CO 2 Source Sink Inversion History Computational Requirements

CO 2 Source / Sink Inversion – History, Computational Requirements Anna M. Michalak Department of Civil & Environmental Engineering Department of Atmospheric, Oceanic & Space Sciences University of Michigan

Inverse Modeling 2 A. M. Michalak (amichala@umich. edu)

Forward vs. Inverse Modeling Forward modeling Inverse modeling 3 A. M. Michalak (amichala@umich. edu)

CO 2 Fluxes Present Knowledge 5. 5 ± 0. 3 3. 3 ± 0. 2 Peta (1015 ) grams of carbon/year To Atmosphere 1. 6 ± 0. 8 Ocean Uptake Atmospheric Carbon Fossil Fuels Land Use Change To Land/Ocean = Atmospheric Storage Unidentified Sink 2. 0 ± 0. 6 1. 8 ± 1. 5 + Human Input Source: Diane Wickland (NASA) A. M. Michalak (amichala@umich. edu) - Uptake 4

Global Distribution of Atmospheric Carbon Dioxide Atmospheric growth rate ~ 3 ± 0. 1 Gt C/year Source: NOAA-CMDL A. M. Michalak (amichala@umich. edu) 5

Where is the Missing Sink (c. 1995)? Requires uptake O 2/N 2, inverse modeling suggests terrestrial Northern hemisphere!! A. M. Michalak (amichala@umich. edu) Source: Kevin Gurney, CSU 6

Carbon and Climate Futures? Given nearly identical human emissions, models project dramatically different futures. 7 Carbon cycle feedbacks are among the largest sources of uncertainty for future climate. A. M. Michalak (amichala@umich. edu)

Spatio-temporal variability of CO 2 Simulated 2 -hourly column CO 2 A. M. Michalak (amichala@umich. edu) Source: Olsen & Randerson (2004) 8

Sources of Atmospheric CO 2 Information North American Carbon Program 9 A. M. Michalak (amichala@umich. edu)

Regional Flux Estimation Example measurement site: WLEF tall tower (447 m) in Wisconsin CO 2 flux measurements at: 30, 122 and 396 m CO 2 mixing ratio measurements at: 11, 30, 76, 122, 244 and 396 m Photo credit: B. Stephens, UND Citation crew, COBRA 10 A. M. Michalak (amichala@umich. edu)

Local Flux Estimation Example Measurement Site – UMBS Flux Hemispherical image from the top of the 46 meter UMBS~Flux meteorological tower Instrumentation above the UMBS canopy is used to estimate canopy-level carbon uptake Source: Peter Curtis, Ohio State U. A. M. Michalak (amichala@umich. edu) The UMBS meteorological tower is 46 m tall with gas sampling ports at 8 different heights 11

What Surface Fluxes to Atmospheric Samples See? Latitude Height Above Ground Level (km) 24 June 2000: Particle Trajectories Longitude -24 hours -48 hours -72 hours -96 hours -120 hours Longitude 12 Source: Arlyn Andrews, NOAA-CMDL A. M. Michalak (amichala@umich. edu)

Linear Transport • Use transport model to generate H • Observe y at n times / locations • Invert H to find s data transport fluxes Were the problem simple: 14 A. M. Michalak (amichala@umich. edu)

Need for Additional Information • Current network of atmospheric sampling sites requires additional information to constrain fluxes: § Problem is ill-conditioned § Problem is under-determined (at least in some areas) § There are various sources of error: • Measurement error • Transport model error • Aggregation error • One solution is to assimilate additional information through a Bayesian approach 15 A. M. Michalak (amichala@umich. edu)

Bayesian Inference Applied to Inverse Modeling for Trace Gas Surface Flux Estimation Posterior probability of surface flux distribution Likelihood of fluxes given atmospheric distribution y : available observations (n× 1) s : surface flux distribution (m× 1) Prior information about fluxes p(y) probability of measurements 16 A. M. Michalak (amichala@umich. edu)

Bayesian Formalism • Use data, y, prior flux estimates, sp, and model (with Green’s function matrix H) to estimate fluxes, s • Estimate obtained by minimizing: • Solution is • Estimates, ŝ have covariance • Residuals: 17 A. M. Michalak (amichala@umich. edu)

Large Regions Inversion Trans. Com 3 Sites & Basis Regions Trans. Com, Gurney et al 2003 A. M. Michalak (amichala@umich. edu) 18

Transport Gridscale Inversions Rödenbeck et al. 2003 A. M. Michalak (amichala@umich. edu) 19

Deterministic vs. Stochastic Components of Flux Estimates Xβ – Constant Component Remember: QHTξ Xβ – Variable Component ŝ (flux best estimates) 20 A. M. Michalak (amichala@umich. edu) January 2000

Uncertainty on Best Estimates (Variable Trend) Land Jan 1999 Ocean 21 A. M. Michalak (amichala@umich. edu)