Presentation on theme: "Anna M. Michalak Department of Civil and Environmental Engineering"— Presentation transcript:
1 Geostatistical Inverse Modeling for Characterizing the Global Carbon Cycle Anna M. MichalakDepartment of Civil and Environmental EngineeringDepartment of Atmospheric, Oceanic and Space SciencesThe University of Michigan
3 The Future of Natural Carbon Sinks LandUncertainty associated with the future of natural carbon sinks is one of two major sources of uncertainty in future climate projections300 ppmOceansSubset of Fig. 1 from Friedlingstein et al. (2006) showing (a) atmospheric CO2 for the coupled carbon and climate simulations for several models and (c) Land carbon fluxes for these coupled runs. The differences in predicted land fluxes and ocean fluxes (not shown) cause a 300ppm difference in predicted CO2 concentrations in the year 2100.Friedlingstein et al. (2006) showing projections from coupled carbon and climate simulations for several models.
5 Tyler Erickson, Michigan Tech Research Institute 55
6 Carbon Flux Inference Characteristics Inverse problemIll-posedUnderdeterminedSpace-time variabilityMultiscaleNonstationaryAvailable ancillary data (with uncertainties)Deterministic process models have (non-Gaussian) errors (biospheric and atmospheric models)Large datasets (but still data poor), soon to be huge datasets with the advent of space-based CO2 observationsLarge to huge parameter space, depending on spatial / temporal resolution of estimationNeed topick your battlesintelligently!
12 Synthesis Bayesian Inversion Biospheric modelPrior flux estimates (sp)Auxiliary variablesCO2 observations (y)InversionFlux estimates and covariance ŝ, VŝTransport modelSensitivity of observations to fluxes (H)Meteorological fieldsResidual covariance structure (Q, R)
13 Geostatistical Inversion select significant variablesAuxiliary variablesModel selectionCO2 observations (y)Flux estimates and covariance ŝ, VŝInversionTransport modelSensitivity of observations to fluxes (H)Trend estimate and covariance β, VβMeteorological fieldsResidual covariance structure (Q, R)Covariance structure characterizationoptimize covariance parameters
14 Geostatistical Approach to Inverse Modeling Geostatistical inverse modeling objective function:H = transport information, s = unknown fluxes, y = CO2 measurementsX and = model of the trendR = model data mismatch covarianceQ = spatio-temporal covariance matrix for the flux deviations from the trendDeterministiccomponentStochasticcomponent14
15 Model SelectionDozen of types of ancillary data, many of which are from remote sensing platforms, are availableNeed objective approach for selecting variables, and potentially their functional form to be included in XModified expression for weighted sum of squares:Now we can apply statistical model selection tools:Hypothesis based, e.g. F-testCriterion based, e.g. modified BIC (with branch-and-bound algorithm for computational feasibility)Modified BIC (using branch-and-bound algorithm for computational efficiency)
16 Covariance Optimization Need to characterize covariance structure of unobserved parameters (i.e. carbon fluxes) Q using information on secondary variables (i.e. carbon concentrations) and selected ancillary variablesAlso need to characterize the model-data mismatch (sum of multiple types of errors) RRestricted Maximum Likelihood, again marginalizing w.r.t. :In some cases, atmospheric monitoring network is insufficient to capture sill and range parameters of Q
17 Other Implementation Choices No prior information on drift coefficients , which are estimated concurrently with overall spatial process sNo prior information on Q and R parameters, which are estimated in an initial step, but then assumed knownThis setup, combined with Gaussian assumptions on residuals, yields a linear system of equations analogous to universal cokriging:
19 Timeline of Development First presentation of approach:Michalak, Bruhwiler, Tans (JGR-A 2004)Application to estimation of global carbon budget, with and without the use of ancillary spatiotemporal data, model selection using modified F-test:Mueller, Gourdji, Michalak (JGR-A, 2008)Gourdji, Mueller, Schaefer, Michalak (JGR-A 2008)Approach development for North American carbon budget, with the addition of temporal correlation:Gourdji, Hirsch, Mueller, Andrews, Michalak (ACP, in review)Application to estimation of NA carbon budget, model selection using modified BIC:Gourdji, Michalak, et al. (in prep)Related applications for carbon flux analysis and modeling:Yadav, Mueller, Michalak (GCB, in review)Huntzinger, Michalak, Gourdji, Mueller (JGR-B, in review)Mueller, Yadav, Curtis, Vogel, Michalak (GBC, in review)
20 Estimates from North American Study +Evapotrans, Precip, Radiation, Soil Moisture, Temperature (NARR from NCEP Reanalysis), Fossil Fuels (combo of Vulcan & EDGAR for CA/MX), Fire Power, LAI (MODIS)=May 200420
21 Grid Scale Seasonal Cycle Inversion results compared to 15 forward modelsSignificant differences between inversion & forward models during the growing season, also near measurement towers21
22 Annual Average Eco-Region Flux Net flux (PgC/yr)- 2σ+ 2σCanada + Alaska-0.64-0.79-0.49United States-0.33-0.47-0.18Central America0.12-0.040.29total-0.84-1.11-0.57Note that many of these models are near 0 for all biomes. Number of models for each ecoregion: Trop=8, EastFor=12, NWConif=12, BorFor=13, Tundra=13, TempGSS=10, Desert=11Eco-region scale annual inversion fluxes fall within the spread of forward models, except in Boreal Forests and Desert & Xeric Shrub22
23 Carbon Flux Inference Contributions Inverse problemIll-posedUnderdeterminedSpace-time variabilityMultiscaleNonstationaryAvailable ancillary data (with uncertainties)Deterministic process models have (non-Gaussian) errors (biospheric and atmospheric models)Large datasets (but still data poor), soon to be huge datasets with the advent of space-based CO2 observationsLarge to huge parameter space, depending on spatial / temporal resolution of estimation
24 Carbon Flux Inference Opportunities Inverse problemIll-posedUnderdeterminedSpace-time variabilityMultiscaleNonstationaryAvailable ancillary data (with uncertainties)Deterministic process models have (non-Gaussian) errors (biospheric and atmospheric models)Large datasets (but still data poor), soon to be huge datasets with the advent of space-based CO2 observationsLarge to huge parameter space, depending on spatial / temporal resolution of estimation
25 Acknowledgements Collaborators on carbon flux modeling work: Research group: Abhishek Chatterjee, Sharon Gourdji, Charles Humphriss, Deborah Huntzinger, Miranda Malkin, Kim Mueller, Yoichi Shiga, Landon Smith, Vineet YadavNOAA-ESRL: Pieter Tans, Adam Hirsch, Lori Bruhwiler, Arlyn Andrews, Gabrielle Petron, Mike TrudeauPeter Curtis (Ohio State U.), Ian Enting (U. Melbourne), Tyler Erickson (MTRI), Kevin Gurney (Purdue U.), Randy Kawa (NASA Goddard), John C. Lin (U. Waterloo), Kevin Schaefer (NSIDC), Chris Vogel (UMBS), NACP Regional Interim Synthesis ParticipantsFunding sources:25
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