Impacts of spatial and temporal correlations in regional atmospheric inverse estimates of greenhouse gas

fluxesTimothy W. Hilton1, Kenneth J. Davis1, Thomas Lauvaux1, Liza I. Diaz1, Martha P. Butler1, Klaus Keller1, Natasha L.

Miles1, Arlyn Andrews2 and Nathan M. Urban3

1The Pennsylvania State University2NOAA Earth Systems Research Lab

3Princeton University

SIAM, Long Beach, CA, 22 March, 2011

Inverse Modeling of CO2

Air Parcel Air Parcel

Air Parcel

Sources Sinks

wind wind

SampleSample

Changes in CO2 in the air tell us about sources and sinks

Toolbox (used at Penn State)

Air Parcel Air Parcel

Air Parcel

Sources Sinks

wind wind

SampleSample

Network of tower-based GHG sensors:(9 sites with CO2 for the MCI)(~11 sites with CO2, CH4, CO and 14CO2 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 CO2 at observation points

• Compare modeled and observed CO2 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 COFate of CO22 emissions 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, 2002Source: http://www.aip.org/pt/vol-55/iss-8/captions/p30cap2.html

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 = 1.8x1010 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!

Interannualvariability!

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 CO2 fertilization

• Longer growing seasons/better growing conditions - changes in climate

Methods

Flux of carbon across this plane= tower or aircraft flux approach

-

Change inforest biomassover time = forest inventory approach

Change in atmospheric concentration of CO2 overtime = inversion or ABL budget approach.

Change in CO2 concentration in a smallbox 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

Flux of C across this plane

+ Rate of accumulation of C below the flux sensor

= Net Ecosystem-Atmosphere Exchange (NEE) of C

Net sideways transport = 0

Sonic anemometer

Infrared gas analyzer

Campbell Scientific, Inc.LI-COR, Inc.

Net ecosystem-atmosphere exchange of CO2 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 2000-2005 (left).Summer NEE for 2002, 2004 (above).Peters et al, 2007, PNAS

COCO22 Concentration Network: 2008 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

observationsLAI

Carbon cycle model (ensemble?)

WRF or PCTM-SiB

Data assimilation algorithm

Prior parameter values and pdfsCarbon 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

pdfsCorrected C fluxes

Carbon data assimilation framework

Global inversion: PCTM-SiB and PCTM-CASA

Butler, Ph.D. dissertation, pubs in prepCorrect 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 CO2 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 110-140 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 10-30 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 (1995-1997) (Bakwin et al. 1998)

Typical Diurnal Cycle

350360370380390400

0 6 12 18 24

Hours (GMT)

CO2 (ppm)

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 (1995-1997) (Bakwin et al. 1998)

Typical Diurnal Cycle

350360370380390400

0 6 12 18 24

Hours (GMT)

CO2 (ppm)

Typical Diurnal Cycle

340

360

380

400

0 6 12 18 24

Hours (GMT)

CO2 (ppm)LEF

Ring2

Spatial gradient magnitude (daytime):

Growing seasons 2007-08

• 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 40 - 50 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 mapCorn for Grain 2007

Yield per Harvested Acre by County

Courtesy of K. Corbin

NOAA-ESRL Carbon Tracker

Ring2 sites not included as input for 2007

http://carbontracker.noaa.gov

14-day smoother applied to CT outputmid-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 solid2008 dashed

2007 2008

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

observationsLand cover,

climate

Carbon cycle model (ensemble?)LUE/R model

Data assimilation algorithm

MCMC and DE

Prior parameter values and pdfsQ10, 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

predictionsUpper 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 IntensiveExceptionally dense atmospheric CO2 measurement network

SchuhB53F-03

Percentage error reduction map: WRF-SiBCrop-LPDM inversion10x10 km2, weekly flux corrections.

Example from July, 2007.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 ~ 500-800 km

• 2 groups: 33-39 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

COCO22 Concentration Network: 2008 Concentration Network: 2008

Midcontinent intensive, 2007-2009

INFLUX, 2010-2012

Gulf coast intensive, 2013-2014