Improving Understanding of Global and Regional Carbon
Dioxide Flux Variability through Assimilation of in Situ and Remote Sensing Data in a Geostatistical Framework
Anna M. Michalak
Department of Civil and Environmental EngineeringDepartment of Atmospheric, Oceanic and Space SciencesThe University of Michigan
Outline Introduction to geostatistics Inverse modeling approaches to estimating flux
distributions Geostatistical approach to quantifying fluxes:
Global flux estimation Use of auxiliary data Regional scale synthesis
Spatial Correlation Measurements in close proximity to each other generally
exhibit less variability than measurements taken farther apart.
Assuming independence, spatially-correlated data may lead to:
1. Biased estimates of model parameters2. Biased statistical testing of model parameters
Spatial correlation can be accounted for by using geostatistical techniques
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map of an alpine basin
snow depth measurements
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Q: What is the mean snow depth in the watershed?
Geostatistics in Practice Main uses:
Data integration Numerical models for prediction
Numerical assessment (model) of uncertainty
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Geostatistical Inverse Modeling
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Geostatistical Inverse Modeling
Geostatistical Bayesian / Independent Errors
Key Points If the parameter(s) that you are modeling exhibits
spatial (and/or temporal) autocorrelation, this feature must be taken into account to avoid biased solutions
Spatial (and/or temporal) autocorrelation can be used as a source of information in helping to constrain parameter distributions
The field of geostatistics provides a framework for addressing the above two issues
ASIDE: CO2 Measurements from Space
Factors such as clouds, aerosols and computational limitations limit sampling for existing and upcoming satellite missions such as the Orbiting Carbon Observatory
A sampling strategy based on XCO2 spatial structure assures that the satellite gathers enough information to fill data gaps within required precision
Alkhaled et al. (in prep.)
XCO2 Variability Regional spatial covariance
structure is used to evaluate: Regional sampling
densities required for a set interpolation precision
Minimum sampling requirements and optimal sampling locations
Variance
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Source: Arlyn Andrews, NOAA-GMD
What Surface Fluxes do Atmospheric Measurements See?
Need for Additional Information Current network of atmospheric sampling sites
requires additional information to constrain fluxes: Problem is ill-conditioned Problem is under-determined (at least in some areas) There are various sources of uncertainty:
Measurement error Transport model error Aggregation error Representation error
One solution is to assimilate additional information through a Bayesian approach
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dp|p
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Posterior probability of surface flux distribution
Prior informationabout fluxes
p(y) probability ofmeasurements
Likelihood of fluxes givenatmospheric distribution
y : available observations (n×1)
s : surface flux distribution (m×1)
Bayesian Inference Applied to Inverse Modeling for Surface Flux Estimation
Synthesis Bayesian Inversion
Meteorological Fields
TransportModel
Sensitivity of observations to
fluxes (H)
Residual covariance
structure (Q, R)
Prior flux
estimates (sp)
CO2
Observations (y)
Inversion
Flux estimates and covariance
ŝ, Vŝ
BiosphericModel
AuxiliaryVariables
?
?
Geostatistical Approach to Inverse Modeling Geostatistical inverse modeling objective function:
H = transport information, s = unknown fluxes, y = CO2 measurements
X and define the model of the trend R = model data mismatch covariance Q = spatio-temporal covariance matrix for the flux deviations
from the trend
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1 1( ) ( ) ( ) ( )
2 2T TL s β y Hs R y Hs s Xβ Q s Xβ
Deterministiccomponent
Stochasticcomponent
Synthesis Bayesian Inversion
Meteorological Fields
TransportModel
Sensitivity of observations to
fluxes (H)
Residualcovariance
structure (Q, R)
Prior flux estimates (sp)
CO2
Observations (y)
InversionFlux estimates and covariance
ŝ, Vŝ
BiosphericModel
AuxiliaryVariables
Geostatistical Inversion
Meteorological Fields
TransportModel
Sensitivity of observations to
fluxes (H)
Residual covariance
structure (Q, R)
AuxiliaryVariables
CO2
Observations (y)
VarianceRatioTest
Inversion
RMLOptimization
Flux estimates and covariance
ŝ, Vŝ
Trend estimate and covariance
β, Vβ
select significant variables
optimize covariance parameters
Key Questions Can the geostatistical approach estimate:
Sources and sinks of CO2 without relying on prior estimates?
Spatial and temporal autocorrelation structure of residuals?
Significance of available auxiliary data? Relationship between auxiliary data and flux
distribution? If so, what do we learn about:
Flux variability (spatial and temporal) Influence of prior flux estimates in previous studies Impact of aggregation error
What are the opportunities for further expanding this approach to move from attribution to diagnosis and prediction?
Recovery of Annually Averaged Fluxes
Best estimate “Actual” fluxes
Michalak, Bruhwiler & Tans (JGR, 2004)
Recovery of Annually Averaged Fluxes
Best estimate Standard Deviation
Michalak, Bruhwiler & Tans (JGR, 2004)
Key Questions Can the geostatistical approach estimate
Sources and sinks of CO2 without relying on prior estimates?
Spatial and temporal autocorrelation structure of residuals?
Significance of available auxiliary data? Relationship between auxiliary data and flux
distribution? If so, what do we learn about:
Flux variability (spatial and temporal) Influence of prior flux estimates in previous studies Impact of aggregation error
What are the opportunities for further expanding this approach to move from attribution to diagnosis and prediction?
Auxiliary Data and Carbon Flux Processes
Image Source: NCAR
Terrestrial Flux:Photosynthesis(FPAR, LAI, NDVI)
Respiration(temperature)
Oceanic Flux:Gas transfer
(sea surface temperature, air temperature)
AnthropogenicFlux:Fossil fuel combustion(GDP density, population)
Other:Spatial trends
(sine latitude, absolute value latitude)
Environmental parameters:
(precipitation, %landuse, Palmer drought index)
Which Model is Best?
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Available dataReal (unknown) determininistic componentConstant meanLinear trendLinear + QuadraticLinear+Quadratic+Cubic
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Available dataReal (unknown) determininistic componentConstant meanLinear trendLinear + QuadraticLinear+Quadratic+Cubic
Geostatistical Approach to Inverse Modeling Geostatistical inverse modeling objective function:
H = transport information, s = unknown fluxes, y = CO2 measurements
X and define the model of the trend R = model data mismatch covariance Q = spatio-temporal covariance matrix for the flux deviations
from the trend
1 1,
1 1( ) ( ) ( ) ( )
2 2T TL s β y Hs R y Hs s Xβ Q s Xβ
Deterministiccomponent
Stochasticcomponent
Global Gridscale CO2 Flux Estimation Estimate monthly CO2 fluxes (ŝ) and their uncertainty on
3.75° x 5° global grid from 1997 to 2001 in a geostatistical inverse modeling framework using: CO2 flask data from NOAA-ESRL network (y) TM3 (atmospheric transport model) (H) Auxiliary environmental variables correlated with CO2
flux
Three models of trend flux (Xβ) considered: Simple monthly land and ocean constants Terrestrial latitudinal flux gradient and ocean constants Terrestrial gradient, ocean constants and auxiliary
variables
Combine physical understanding with results of VRT to choose final set of auxiliary variables:
% Ag LAI SST% Forest fPAR dSSt/dt% Shrub NDVI Palmer Drought Index% Grass Precipitation GDP Density
Land Air Temp. Population Density
Combine physical understanding with results of VRT to choose final set of auxiliary variables:
% Ag LAI SST% Forest fPAR dSSt/dt% Shrub NDVI Palmer Drought Index% Grass Precipitation GDP Density
Land Air Temp. Population Density
Selected Auxiliary Variables
Inversion estimates drift coefficients (β):
Aux. Variable
CV X (GtC/yr)
GDP
LAI
fPAR
% Shrub
L. Temp
GDP 0.09 0.247 2.4 1 0.01 -0.19 0.24 0.10
LAI -0.67 0.094 -44.6 --- 1 -0.93 0.03 -0.05
fPAR 0.60 0.094 49.3 --- --- 1 -0.15 -0.15
% Shrub -0.11 0.175 -4.4 --- --- --- 1 0.02
LandTemp 0.06 0.485 1.7 --- --- --- --- 1
Gourdji et al. (in prep.)
Deterministiccomponent
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Ts QHX ˆ
Building up the best estimate in January 2000
Gourdji et al. (in prep.)
Regional comparison of seasonal cycle
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TemperateNorth America
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Tropical America1 3 5 7 9 11
South America1 3 5 7 9 11
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South Pacific1 3 5 7 9 11
Northern Ocean North Atlantic
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South Atlantic Southern Ocean Tropical Indian Southern Indian
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Variable Trend Estimates (ŝ) Variable Trend +/- 2σŝ
TransCom Estimates (Baker et al., 2006)
+/σ
Aggregated Bottom Up Estimates(Randerson et al. 1997, Brenkert 1998,Takahashi et al. 2002)
Modified Trend Estimates (ŝ)Simple Trend Estimat
Gourdji et al. (in prep.)
Comparison of annual average non-fossil fuel flux
Gourdji et al. (in prep.)
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Simple Trend Best EstimatesModified Trend Best EstimatesTranscom (Baker et al., 2006) +/- 2
Rodenbeck et al. (2003) +/- 2
Key Questions Can the geostatistical approach estimate
Sources and sinks of CO2 without relying on prior estimates?
Spatial and temporal autocorrelation structure of residuals?
Significance of available auxiliary data? Relationship between auxiliary data and flux
distribution? If so, what do we learn about:
Flux variability (spatial and temporal) Influence of prior flux estimates in previous studies Impact of aggregation error
What are the opportunities for further expanding this approach to move from attribution to diagnosis and prediction?
Opportunities for Regional Synthesis
Photo credit: B. Stephens, UND Citation crew, COBRA
Continuous tall-tower data available
More consistent relationship to auxiliary variables
Flux tower and aircraft campaign data available for validation
NACP offers opportunities for intercomparison / collaborations
WLEF tall tower (447m) in Wisconsin with CO2 mixing ratio measurements at 11, 30, 76, 122, 244 and 396 m
North American CO2 Flux Estimation Estimate North American
CO2 fluxes at 1°x1° resolution & daily/weekly/monthly timescales using: CO2 concentrations
from 3 tall towers in Wisconsin (Park Falls), Maine (Argyle) and Texas (Moody)
STILT – Lagrangian atmospheric transport model
Auxiliary remote-sensing and in situ environmental data
Pseudodata and recovered fluxes (Source: Adam Hirsch, NOAA-ESRL)
Analysis steps:Compile auxiliary variablesSelect significant variables to include in model of the trend
Estimate covariance parameters:
Model-data mismatchFlux deviations from overall trend.
Perform inversion, estimating both (i) the relationship between auxiliary variables and flux , and (ii) the flux distribution s.
A posteriori covariance includes the uncertainties of fluxes, trend parameters, and all cross-covariances
Assimilation of Remote Sensing and Atmospheric Data
Key Questions Can the geostatistical approach estimate
Sources and sinks of CO2 without relying on prior estimates?
Spatial and temporal autocorrelation structure of residuals?
Significance of available auxiliary data? Relationship between auxiliary data and flux
distribution? If so, what do we learn about:
Flux variability (spatial and temporal) Influence of prior flux estimates in previous studies Impact of aggregation error
What are the opportunities for further expanding this approach to move from attribution to diagnosis and prediction?
Conclusions Atmospheric data information content is sufficient to:
Quantify model-data mismatch and flux covariance structure
Identify significant auxiliary environmental variables and estimate their relationship with flux
Constrain continental fluxes independently of biospheric model and oceanic exchange estimates
Uncertainties at grid scale are high, but uncertainties of continental and global estimates are comparable to synthesis Bayesian studies
Auxiliary data inform regional (grid) scale flux variability; seasonal cycle at larger scales is consistent across models
Use of auxiliary variables within a geostatistical framework can be used to derive process-based understanding directly from an inverse model
Acknowledgements Collaborators:
Research group: Alanood Alkhaled, Abhishek Chatterjee, Sharon Gourdji, Charles Humphriss, Meng Ying Li, Miranda Malkin, Kim Mueller, Shahar Shlomi, and Yuntao Zhou
NOAA-ESRL: Pieter Tans, Adam Hirsch, Lori Bruhwiler and Wouter Peters
JPL: Bhaswar Sen, Charles Miller Kevin Gurney (Purdue U.), John C. Lin (U. Waterloo), Ian Enting (U.
Melbourne), Peter Curtis (Ohio State U.) Data providers:
NOAA-ESRL cooperative air sampling network Seth Olsen (LANL) and Jim Randerson (UCI) Christian Rödenbeck, MPIB Kevin Schaefer, NSIDC
Funding sources: