SUPECA kinetics for scaling redox reactions in networks of mixed substrates and consumers and an example application to aerobic soil respiration
Abstract
Several land biogeochemical models used for studying carbon–climate feedbacks have begun explicitly representing microbial dynamics. However, to our knowledge, there has been no theoretical work on how to achieve a consistent scaling of the complex biogeochemical reactions from microbial individuals to populations, communities, and interactions with plants and mineral soils. We focus here on developing a mathematical formulation of the substrate–consumer relationships for consumer-mediated redox reactions of the form A+BE→ products, where products could be, e.g., microbial biomass or bioproducts. Under the quasi-steady-state approximation, these substrate–consumer relationships can be formulated as the computationally difficult full equilibrium chemistry problem or approximated analytically with the dual Monod (DM) or synthesizing unit (SU) kinetics. We find that DM kinetics is scaling inconsistently for reaction networks because (1) substrate limitations are not considered, (2) contradictory assumptions are made regarding the substrate processing rate when transitioning from single- to multi-substrate redox reactions, and (3) the product generation rate cannot be scaled from one to multiple substrates. In contrast, SU kinetics consistently scales the product generation rate from one to multiple substrates but predicts unrealistic results as consumer abundances reach large values with respect to their substrates. We attribute this deficit to SU's failure to incorporate substrate limitation inmore »
- Authors:
- Publication Date:
- Research Org.:
- Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Biological and Environmental Research (BER)
- OSTI Identifier:
- 1378394
- Alternate Identifier(s):
- OSTI ID: 1408471
- Grant/Contract Number:
- AC02-05CH11231
- Resource Type:
- Published Article
- Journal Name:
- Geoscientific Model Development (Online)
- Additional Journal Information:
- Journal Name: Geoscientific Model Development (Online) Journal Volume: 10 Journal Issue: 9; Journal ID: ISSN 1991-9603
- Publisher:
- Copernicus Publications, EGU
- Country of Publication:
- Germany
- Language:
- English
- Subject:
- 58 GEOSCIENCES; 37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY
Citation Formats
Tang, Jin-Yun, and Riley, William J. SUPECA kinetics for scaling redox reactions in networks of mixed substrates and consumers and an example application to aerobic soil respiration. Germany: N. p., 2017.
Web. doi:10.5194/gmd-10-3277-2017.
Tang, Jin-Yun, & Riley, William J. SUPECA kinetics for scaling redox reactions in networks of mixed substrates and consumers and an example application to aerobic soil respiration. Germany. https://doi.org/10.5194/gmd-10-3277-2017
Tang, Jin-Yun, and Riley, William J. Tue .
"SUPECA kinetics for scaling redox reactions in networks of mixed substrates and consumers and an example application to aerobic soil respiration". Germany. https://doi.org/10.5194/gmd-10-3277-2017.
@article{osti_1378394,
title = {SUPECA kinetics for scaling redox reactions in networks of mixed substrates and consumers and an example application to aerobic soil respiration},
author = {Tang, Jin-Yun and Riley, William J.},
abstractNote = {Several land biogeochemical models used for studying carbon–climate feedbacks have begun explicitly representing microbial dynamics. However, to our knowledge, there has been no theoretical work on how to achieve a consistent scaling of the complex biogeochemical reactions from microbial individuals to populations, communities, and interactions with plants and mineral soils. We focus here on developing a mathematical formulation of the substrate–consumer relationships for consumer-mediated redox reactions of the form A+BE→ products, where products could be, e.g., microbial biomass or bioproducts. Under the quasi-steady-state approximation, these substrate–consumer relationships can be formulated as the computationally difficult full equilibrium chemistry problem or approximated analytically with the dual Monod (DM) or synthesizing unit (SU) kinetics. We find that DM kinetics is scaling inconsistently for reaction networks because (1) substrate limitations are not considered, (2) contradictory assumptions are made regarding the substrate processing rate when transitioning from single- to multi-substrate redox reactions, and (3) the product generation rate cannot be scaled from one to multiple substrates. In contrast, SU kinetics consistently scales the product generation rate from one to multiple substrates but predicts unrealistic results as consumer abundances reach large values with respect to their substrates. We attribute this deficit to SU's failure to incorporate substrate limitation in its derivation. To address these issues, we propose SUPECA (SU plus the equilibrium chemistry approximation – ECA) kinetics, which consistently imposes substrate and consumer mass balance constraints. We show that SUPECA kinetics satisfies the partition principle, i.e., scaling invariance across a network of an arbitrary number of reactions (e.g., as in Newton's law of motion and Dalton's law of partial pressures). We tested SUPECA kinetics with the equilibrium chemistry solution for some simple problems and found SUPECA outperformed SU kinetics. As an example application, we show that a steady-state SUPECA-based approach predicted an aerobic soil respiration moisture response function that agreed well with laboratory observations. We conclude that, as an extension to SU and ECA kinetics, SUPECA provides a robust mathematical representation of complex soil substrate–consumer interactions and can be applied to improve Earth system model (ESM) land models.},
doi = {10.5194/gmd-10-3277-2017},
journal = {Geoscientific Model Development (Online)},
number = 9,
volume = 10,
place = {Germany},
year = {Tue Sep 05 00:00:00 EDT 2017},
month = {Tue Sep 05 00:00:00 EDT 2017}
}
https://doi.org/10.5194/gmd-10-3277-2017
Web of Science
Works referenced in this record:
Multiple soil nutrient competition between plants, microbes, and mineral surfaces: model development, parameterization, and example applications in several tropical forests
journal, January 2016
- Zhu, Q.; Riley, W. J.; Tang, J.
- Biogeosciences, Vol. 13, Issue 1
Some Characteristics of Simple Types of Predation and Parasitism
journal, July 1959
- Holling, C. S.
- The Canadian Entomologist, Vol. 91, Issue 7
Long residence times of rapidly decomposable soil organic matter: application of a multi-phase, multi-component, and vertically resolved model (BAMS1) to soil carbon dynamics
journal, January 2014
- Riley, W. J.; Maggi, F.; Kleber, M.
- Geoscientific Model Development, Vol. 7, Issue 4
Carbon cost of plant nitrogen acquisition: global carbon cycle impact from an improved plant nitrogen cycle in the Community Land Model
journal, January 2016
- Shi, Mingjie; Fisher, Joshua B.; Brzostek, Edward R.
- Global Change Biology, Vol. 22, Issue 3
An analytical model of the decomposition of soil organic matter
journal, January 1979
- Smith, O. L.
- Soil Biology and Biochemistry, Vol. 11, Issue 6
Long-Term Effects of Crop Management in Wheat-Fallow: II. CENTURY Model Simulations
journal, January 1994
- Parton, William J.; Rasmussen, P. E.
- Soil Science Society of America Journal, Vol. 58, Issue 2
Dynamic model of flexible phytoplankton nutrient uptake
journal, December 2011
- Bonachela, J. A.; Raghib, M.; Levin, S. A.
- Proceedings of the National Academy of Sciences, Vol. 108, Issue 51
Effect of climate data on simulated carbon and nitrogen balances for Europe: CLIMATE DATA EFFECTS
journal, May 2016
- Blanke, Jan Hendrik; Lindeskog, Mats; Lindström, Johan
- Journal of Geophysical Research: Biogeosciences, Vol. 121, Issue 5
Bacterial dry matter content and biomass estimations.
journal, January 1984
- Bratbak, G.; Dundas, I.
- Applied and Environmental Microbiology, Vol. 48, Issue 4
Analytical investigation on 3D non-Boussinesq mountain wave drag for wind profiles with vertical variations
journal, March 2007
- Tang, Jin-yuan; Tang, Jie; Wang, Yuan
- Applied Mathematics and Mechanics, Vol. 28, Issue 3
Kinetics of nutrient-limited transport and microbial growth.
journal, January 1985
- Button, D. K.
- Microbiological Reviews, Vol. 49, Issue 3
Nutrient Cycling and Nutrient Use Efficiency
journal, April 1982
- Vitousek, Peter
- The American Naturalist, Vol. 119, Issue 4
Technical Note: A generic law-of-the-minimum flux limiter for simulating substrate limitation in biogeochemical models
journal, January 2016
- Tang, J. Y.; Riley, W. J.
- Biogeosciences, Vol. 13, Issue 3
A theoretical model for nutrient uptake in phytoplankton
journal, January 1991
- Aksnes, Dl; Egge, Jk
- Marine Ecology Progress Series, Vol. 70
Hydraulic properties of adsorbed water films in unsaturated porous media: HYDRAULIC PROPERTIES OF ADSORBED WATER FILMS
journal, June 2009
- Tokunaga, Tetsu K.
- Water Resources Research, Vol. 45, Issue 6
The validity of the application of simple kinetic analysis to heterogeneous microbial populations1
journal, January 1973
- Williams, P. J. Leb.
- Limnology and Oceanography, Vol. 18, Issue 1
Root traits explain observed tundra vegetation nitrogen uptake patterns: Implications for trait-based land models: Tundra N Uptake Model-Data Comparison
journal, December 2016
- Zhu, Qing; Iversen, Colleen M.; Riley, William J.
- Journal of Geophysical Research: Biogeosciences, Vol. 121, Issue 12
Soil Microbial Respiration at Different Water Potentials and Temperatures: Theory and Mathematical Modeling
journal, January 1994
- Grant, R. F.; Rochette, P.
- Soil Science Society of America Journal, Vol. 58, Issue 6
Coupled groundwater flow and transport: 1. Verification of variable density flow and transport models
journal, February 1998
- Kolditz, Olaf; Ratke, Rainer; Diersch, Hans-Jörg G.
- Advances in Water Resources, Vol. 21, Issue 1
Emergent Biogeography of Microbial Communities in a Model Ocean
journal, March 2007
- Follows, M. J.; Dutkiewicz, S.; Grant, S.
- Science, Vol. 315, Issue 5820
A trait-based approach for downscaling complexity in plankton ecosystem models
journal, November 2009
- Merico, Agostino; Bruggeman, Jorn; Wirtz, Kai
- Ecological Modelling, Vol. 220, Issue 21
Transport of dissolved hydrocarbons influenced by oxygen-limited biodegradation: 1. Theoretical development
journal, December 1986
- Borden, Robert C.; Bedient, Philip B.
- Water Resources Research, Vol. 22, Issue 13
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
Modeling Microbial Dynamics in Heterogeneous Environments: Growth on Soil Carbon Sources
journal, December 2011
- Resat, Haluk; Bailey, Vanessa; McCue, Lee Ann
- Microbial Ecology, Vol. 63, Issue 4
Terrestrial Carbon Cycle: Climate Relations in Eight CMIP5 Earth System Models
journal, November 2013
- Shao, Pu; Zeng, Xubin; Sakaguchi, Koichi
- Journal of Climate, Vol. 26, Issue 22
A Theoretical Study Relating the Concentration and Diffusion of Oxygen to the Biology of Organisms in soil
journal, July 1968
- Griffin, D. M.
- New Phytologist, Vol. 67, Issue 3
Improved modelling of soil nitrogen losses
journal, July 2015
- Zhu, Qing; Riley, William J.
- Nature Climate Change, Vol. 5, Issue 8
Modeling Oxygen Diffusion in Aggregated Soils: I. Anaerobiosis inside the Aggregates
journal, January 1994
- Renault, Pierre; Stengel, Pierre
- Soil Science Society of America Journal, Vol. 58, Issue 4
The Functional Response of Invertebrate Predators to Prey Density
journal, January 1966
- Holling, C. S.
- Memoirs of the Entomological Society of Canada, Vol. 98, Issue S48
Modeling the impact of soil aggregate size on selenium immobilization
journal, January 2013
- Kausch, M. F.; Pallud, C. E.
- Biogeosciences, Vol. 10, Issue 3
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
Quantifying wetland methane emissions with process-based models of different complexities
journal, January 2010
- Tang, J.; Zhuang, Q.; Shannon, R. D.
- Biogeosciences, Vol. 7, Issue 11
An improved analysis of forest carbon dynamics using data assimilation
journal, January 2005
- Williams, Mathew; Schwarz, Paul A.; Law, Beverly E.
- Global Change Biology, Vol. 11, Issue 1
The Growth of Bacterial Cultures
journal, October 1949
- Monod, J.
- Annual Review of Microbiology, Vol. 3, Issue 1
Meta-analysis of high-latitude nitrogen-addition and warming studies implies ecological mechanisms overlooked by land models
journal, January 2014
- Bouskill, N. J.; Riley, W. J.; Tang, J. Y.
- Biogeosciences, Vol. 11, Issue 23
Modeling coupled enzymatic and solute transport controls on decomposition in drying soils
journal, April 2016
- Manzoni, S.; Moyano, F.; Kätterer, T.
- Soil Biology and Biochemistry, Vol. 95
Transient competitive complexation in biological kinetic isotope fractionation explains nonsteady isotopic effects: Theory and application to denitrification in soils
journal, January 2009
- Maggi, Federico; Riley, William J.
- Journal of Geophysical Research, Vol. 114, Issue G4
Equifinality in parameterization of process-based biogeochemistry models: A significant uncertainty source to the estimation of regional carbon dynamics: EQUIFINALITY IN REGIONAL CARBON DYNAMICS
journal, October 2008
- Tang, Jinyun; Zhuang, Qianlai
- Journal of Geophysical Research: Biogeosciences, Vol. 113, Issue G4
Trait-Based Community Ecology of Phytoplankton
journal, December 2008
- Litchman, Elena; Klausmeier, Christopher A.
- Annual Review of Ecology, Evolution, and Systematics, Vol. 39, Issue 1
Nutrient uptake rate as a function of cell size and surface transporter density: A Michaelis-like approximation to the model of Pasciak and Gavis
journal, October 2008
- Armstrong, Robert A.
- Deep Sea Research Part I: Oceanographic Research Papers, Vol. 55, Issue 10
Mineral properties, microbes, transport, and plant-input profiles control vertical distribution and age of soil carbon stocks
journal, April 2017
- Dwivedi, D.; Riley, W. J.; Torn, M. S.
- Soil Biology and Biochemistry, Vol. 107
Enzyme Kinetics at High Enzyme Concentration
journal, May 2000
- Schnell, S.
- Bulletin of Mathematical Biology, Vol. 62, Issue 3
On the relationships between the Michaelis–Menten kinetics, reverse Michaelis–Menten kinetics, equilibrium chemistry approximation kinetics, and quadratic kinetics
journal, January 2015
- Tang, J. Y.
- Geoscientific Model Development, Vol. 8, Issue 12
Physics of chemoreception
journal, November 1977
- Berg, H. C.; Purcell, E. M.
- Biophysical Journal, Vol. 20, Issue 2
Future challenges in coupled C–N–P cycle models for terrestrial ecosystems under global change: a review
journal, November 2016
- Achat, David L.; Augusto, Laurent; Gallet-Budynek, Anne
- Biogeochemistry, Vol. 131, Issue 1-2
A new theory of plant-microbe nutrient competition resolves inconsistencies between observations and model predictions
journal, March 2017
- Zhu, Qing; Riley, William J.; Tang, Jinyun
- Ecological Applications, Vol. 27, Issue 3
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
Harmonized soil property values for broad-scale modelling (WISE30sec) with estimates of global soil carbon stocks
journal, May 2016
- Batjes, N. H.
- Geoderma, Vol. 269
A trait-based approach for modelling microbial litter decomposition
journal, May 2012
- Allison, S. D.
- Ecology Letters, Vol. 15, Issue 9
Erratum: Ever-fluctuating single enzyme molecules: Michaelis-Menten equation revisited
journal, March 2006
- English, Brian P.; Min, Wei; van Oijen, Antoine M.
- Nature Chemical Biology, Vol. 2, Issue 3
Extending the quasi-steady state approximation by changing variables
journal, January 1996
- Borghans, J.
- Bulletin of Mathematical Biology, Vol. 58, Issue 1
Uncertainties in CMIP5 Climate Projections due to Carbon Cycle Feedbacks
journal, January 2014
- Friedlingstein, Pierre; Meinshausen, Malte; Arora, Vivek K.
- Journal of Climate, Vol. 27, Issue 2
Modeling and measuring biogeochemical reactions: system consistency, data needs, and rate formulations
journal, August 2001
- Yeh, Gour-Tsyh; Burgos, William D.; Zachara, John M.
- Advances in Environmental Research, Vol. 5, Issue 3
Effects of model structural uncertainty on carbon cycle projections: biological nitrogen fixation as a case study
journal, April 2015
- Wieder, William R.; Cleveland, Cory C.; Lawrence, David M.
- Environmental Research Letters, Vol. 10, Issue 4
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
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
A Note on the Kinetics of Enzyme Action
journal, January 1925
- Briggs, George Edward; Haldane, John Burdon Sanderson
- Biochemical Journal, Vol. 19, Issue 2
Integrating microbial physiology and physio-chemical principles in soils with the MIcrobial-MIneral Carbon Stabilization (MIMICS) model
journal, January 2014
- Wieder, W. R.; Grandy, A. S.; Kallenbach, C. M.
- Biogeosciences, Vol. 11, Issue 14
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
The mode of Action of Urease and of Enzymes in General
journal, October 1914
- Van Slyke, Donald D.; Cullen, Glenn E.
- Journal of Biological Chemistry, Vol. 19, Issue 2
Flow Partitioning in Fully Saturated Soil Aggregates
journal, March 2014
- Yang, Xiaofan; Richmond, Marshall C.; Scheibe, Timothy D.
- Transport in Porous Media, Vol. 103, Issue 2
Microbial activity in response to water-filled pore space of variably eroded southern Piedmont soils
journal, January 1999
- Franzluebbers, A. J.
- Applied Soil Ecology, Vol. 11, Issue 1
A global sensitivity analysis and Bayesian inference framework for improving the parameter estimation and prediction of a process-based Terrestrial Ecosystem Model
journal, January 2009
- Tang, Jinyun; Zhuang, Qianlai
- Journal of Geophysical Research, Vol. 114, Issue D15
Parameter estimation in surface exchange models using nonlinear inversion: how many parameters can we estimate and which measurements are most useful?
journal, May 2001
- Wang, Ying-Ping; Leuning, Ray; Cleugh, Helen A.
- Global Change Biology, Vol. 7, Issue 5
Carbon and nitrogen dynamics along the decay continuum: Plant litter to soil organic matter
journal, April 1989
- Melillo, Jerry M.; Aber, John D.; Linkins, Arthur E.
- Plant and Soil, Vol. 115, Issue 2
Barriers to predicting changes in global terrestrial methane fluxes: analyses using CLM4Me, a methane biogeochemistry model integrated in CESM
journal, January 2011
- Riley, W. J.; Subin, Z. M.; Lawrence, D. M.
- Biogeosciences, Vol. 8, Issue 7
Global patterns and substrate-based mechanisms of the terrestrial nitrogen cycle
journal, March 2016
- Niu, Shuli; Classen, Aimée T.; Dukes, Jeffrey S.
- Ecology Letters, Vol. 19, Issue 6
Quasi steady-state approximations in complex intracellular signal transduction networks – a word of caution
journal, June 2007
- Pedersen, Morten Gram; Bersani, Alberto Maria; Bersani, Enrico
- Journal of Mathematical Chemistry, Vol. 43, Issue 4
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
Weaker soil carbon–climate feedbacks resulting from microbial and abiotic interactions
journal, November 2014
- Tang, Jinyun; Riley, William J.
- Nature Climate Change, Vol. 5, Issue 1
Microbe-driven turnover offsets mineral-mediated storage of soil carbon under elevated CO2
journal, November 2014
- Sulman, Benjamin N.; Phillips, Richard P.; Oishi, A. Christopher
- Nature Climate Change, Vol. 4, Issue 12
Are oxygen limitations under recognized regulators of organic carbon turnover in upland soils?
journal, January 2016
- Keiluweit, Marco; Nico, Peter S.; Kleber, Markus
- Biogeochemistry, Vol. 127, Issue 2-3
The effect of vertically resolved soil biogeochemistry and alternate soil C and N models on C dynamics of CLM4
journal, January 2013
- Koven, C. D.; Riley, W. J.; Subin, Z. M.
- Biogeosciences, Vol. 10, Issue 11
Nitrogen Mineralization: Challenges of a Changing Paradigm
journal, March 2004
- Schimel, Joshua P.; Bennett, Jennifer
- Ecology, Vol. 85, Issue 3
Radiocarbon constraints imply reduced carbon uptake by soils during the 21st century
journal, September 2016
- He, Y.; Trumbore, S. E.; Torn, M. S.
- Science, Vol. 353, Issue 6306
Explicitly representing soil microbial processes in Earth system models: Soil microbes in earth system models
journal, October 2015
- Wieder, William R.; Allison, Steven D.; Davidson, Eric A.
- Global Biogeochemical Cycles, Vol. 29, Issue 10
Three-dimensional model for multi-component reactive transport with variable density groundwater flow
journal, May 2006
- Mao, X.; Prommer, H.; Barry, D. A.
- Environmental Modelling & Software, Vol. 21, Issue 5
Convergent modelling of past soil organic carbon stocks but divergent projections
journal, January 2015
- Luo, Z.; Wang, E.; Zheng, H.
- Biogeosciences, Vol. 12, Issue 14
Predicting the Responses of Soil Nitrite-Oxidizers to Multi-Factorial Global Change: A Trait-Based Approach
journal, May 2016
- Le Roux, Xavier; Bouskill, Nicholas J.; Niboyet, Audrey
- Frontiers in Microbiology, Vol. 7
A general model for multiple substrate biodegradation. Application to co-metabolism of structurally non-analogous compounds
journal, December 2003
- Brandt, B.
- Water Research, Vol. 37, Issue 20
Sensitivity-guided reduction of parametric dimensionality for multi-objective calibration of watershed models
journal, August 2009
- van Werkhoven, Kathryn; Wagener, Thorsten; Reed, Patrick
- Advances in Water Resources, Vol. 32, Issue 8
The Synthesizing Unit as model for the stoichiometric fusion and branching of metabolic fluxes
journal, July 1998
- Kooijman, S. A. L. M.
- Biophysical Chemistry, Vol. 73, Issue 1-2
Sensitivity of decomposition rates of soil organic matter with respect to simultaneous changes in temperature and moisture
journal, February 2015
- Sierra, Carlos A.; Trumbore, Susan E.; Davidson, Eric A.
- Journal of Advances in Modeling Earth Systems, Vol. 7, Issue 1
A total quasi-steady-state formulation of substrate uptake kinetics in complex networks and an example application to microbial litter decomposition
journal, January 2013
- Tang, J. Y.; Riley, W. J.
- Biogeosciences, Vol. 10, Issue 12
A Technique for Estimating Denitrification Rates at Different soil Temperatures, Water Contents, and Nitrate Concentrations
journal, January 1991
- Grant, R. F.
- Soil Science, Vol. 152, Issue 1
Simulation of carbon and nitrogen transformations in soil: Mineralization
journal, October 1993
- Grant, R. F.; Juma, N. G.; McGill, W. B.
- Soil Biology and Biochemistry, Vol. 25, Issue 10
Role of substrate unbinding in Michaelis-Menten enzymatic reactions
journal, March 2014
- Reuveni, S.; Urbakh, M.; Klafter, J.
- Proceedings of the National Academy of Sciences, Vol. 111, Issue 12
Parametric sensitivity analysis of precipitation at global and local scales in the Community Atmosphere Model CAM5
journal, April 2015
- Qian, Yun; Yan, Huiping; Hou, Zhangshuan
- Journal of Advances in Modeling Earth Systems, Vol. 7, Issue 2
A new top boundary condition for modeling surface diffusive exchange of a generic volatile tracer: theoretical analysis and application to soil evaporation
journal, January 2013
- Tang, J. Y.; Riley, W. J.
- Hydrology and Earth System Sciences, Vol. 17, Issue 2
Modelling changes in nitrogen cycling to sustain increases in forest productivity under elevated atmospheric CO 2 and contrasting site conditions
journal, January 2013
- Grant, R. F.
- Biogeosciences, Vol. 10, Issue 11
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