of litter decomposition in terrestrial ecosystems: global patterns and controlling factors
journal, March 2008

  • Zhang, Deqiang; Hui, Dafeng; Luo, Yiqi
  • Journal of Plant Ecology, Vol. 1, Issue 2
  • DOI: 10.1093/jpe/rtn002