Impacts of spatial and temporal correlations in regional atmospheric inverse estimates of greenhouse gas fluxes Timothy W. Hilton 1, Kenneth J. Davis 1, Thomas Lauvaux 1, Liza I. Diaz 1, Martha P. Butler 1, Klaus Keller 1, Natasha L. Miles 1, Arlyn Andrews 2 and Nathan M. Urban 3 1 The Pennsylvania State University 2 NOAA Earth Systems Research Lab 3 Princeton University SIAM, Long Beach, CA, 22 March, 2011

Inverse Modeling of CO 2 Air Parcel Sources Sinks wind Sample Changes in CO 2 in the air tell us about sources and sinks

Toolbox (used at Penn State) Air Parcel Sources Sinks wind Sample Network of tower-based GHG sensors: (9 sites with CO 2 for the MCI) (~11 sites with CO 2, CH 4, CO and 14 CO 2 for INFLUX) Atmospheric transport model: (WRF, 10km for the MCI) (WRF, 2km for INFLUX) Prior flux estimate: (SiB-Crop for MCI) (Hestia for INFLUX) Boundary conditions (CO2/met):(Carbon Tracker and NOAA aircraft profiles, NCEP meteorology)

Toolbox, continued Lagragian Particle Dispersion Model (LPDM, Uliasz). –Determines “influence function” – the areas that contribute to GHG concentrations at measurement points. Independent data for evaluation of our results. –Agricultural inventory, flux towers and some aircraft data for the MCI –Fossil fuel inventory, (flux towers?) and abundant in situ aircraft data for INFLUX

Inversion method Simulate atmospheric transport. Run LPDM to determine influence functions Convolute influence functions with prior flux estimates to predict CO 2 at observation points Compare modeled and observed CO 2 and minimize the difference by adjusting the fluxes and boundary conditions.

Inversion method (graphic) Estimated together The spatial and temporal correlations in fluxes and concentrations has a large impact on the optimized fluxes and estimated uncertainties. Dense observations of fluxes and concentrations can be used to evaluate the spatial and temporal correlations that exist. How many unknowns? How many independent data points?

Fate of CO 2 emissions Roughly constant fraction (~45%) of fossil fuel emissions absorbed Large interannual variability in sink strength Governed by climate variability (e.g. ENSO)? Anthropogenic land-use emissions ~ 2 GtC yr -1  implies even larger sink Sarmiento and Gruber, 2002 Source: Sarmiento and Gruber, Physics Today, 2003

Atmospheric inventory results Gurney et al, 2002, Nature

Annual NEE is highly variable across inversions. Evidence of covariance in boreal vs. temperate N. America? 0.5 PgC yr-1 uncertainty bound may be optimistic? Evidence of coherence in the interannual variability. “Inverse” models - annual NEE

Other extreme Pixel by pixel, time step by time step MCI example – (1000 km) 2 domain, 10 km transport model resolution, 1 year temporal domain, 20 second model time step = 1000x1000/10/10*365*24*60*60/20 = 1.8x10 10 unknown fluxes. Computationally unreasonable, and not very realistic. Every pixel and time step is not independent.

Outline Background State of the science Recent results, work in progress

1 ppm yr -1 ~ 2 PgC yr -1. Fossil fuel emissions are ~ 6 PgC yr -1. Sink is implied! Interannual variability!

Global Carbon Cycle IPCC, 2007, after Sarmiento and Gruber, 2002

Possible terrestrial carbon sink mechanisms Regrowth of logged forests or woody enroachment in grasslands Nitrogen or CO 2 fertilization Longer growing seasons/better growing conditions - changes in climate

Methods Flux of carbon across this plane = tower or aircraft flux approach - Change in forest biomass over time = forest inventory approach Change in atmospheric concentration of CO 2 over time = inversion or ABL budget approach. Change in CO 2 concentration in a small box over time = chamber flux approach

Carbon cycle observations: Gap in scales Carbon fluxes Terrestrial carbon stocks Atmospheric carbon Surface radiances

Challenges Accurate diagnosis of the carbon cycle is limited to very small (flux tower footprints, FIA plots) or very large (globe, zonal bands) spatial scales. –convergence at regional scales has not yet been achieved Predictive skill is poor for all domains –demonstrated by limited ability to hind-cast multi-year flux tower records, and wide range of predictions among coupled carbon-climate models.

Method – eddy covariance

Sonic anemometer Infrared gas analyzer Campbell Scientific, Inc. LI-COR, Inc.

Net ecosystem-atmosphere exchange of CO 2 in northern Wisconsin

WLEF Lost Creek Willow Creek Sylvania

Atmospheric inventory results Gurney et al, 2002, Nature

Atmospheric inversion example - NOAA’s Carbon Tracker Annual NEE (gC m -2 yr -1 ) for (left). Summer NEE for 2002, 2004 (above). Peters et al, 2007, PNAS

CO 2 Concentration Network: 2008

Input data for domain of observations Carbon cycle model (ensemble?) Data assimilation algorithm Prior parameter values and pdfs Model predictions (including carbon fluxes) Carbon cycle model (ensemble?) Input data for domain of prediction Optimized, probabilistic flux predictions Observations of predicted variables Optimized parameters and pdfs Carbon data assimilation framework

Input data for domain of observations LAI Carbon cycle model (ensemble?) WRF or PCTM-SiB Data assimilation algorithm Prior parameter values and pdfs Carbon fluxes, perhaps informed by flux towers Model predictions (including carbon fluxes) Atmospheric CO2 Carbon cycle model (ensemble?) Input data for domain of prediction Optimized, probabilistic flux predictions Observations of predicted variables Atmospheric CO2 Optimized parameters and pdfs Corrected C fluxes Carbon data assimilation framework

Global inversion: PCTM-SiB and PCTM-CASA Butler, Ph.D. dissertation, pubs in prep Correct fluxes over coherent blocks, as in TRANSCOM Higher resolution over N. America where more data are available

North American results: annual mean Note the reduction of uncertainty in regions with flux towers (without much change to the estimated flux)

Mid-continent intensive (MCI) Overarching Goal Compare and reconcile to the extent possible, regional carbon flux estimates from “top-down” inverse modeling with the “bottom-up” inventories

MCI observation sites: Campaign (2007-8)

MCI region CO 2 seasonal cycle 31-day running mean Strong coherent seasonal cycle across stations West Branch (wbi) and Centerville (ce) differ significantly from 2007 to 2008 Large variance in seasonal drawdown

Outline Overall goal of Mid-Continental Intensive: Seek convergence between top-down (tower-based) and bottom-up (inventory-based) ecological estimates of the regional flux Plan: to “oversample” the atmosphere in the study region for more than a full year Atmospheric results –NOAA aircraft –Purdue Univ ALAR –Penn State Ring 2 (regional network of 5 cavity ring-down spectroscopy (Picarro, Inc) instruments –NOAA tall towers (WBI and LEF) –NOAA Carbon Tracker –Colorado State SiB3-RAMS model “Ring 2” Cavity Ring- Down systems PSU Ameriflux systems NOAA Tall Towers LEF

PSU Ring 2 Regional network of 5 cavity ring-down spectroscopy (Picarro, Inc.) instruments –Centerville, IA –Galesville, WI –Kewanee, IL –Mead, NE –Round Lake, MN 30 and m AGL NOAA tall towers in MCI region Two-cell non-dispersive infrared spectroscopy (LiCor, Inc.) instruments LEF: 11, 30, 76, 122, 244, 396 m AGL WBI: 31, 99, 379 m AGL

Synoptic variability in boundary-layer CO2 mixing ratios Seasonal drawdown Differences amongst the sites 2007 vs 2008 Day to day variability

Difference in daily value from one day to the next: as large as ppm Synoptic variability in boundary-layer CO2 mixing ratios Seasonal drawdown Differences amongst the sites 2007 vs 2008 Day to day variability

Temporal variability: Night – Day [CO2] Difference between nighttime and daytime values at ~120 m AGL can be over 80 ppm for Ring 2 Average magnitude of the diurnal cycle at 122 m for July at LEF: 10 ppm ( ) (Bakwin et al. 1998)

Temporal variability: Night – Day [CO2] Difference between nighttime and daytime values at ~120 m AGL can be over 80 ppm for Ring 2 Average magnitude of the diurnal cycle at 122 m for July at LEF: 10 ppm ( ) (Bakwin et al. 1998) LEF Ring2

Spatial gradient magnitude (daytime): Growing seasons Majority < 0.02 ppm/km But in 6% of cases, the spatial gradient is between 0.04 and 0.06 ppm/km (Daytime!) % of site-days Seasonal pattern Differences as large as ppm between Ring 2 sites! Daytime! Significant day-to-day variability Largest difference amongst the sites for each daily value

Seasonal cycle 31-day running mean Strong coherent seasonal cycle across stations West Branch (wbi) and Centerville (ce) differ significantly from 2007 to 2008 Large variance in seasonal drawdown, despite being separated by, at most, 550 km. (mm, ce, lef) vs (kw, rl, wbi)

Seasonal cycle 31-day running mean Strong coherent seasonal cycle across stations West Branch (wbi) and Centerville (ce) differ significantly from 2007 to 2008 Large variance in seasonal drawdown, despite being separated by, at most, 550 km. (mm, ce, lef) vs (kw, rl, wbi)

Seasonal cycle 31-day running mean Strong coherent seasonal cycle across stations West Branch (wbi) and Centerville (ce) differ significantly from 2007 to 2008 Large variance in seasonal drawdown, despite being separated by, at most, 550 km. (mm, ce, lef) vs (kw, rl, wbi)

Dominant vegetation map Corn for Grain 2007 Yield per Harvested Acre by County Courtesy of K. Corbin

NOAA-ESRL Carbon Tracker Ring2 sites not included as input for

14-day smoother applied to CT output mid-afternoon values only (19:30 GMT) Overall drawdown in CT2008 is too weak, but some features of modeled variability are consistent with obs, e.g., there is a lot of variability and MM has less drawdown than WBI, RL and KW in both model and obs. A. Andrews 2007

Flooding in the Midwest: June 2008 Dell Creek breach of Lake Delton, WI U.S. Air Force Cedar Rapids, IA Don Becker (USGS)

Seasonal cycle Strong coherent seasonal cycle across stations West Branch (wbi) and Centerville (ce) differ significantly from 2007 to 2008 Large variance in seasonal drawdown, despite being separated by, at most, 550 km (mm, ce, lef) vs (kw, rl, wbi)

Delay in seasonal drawdown 2008 growing season is uniformly delayed by about one month, compared to 2007 Effect of June 2008 flood? Recovery: increased uptake later in the growing season 2007 solid 2008 dashed

Sources of uncertainty in model-data syntheses Model structural error –Bayesian model averaging? Input/driver data uncertainty –Propagation of error? Parametric uncertainty –Bayesian methods to derive pdfs. Complex model-data error structures –Temporal and spatial correlations –Non-Gaussian residuals –Heteroskedastic residuals

Input data for domain of observations Land cover, climate Carbon cycle model (ensemble?) LUE/R model Data assimilation algorithm MCMC and DE Prior parameter values and pdfs Q10, LUE, etc Model predictions (including carbon fluxes) Upper midwest forest C fluxes Carbon cycle model (ensemble?) Input data for domain of prediction Extrapolate over space Optimized, probabilistic flux predictions Upper midwest forest flux maps Observations of predicted variables ChEAS flux measurements Optimized parameters and pdfs Carbon data assimilation framework

Results Example of sources of uncertainty in flux maps Example of the importance of assumptions about spatial correlation in model-data errors Example of using global models, and the promise of connecting across scales

What is the correct spatial (and temporal) coherence in model-data residuals? And does it really matter? Gap-filled fluxes from the 5 sites used in TRIFFID analysis Harvard and Howland: Coherent between 1996 and 2000, then breaks down. UMBS and Morgan Monroe: coherent (similar PFT, climate) WLEF: 2002 missing, coherent with UMBS and Morgan Monroe

Midcontinental Intensive Exceptionally dense atmospheric CO 2 measurement network Schuh B53F-03

Percentage error reduction map: WRF-SiBCrop-LPDM inversion 10x10 km 2, weekly flux corrections. Example from July, Flux corrections assumed to be correlated according to vegetation cover with a length scale of 50 km.

Percentage error reduction map assuming no spatial correlation. Note the dramatic difference in the area influenced by the atmospheric data. Influence becomes intensely local.

Conclusions 2 Example of the importance of assumptions about spatial correlation in model-data errors –Assuming independent, Gaussian errors enables progress, but is almost certainly wrong, especially in a data-limited environment. –Spatial and temporal correlations in model-data residuals can have a large impact on our solutions, and a larger impact on our assessment of uncertainty in our solutions. –Flux towers can inform atmospheric inversions (see also, Raczka, B54A-05).

Corn-dominated sites MCI Tower-Based CO2 Observational Network Aircraft profile sites, flux towers omitted for clarity.

Large variance in seasonal drawdown, despite being separated by ~ km 2 groups: ppm drawdown and 24 – 29 ppm drawdown (difference of about 10 ppm) Mauna Loa Miles et al, in preparation MCI 31 day running mean daily daytime average CO2

CO 2 Concentration Network: 2008 Midcontinent intensive, INFLUX, Gulf coast intensive,