1. Space-Time Variability in Carbon Cycle Data Assimilation Scott Denning, Peter Rayner, Dusanka Zupanski, Marek Uliasz, Nick Parazoo, Ravi Lokupitiya, Andrew Schuh, Ian Baker, and Ken Davis Acknowledgements: Support by US NOAA, NASA, DoE

2. 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

3. 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

4. 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)

5. 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

6. 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 (ecosystem resp is secondary!) Seasonal variations are controlled hemispherically by phenology Synoptic variations controlled regionally, over scales of 100 - 1000 km. Let’s target these.

7. 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 “Ring of Towers” in Wisconsin Daily min [CO 2 ], 2004

8. 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)

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

12. Filtered: diurnal cycle removed

14. 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

15. 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

22. Wow! no info over Great Lakes

23. Next Step: Predict  If we had a deterministic equation that predict the next  from the current  we could improve our estimates over time Fold  into model state, not parameters Spatial covariance would be based on “model physics” rather than an assumed exponential decorrelation length Assimilation will progressively “learn” about both fluxes and covariance structure

24. Coupled Modeling and Assimilation System CSU RAMS Radiation Clouds CO 2 Transport and Mixing Ratio Winds Surface layerPrecipitation PBL (T, q) Biogeochemistry Microbial pools Litter pools Slow soil C RootsWoodLeaves passive soil C allocation autotrophic resp heterotrophic resp SiB3 Snow (0-5 layers) Photosynthesis Soil T & moisture (10 layers) Canopy air space Sfc T Leaf T HLENEE CO 2 Adding C allocation and biogeochemistry to SiB- RAMS Parameterize using eddy covariance and satellite data Optimize model state variables (C stocks), not parameters or unpredictable biases Propagate flux covariance using BGC instead of a persistence forecast

25. Summary/Recommendations Space/time variations of NEE are complex and fine- grained, resulting from hard-to-model processes Variations in [CO 2 ] dominated by “trivial” diurnal & seasonal cycles that contain little information about time-mean regional NEE Target synoptic variations to focus on regional scales Model parameters control higher-frequency variability … optimize against eddy flux & RS Time-mean NEE(x,y) depends on BGC model state (C stocks) rather than parameters … optimize these based on time-integrated model-data mismatch 70 days of 2-hourly data sufficient to estimate stationary model bias on 20-km grid over 360,000 km 2