, Volume 164, Issue 1, pp 25–40 | Cite as

Estimating parameters of a forest ecosystem C model with measurements of stocks and fluxes as joint constraints

  • Andrew D. Richardson
  • Mathew Williams
  • David Y. Hollinger
  • David J. P. Moore
  • D. Bryan Dail
  • Eric A. Davidson
  • Neal A. Scott
  • Robert S. Evans
  • Holly Hughes
  • John T. Lee
  • Charles Rodrigues
  • Kathleen Savage
Physiological ecology - Original Paper


We conducted an inverse modeling analysis, using a variety of data streams (tower-based eddy covariance measurements of net ecosystem exchange, NEE, of CO2, chamber-based measurements of soil respiration, and ancillary ecological measurements of leaf area index, litterfall, and woody biomass increment) to estimate parameters and initial carbon (C) stocks of a simple forest C-cycle model, DALEC, using Monte Carlo procedures. Our study site is the spruce-dominated Howland Forest AmeriFlux site, in central Maine, USA. Our analysis focuses on: (1) full characterization of data uncertainties, and treatment of these uncertainties in the parameter estimation; (2) evaluation of how combinations of different data streams influence posterior parameter distributions and model uncertainties; and (3) comparison of model performance (in terms of both predicted fluxes and pool dynamics) during a 4-year calibration period (1997–2000) and a 4-year validation period (“forward run”, 2001–2004). We find that woody biomass increment, and, to a lesser degree, soil respiration, measurements contribute to marked reductions in uncertainties in parameter estimates and model predictions as these provide orthogonal constraints to the tower NEE measurements. However, none of the data are effective at constraining fine root or soil C pool dynamics, suggesting that these should be targets for future measurement efforts. A key finding is that adding additional constraints not only reduces uncertainties (i.e., narrower confidence intervals) on model predictions, but at the same time also results in improved model predictions by greatly reducing bias associated with predictions during the forward run.


Carbon cycle Data-model fusion Eddy covariance Howland Forest Inverse modeling Parameter estimation Uncertainty 



Research at the Howland Forest was supported by the Office of Science (BER), US Department of Energy, through the Terrestrial Carbon Program under Interagency Agreement No. DE-AI02-07ER64355 and through the Northeastern Regional Center of the National Institute for Climatic Change Research. The Howland CO2 flux, climate, and ancillary ecological datasets are available at http://public.ornl.gov/ameriflux/Data/index.cfm subject to AmeriFlux “Fair-use” policies.


  1. Aber JD, Reich PB, Goulden ML (1996) Extrapolating leaf CO2 exchange to the canopy: a generalized model of forest photosynthesis compared with measurements by eddy correlation. Oecologia 106:257–265CrossRefGoogle Scholar
  2. Amthor JS et al (2001) Boreal forest CO2 exchange and evapotranspiration predicted by nine ecosystem process models: intermodel comparisons and relationships to field measurements. J Geophys Res Atmos 106:33623–33648CrossRefGoogle Scholar
  3. Ascough JC, Maier HR, Ravalico JK, Strudley MW (2008) Future research challenges for incorporation of uncertainty in environmental and ecological decision-making. Ecol Model 219:383–399CrossRefGoogle Scholar
  4. Baldocchi DD (2003) Assessing the eddy covariance technique for evaluating carbon dioxide exchange rates of ecosystems: past, present and future. Glob Chang Biol 9:479–492CrossRefGoogle Scholar
  5. Barrett DJ et al (2005) Prospects for improving savanna biophysical models by using multiple-constraints model-data assimilation methods. Aust J Bot 53:689–714CrossRefGoogle Scholar
  6. Braswell BH, Sacks WJ, Linder E, Schimel DS (2005) Estimating diurnal to annual ecosystem parameters by synthesis of a carbon flux model with eddy covariance net ecosystem exchange observations. Glob Chang Biol 11:335–355CrossRefGoogle Scholar
  7. Chen M, Liu S, Tieszen LL, Hollinger DY (2008) An improved state-parameter analysis of ecosystem models using data assimilation. Ecol Model 219:317–326CrossRefGoogle Scholar
  8. Davidson EA, Richardson AD, Savage KE, Hollinger DY (2006) A distinct seasonal pattern of the ratio of soil respiration to total ecosystem respiration in a spruce-dominated forest. Glob Chang Biol 12:230–239CrossRefGoogle Scholar
  9. Enting IG (2008) Assessing the information content in environmental modelling: a carbon cycle perspective. Entropy 10:556–575CrossRefGoogle Scholar
  10. Fernandez IJ, Rustad LE, Lawrence GB (1993) Estimating total soil mass, nutrient content, and trace metals in soils under a low elevation spruce-fir forest. Can J Soil Sci 73:317–328CrossRefGoogle Scholar
  11. Fox A et al (2009) The REFLEX project: comparing different algorithms and implementations for the inversion of a terrestrial ecosystem model against eddy covariance data. Agric For Meteorol 149:1597–1615CrossRefGoogle Scholar
  12. Franks SW, Beven KJ (1997) Bayesian estimation of uncertainty in land surface-atmosphere flux predictions. J Geophys Res Atmos 102:23991–23999CrossRefGoogle Scholar
  13. Franks SW, Beven KJ, Quinn PF, Wright IR (1997) On the sensitivity of soil-vegetation-atmosphere transfer (SVAT) schemes: equifinality and the problem of robust calibration. Agric For Meteorol 86:63–75CrossRefGoogle Scholar
  14. Franks SW, Beven KJ, Gash JHC (1999) Multi-objective conditioning of a simple SVAT model. Hydrol Earth Syst Sci 3:477–489CrossRefGoogle Scholar
  15. Friend AD et al (2007) FLUXNET and modelling the global carbon cycle. Glob Chang Biol 13:610–633CrossRefGoogle Scholar
  16. Goulden ML, Munger JW, Fan SM, Daube BC, Wofsy SC (1996) Exchange of carbon dioxide by a deciduous forest: response to interannual climate variability. Science 271:1576–1578CrossRefGoogle Scholar
  17. Gove JH, Hollinger DY (2006) Application of a dual unscented Kalman filter for simultaneous state and parameter estimation in problems of surface-atmosphere exchange. J Geophys Res Atmos 111:D08S07. doi: 10.1029/2005JD006021Google Scholar
  18. Gupta HV, Bastidas LA, Sorooshian S, Shuttleworth WJ, Yang ZL (1999) Parameter estimation of a land surface scheme using multicriteria methods. J Geophys Res Atmos 104:19491–19503CrossRefGoogle Scholar
  19. Hänninen H, Kramer K (2007) A framework for modelling the annual cycle of trees in boreal and temperate regions. Silva Fenn 41:167–205Google Scholar
  20. Hanson PJ et al (2004) Oak forest carbon and water simulations: model intercomparisons and evaluations against independent data. Ecol Monogr 74:443–489CrossRefGoogle Scholar
  21. Hollinger DY, Kelliher FM, Byers JN, Hunt JE, McSeveny TM, Weir PL (1994) Carbon dioxide exchange between an undisturbed old-growth temperate forest and the atmosphere. Ecology 75:134–150CrossRefGoogle Scholar
  22. Hollinger DY, Goltz SM, Davidson EA, Lee JT, Tu K, Valentine HT (1999) Seasonal patterns and environmental control of carbon dioxide and water vapour exchange in an ecotonal boreal forest. Glob Chang Biol 5:891–902CrossRefGoogle Scholar
  23. Hollinger DY et al (2004) Spatial and temporal variability in forest-atmosphere CO2 exchange. Glob Chang Biol 10:1689–1706CrossRefGoogle Scholar
  24. Ibrom A et al (2006) A comparative analysis of simulated and observed photosynthetic CO2 uptake in two coniferous forest canopies. Tree Physiol 26:845–864CrossRefPubMedGoogle Scholar
  25. Kaminski T, Knorr W, Rayner PJ, Heimann M (2002) Assimilating atmospheric data into a terrestrial biosphere model: a case study of the seasonal cycle. Glob Biogeochem Cycles 16:1066. doi: 1010.1029/2001GB001463CrossRefGoogle Scholar
  26. Knorr W, Kattge J (2005) Inversion of terrestrial ecosystem model parameter values against eddy covariance measurements by Monte Carlo sampling. Glob Chang Biol 11:1333–1351CrossRefGoogle Scholar
  27. Kramer K et al (2002) Evaluation of six process-based forest growth models using eddy-covariance measurements of CO2 and H2O fluxes at six forest sites in Europe. Glob Chang Biol 8:213–230CrossRefGoogle Scholar
  28. Larocque GR, Bhatti JS, Boutin R, Chertov O (2008) Uncertainty analysis in carbon cycle models of forest ecosystems: research needs and development of a theoretical framework to estimate error propagation. Ecol Model 219:400–412CrossRefGoogle Scholar
  29. Levine ER, Knox RG, Lawrence WT (1994) Relationships between soil properties and vegetation at the Northern Experimental Forest, Howland, Maine. Remote Sens Environ 47:231–241CrossRefGoogle Scholar
  30. Medvigy D, Wofsy SC, Munger JW, Hollinger DY, Moorcroft PR (2009) Mechanistic scaling of ecosystem function and dynamics in space and time: Ecosystem Demography model version 2. J Geophys Res 114:G01002. doi: 10.1029/2008JG000812Google Scholar
  31. Metropolis N, Rosenbluth AW, Rosenbluth MN, Teller AH, Teller E (1953) Equations of state calculations by fast computing machines. J Chem Phys 21:1087–1092CrossRefGoogle Scholar
  32. Mo XG, Beven K (2004) Multi-objective parameter conditioning of a three-source wheat canopy model. Agric For Meteorol 122:39–63CrossRefGoogle Scholar
  33. Mo XG, Chen JM, Ju WM, Black TA (2008) Optimization of ecosystem model parameters through assimilating eddy covariance flux data with an ensemble Kalman filter. Ecol Model 217:157–173CrossRefGoogle Scholar
  34. Moffat AM et al (2007) Comprehensive comparison of gap-filling techniques for eddy covariance net carbon fluxes. Agric For Meteorol 147:209–232CrossRefGoogle Scholar
  35. Moore DJP, Hu J, Sacks WJ, Schimel DS, Monson RK (2008) Estimating transpiration and the sensitivity of carbon uptake to water availability in a subalpine forest using a simple ecosystem process model informed by measured net CO2 and H2O fluxes. Agric For Meteorol 148:1467–1477CrossRefGoogle Scholar
  36. Pappenberger F, Beven KJ (2006) Ignorance is bliss: or seven reasons not to use uncertainty analysis. Water Resour Res 42:W05302. doi:05310.01029/02005WR004820CrossRefGoogle Scholar
  37. Petersen PH, Stöckl D, Westgard JO, Sandberg S, Linnet K, Thienpont L (2001) Models for combining random and systematic errors: assumptions and consequences for different models. Clin Chem Lab Med 39:589–595PubMedGoogle Scholar
  38. Prihodko L, Denning AS, Hanan NP, Baker I, Davis K (2008) Sensitivity, uncertainty and time dependence of parameters in a complex land surface model. Agric For Meteorol 148:268–287CrossRefGoogle Scholar
  39. Quaife T et al (2008) Assimilating canopy reflectance data into an ecosystem model with an Ensemble Kalman Filter. Remote Sens Environ 112:1347–1364CrossRefGoogle Scholar
  40. Raupach MR et al (2005) Model-data synthesis in terrestrial carbon observation: methods, data requirements and data uncertainty specifications. Glob Chang Biol 11:378–397CrossRefGoogle Scholar
  41. Reichstein M et al (2003) Inverse modeling of seasonal drought effects on canopy CO2/H2O exchange in three Mediterranean ecosystems. J Geophys Res Atmos 108:4726. doi: 4710.1029/2003JD003430CrossRefGoogle Scholar
  42. Renzullo LJ et al (2008) Multi-sensor model-data fusion for estimation of hydrologic and energy flux parameters. Remote Sens Environ 112:1306–1319CrossRefGoogle Scholar
  43. Richardson AD, Hollinger DY (2005) Statistical modeling of ecosystem respiration using eddy covariance data: maximum likelihood parameter estimation, and Monte Carlo simulation of model and parameter uncertainty, applied to three simple models. Agric For Meteorol 131:191–208CrossRefGoogle Scholar
  44. Richardson AD, Hollinger DY (2007) A method to estimate the additional uncertainty in gap-filled NEE resulting from long gaps in the CO2 flux record. Agric For Meteorol 147:199–208CrossRefGoogle Scholar
  45. Richardson AD et al (2006a) Comparing simple respiration models for eddy flux and dynamic chamber data. Agric For Meteorol 141:219–234CrossRefGoogle Scholar
  46. Richardson AD et al (2006b) A multi-site analysis of random error in tower-based measurements of carbon and energy fluxes. Agric For Meteorol 136:1–18CrossRefGoogle Scholar
  47. Richardson AD, Hollinger DY, Aber JD, Ollinger SV, Braswell BH (2007) Environmental variation is directly responsible for short- but not long-term variation in forest-atmosphere carbon exchange. Glob Chang Biol 13:788–803CrossRefGoogle Scholar
  48. Richardson AD et al (2008) Statistical properties of random CO2 flux measurement uncertainty inferred from model residuals. Agric For Meteorol 148:38–50CrossRefGoogle Scholar
  49. Sacks WJ, Schimel DS, Monson RK, Braswell BH (2006) Model-data synthesis of diurnal and seasonal CO2 fluxes at Niwot Ridge, Colorado. Glob Chang Biol 12:240–259CrossRefGoogle Scholar
  50. Savage KE, Davidson EA (2001) Interannual variation of soil respiration in two New England forests. Glob Biogeochem Cycles 15:337–350CrossRefGoogle Scholar
  51. Savage KE, Davidson EA, Richardson AD (2008) A conceptual and practical approach to data quality and analysis procedures for high-frequency soil respiration measurements. Funct Ecol 22:1000–1007CrossRefGoogle Scholar
  52. Savage K, Davidson EA, Richardson AD, Hollinger DY (2009) Three scales of temporal resolution from automated soil respiration measurements. Agric For Meteorol 149:2012–2021CrossRefGoogle Scholar
  53. Siqueira MB et al (2006) Multiscale model intercomparisons of CO2 and H2O exchange rates in a maturing southeastern US pine forest. Glob Chang Biol 12:1189–1207CrossRefGoogle Scholar
  54. Stoy PC et al (2009) Biosphere-atmosphere exchange of CO2 in relation to climate: a cross-biome analysis across multiple time scales. Biogeosciences 6:2297–2312CrossRefGoogle Scholar
  55. Trudinger CM et al (2007) OptIC project: an intercomparison of optimization techniques for parameter estimation in terrestrial biogeochemical models. J Geophys Res Biogeosci 112:G02027. doi: 02010.01029/02006JG000367CrossRefGoogle Scholar
  56. Trumbore S (2000) Age of soil organic matter and soil respiration: radiocarbon constraints on belowground C dynamics. Ecol Appl 10:399–411CrossRefGoogle Scholar
  57. Trumbore S (2006) Carbon respired by terrestrial ecosystems—recent progress and challenges. Glob Chang Biol 12:141–153CrossRefGoogle Scholar
  58. Wang YP, Leuning R, Cleugh HA, Coppin PA (2001) Parameter estimation in surface exchange models using nonlinear inversion: how many parameters can we estimate and which measurements are most useful? Glob Chang Biol 7:495–510CrossRefGoogle Scholar
  59. Wang YP, Baldocchi D, Leuning R, Falge E, Vesala T (2007) Estimating parameters in a land-surface model by applying nonlinear inversion to eddy covariance flux measurements from eight FLUXNET sites. Glob Chang Biol 13:652–670CrossRefGoogle Scholar
  60. Wang Y-P, Trudinger CM, Enting IG (2009) A review of applications of model-data fusion to studies of terrestrial carbon fluxes at different scales. Agric For Meteorol 149:1829–1842CrossRefGoogle Scholar
  61. Williams M, Rastetter EB, Fernandes DN, Goulden ML, Shaver GR, Johnson LC (1997) Predicting gross primary productivity in terrestrial ecosystems. Ecol Appl 7:882–894CrossRefGoogle Scholar
  62. Williams M, Schwarz PA, Law BE, Irvine J, Kurpius MR (2005) An improved analysis of forest carbon dynamics using data assimilation. Glob Chang Biol 11:89–105CrossRefGoogle Scholar
  63. Williams M et al (2009) Improving land surface models with FLUXNET data. Biogeosciences 6:1341–1359CrossRefGoogle Scholar
  64. Xu T, White L, Hui DF, Luo YQ (2006) Probabilistic inversion of a terrestrial ecosystem model: analysis of uncertainty in parameter estimation and model prediction. Glob Biogeochem Cycles 20:GB2007. doi: 2010.1029/2005GB002468Google Scholar
  65. Young HE, Ribe JH, Wainwright K (1980) Weight tables for tree and shrub species in Maine. Life Sciences and Agricultural Experiment Station, University of Maine, OronoGoogle Scholar
  66. Zobitz JM et al (2008) Integration of process-based soil respiration models with whole-ecosystem CO2 measurements. Ecosystems 11:250–269CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Andrew D. Richardson
    • 1
  • Mathew Williams
    • 2
  • David Y. Hollinger
    • 3
  • David J. P. Moore
    • 4
  • D. Bryan Dail
    • 5
  • Eric A. Davidson
    • 6
  • Neal A. Scott
    • 7
  • Robert S. Evans
    • 3
  • Holly Hughes
    • 6
  • John T. Lee
    • 5
  • Charles Rodrigues
    • 5
  • Kathleen Savage
    • 6
  1. 1.Department of Organismic and Evolutionary Biology, Harvard University HerbariaHarvard UniversityCambridgeUSA
  2. 2.School of GeoSciencesUniversity of EdinburghEdinburghUK
  3. 3.Northern Research StationUSDA Forest ServiceDurhamUSA
  4. 4.Department of Geography, Environmental Monitoring and Modelling Research GroupKing’s College LondonLondonUK
  5. 5.Department of Plant, Soil, and Environmental SciencesUniversity of MaineOronoUSA
  6. 6.Woods Hole Research CenterFalmouthUSA
  7. 7.Department of GeographyQueen’s UniversityKingstonCanada

Personalised recommendations