Advertisement

Environmental and Ecological Statistics

, Volume 20, Issue 1, pp 129–146 | Cite as

A constrained least-squares approach to combine bottom-up and top-down CO2 flux estimates

  • Daniel CooleyEmail author
  • F. Jay Breidt
  • Stephen M. Ogle
  • Andrew E. Schuh
  • Thomas Lauvaux
Article

Abstract

Terrestrial CO2 flux estimates are obtained from two fundamentally different methods generally termed bottom-up and top-down approaches. Inventory methods are one type of bottom-up approach which uses various sources of information such as crop production surveys and forest monitoring data to estimate the annual CO2 flux at locations covering a study region. Top-down approaches are various types of atmospheric inversion methods which use CO2 concentration measurements from monitoring towers and atmospheric transport models to estimate CO2 flux over a study region. Both methods can also quantify the uncertainty associated with their estimates. Historically, these two approaches have produced estimates that differ considerably. The goal of this work is to construct a statistical model which sensibly combines estimates from the two approaches to produce a new estimate of CO2 flux for our study region. The two approaches have complementary strengths and weaknesses, and our results show that certain aspects of the uncertainty associated with each of the approaches are greatly reduced by combining the methods. Our model is purposefully simple and designed to take the two approaches’ estimates and measures of uncertainty at ‘face value’. Specifically, we use a constrained least-squares approach to appropriately weigh the estimates by the inverse of their variance, and the constraint imposes agreement between the two sources. Our application involves nearly 18,000 flux estimates for the upper midwest United States. The constrained dependencies result in a non-sparse covariance matrix, but computation requires only minutes due to the structure of the model.

Keywords

Atmospheric inversion Carbon inventory Climate change 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bocquet M (2008) Inverse modelling of atmospheric tracers: non-Gaussian methods and second-order sensitivity analysis. Nonlinear Process Geophys 15(1): 127–143CrossRefGoogle Scholar
  2. Chan E, Lin J (2011) What is the value of agricultural census data in carbon cycle studies?. J Geophys Res 116(G03012): G03012CrossRefGoogle Scholar
  3. Chevallier F, Ciais P, Conway TJ, Aalto T, Anderson BE, Bousquet P, Brunke EG, Ciattaglia L, Esaki Y, Fröhlich M et al (2010) CO2 surface fluxes at grid point scale estimated from a global 21 year reanalysis of atmospheric measurements. J Geophys Res 115(D21): D21307CrossRefGoogle Scholar
  4. Cressie N (1993) Statistics for spatial data. Wiley, New YorkGoogle Scholar
  5. EPA (2011) Inventory of U.S. greenhouse gas emissions and sinks: 1990–2009. Technical report, U.S. Environmental Protection Agency, Washington, DCGoogle Scholar
  6. Furrer R (2008) Spam: SPArse Matrix. R package version 0.14-1Google Scholar
  7. Göckede M, Michalak AM, Vickers D, Turner DP, Law BE (2010) Atmospheric inverse modeling to constrain regional-scale CO2 budgets at high spatial and temporal resolution. J Geophys Res 115:D15113Google Scholar
  8. Gourdji S, Mueller K, Yadav V, Huntzinger D, Andrews A, Trudeau M, Petron G, Nehrkorn T, Eluszkiewicz J, Henderson J et al (2012) North american CO2 exchange: inter-comparison of modeled estimates with results from a fine-scale atmospheric inversion. Biogeosciences 9: 457–475CrossRefGoogle Scholar
  9. Graybill F (1976) Theory and application of the linear model. Duxbury, North Scituate, MassachusettsGoogle Scholar
  10. Gurney KR, Mendoza DL, Zhou Y, Fischer ML, Miller CC, Geethakumar S, de la Ruedu Can S (2009) High resolution fossil fuel combustion CO2 emission fluxes for the United States. Environ Sci Technol 43(14): 5535–5541PubMedCrossRefGoogle Scholar
  11. IPCC (2006) 2006 IPCC guidelines for national greenhouse gas inventories. In: Eggleston HS, Buendia L, Miwa K, Ngara T, Tanabe K (eds) Institute for Global Environmental Strategies, Kanagawa, Japan.Google Scholar
  12. IPCC (2007) Climate change 2007: the physical science basis. In: Solomon S, Qin D, Manning M, Chen Z, Marquis M, Averyt KB, Tignor M, Miller HL (eds) Contribution of working group I to the fourth assessment report of the intergovernmental panel on climate change. Cambridge University Press, CambridgeGoogle Scholar
  13. Lauvaux T, Pannekoucke O, Sarrat C, Chevallier F, Ciais P, Noilhan J, Rayner PJ (2009) Structure of the transport uncertainty in mesoscale inversions of CO2 sources and sinks using ensemble model simulations. Biogeosciences 6(6): 1089–1102CrossRefGoogle Scholar
  14. Lauvaux T, Schuh AE, Uliasz M, Richardson S, Miles N, Andrews AE, Sweeney C, Diaz LI, Martins D, Shepson PB, Davis KJ (2011) Constraining the CO2 budget of the corn belt: exploring uncertainties from the assumptions in a mesoscale inverse system. Atmos Chem Phys 12: 337–354. doi: 10.5194/acpd-11-20855-2011 CrossRefGoogle Scholar
  15. Le Quéré C, Raupach M, Canadell J, Marland G et al (2009) Trends in the sources and sinks of carbon dioxide. Nat Geosci 2(12): 831–836CrossRefGoogle Scholar
  16. Lokupitiya E, Denning S, Paustian K, Baker I, Schaefer K, Verma S, Meyers T, Bernacchi CJ, Suyker A, Fischer M (2009) Incorporation of crop phenology in simple biosphere model (sibcrop) to improve land-atmosphere carbon exchanges from croplands. Biogeosciences 6: 1103CrossRefGoogle Scholar
  17. Ogle S, Breidt F, Easter M, Williams S, Killian K, Paustian K (2010) Scale and uncertainty in modeled soil organic carbon stock changes for US croplands using a process-based model. Glob Chang Biol 16: 810–822CrossRefGoogle Scholar
  18. Pacala SW, Hurtt G, Baker D, Peylin P, Houghton R, Heath L, Sundquist RB, Stallard E, Ciais R, Moorcroft P, Caspersen P, Shevliakova J, Moore E, Kohlmaier B, Holland G, Gloor E, Harmon M, Fan M, Sarmiento S, Goodale J, Schimel C, Field DC (2001) Consistent land- and atmosphere-based U.S. carbon sink estimates. Science 292: 2316–2320PubMedCrossRefGoogle Scholar
  19. Paustian K, Andren O, Janzen HH, Lal R, Smith P, Tian G, Tiessen H, Noordwijk MV, Woomer PL (1997) Agricultural soils as a sink to mitigate CO2 emissions. Soil Use Manag 13: 230–244CrossRefGoogle Scholar
  20. Peters W, Jacobson AR, Sweeney C, Andrews AE, Conway TJ, Masarie K, Miller JB, Bruhwiler LMP, Pétron G, Hirsch AI et al (2007) An atmospheric perspective on North American carbon dioxide exchange: carbontracker. Proc Natl Acad Sci 104(48): 18925PubMedCrossRefGoogle Scholar
  21. Schabenberger O, Gotway CA (2005) Statistical methods for spatial data analysis. Texts in statistical science. Chapman and Hall/CRC, Boca RatonGoogle Scholar
  22. Schimel D, House JI, Hibbard KA, Bousquet P, Ciais P, Peylin P, Braswell BH, Apps MJ, Baker D, Bondeau A, Canadell J, Churkina G, Cramer W, Denning AS, Field CB, Friedlingstein P, Goodale C, Heimann M, Houghton RA, Melillo JM, Moore B, Murdiyarso D, Noble I, Pacala SW, Prentice IC, Raupach MR, Rayner PJ, Scholes RJ, Steffen WL, Wirth C (2001) Recent patterns and mechanisms of carbon exchange by terrestrial ecosystems. Nature 414: 169–172PubMedCrossRefGoogle Scholar
  23. Schuh AE, Denning AS, Corbin KD, Baker IT, Uliasz M, Parazoo N, Andrews AE, Worthy DEJ (2010) A regional high-resolution carbon flux inversion of North America for 2004. Biogeosciences 7: 1625–1644CrossRefGoogle Scholar
  24. Smith J, Heath L, Nichols M (2007) U.S. forest carbon calculation tool: forestland carbon stocks and net annual stock change. Technical report, US Forest Service, Newtown, Pennsylvania. General Technical Report NRS13. Northern Research StationGoogle Scholar
  25. Sweeney C, Karion A, Wolter S, Neff D, Higgs JA, Heller M, Guenther D, Miller B, Montzka S, Miller J, Conway T, Dlugokencky E, Novelli P, Masarie K, Oltman S, Tans P (2011) Carbon dioxide climatology of the NOAA/ESRL greenhouse gas aircraft network. J Geophys Res (in prep). 20858, 20868Google Scholar
  26. Tarantola A (2005) Inverse problem theory and methods for model parameter estimation. Society for Industrial MathematicsGoogle Scholar
  27. Uliasz M (1994) Lagrangian particle dispersion modeling in mesoscale applications. Environ Model 2: 71–101Google Scholar
  28. USDA-NASS (2010) Data and statistics. Technical report, United States Department of Agriculture, National Agriculture Statistics Service, Washington, DCGoogle Scholar
  29. West T, Bandaru V, Brandt C, Schuh A, Ogle S (2011) Regional uptake and release of crop carbon in the United States. Biogeosciences 8: 631–654CrossRefGoogle Scholar
  30. West T, Singh N, Marland G, Bhaduri B, Roddy A (2009) The human carbon budget: an estimate of the spatial distribution of metabolic carbon consumption and release in the United States. Biogeochemistry 94: 29–41CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • Daniel Cooley
    • 1
    Email author
  • F. Jay Breidt
    • 1
  • Stephen M. Ogle
    • 2
  • Andrew E. Schuh
    • 3
  • Thomas Lauvaux
    • 4
  1. 1.Department of StatisticsColorado State UniversityFort CollinsUSA
  2. 2.Natural Resources Ecology LaboratoryColorado State UniversityFort CollinsUSA
  3. 3.Department of Atmospheric SciencesColorado State UniversityFort CollinsUSA
  4. 4.Department of MeteorologyPennsylvania State University, State CollegeUniversity ParkUSA

Personalised recommendations