Regional Flux Estimation using the Ring of Towers Scott Denning, Ken Davis, Scott Richardson, Marek Uliasz, Dusanka Zupanski, Kathy Corbin, Andrew Schuh, Nick Parazoo, Ian Baker, Tasha Miles, and Peter Rayner

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 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 seen by RS

Temporal Variations in NEE Flux is nothing like a constant value to be estimated! “Coherent” diurnal cycles?, but … Day-to-day variability of ~ factor of 2 due to passing weather disturbances WLEF

Pesky Variability in the Real World Managed forests, variable soils, suburban landscapes, urban parks Disturbance and succession: fires, harvest, etc Crops: Wheat vs Corn vs Soybeans Irrigation, fertilization, tillage practice Wisconsin (ChEAS) flux towers Attempt to “upscale” annual NEE over 40 km: –WLEF = a 1 * WC + a 2 * LC, –but only if a 2 < 0 –decorrelation length scale is very small on annual NEE! High-Frequency Variations in Space …

What Causes Long-Term Model Bias? Parameters (maybe, but more likely to control variability than bias) State! –Respiration: soil carbon, coarse woody debris –GPP: stand age, nutrient availability, management Missing equations! Physiology is easier to model than site history and management

Our 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” model biases for slow BGC GOAL: Time-varying maps of sources/sinks consistent with observed vegetation, fluxes, and CO 2 as well as process knowledge

Observational Constraints Satellite imagery & veg maps –spatial and seasonal variations Flux towers –Ecosystem physiology for different veg types –GPP, Resp, stomates, drought response Atmospheric CO 2 –Average source/sink over large upstream area

Continental NEE and [CO2] Variance dominated by diurnal and seasonal cycles, but target is source/sink processes on interannual to decadal time scales Diurnal variations controlled locally by nocturnal stability (ecosystem resp is secondary!) Seasonal variations controlled hemispherically by phenology Synoptic variations controlled regionally, over scales of km. Target these.

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 ppm, strongest in summer Events can be traced across multiple sites What causes these huge coherent changes? Daily min [CO 2 ], 2004

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

Modeling & Analysis Tools (alphabet soup) Ecosystem model (Simple Biosphere, SiB) Weather and atmospheric transport (Regional Atmospheric Modeling System, RAMS) Large-scale 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)

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

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?

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

Ring of Towers inexpensive instruments deployed on six 75-m towers in 2004 ~200 km radius 1-minute data May- August

Ring of Towers Data mid-day onlyJune 9- July 5, ppm over 200 km u ~ 10 m/s  z ~ 1500 m ~ 13  mol m -2 s -1

Coupled Model: SiB-RAMS-LPDM SiB3 – Simple Biosphere Model [Sellers et al., 1996] – Calculates the transfer of energy, water, and carbon between the atmosphere and the vegetated surface of the earth – Photosynthesis model of Farquhar et al. [1980] and stomatal model of Collatz et al [1991, 1992] – Ecosystem respiration depends on soil temperature, water, FPAR, with pool size chosen to enforce annual carbon balance – Parameters specified from MODIS Vegetation imagery (1 km) RAMS5 – Regional Atmospheric Modeling System – Comprehensive mesoscale meteorological modeling system (Cotton et al., 2002), with telescoping, nested grid scheme – Bulk cloud microphysics parameterization –Meteorological fields initialized and lateral boundaries nudged using the NCEP mesoscale Eta analysis (  x = 40 km) –Deep cumulus after Grell (1995); Shallow cloud transports after Freitas (2001) –Lateral CO2 boundary condition from global SiB-PCTM analysis LPDM - Lagrangian Particle Dispersion Model –Backward-in time particle trajectories from receptors –Driven from 15-minute RAMS output

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

Back-trajectory Analysis 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

Treatment of Variations for Inversion Fine-scale variations (hourly, 20-km pixels) from weather forcing and satellite vegetation data 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

Maximum Likelihood Ensemble Filter (MLEF) Closely related to Ensemble Kalman Filter No adjoint, forward modeling of ensemble of perturbed states or parameters Propagate estimates of  GPP (x,y) and  Resp (x,y) along with (sample of) full covariance matrix Model “learns” about parameters, state variables, and covariance structure over each data assimilation cycle Explain on whiteboard?

Pseudodata Ring Inversions 6 short towers plus 396 m at WLEF 2-hour averaged data (from 1 min) SiB-RAMS nest at  x=10 km LPDM on RAMS output, convolve with GPP and Resp, influence functions integrated for 10 days Add Gaussian noise to initial  ’s and obs Estimate  GPP and  Resp for 30x30 grid boxes centered at WLEF at  x=20 km N unk = 30 x 30 x 2 = 1800

Synthetic “Ring” Experiment: MLEF Solve  for  ( x,y ) on a 20-km grid “Truth” divided in half (E vs W) Noise added at different scales (8  x N vs 4  x S) Prior:  = 0.75 Prior smoothing = 6  x … solve 6 towers, obs every 2 hours  = 0.5 _  = 1.1 _

Wow! no info over Great Lakes

MLEF Result after 70 Days Easily finds E-W diffs Some skill locating anomalies Better N-S diff in covariance than prior No flux over lakes, so no skill there!    

NACP “Mid-Continent Intensive” (2007)

31 Towers in 2007

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 would progressively “learn” about both fluxes and covariance structure

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 Add C allocation and biogeochemistry to SiB- RAMS Parameterize using eddy covariance and satellite data Optimize model state variables, not parameters or unpredictable biases Propagate flux covariance using BGC instead of a persistence forecast