1. Forward and Inverse Modeling of Atmospheric CO 2 Scott Denning, Nick Parazoo, Kathy Corbin, Marek Uliasz, Andrew Schuh, Dusanka Zupanski, Ken Davis, and Peter Rayner Acknowledgements: Support by US NOAA, NASA, DoE

3. Signal? Noise? Which is which? Cape Grim Usual approach is to exclude “spikes” as non-“background” Law et al inverted the “spikes” instead!

4. Effects of height-time concentration variation near the ground 358 ppm OASIS, Oct 1995, Wagga, NSW

5. Continental NEE and [CO 2 ] Variance in [CO 2 ] is strongly dominated by diurnal and seasonal cycles, but target is source/sink processes on interannual to decadal time scales Diurnal variations are controlled locally by nocturnal stability (variations in ecosystem resp are secondary!) Seasonal variations are controlled hemispherically by phenology Synoptic variations controlled regionally, over scales of 100 - 1000 km. Let’s target these.

6. wpl sobs frs sgp wkt hrv amt lef ring Seasonal and Synoptic Variations Strong coherent seasonal cycle across stations SGP shows earlier drawdown (winter wheat), then relaxes to hemispheric signal Synoptic variance of 10- 20 ppm, strongest in summer Events can be traced across multiple sites What causes these huge coherent changes? Daily min [CO 2 ], 2004

7. Modeling & Analysis Tools (alphabet soup) Ecosystem model (Simple Biosphere, SiB) Weather and atmospheric transport (Regional Atmospheric Modeling System, RAMS) Large-scale continental inflow (Parameterized Chemical Transport Model, PCTM) Airmass trajectories (Lagrangian Particle Dispersion Model, LPDM) Optimization procedure to estimate persistent model biases upstream (Maximum Likelihood Ensemble Filter, MLEF)

9. Frontal Composites of Weather The time at which magnitude of gradient of density (  ) changes the most rapidly defines the trough (minimum GG , cold front) and ridge (maximum GG  ) Frontal Locator Function Oklahoma WisconsinAlberta

10. Frontal CO 2 “Climatology” Multiple cold fronts averaged together (diurnal & seasonal cycle removed) Some sites show frontal drop in CO 2, some show frontal rise … controls? Simulated shape and phase similar to observations What causes these?

11. Deformational Flow Anomalies organize along cold front dC/dx ~ 15ppm/3-5° shear deformation - tracer field rotated by shear vorticity stretching deformation - tracer field deformed by stretching gradient strength

12. Lateral Boundary Forcing Flask sampling shows N-S gradients of 5-10 ppm in [CO 2 ] over Atlantic and Pacific Synoptic waves (weather) drive quasi- periodic reversals in meridional ( v ) wind with ~5 day frequency Expect synoptic variations of ~ 5 ppm over North America, unrelated to NEE! Regional inversions must specify correct time-varying lateral boundary conditions Sensitivity exp: turn off all NEE in Western Hemisphere, analyze CO2(t)

15. Run 1: Surfaces fluxes defined everywhere on Earth Run 2: Surface fluxes set to 0 in Western Hemisphere, including NA Correlation of the 2 experiments in July (mid-day values only) shows the importance of lateral flow over NA (R 2 = 35-70% in SE!)

16. Regional Fluxes are Hard! Eddy covariance flux footprint is only a few hundred meters upwind Heterogeneity of fluxes too fine-grained to be captured, even by many flux towers –Temporal variations ~ hours to days –Spatial variations in annual mean ~ 1 km Some have tried to “paint by numbers,” –measure flux in a few places and then apply everywhere else using remote sensing Annual source/sink isn’t a result of vegetation type or LAI, but rather a complex mix of management history, soils, nutrients, topography not easily seen by RS

17. A Different Strategy Divide carbon balance into “fast” processes that we know how to model, and “slow” processes that we don’t Use coupled model to simulate fluxes and resulting atmospheric CO 2 Measure real CO 2 variations Figure out where the air has been Use mismatch between simulated and observed CO 2 to “correct” persistent model biases GOAL: Time-varying maps of sources/sinks consistent with observed vegetation, fluxes, and CO 2 as well as process knowledge

18. Treatment of Variations for Inversion Fine-scale variations (hourly, pixel-scale) from weather forcing, NDVI as processed by forward model logic (SiB-RAMS) Multiplicative biases (caused by “slow” BGC that’s not in the model) derived by from observed hourly [CO 2 ] SiB   unknown!   Flux-convolved influence functions derived from SiB-RAMS

19. Average NEE SiB-RAMS Simulated Net Ecosystem Exchange (NEE)

21. Filtered: diurnal cycle removed

23. Ring of Towers: May-Aug 2004 1-minute [CO 2 ] from six 75-m telecom towers, ~200 km radius Simulate in SiB-RAMS Adjust  (x,y) to optimize mid-day CO 2 variations

24. Back-trajectory “ Influence Functions ” Release imaginary “particles” every hour from each tower “receptor” Trace them backward in time, upstream, using flow fields saved from RAMS Count up where particles have been that reached receptor at each obs time Shows quantitatively how much each upstream grid cell contributed to observed CO 2 Partial derivative of CO 2 at each tower and time with respect to fluxes at each grid cell and time

25. 31 Towers in 2007

26. Estimating the  ’ s Full Kalman Filter (Bayesian synthesis) Maximum Likelihood Ensemble Filter (MLEF, Zupanski et al) Markov-Chain Monte Carlo (MCMC) Problem is terribly underconstrained! The science (art?) is in the specification of covariance structures Marek and Andrew will discuss …