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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Parameter Bias Example

map of an alpine basin

snow depth measurements

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kriging estimate of mean snow depth(assumes spatial correlation)

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Q: What is the mean snow depth in the watershed?

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Variogram Model Used to describe spatial correlation

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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24 June 2000: Particle Trajectories

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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

sssy

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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

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AuxiliaryVariables

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TransCom, Gurney et al. 2003

Large Regions Inversion

Transport Model Gridscale Inversions

Rödenbeck et al. 2003

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Variogram Model Used to describe spatial correlation

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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Deterministiccomponent

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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?

Fluxes Used in Pseudodata Study

Michalak, Bruhwiler & Tans (JGR, 2004)

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)

Sample Auxiliary Data

Gourdji et al. (in prep.)

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

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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

Measurement Locations

Gourdji et al. (in prep.)Mueller et al. (in prep.)

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.)

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Building up the best estimate in January 2000

Gourdji et al. (in prep.)

A posteriori uncertainty for January 2000

Gourdji et al. (in prep.)

Transcom Regions

TransCom, Gurney et al. 2003

Regional comparison of seasonal cycle

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Variable Trend Estimates (ŝ) Variable Trend +/- 2σŝ

TransCom Estimates (Baker et al., 2006)

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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.)

Regional comparison of seasonal cycle #2

Gourdji et al. (in prep.)

Comparison of annual average non-fossil fuel flux

Gourdji et al. (in prep.)

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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:

QUESTIONS?

Anna.Michalak@umich.eduhttp://www.umich.edu/~amichala/