A BIRD S EYE VIEW OF THE CARBON CYCLE. Anna M. Michalak

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1 A BIRD S EYE VIEW OF THE CARBON CYCLE Anna M. Michalak

2 Current natural carbon sinks Huntzinger et al. (Ecol Model, 2012)

3 How can the atmosphere help?

4 In situ atmospheric CO 2 observations! Source: NOAA-ESRL

5 Satellite atmospheric CO 2 observations AIRS on Aqua OCO-2 GOSAT ASCENDS Geo satellite(s) TES, SCIAMACHY, etc. etc.

6 Global trends! Source: NOAA-ESRL

7 Regional variability Source: NOAA-ESRL!

8 Tyler Erickson, Michigan Tech Research Institute 8

9 Flux model evaluation

10 What aspects of flux differences are observable?

11 + Large- Scale Spa,al Seasonal Cycle Fine- Scale Spa,al Diurnal Cycle Good news: Atmospheric data can dis3nguish among models. What is driving the difference? Huntzinger et al. (JGR 2011)

12 Large- Scale Spa,al Seasonal Cycle Fine- Scale Spa,al Diurnal Cycle Atmospheric signal can detect differences in net flux over large regions and 3ming of the seasonal cycle Huntzinger et al. (JGR 2011)

13 Large- Scale Spa,al Seasonal Cycle Fine- Scale Spa,al Diurnal Cycle Atmospheric signal can detect differences in fine scale variability during the growing season What is the rela3ve importance of the spa3al distribu3on of fluxes compared to 3ming and strength of their diurnal cycle? Huntzinger et al. (JGR 2011)

14 Large- Scale Spa,al Seasonal Cycle Fine- Scale Spa,al Diurnal Cycle Diurnal cycle has a large impact on the CO 2 signals Background Model Comparison Summary Huntzinger et Future al. (JGR Directions 2011)

15 ACOS GOSAT Level 3 Estimate Observations (a) (b) σ ŷ < 2.5 ppm (a) (b) σ ŷ < 1.5 ppm (c) (c) Uncertainty 2 1 σ ŷ < 1 ppm 0 [ppm] Hammerling, Michalak, O Dell, Kawa (GRL, 2012) [# of periods] [ppm]

16 Hammerling, Michalak, O Dell, Kawa (GRL, 2012) September July August 100% 80% October 60% 40% November December December 20% 0%

17 Flux model updating Inversion Carbon Budget ε

18 Atmospheric inverse modeling Photosynthesis Total CO 2 flux Ecosystem Respiration Fossil Fuel Emissions Disturbance + Land use Change Measurement location Source: Kim Mueller, U. Michigan (now a UCAR/AMS congressional fellow)

19 Bayesian Inverse Problem Biospheric model Prior flux estimates (s p ) Auxiliary variables CO 2 observations (y) Inversion Flux estimates and covariance Transport model Sensitivity of observations to fluxes (H) ŝ, V ŝ Meteorological fields Residual covariance structure (Q, R)

20 Examples of Bayesian Inversion Studies TransCom3: Estimates: Continental; Monthly Prior: CASA Observations: in situ Numerics: Batch Now 100s of publications CarbonTracker: Estimates: Ecoregion; Weekly Prior: CASA (+ others) Observations: in situ Numerics: Ensemble SRF JPL CMS flux: Estimates: 4 o x 5 o ; monthly Prior: CASA, CASA-GFED Observations: GOSAT Numerics: 4d-VAR

21 Atmospheric inverse modeling Inversion ε Carbon Budget

22 Synthesis Bayesian inversion Biospheric model Prior flux estimates (s p ) Auxiliary variables (X) Transport model CO 2 observations (y) Sensitivity of observations to fluxes (H) Inversion Flux estimates and covariance ŝ, V ŝ Meteorological fields Residual covariance structure (Q, R) Michalak et al. (JGR, 2004), Mueller et al. (JGR, 2008), Gourdji et al. (JGR, 2008; ACP 2010; BGD 2011), Miller et al. (JGR, 2012)

23 Geostatistical inversion model select significant variables Auxiliary variables (X) Model selection CO 2 observations (y) Flux estimates and covariance ŝ, V ŝ Inversion Transport model Sensitivity of observations to fluxes (H) Trend estimate and covariance β, V β Meteorological fields Residual covariance structure (Q, R) Covariance structure characterization optimize covariance parameters Michalak et al. (JGR, 2004), Mueller et al. (JGR, 2008), Gourdji et al. (JGR, 2008; ACP 2010; BGD 2011), Miller et al. (JGR, 2012)

24 Geostatistical inversion model L T 1 T 1 s, β = ( y Hs) R ( y Hs) + ( s Xβ) Q ( s Xβ) y = atmospheric CO 2 concentration measurements H = transport or sensitivity matrix s = (unknown) CO 2 flux distribution X and β = model of the trend R = model-data mismatch covariance Q = spatiotemporal covariance of flux residuals Michalak et al. (JGR, 2004), Mueller et al. (JGR, 2008), Gourdji et al. (JGR, 2008; ACP 2010; BGD 2011), Miller et al. (JGR, 2012)

25 Gourdji et al. (JGR 2008);Mueller et al. (JGR 2008) Global GIM CO 2 flux estimation Contributions of components to flux in July 2000: (a) GDP Density (b) Population density (c) LAI (d) fpar (e) % shrub cover (f) Latitudinal gradient & ocean constant (g) Stochastic residual (h) Full best estimates Estimates: 4 o x 5 o ; monthly Prior: Individual aux. vars. Observations: in situ Numerics: Batch

26 Gourdji et al. (ACP 2010; BG 2012) Seasonal spatial patterns Estimates: 1o x 1o; 3-hourly Prior: Individual aux. vars. Observations: in situ Numerics: Batch

27 Scale dependence Mixed Hardwood Forest Mixed hardwood forest UMBS Tonzi Ranch Woody savannas Yadav et al. (BG 2010); Mueller, et al. (GBC 2010)

28 Challenges Low sensitivity and/or indirect observations Heterogeneity Uncertainty / biases / systematic errors Massive data volume Massive state space

29 Challenges Low sensitivity and/or indirect observations Inverse problems Ill-posed problems Use of ancillary data Heterogeneity Uncertainty / biases / systematic errors Massive data volume Massive state space

30 Challenges Low sensitivity and/or indirect observations Heterogeneity Multiscale Space-time variability Nonstationarity Uncertainty / biases / systematic errors Massive data volume Massive state space

31 Challenges Low sensitivity and/or indirect observations Heterogeneity Uncertainty / biases / systematic errors Epistemic error Non-Gaussian errors Multiple sources of uncertainty Massive data volume Massive state space

32 Challenges Low sensitivity and/or indirect observations Heterogeneity Uncertainty / biases / systematic errors Massive data volume Massive state space

33 Summary and conclusions Development of statistical approaches, guided by scientific understanding, presents an opportunity to maximize information retrieved from observations Flux information provided by atmospheric observations is (space- and time-) scale dependent Flux diagnosis and attribution methods should not prescribe unknown variability

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35 All models are wrong we make tenta3ve assump3ons about the real world which we know are false but which we believe may be useful the sta3s3cian knows, for example, that in nature there never was a normal distribu3on, there never was a straight line, yet with normal and linear assump3ons, known to be false, he can oien derive results which match, to a useful approxima3on, those found in the real world. (Box, 1976)