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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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Anna m michalak department of civil and environmental engineering

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)


Anna m michalak department of civil and environmental engineering

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

x104 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


Anna m michalak department of civil and environmental engineering

Source: NOAA-ESRL


What surface fluxes do atmospheric measurements see

-24 hours

-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

  • 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

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

TransCom, Gurney et al. 2003


Transport model gridscale inversions

Transport Model Gridscale Inversions

Rödenbeck et al. 2003


Variogram model1

Variogram Model

  • Used to describe spatial correlation

1

2

3

4


Geostatistical approach to inverse modeling

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

Deterministic

component

Stochastic

component


Synthesis bayesian inversion1

Synthesis Bayesian Inversion

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

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

  • 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

Michalak, Bruhwiler & Tans (JGR, 2004)


Recovery of annually averaged fluxes

Recovery of Annually Averaged Fluxes

Best estimate

“Actual” fluxes

Michalak, Bruhwiler & Tans (JGR, 2004)


Recovery of annually averaged fluxes1

Recovery of Annually Averaged Fluxes

Best estimate

Standard Deviation

Michalak, Bruhwiler & Tans (JGR, 2004)


Key questions1

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

Auxiliary Data and Carbon Flux Processes

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

Gourdji et al. (in prep.)


Which model is best

Which Model is Best?


Geostatistical approach to inverse modeling1

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

Deterministic

component

Stochastic

component


Global gridscale co 2 flux estimation

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

Measurement Locations

Gourdji et al. (in prep.)

Mueller et al. (in prep.)


Selected auxiliary variables

Selected Auxiliary Variables

Combine physical understanding with results of VRT to choose final set of auxiliary variables:

% AgLAISST

% ForestfPARdSSt/dt

% ShrubNDVIPalmer Drought Index

% GrassPrecipitationGDP Density

Land Air Temp.Population Density

Combine physical understanding with results of VRT to choose final set of auxiliary variables:

% AgLAISST

% ForestfPARdSSt/dt

% ShrubNDVIPalmer Drought Index

% GrassPrecipitationGDP 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

Deterministic

component

Stochastic

component

Gourdji et al. (in prep.)


A posteriori uncertainty for january 2000

A posteriori uncertainty for January 2000

Gourdji et al. (in prep.)


Transcom regions

Transcom Regions

TransCom, Gurney et al. 2003


Regional comparison of seasonal cycle

Regional comparison of seasonal cycle

Gourdji et al. (in prep.)


Regional comparison of seasonal cycle 2

Regional comparison of seasonal cycle #2

Gourdji et al. (in prep.)


Comparison of annual average non fossil fuel flux

Comparison of annual average non-fossil fuel flux

Gourdji et al. (in prep.)


Key questions2

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

Opportunities for Regional Synthesis

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 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)


Assimilation of remote sensing and atmospheric data

Assimilation of Remote Sensing and Atmospheric Data

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

  • 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

  • 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

  • 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:


Anna m michalak department of civil and environmental engineering

QUESTIONS?

[email protected]

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


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