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

Title: Diagnosing the Dynamics of Observed and Simulated Ecosystem Gross Primary Productivity with Time Causal Information Theory Quantifiers

Abstract

Data analysis and model-data comparisons in the environmental sciences require diagnostic measures that quantify time series dynamics and structure, and are robust to noise in observational data. This paper investigates the temporal dynamics of environmental time series using measures quantifying their information content and complexity. The measures are used to classify natural processes on one hand, and to compare models with observations on the other. The present analysis focuses on the global carbon cycle as an area of research in which model-data integration and comparisons are key to improving our understanding of natural phenomena. We investigate the dynamics of observed and simulated time series of Gross Primary Productivity (GPP), a key variable in terrestrial ecosystems that quantifies ecosystem carbon uptake. However, the dynamics, patterns and magnitudes of GPP time series, both observed and simulated, vary substantially on different temporal and spatial scales. Here we demonstrate that information content and complexity, or Information Theory Quantifiers (ITQ) for short, serve as robust and efficient data-analytical and model benchmarking tools for evaluating the temporal structure and dynamical properties of simulated or observed time series at various spatial scales. At continental scale, we compare GPP time series simulated with two models and an observations-basedmore » product. This analysis reveals qualitative differences between model evaluation based on ITQ compared to traditional model performance metrics, indicating that good model performance in terms of absolute or relative error does not imply that the dynamics of the observations is captured well. Furthermore, we show, using an ensemble of site-scale measurements obtained from the FLUXNET archive in the Mediterranean, that model-data or model-model mismatches as indicated by ITQ can be attributed to and interpreted as differences in the temporal structure of the respective ecological time series. At global scale, our understanding of C fluxes relies on the use of consistently applied land models. Here, we use ITQ to evaluate model structure: The measures are largely insensitive to climatic scenarios, land use and atmospheric gas concentrations used to drive them, but clearly separate the structure of 13 different land models taken from the CMIP5 archive and an observations-based product. In conclusion, diagnostic measures of this kind provide data-analytical tools that distinguish different types of natural processes based solely on their dynamics, and are thus highly suitable for environmental science applications such as model structural diagnostics.« less

Authors:
 [1]; ORCiD logo [2];  [3];  [4];  [1];  [5];  [1];  [6];  [7]
  1. Max Planck Society, Jena (Germany). Max Planck Inst. for Biogeochemistry
  2. Norwegian Inst. of Bioeconomy Research (NIBIO), Akershus, As (Norway); Univ. Federal de Alagoas, Maceio , Alagoas (Brazil). Inst. de Fisica
  3. Max Planck Society, Jena (Germany). Max Planck Inst. for Biogeochemistry; German Centre for Integrative Biodiversity Research (iDiv), Leipzig (Germany)
  4. Univ. of Bayreuth (Germany)
  5. The Inversion Lab., Hamburg (Germany)
  6. Univ. Federal de Alagoas, Maceio , Alagoas (Brazil). Inst. de Fisica; Inst. Tecnologico de Buenos Aires (ITBA) and CONICET, Buenos Aires (Argentina); Univ. de los Andes, Las Condes, Santiago (Chile). Facultad de Ingenieria y Ciencias Aplicadas, Complex Systems Group
  7. Pacific Northwest National Laboratory, Richland, WA (United States)
Publication Date:
Research Org.:
Max Planck Society, Jena (Germany). Max Planck Inst. for Biogeochemistry
Sponsoring Org.:
USDOE; National Science Foundation (NSF); Consejo Nacional de Investigaciones Científicas y Tecnicas (CONICET)
Contributing Org.:
Max Planck Institute for Biochemistry; University of Tuscia; Universite Laval; Environment Canada
OSTI Identifier:
1378442
Grant/Contract Number:  
310003/2016-4
Resource Type:
Accepted Manuscript
Journal Name:
PLoS ONE
Additional Journal Information:
Journal Volume: 11; Journal Issue: 10; Journal ID: ISSN 1932-6203
Publisher:
Public Library of Science
Country of Publication:
United States
Language:
English
Subject:
54 ENVIRONMENTAL SCIENCES

Citation Formats

Sippel, Sebastian, Lange, Holger, Mahecha, Miguel D., Hauhs, Michael, Bodesheim, Paul, Kaminski, Thomas, Gans, Fabian, Rosso, Osvaldo A., and Bond-Lamberty, Ben. Diagnosing the Dynamics of Observed and Simulated Ecosystem Gross Primary Productivity with Time Causal Information Theory Quantifiers. United States: N. p., 2016. Web. https://doi.org/10.1371/journal.pone.0164960.
Sippel, Sebastian, Lange, Holger, Mahecha, Miguel D., Hauhs, Michael, Bodesheim, Paul, Kaminski, Thomas, Gans, Fabian, Rosso, Osvaldo A., & Bond-Lamberty, Ben. Diagnosing the Dynamics of Observed and Simulated Ecosystem Gross Primary Productivity with Time Causal Information Theory Quantifiers. United States. https://doi.org/10.1371/journal.pone.0164960
Sippel, Sebastian, Lange, Holger, Mahecha, Miguel D., Hauhs, Michael, Bodesheim, Paul, Kaminski, Thomas, Gans, Fabian, Rosso, Osvaldo A., and Bond-Lamberty, Ben. Thu . "Diagnosing the Dynamics of Observed and Simulated Ecosystem Gross Primary Productivity with Time Causal Information Theory Quantifiers". United States. https://doi.org/10.1371/journal.pone.0164960. https://www.osti.gov/servlets/purl/1378442.
@article{osti_1378442,
title = {Diagnosing the Dynamics of Observed and Simulated Ecosystem Gross Primary Productivity with Time Causal Information Theory Quantifiers},
author = {Sippel, Sebastian and Lange, Holger and Mahecha, Miguel D. and Hauhs, Michael and Bodesheim, Paul and Kaminski, Thomas and Gans, Fabian and Rosso, Osvaldo A. and Bond-Lamberty, Ben},
abstractNote = {Data analysis and model-data comparisons in the environmental sciences require diagnostic measures that quantify time series dynamics and structure, and are robust to noise in observational data. This paper investigates the temporal dynamics of environmental time series using measures quantifying their information content and complexity. The measures are used to classify natural processes on one hand, and to compare models with observations on the other. The present analysis focuses on the global carbon cycle as an area of research in which model-data integration and comparisons are key to improving our understanding of natural phenomena. We investigate the dynamics of observed and simulated time series of Gross Primary Productivity (GPP), a key variable in terrestrial ecosystems that quantifies ecosystem carbon uptake. However, the dynamics, patterns and magnitudes of GPP time series, both observed and simulated, vary substantially on different temporal and spatial scales. Here we demonstrate that information content and complexity, or Information Theory Quantifiers (ITQ) for short, serve as robust and efficient data-analytical and model benchmarking tools for evaluating the temporal structure and dynamical properties of simulated or observed time series at various spatial scales. At continental scale, we compare GPP time series simulated with two models and an observations-based product. This analysis reveals qualitative differences between model evaluation based on ITQ compared to traditional model performance metrics, indicating that good model performance in terms of absolute or relative error does not imply that the dynamics of the observations is captured well. Furthermore, we show, using an ensemble of site-scale measurements obtained from the FLUXNET archive in the Mediterranean, that model-data or model-model mismatches as indicated by ITQ can be attributed to and interpreted as differences in the temporal structure of the respective ecological time series. At global scale, our understanding of C fluxes relies on the use of consistently applied land models. Here, we use ITQ to evaluate model structure: The measures are largely insensitive to climatic scenarios, land use and atmospheric gas concentrations used to drive them, but clearly separate the structure of 13 different land models taken from the CMIP5 archive and an observations-based product. In conclusion, diagnostic measures of this kind provide data-analytical tools that distinguish different types of natural processes based solely on their dynamics, and are thus highly suitable for environmental science applications such as model structural diagnostics.},
doi = {10.1371/journal.pone.0164960},
journal = {PLoS ONE},
number = 10,
volume = 11,
place = {United States},
year = {2016},
month = {10}
}

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

Citation Metrics:
Cited by: 6 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

A Mathematical Theory of Communication
journal, July 1948


Soil respiration across scales: The importance of a model–data integration framework for data interpretation
journal, June 2008

  • Reichstein, Markus; Beer, Christian
  • Journal of Plant Nutrition and Soil Science, Vol. 171, Issue 3
  • DOI: 10.1002/jpln.200700075

Ordinal analysis of time series
journal, October 2005


Entropy-Complexity Characterization of Brain Development in Chickens
journal, August 2014


Characterization of vehicle behavior with information theory
journal, October 2015

  • Aquino, Andre L. L.; Cavalcante, Tamer S. G.; Almeida, Eliana S.
  • The European Physical Journal B, Vol. 88, Issue 10
  • DOI: 10.1140/epjb/e2015-60384-x

Complexity-Entropy Causality Plane as a Complexity Measure for Two-Dimensional Patterns
journal, August 2012


Evaluation of ecosystem dynamics, plant geography and terrestrial carbon cycling in the LPJ dynamic global vegetation model
journal, February 2003


Comparing observations and process-based simulations of biosphere-atmosphere exchanges on multiple timescales: MODEL EVALUATION ON MULTIPLE TIMESCALES
journal, April 2010

  • Mahecha, M. D.; Reichstein, M.; Jung, M.
  • Journal of Geophysical Research: Biogeosciences, Vol. 115, Issue G2
  • DOI: 10.1029/2009JG001016

Ambiguities in Bandt–Pompe’s methodology for local entropic quantifiers
journal, April 2012

  • Olivares, Felipe; Plastino, Angelo; Rosso, Osvaldo A.
  • Physica A: Statistical Mechanics and its Applications, Vol. 391, Issue 8
  • DOI: 10.1016/j.physa.2011.12.033

Quantifiers for randomness of chaotic pseudo-random number generators
journal, August 2009

  • De Micco, L.; Larrondo, H. A.; Plastino, A.
  • Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 367, Issue 1901
  • DOI: 10.1098/rsta.2009.0075

Entropy analysis of the dynamics of El Niño/Southern Oscillation during the Holocene
journal, November 2010

  • Saco, Patricia M.; Carpi, Laura C.; Figliola, Alejandra
  • Physica A: Statistical Mechanics and its Applications, Vol. 389, Issue 21
  • DOI: 10.1016/j.physa.2010.07.006

A comprehensive benchmarking system for evaluating global vegetation models
journal, January 2013


A submonthly database for detecting changes in vegetation-atmosphere coupling: THE VEGETATION-ATMOSPHERE COUPLING INDEX
journal, November 2015

  • Zscheischler, Jakob; Orth, René; Seneviratne, Sonia I.
  • Geophysical Research Letters, Vol. 42, Issue 22
  • DOI: 10.1002/2015GL066563

Complexity–entropy analysis of daily stream flow time series in the continental United States
journal, November 2013

  • Serinaldi, Francesco; Zunino, Luciano; Rosso, Osvaldo A.
  • Stochastic Environmental Research and Risk Assessment, Vol. 28, Issue 7
  • DOI: 10.1007/s00477-013-0825-8

Intensive entropic non-triviality measure
journal, March 2004

  • Lamberti, P. W.; Martin, M. T.; Plastino, A.
  • Physica A: Statistical Mechanics and its Applications, Vol. 334, Issue 1-2
  • DOI: 10.1016/j.physa.2003.11.005

The meanings of entropy
journal, February 2005


An Overview of CMIP5 and the Experiment Design
journal, April 2012

  • Taylor, Karl E.; Stouffer, Ronald J.; Meehl, Gerald A.
  • Bulletin of the American Meteorological Society, Vol. 93, Issue 4
  • DOI: 10.1175/BAMS-D-11-00094.1

Will the tropical land biosphere dominate the climate–carbon cycle feedback during the twenty-first century?
journal, April 2007


The next generation of scenarios for climate change research and assessment
journal, February 2010

  • Moss, Richard H.; Edmonds, Jae A.; Hibbard, Kathy A.
  • Nature, Vol. 463, Issue 7282
  • DOI: 10.1038/nature08823

Towards a benchmark for land surface models: TOWARDS A BENCHMARK FOR LAND SURFACE MODELS
journal, November 2005


ESMValTool (v1.0) – a community diagnostic and performance metrics tool for routine evaluation of Earth system models in CMIP
journal, January 2016

  • Eyring, Veronika; Righi, Mattia; Lauer, Axel
  • Geoscientific Model Development, Vol. 9, Issue 5
  • DOI: 10.5194/gmd-9-1747-2016

Towards a public, standardized, diagnostic benchmarking system for land surface models
journal, January 2012


Detecting and quantifying temporal correlations in stochastic resonance via information theory measures
journal, April 2009


Harmonized European Long-Term Climate Data for Assessing the Effect of Changing Temporal Variability on Land–Atmosphere CO 2 Fluxes
journal, July 2014


A framework for benchmarking land models
journal, January 2012


A statistical measure of complexity
journal, December 1995


Ordinal pattern and statistical complexity analysis of daily stream flow time series
journal, June 2013


The (in)visible hand in the Libor market: an information theory approach
journal, August 2015

  • Bariviera, Aurelio Fernandez; Guercio, María Belén; Martinez, Lisana B.
  • The European Physical Journal B, Vol. 88, Issue 8
  • DOI: 10.1140/epjb/e2015-60410-1

Permutation Entropy and Its Main Biomedical and Econophysics Applications: A Review
journal, August 2012

  • Zanin, Massimiliano; Zunino, Luciano; Rosso, Osvaldo A.
  • Entropy, Vol. 14, Issue 8
  • DOI: 10.3390/e14081553

Bandt–Pompe approach to the classical-quantum transition
journal, September 2007


Contrasting chaos with noise via local versus global information quantifiers
journal, April 2012


Time Scales of a Chaotic Semiconductor Laser With Optical Feedback Under the Lens of a Permutation Information Analysis
journal, February 2011

  • Soriano, Miguel C.; Zunino, Luciano; Rosso, Osvaldo A.
  • IEEE Journal of Quantum Electronics, Vol. 47, Issue 2
  • DOI: 10.1109/JQE.2010.2078799

The organization of intrinsic computation: Complexity-entropy diagrams and the diversity of natural information processing
journal, December 2008

  • Feldman, David P.; McTague, Carl S.; Crutchfield, James P.
  • Chaos: An Interdisciplinary Journal of Nonlinear Science, Vol. 18, Issue 4
  • DOI: 10.1063/1.2991106

Info-quantifiers’ map-characterization revisited
journal, November 2010

  • Rosso, Osvaldo A.; De Micco, Luciana; Plastino, A.
  • Physica A: Statistical Mechanics and its Applications, Vol. 389, Issue 21
  • DOI: 10.1016/j.physa.2010.06.055

Towards a comprehensive assessment of model structural adequacy: ASSESSMENT OF MODEL STRUCTURAL ADEQUACY
journal, August 2012

  • Gupta, Hoshin V.; Clark, Martyn P.; Vrugt, Jasper A.
  • Water Resources Research, Vol. 48, Issue 8
  • DOI: 10.1029/2011WR011044

Generalized statistical complexity measures: Geometrical and analytical properties
journal, September 2006

  • Martin, M. T.; Plastino, A.; Rosso, O. A.
  • Physica A: Statistical Mechanics and its Applications, Vol. 369, Issue 2
  • DOI: 10.1016/j.physa.2005.11.053

Evaluation of terrestrial carbon cycle models for their response to climate variability and to CO 2 trends
journal, April 2013

  • Piao, Shilong; Sitch, Stephen; Ciais, Philippe
  • Global Change Biology, Vol. 19, Issue 7
  • DOI: 10.1111/gcb.12187

Extreme events in gross primary production: a characterization across continents
journal, January 2014


A symbolic information approach to determine anticipated and delayed synchronization in neuronal circuit models
journal, December 2015

  • Montani, Fernando; Rosso, Osvaldo A.; Matias, Fernanda S.
  • Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 373, Issue 2056
  • DOI: 10.1098/rsta.2015.0110

Permutation Entropy: A Natural Complexity Measure for Time Series
journal, April 2002


A permutation information theory tour through different interest rate maturities: the Libor case
journal, December 2015

  • Bariviera, Aurelio Fernández; Guercio, María Belén; Martinez, Lisana B.
  • Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 373, Issue 2056
  • DOI: 10.1098/rsta.2015.0119

Causality and the entropy–complexity plane: Robustness and missing ordinal patterns
journal, January 2012

  • Rosso, Osvaldo A.; Carpi, Laura C.; Saco, Patricia M.
  • Physica A: Statistical Mechanics and its Applications, Vol. 391, Issue 1-2
  • DOI: 10.1016/j.physa.2011.07.030

Pattern-oriented modelling: a ‘multi-scope’ for predictive systems ecology
journal, January 2012

  • Grimm, Volker; Railsback, Steven F.
  • Philosophical Transactions of the Royal Society B: Biological Sciences, Vol. 367, Issue 1586
  • DOI: 10.1098/rstb.2011.0180

Fisher information description of the classical–quantal transition
journal, June 2011

  • Kowalski, A. M.; Martín, M. T.; Plastino, A.
  • Physica A: Statistical Mechanics and its Applications, Vol. 390, Issue 12
  • DOI: 10.1016/j.physa.2011.02.009

Statistical complexity and disequilibrium
journal, May 2003


The Amigó paradigm of forbidden/missing patterns: a detailed analysis
journal, December 2012


Efficiency characterization of a large neuronal network: A causal information approach
journal, May 2014

  • Montani, Fernando; Deleglise, Emilia B.; Rosso, Osvaldo A.
  • Physica A: Statistical Mechanics and its Applications, Vol. 401
  • DOI: 10.1016/j.physa.2013.12.053

Soil carbon model alternatives for ECHAM5/JSBACH climate model: Evaluation and impacts on global carbon cycle estimates
journal, January 2011

  • Thum, T.; Räisänen, P.; Sevanto, S.
  • Journal of Geophysical Research, Vol. 116, Issue G2
  • DOI: 10.1029/2010JG001612

Ordinal time series analysis
journal, March 2005


On the separation of net ecosystem exchange into assimilation and ecosystem respiration: review and improved algorithm
journal, September 2005


Evaluating the Land and Ocean Components of the Global Carbon Cycle in the CMIP5 Earth System Models
journal, September 2013


Analysis of symbolic sequences using the Jensen-Shannon divergence
journal, March 2002


Causal information quantification of prominent dynamical features of biological neurons
journal, December 2015

  • Montani, Fernando; Baravalle, Roman; Montangie, Lisandro
  • Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 373, Issue 2056
  • DOI: 10.1098/rsta.2015.0109

Sampling period, statistical complexity, and chaotic attractors
journal, April 2012

  • De Micco, Luciana; Fernández, Juana Graciela; Larrondo, Hilda A.
  • Physica A: Statistical Mechanics and its Applications, Vol. 391, Issue 8
  • DOI: 10.1016/j.physa.2011.12.042

Bivariate colour maps for visualizing climate data: BIVARIATE COLOUR MAPS
journal, April 2010

  • Teuling, A. J.; Stöckli, R.; Seneviratne, S. I.
  • International Journal of Climatology, Vol. 31, Issue 9
  • DOI: 10.1002/joc.2153

Weighted-permutation entropy: A complexity measure for time series incorporating amplitude information
journal, February 2013


Distinguishing Noise from Chaos
journal, October 2007


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


Climate extremes and the carbon cycle
journal, August 2013

  • Reichstein, Markus; Bahn, Michael; Ciais, Philippe
  • Nature, Vol. 500, Issue 7462
  • DOI: 10.1038/nature12350

Permutation-information-theory approach to unveil delay dynamics from time-series analysis
journal, October 2010


Distinguishing chaotic and stochastic dynamics from time series by using a multiscale symbolic approach
journal, October 2012


Randomizing nonlinear maps via symbolic dynamics
journal, June 2008

  • De Micco, L.; González, C. M.; Larrondo, H. A.
  • Physica A: Statistical Mechanics and its Applications, Vol. 387, Issue 14
  • DOI: 10.1016/j.physa.2008.02.037

Modelling the role of agriculture for the 20th century global terrestrial carbon balance
journal, March 2007


Global covariation of carbon turnover times with climate in terrestrial ecosystems
journal, September 2014

  • Carvalhais, Nuno; Forkel, Matthias; Khomik, Myroslava
  • Nature, Vol. 514, Issue 7521
  • DOI: 10.1038/nature13731

Towards a public, standardized, diagnostic benchmarking system for land surface models
journal, January 2012


ESMValTool (v1.0) – a community diagnostic and performance metrics tool for routine evaluation of Earth System Models in CMIP
journal, January 2015

  • Eyring, V.; Righi, M.; Evaldsson, M.
  • Geoscientific Model Development Discussions, Vol. 8, Issue 9
  • DOI: 10.5194/gmdd-8-7541-2015

A Mathematical Theory of Communication
journal, October 1948


    Works referencing / citing this record:

    The intrinsic predictability of ecological time series and its potential to guide forecasting
    journal, March 2019

    • Pennekamp, Frank; Iles, Alison C.; Garland, Joshua
    • Ecological Monographs, Vol. 89, Issue 2
    • DOI: 10.1002/ecm.1359

    Bandt-Pompe symbolization dynamics for time series with tied values: A data-driven approach
    journal, July 2018

    • Traversaro, Francisco; Redelico, Francisco O.; Risk, Marcelo R.
    • Chaos: An Interdisciplinary Journal of Nonlinear Science, Vol. 28, Issue 7
    • DOI: 10.1063/1.5022021

    Analysis of ischaemic crisis using the informational causal entropy-complexity plane
    journal, July 2018

    • Legnani, Walter; Traversaro, Francisco; Redelico, Francisco O.
    • Chaos: An Interdisciplinary Journal of Nonlinear Science, Vol. 28, Issue 7
    • DOI: 10.1063/1.5026422

    Permutation Entropy and Statistical Complexity Analysis of Brazilian Agricultural Commodities
    journal, December 2019

    • de Araujo, Fernando Henrique Antunes; Bejan, Lucian; Rosso, Osvaldo A.
    • Entropy, Vol. 21, Issue 12
    • DOI: 10.3390/e21121220

    The intrinsic predictability of ecological time series and its potential to guide forecasting
    text, January 2019


    The intrinsic predictability of ecological time series and its potential to guide forecasting
    text, January 2019

    • Pennekamp, Frank; Iles, Alison C.; Garland, Joshua
    • Ecological Society of America
    • DOI: 10.5167/uzh-164914