Forward and Inverse Modeling of Atmospheric CO 2

1. Forward and Inverse Modeling of Atmospheric CO2 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? Usual approach is to exclude “spikes” as non-“background” Cape Grim Law et al inverted the “spikes” instead!

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

5. Continental NEE and [CO2] • Variance in [CO2] 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 amt lef ring hrv sgp wkt Seasonal and Synoptic Variations Daily min [CO2], 2004 • 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?

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 Oklahoma Wisconsin Alberta • 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

10. Frontal CO2 “Climatology” • Multiple cold fronts averaged together (diurnal & seasonal cycle removed) • Some sites show frontal drop in CO2, 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° gradient strength • shear • deformation • tracer field • rotated by • shear vorticity • stretching • deformation • tracer field • deformed • by stretching

12. Lateral Boundary Forcing • Flask sampling shows N-S gradients of 5-10 ppm in [CO2] 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 (R2 = 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 CO2 • Measure real CO2 variations • Figure out where the air has been • Use mismatch between simulated and observed CO2 to “correct” persistent model biases • GOAL: Time-varying maps of sources/sinks consistent with observed vegetation, fluxes, and CO2 as well as process knowledge

18. SiB SiB     unknown! unknown! Flux-convolved influence functions derived from SiB-RAMS 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 [CO2]

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

21. Filtered: diurnal cycle removed

22. Filtered: diurnal cycle removed

23. Ring of Towers: May-Aug 2004 • 1-minute [CO2] from six 75-m telecom towers, ~200 km radius • Simulate in SiB-RAMS • Adjust (x,y) to optimize mid-day CO2 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 CO2 • Partial derivative of CO2 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 …