Gradual Global Environmental Change in the Real World and Step Manipulative Experiments in Laboratory and Field: The Necessity of Inverse Analysis

  • Yiqi LuoEmail author
  • Dafeng Hui


Ecosystem responses to perturbation generated by a step increase in climatic variables, such as CO2 concentration and temperature as in field manipulative experiments, are different from responses as a result of a gradual increase in climatic variables as in the real world. This chapter discusses how results from manipulative experiments can be analyzed to improve our predictive understanding of ecosystem responses to future gradual climate change. We first describe gradual changes in several global environmental variables and the corresponding manipulative experiments. Then we review a modeling study by Luo and Reynolds (1999) on differential responses of ecosystems to gradual vs. step changes in CO2 concentration. We also review results from several experiments to verify that ecosystem responses to step CO2 increases are different from those to gradual changes. Finally, we introduce a framework of analysis techniques – inverse analysis – that extract information from experimental data toward predictive understanding in ecological research. The inverse analysis fundamentally focuses on data analysis for parameter estimation and evaluation of alternative model structures so as to improve our predictive understanding from both experimental observations and prior knowledge about the ecosystem processes.


Soil Respiration Inverse Analysis Ecosystem Response Manipulative Experiment Global Change Factor 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



We thank Dr. Miao and three anonymous reviewers for their constructive comments and suggestions that made this chapter much improved. Our work has been supported by grants from the Office of Science (BER), U.S. Department of Energy, grant DE-FG03-99ER62800 DE-FG02-006ER64319, and National Science Foundation (DEB0444518).


  1. Andrews, J.A., and W.H. Schlesinger. 2001. Soil CO2 dynamics in a temperate forest with experimental CO2 enrichment. Global Biogeochemical Cycles 15:149–162.CrossRefGoogle Scholar
  2. Ägren, G.I. 1985. Theory for growth of plants derived from the nitrogen productivity concept. Physiologia Plantarum 64:17–28.CrossRefGoogle Scholar
  3. Allen, L.H., Jr., B.G. Drake, H.H. Rogers, and J.H. Shinn. 1992. Field techniques for exposure of plants and ecosystems to elevated CO2 and other trace gases. Critical Reviews in Plant Science 11:85–119.Google Scholar
  4. Ashmore, M. R. 2005. Assessing the future global impacts of ozone on vegetation. Plant Cell Environ. 28: 949–964.CrossRefGoogle Scholar
  5. Barrett, D.J. 2002. Steady state turnover time of carbon in the Australian terrestrial biosphere. Global Biogeochemical Cycles 16, 1108, doi:10.1029/2002GB001860.Google Scholar
  6. Braswell, B.H., W.J. Sacks, E. Linder, and D.S. Schimel. 2005. Estimating diurnal to annual ecosystem parameters by synthesis of a carbon flux model with eddy covariance net ecosystem exchange observations. Global Change Biology 11: 335–355.CrossRefGoogle Scholar
  7. Cheng, W., D.C. Coleman, C.R. Corroll, and C.A. Hoffman. 1994. Investigating short-term carbon flows in the rhizospheres of different plant species, using isotopic trapping. Agronomy Journal 86:782–788.CrossRefGoogle Scholar
  8. Comins, H.N., and R.E. McMurtrie. 1993. Long-term biotic response of nutrient-limited forest ecosystems to CO2-enrichment: Equilibrium behavior of integrated plant-soil models. Ecological Applications 3:666–681.CrossRefGoogle Scholar
  9. Cramer, W., A. Bondeau, F.I. Woodward, et al. 2001. Global response of terrestrial ecosystem structure and function to CO2 and climate change: results from six dynamic global vegetation models. Global Change Biology 7: 357–373.CrossRefGoogle Scholar
  10. Dermody, O., J.F. Weltzin, E.C. Engel, P. Allen, and R.J. Norby. 2007. How do elevated [CO2], warming, and reduced precipitation interact to affect soil moisture and LAI in an old field ecosystem? Plant and Soil 301: 255–266.CrossRefGoogle Scholar
  11. Ellsworth, D.S. 2000. Seasonal CO2 assimilation and stomatal limitations in a Pinus taeda canopy. Tree Physiology 20: 435–445.PubMedGoogle Scholar
  12. Farquhar, G.D., S. von Caemmerer, and J.A. Berry. 1980. A biochemical model of photosynthetic CO2 assimilation in leaves of C3 species. Planta 149:79–90.CrossRefGoogle Scholar
  13. Fay, P.A., J.D. Carlisle, A.K. Knapp, et al. 2000. Altering rainfall timing and quantity in a mesic grassland ecosystem: Design and performance of rainfall manipulation shelters. Ecosystems 3: 308–319.CrossRefGoogle Scholar
  14. Fay, P.A., J.D. Carlisle, A.K. Knapp, et al. 2003. Productivity responses to altered rainfall patterns in a C4-dominated grassland. Oecologia 137: 245–251.CrossRefPubMedGoogle Scholar
  15. Friedli, H., H. Loestcher, H. Oeschger, U. Siegenthaler, and B. Stauffer. 1986. Ice core record of the 13C/12C record of atmospheric CO2 in the past two centuries. Nature 324:237–238.CrossRefGoogle Scholar
  16. Gill, R.A., H.W. Polley, H.B. Johnson, L.J. Anderson, H. Maherali, and R.B. Jackson. 2002. Nonlinear grassland responses to past and future atmospheric CO2. Nature 417: 279–282.CrossRefPubMedGoogle Scholar
  17. Hanan, N.P., G. Burba, S.B. Verma, J.A. Berry, A. Suyker, and E.A. Walter-Shea. 2002. Inversion of net ecosystem CO2 flux measurements for estimation of canopy PAR absorption. Global Change Biology 8: 563–574.CrossRefGoogle Scholar
  18. Harley, P.C., R.B. Thomas, J.F. Reynolds, and B.R. Strain. 1992. Modeling photosynthesis of cotton grown in elevated CO2. Plant, Cell and Environment 15: 271–282.CrossRefGoogle Scholar
  19. Harte, J., and R. Shaw. 1995. Shifting dominance within a montane vegetation community – results of a climate warming experiment. Science 267: 876–880.CrossRefPubMedGoogle Scholar
  20. Hartley, I.P., A. Heinemeyer, and P. Ineson P. 2007. Effects of three years of soil warming and shading on the rate of soil respiration: substrate availability and not thermal acclimation mediates observed response. Global Change Biology 13: 1761–1770.CrossRefGoogle Scholar
  21. Hendrey, G.R., D.S. Ellsworth, K.F. Lewin, et al. 1999. A free-air enrichment system for exposing tall forest vegetation to elevated atmospheric CO2. Global Change Biology 5: 293–309.CrossRefGoogle Scholar
  22. Herrick, J.D., and S.B. Thomas. 2001. No photosynthetic down-regulation in sweetgum trees (Liquidambar styraciflua L.) after three years of CO2 enrichment at the Duke Forest FACE experiment. Plant Cell and Environment 24: 53–64.CrossRefGoogle Scholar
  23. Hui, D., D.A. Sims, D.W. Johnson, W. Cheng, and Y. Luo. 2002. Effects of gradual versus step increase in carbon dioxide on Plantago photosynthesis and growth in a microcosm study. Environmental and Experimental Botany 47:51–66.CrossRefGoogle Scholar
  24. Hui, D., and Y. Luo. 2004. Evaluation of soil CO2 production and transport in Duke Forest using a process-based modeling approach. Global Biogeochemical Cycles 18, GB4029, doi:10.1029/2004GB002297.Google Scholar
  25. Hui, D., Y. Luo, D. Schimel, J.S. Clark, A. Hastings, K. Ogle, M. Williams. 2008. Converting raw data into ecologically meaningful products. Eos, Transactions, American Geophysical Union 89: 5.CrossRefGoogle Scholar
  26. Huxman, T.E., M.D. Smith, P.A. Fay, et al. 2004. Convergence across biomes to a common rain-use efficiency. Nature 429: 651–654.CrossRefPubMedGoogle Scholar
  27. Intergovernmental Panel on Climate Change (IPCC), Climate Change 1992 (IPCC, Geneva, 1992);
  28. Intergovernmental Panel on Climate Change (IPCC), Climate Change 2007 (IPCC, Geneva, 2007);
  29. Jenkinson, D.S., and J.H. Rayner. 1977. The turnover of soil organic matter in some of the Rothamsted classical experiments. Soil Science 123: 298–305.CrossRefGoogle Scholar
  30. Kimball, B.A. 2005. Theory and performance of an infrared heater for ecosystem warming. Global Change Biology 11:2041–2056.Google Scholar
  31. Klanderud, K., and O. Totland. 2007. The relative role of dispersal and local interactions for alpine plant community diversity under simulated climate warming. Oikos 116: 1279–1288.CrossRefGoogle Scholar
  32. Klironomos, J.N., M.F. Allen, M.C. Rillig, J. Piotrowski, S. Makvandi-Nejad, B.E. Wolfe, and J.R. Powell. 2005. Abrupt rise in atmospheric CO2 overestimates community response in a model plant–soil system. Nature 433, 621–624.CrossRefPubMedGoogle Scholar
  33. Knorr, W., and J. Kattge. 2005. Inversion of terrestrial ecosystem model parameter values against eddy covariance measurements by Monte Carlo sampling. Global Change Biology 11: 1333–1351.CrossRefGoogle Scholar
  34. Koch, G.W. 1993. The use of natural situations of CO2 enrichment in studies of vegetation responses to increasing atmospheric CO2. Pages 381–391 in E.D. Schulze, and H.A. Mooney, editors. Design and Execution of Experiments on CO2 Enrichment. Commission of the European Communities, Brussels.Google Scholar
  35. Körner, C. 1995. Towards a better experimental basis for upscaling plant-responses to elevated CO2 and climate warming. Plant Cell and Environment 18: 1101–1110.CrossRefGoogle Scholar
  36. Körner, C., R. Asshoff, O. Bignucolo, S. Hättenschwiler, S.G. Keel, S. Peláez-Riedl, S. Pepin, R.T.W. Siegwolf, and G. Zotz. 2005. Carbon flux and growth in mature deciduous forest trees exposed to elevated CO2. Science 309: 1360–1362.CrossRefPubMedGoogle Scholar
  37. Laidler, K.J., and J.H. Meiser. 1982. Physical Chemistry. The Benjamin/Cummings Publishing Company. Menlo Park, CA.Google Scholar
  38. Long, S.P., and P.R. Hutchin. 1991. Primary production in grasslands and coniferous forests with climate change – an over view. Ecological Applications 1: 139–156.CrossRefGoogle Scholar
  39. Luo, Y. 2001. Transient ecosystem responses to free-air CO2 enrichment: Experimental evidence and methods of analysis. New Phytologist 152: 3–8.CrossRefGoogle Scholar
  40. Luo, Y. 2007. Terrestrial Carbon-Cycle Feedback to Climate Warming. Annual Review of Ecology, Evolution, and Systematics 38: 683–712.CrossRefGoogle Scholar
  41. Luo, Y., C.B. Field, and H.A. Mooney. 1994. Predicting responses of photosynthesis and root fraction to elevated CO2: Interactions among carbon, nitrogen, and growth. Plant, Cell and Environment 17: 1194–1205.CrossRefGoogle Scholar
  42. Luo Y., B. Medlyn, D. Hui, D. Ellsworth, J. Reynolds, and G. Katul. 2001a. Gross primary productivity in Duke Forest: Modeling synthesis of CO2 experiment and eddy-flux data. Ecological Applications 11: 239–252.Google Scholar
  43. Luo, Y., and H. A. Mooney. 1996. Stimulation of global photosynthetic carbon influx by an increase in atmospheric carbon dioxide concentration. Pages 381–397 in G. W. Koch, and H. A. Mooney, editors. Carbon Dioxide and Terrestrial Ecosystems. Academic Press, San Diego.CrossRefGoogle Scholar
  44. Luo, Y., and J.F. Reynolds. 1999. Validity of extrapolating field CO2 experiments to predict carbon sequestration in natural ecosystems. Ecology 80: 1568–1583.CrossRefGoogle Scholar
  45. Luo, Y., D.A. Sims, K.L. Griffin. 1998. Nonlinearity of photosynthetic responses to growth in rising atmospheric CO2: An experimental and modeling study. Global Change Biology 4: 173–183.CrossRefGoogle Scholar
  46. Luo, Y., B. Su, W.S. Currie, J.S. Dukes, A. Finzi, U. Hartwig, B. Hungate, R.E. McNurtrie, R. Oren, W.J. Parton, D.E. Pataki, M.R. Shaw, D.R. Zak, C.B. Field. 2004. Progressive nitrogen limitation of ecosystem responses to rising atmospheric carbon dioxide. BioScience 54: 731–739.Google Scholar
  47. Luo, Y., L. White, J. Canadell, E. DeLucia, D. Ellsworth, A. Finzi, J. Lichter, and W. Schlesinger. 2003. Sustainability of terrestrial carbon sequestration: A case study in Duke Forest with inversion approach. Global Biogeochemical Cycles. 17, 1021, doi:10.1029/2002GB001923Google Scholar
  48. Luo, Y., L. Wu, J.A. Andrews, L. White, R. Matamala, K.V.R. Schafer, and W. H. Schlesinger. 2001b. Elevated CO2 differentiates ecosystem carbon processes: Deconvolution analysis of Duke Forest FACE data. Ecological Monographs 71: 357–376.Google Scholar
  49. Luo, Y.Q., D. Hui, and D. Zhang. 2006. Elevated Carbon Dioxide Stimulates Net Accumulations of Carbon and Nitrogen in Terrestrial Ecosystems: A Meta-Analysis. Ecology 87: 53–63.CrossRefPubMedGoogle Scholar
  50. Mack, M.C., E.A.G. Schuur, M.S. Bret-Harte, et al. 2004. Ecosystem carbon storage in arctic tundra reduced by long-term nutrient fertilization. Nature 431: 440–443.CrossRefPubMedGoogle Scholar
  51. McGuire, A.D., S. Sitch, J.S. Clein, R. Dargaville, G. Esser, J. Foley, M. Heimann, F. Joos, et al. 2001. Carbon balance of the terrestrial biosphere in the twentieth century: Analyses of CO2, climate and land use effects with four process-based ecosystem models. Global Biogeochemical Cycles 15: 183–206.CrossRefGoogle Scholar
  52. Melillo, J.M., P.A. Steudler, J.D. Aber, K. Newkirk, H. Lux, F.P. Bowles, C. Catricala, A. Magill, T. Ahrens, and S. Morrisseau. 2002. Soil warming and carbon-cycle feedbacks to the climate system. Science 298: 2173–2176.CrossRefPubMedGoogle Scholar
  53. Miglietta, F., A. Peressotti, F.P. Vaccari, A. Zaldei, P. deAngelis, and G. Scarascia-Mugnozza. 2001. Free-air CO2 enrichment (FACE) of a poplar plantation: the POPFACE fumigation system. New Phytologist 150: 465–476.CrossRefGoogle Scholar
  54. Neftel, A., H. Oeschger, J. Schwander, B. Stauffer, and R. Zumbrunn.1982. Ice core sample measurements give atmospheric CO2 content during the past 40,000 yr. Nature 295: 220–223.CrossRefGoogle Scholar
  55. Norby, R.J., N.T. Edwards, J.S. Riggs, C.H. Abner, S.D. Wullschleger, and C.A. Gunderson. 1997. Temperature-controlled open-top chambers for global change research Global Change Biolog 3: 259–267.CrossRefGoogle Scholar
  56. Olson, J.S. 1963. Energy-storage and balance of producers and decomposers in ecological-systems. Ecology 44: 322–331.CrossRefGoogle Scholar
  57. Parton, W.J., D.S. Schimel, C.V. Cole, and D.S. Ojima. 1987. Analysis of factors controlling soil organic matter levels in Great-Plains grasslands. Soil Science Soc. of America Journal 51: 1173–1179.CrossRefGoogle Scholar
  58. Pataki, D.E., T. Xu, Y. Luo, and J.R. Ehleringer. 2007. Inferring biogenic and anthropogenic CO2 sources across an urban to rural gradient. Oecologia 152: 307–322.CrossRefPubMedGoogle Scholar
  59. Polley, H.W., H.B. Johnson, and J.D. Derner. 2003. Increasing CO2 from subambient to superambient concentrations alters species composition and increases above-ground biomass in a C3/C4 grassland. New Phytologist 160: 319–327.CrossRefGoogle Scholar
  60. Polley, HW., P.C. Mielnick., W.A. Dugas, H.B. Johnson, and J. Sanabria. 2006. Increasing CO2 from subambient to elevated concentrations increases grassland respiration per unit of net carbon fixation. Global Change Biology 12: 1390–1399.CrossRefGoogle Scholar
  61. Raschi, A., F. Milglietta, R. Tognetti, and P.R. van Gardingen, editors. 1997. Plant responses to elevated CO2: evidence from natural springs. Cambridge University Press, New York.Google Scholar
  62. Rastetter, E.B., G.I. Ågren, and G.R. Shaver. 1997. Responses of N-limited ecosystems to increased CO2: A balanced-nutrition, coupled-element-cycles model. Ecological Applications 7: 444–460.Google Scholar
  63. Raupach, M.R., P.J. Rayner, D.J. Barrett, R.S. Defries, M. Heimann, D.S. Ojima, S. Quegan, and C.C. Schmullius. 2005. Model-data synthesis in terrestrial carbon observation: methods, data requirements and data uncertainty specifications. Global Change Biology 11: 378–397.CrossRefGoogle Scholar
  64. Reynolds, J.F., and P.W. Leadley. 1992. Modeling the response of arctic plants to changing climate. Pages 413–438 in F. S. Chapin, III, R. Jefferies, J. F. Reynolds, G. Shaver and J. Svoboda, editors. Arctic Physiological Processes in a Changing Climate, San Diego, CA.Google Scholar
  65. Rouhier, H., G. Billès, L. Billès, and P. Bottner. 1996. Carbon fluxes in the rhizosphere of sweet chestnut seedlings (Castanea sativa) grown under two atmospheric CO2 concentrations: 14C partitioning after pulse labelling. Plant and Soil 180: 101–111.CrossRefGoogle Scholar
  66. Rustad, L.E., J.L. Campbell, G.M. Marion, R.J. Norby, M.J. Mitchell, A.E. Hartley AE, and J. Gurevitch. 2001. A meta-analysis of the response of soil respiration, net nitrogen mineralization, and aboveground plant growth to experimental ecosystem warming. Oecologia 126: 543–562.CrossRefGoogle Scholar
  67. Rustad, L.E. 2006. From transient to steady-state response of ecosystems to atmospheric enrichment and global climate change: conceptual challenges and need for an integrated approach. Plant Ecology 182: 43–62.Google Scholar
  68. Sacks, W.J., D.S. Schimel, R.K. Monson, and B.H. Braswell. 2006. Model-data synthesis of diurnal and seasonal CO2 fluxes at Niwot Ridge, Colorado. Global Change Biology 12: 240–259.CrossRefGoogle Scholar
  69. Shaver, G.R., J. Canadell, F.S. Chapin, J. Gurevitch, J. Harte, G. Henry, P. Ineson, S. Jonasson, J. Melillo, L. Pitelka, L. Rustad. 2000. Global warming and terrestrial ecosystems: A conceptual framework for analysis. Bioscience 50: 871–882.CrossRefGoogle Scholar
  70. Sherry, R.A., X. Zhou, S. Gu, J.A. Arnone III, D.S. Schimel, P.S. Verburg, L.L. Wallace and Y. Luo. 2007. Divergence of Reproductive Phenology under Climate Warming. Proceedings of National Academy of Sciences USA 104: 198–202.CrossRefGoogle Scholar
  71. Schulz, K., A. Jarvis, K. Beven, and H. Soegaard. 2001. The predictive uncertainty of land surface fluxes in response to increasing ambient carbon dioxide. Journal of Climate 14: 2551–2562.CrossRefGoogle Scholar
  72. Sitch, S., P.M. Cox, W.J. Collins, and C. Huntingford. 2007. Indirect radiative forcing of climate change through ozone effects on the land-carbon sink. Nature 448: 791–794.CrossRefPubMedGoogle Scholar
  73. Thompson, M.V., and J.T. Randerson. 1999. Impulse response functions of terrestrial carbon cycle models: method and application. Global Change Biology 5: 371–394.CrossRefGoogle Scholar
  74. Verburg, P.S.J., J.A Arnone III, R.D. Evans, D. LeRoux-Swarthout, D. Obrist, D.W. Johnson, D.E. Schorran, Y. Luo, and J.S. Coleman. 2004. Net ecosystem C exchange in two model grassland ecosystems. Global Change Biology 10: 498–508.CrossRefGoogle Scholar
  75. Wan, S., Y. Luo, and L. Wallace. 2002. Changes in microclimate induced by experimental warming and clipping in tallgrass prairie. Global Change Biology 8: 754–768.CrossRefGoogle Scholar
  76. Weltzin, J.F., M.E. Loik, S. Schwinning, et al. 2003. Assessing the response of terrestrial ecosystems to potential changes in precipitation. Bioscience 53: 941–952.CrossRefGoogle Scholar
  77. White, L., and Y. Luo. 2002. Inverse analysis for estimating carbon transfer coefficients in Duke Forest. Applied Mathematics and Computation 130: 101–120.CrossRefGoogle Scholar
  78. White, L., and Y. Luo. 2005. Model-based CO2 data assessment for terrestrial carbon processes: Implications for sampling strategy in FACE experiments. Applied Mathematics and Computation 167: 419–434.CrossRefGoogle Scholar
  79. White, L., Y. Luo, and T, Xu. 2005. Carbon sequestration: inversion of FACE data and prediction. Applied Mathematics and Computation 163: 783–800.CrossRefGoogle Scholar
  80. Wieder, R.K., and G.E. Lang. 1982. A critique of the analytical methods used in examining decomposition data obtained from litter bags. Ecology 63: 1636–1642.CrossRefGoogle Scholar
  81. Williams, M., P.A. Schwarz, B.E. Law, J. Irvine, and M.R. Kurpius. 2005. An improved analysis of forest carbon dynamics using data assimilation. Global Change Biology 11: 89–105.CrossRefGoogle Scholar
  82. Xu, T., L. White, D. Hui, and Y. Luo. 2006. Probabilistic inversion of a terrestrial ecosystem model: Analysis of uncertainty in parameter estimation and model prediction, Global Biogeochemical Cycles 20, GB2007, doi:10.1029/2005GB002468Google Scholar
  83. Yahdjian, L., and O.E. Sala. 2002. A rainout shelter design for intercepting different amounts of rainfall. Oecologia 133: 95–101.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Department of Botany and MicrobiologyUniversity of OklahomaNormanUSA

Personalised recommendations