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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 Engineering Department of Atmospheric, Oceanic and Space Sciences

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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 Engineering

Department of Atmospheric, Oceanic and Space Sciences

The University of Michigan


Outline
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
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:

    • Biased estimates of model parameters

    • Biased statistical testing of model parameters

  • Spatial correlation can be accounted for by using geostatistical techniques


Parameter bias example
Parameter Bias Example

map of an alpine basin

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

snow depth measurements

kriging estimate of mean snow depth

(assumes spatial correlation)

mean of snow depth measurements

(assumes spatial independence)


5% H0 Rejected

H0 Rejected!

H0 is TRUE

5% H0 Rejected

H0Not Rejected

5% H0 rejected


Variogram model
Variogram Model

  • Used to describe spatial correlation

1

2

3

4


Geostatistics in practice
Geostatistics in Practice

  • Main uses:

    • Data integration

    • Numerical models for prediction

    • Numerical assessment (model) of uncertainty


Geostatistical inverse modeling
Geostatistical Inverse Modeling

Actual flux history

Available data


Geostatistical inverse modeling1
Geostatistical Inverse Modeling

Geostatistical

Bayesian / Independent Errors

31 data

201 fluxes

31 data

101 fluxes

31 data

41 fluxes

31 data

11 fluxes

31 data

21 fluxes


Key points
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 co 2 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

ASIDE: CO2 Measurements from Space

Alkhaled et al. (in prep.)


X co2 variability

x10 limitations limit sampling for existing and upcoming satellite missions such as the Orbiting Carbon Observatory4 km

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


Source: NOAA-ESRL limitations limit sampling for existing and upcoming satellite missions such as the Orbiting Carbon Observatory


What surface fluxes do atmospheric measurements see

-24 hours limitations limit sampling for existing and upcoming satellite missions such as the Orbiting Carbon Observatory

-48 hours

-72 hours

-96 hours

-120 hours

What Surface Fluxes do Atmospheric Measurements See?

24 June 2000: Particle Trajectories

Latitude

Height Above Ground Level (km)

Longitude

Longitude

Source: Arlyn Andrews, NOAA-GMD


Need for additional information
Need for Additional Information limitations limit sampling for existing and upcoming satellite missions such as the Orbiting Carbon Observatory

  • 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


Bayesian inference applied to inverse modeling for surface flux estimation
Bayesian Inference Applied to Inverse Modeling for Surface Flux Estimation

Likelihood of fluxes given

atmospheric distribution

Posterior probability of surface flux distribution

Prior information

about fluxes

p(y) probabilityofmeasurements

y : available observations (n×1)

s: surface flux distribution (m×1)


Synthesis bayesian inversion
Synthesis Bayesian Inversion Flux Estimation

Prior flux estimates (sp)

BiosphericModel

CO2Observations (y)

AuxiliaryVariables

Inversion

Flux estimates and covarianceŝ, Vŝ

?

TransportModel

Sensitivity of observations to fluxes (H)

Meteorological Fields

Residual covariancestructure (Q, R)

?


Large regions inversion
Large Regions Inversion Flux Estimation

TransCom, Gurney et al. 2003


Transport model gridscale inversions
Transport Model Gridscale Inversions Flux Estimation

Rödenbeck et al. 2003


Variogram model1
Variogram Model Flux Estimation

  • Used to describe spatial correlation

1

2

3

4


Geostatistical approach to inverse modeling
Geostatistical Approach to Inverse Modeling Flux Estimation

  • 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

Deterministic

component

Stochastic

component


Synthesis bayesian inversion1
Synthesis Bayesian Inversion Flux Estimation

Prior flux estimates (sp)

BiosphericModel

CO2Observations (y)

AuxiliaryVariables

Inversion

Flux estimates and covarianceŝ, Vŝ

TransportModel

Sensitivity of observations to fluxes (H)

Meteorological Fields

Residualcovariancestructure (Q, R)


Geostatistical inversion
Geostatistical Inversion Flux Estimation

select significant variables

AuxiliaryVariables

VarianceRatioTest

CO2Observations (y)

Flux estimates and covariance ŝ, Vŝ

Inversion

TransportModel

Sensitivity of observations to fluxes (H)

Trend estimate and covariance β, Vβ

Meteorological Fields

Residual covariancestructure (Q, R)

RMLOptimization

optimize covariance parameters


Key questions
Key Questions Flux Estimation

  • 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
Fluxes Used in Pseudodata Study Flux Estimation

Michalak, Bruhwiler & Tans (JGR, 2004)


Recovery of annually averaged fluxes
Recovery of Annually Averaged Fluxes Flux Estimation

Best estimate

“Actual” fluxes

Michalak, Bruhwiler & Tans (JGR, 2004)


Recovery of annually averaged fluxes1
Recovery of Annually Averaged Fluxes Flux Estimation

Best estimate

Standard Deviation

Michalak, Bruhwiler & Tans (JGR, 2004)


Key questions1
Key Questions Flux Estimation

  • 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
Auxiliary Data and Carbon Flux Processes Flux Estimation

Other:

Spatial trends

(sine latitude, absolute value latitude)

Environmental parameters:

(precipitation, %landuse, Palmer drought index)

Anthropogenic

Flux:

Fossil fuel

combustion

(GDP density, population)

Oceanic Flux:

Gas transfer

(sea surface temperature, air temperature)

Terrestrial Flux:

Photosynthesis

(FPAR, LAI, NDVI)

Respiration

(temperature)

Image Source: NCAR


Sample auxiliary data
Sample Auxiliary Data Flux Estimation

Gourdji et al. (in prep.)


Which model is best
Which Model is Best? Flux Estimation


Geostatistical approach to inverse modeling1
Geostatistical Approach to Inverse Modeling Flux Estimation

  • 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

Deterministic

component

Stochastic

component


Global gridscale co 2 flux estimation
Global Gridscale CO Flux Estimation2 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
Measurement Locations Flux Estimation

Gourdji et al. (in prep.)

Mueller et al. (in prep.)


Selected auxiliary variables
Selected Auxiliary Variables Flux Estimation

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:

% AgLAISST

% ForestfPARdSSt/dt

% ShrubNDVI Palmer Drought Index

% Grass PrecipitationGDP Density

Land Air Temp.Population Density

Inversion estimates drift coefficients (β):

Gourdji et al. (in prep.)


Building up the best estimate in january 2000
Building up the best estimate in January 2000 Flux Estimation

Deterministic

component

Stochastic

component

Gourdji et al. (in prep.)


A posteriori uncertainty for january 2000
A posteriori uncertainty for January 2000 Flux Estimation

Gourdji et al. (in prep.)


Transcom regions
Transcom Regions Flux Estimation

TransCom, Gurney et al. 2003


Regional comparison of seasonal cycle
Regional comparison of seasonal cycle Flux Estimation

Gourdji et al. (in prep.)


Regional comparison of seasonal cycle 2
Regional comparison of seasonal cycle #2 Flux Estimation

Gourdji et al. (in prep.)


Comparison of annual average non fossil fuel flux
Comparison of annual average non-fossil fuel flux Flux Estimation

Gourdji et al. (in prep.)


Key questions2
Key Questions Flux Estimation

  • 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
Opportunities for Regional Synthesis Flux Estimation

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

Photo credit: B. Stephens, UND Citation crew, COBRA

WLEF tall tower (447m) in Wisconsin with CO2 mixing ratio measurements at 11, 30, 76, 122, 244 and 396 m


North american co 2 flux estimation
North American CO Flux Estimation2 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)


Assimilation of remote sensing and atmospheric data
Assimilation of Remote Sensing and Atmospheric Data Flux Estimation

Analysis steps:

  • Compile auxiliary variables

  • Select significant variables to include in model of the trend

  • Estimate covariance parameters:

    • Model-data mismatch

    • Flux 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


Key questions3
Key Questions Flux Estimation

  • 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
Conclusions Flux Estimation

  • 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
Acknowledgements Flux Estimation

  • 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? Flux Estimation

[email protected]

http://www.umich.edu/~amichala/


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