Carbon Cycle: An Inverse Problem. Inez Fung

Transcription

1 Carbon Cycle: An Inverse Problem Inez Fung

2 Outstanding Questions Only half of the CO 2 produced by human activities is remaining in the atmosphere Where are the sinks that are absorbing over 40% of the CO 2 that we emit? Land or ocean? Eurasia/orth America? Why does CO 2 buildup vary dramatically with nearly uniform emissions? How will CO 2 sinks respond to climate change?

3 Atm Carbon Models C t + { (C ) = { Atm _transport+ mixing z= 0 ourcesinks Kalnay x b (t i+1 ) = M(x a (t i )) X =conc, fluxes, parameters ychka x (x ) G( u ) i+ 1 = i + X = conc u = fluxes

4 Atmospheric Inverse Modeling of CO 2 Concentration (observed samples) Transport (modeled) + = ources & inks (solved for)

5 An Atm Carbon Cycle Model C t + { (C ) = { z = 0 Atm _transport+ mixing ourcesinks = FF + LandUse + (F F ) + ( F F oa ao ba ab What we ve got: ources/inks known approximately or not well constrained C obs (actually mixing ratios X obs ) biweekly, at ~100 stations near the surface Decent transport model (winds, turbulent mixing) What we want: where has the fossil fuel CO2 gone? {Better estimates of the magnitude and distribution of (e.g. land exchange)} How did the fossil fuel CO2 get there? {improved understanding and representation of processes, e.g. F ab =LUE*AvailableLight; F ba =exp(t); )

6 Pressure (mb) What we ve got: (1) The Model: CAR climate model ource: Fossil fuel combustion (6 PgC/y) C(x,y,z) at steady state urface 4 Zonal mean P Eq Latitude P

7 What We ve got: The data: Atm CO2 (for now) Discrete surface flasks (~weekly) Continuous surface (hourly) observatories Tall towers continuous (hourly) Aircraft profiles (~weekly)

8 What We ve Got: (3) The Flux Priors = F { F + LandUse + ( Foa F ao ) + ( F ba Fab ) "wellknown" C + { (C ) = t { Atm _transport+ mixing z= 0 ourcesinks extrapolation of sparse obs should net land flux (F ba - F ab ) be prop to F ab?

9 Pressure (mb) Example I: A impler Model - reduce 3D atm to 2 hemisphere urface Zonal mean P Eq Latitude P

10 Example I: Interhemispheric Mixing: Two-Box Model, everything is perfect. M t M t M M = + M M =+ + M M ( M M ) M M = 2 + ( ) = teadytate t M M = 2 Interhemispheric exchange time determined from inert tracers (e.g. CFC, with s =0): ~1-2 years

11 Example 1: Interhemispheric Mixing: Two-Box Model, everything is perfect. M t M t M M = + M M =+ + M M ( M M ) M M = 2 + ( ) = teadytate t M M = 2 Interhemispheric exchange time determined from inert tracers (e.g. CFC, with s =0): ~1-2 years

12 Ex I: 2-Box Model Applied to the Carbon Cycle M M = ( ) 2 Consider the case = 6 PgC/yr; = 0 = 1 yr column M M = 3 PgC Recall 1 PgC 0.5 ppmv if mixed in entire atm. 1 PgC 1 ppmv if mixed in a hemisphere. sfc column = sfc 3 ppmv s Guess (3D model) surface gradient 1.5x column mean gradient = 4.5 ppmv M M Britt tephens: new obs of vertical profile

13 Ex I: 2-Box Model Applied to the Carbon Cycle Forward problem: If 100% FF CO2 remained in atm M M = ( ) 2 = 6 PgC/yr; = 0 = 1 yr M M = 3 PgC sfc sfc s sfc = sfc 4.5 ppmv But ( ) = 2.5 ppmv obs Obs only 50% of FF CO2 remains in atm (M + M ) t (M + M ) t = + = sources sinks obs sources = 6 PgC/yr = 3 PgC/yr inks +inks = 3 PgC/yr

14 Ex I: 2-Box Model Applied to the Carbon Cycle Inverse problem Obs operator X=H(M) Model: M M = ( ) 2 Given: sfc sfc ( ) = 2.5 column column obs obs ( ) = 1.7 ppmv M M = 1.7 PgC M M Invert model = 2 = 3.4 PgC/yr (sources sin ks ) (sources sin ks ) = 3.4 PgC/ yr (6 PgC/yr sin ks ) (0 sin ks ) = 3.4 PgC/yr sinks sin ks = 2.6 PgC/yr ppmv Obs Carbon Budget inks +inks = 3 PgC/yr

15 Budget Gradient Where are the Carbon inks? sinks + sin ks =+ 3 PgC/yr sinks sin ks = 2.6 PgC/yr sinks = 2.8PgC/yr; sin ks = 0.2 PgC/yr orthern sinks > outhern inks!!!!!!! Data/Obs : Huge C sink in the large expanse of southern ocean; but large uncertainty in obs ocn better observed large orthern land sink!!!

16 Example II: Perfect 3D atm circulation model. P teady state 60 (1) Forward tep Premise: Atm CO 2 = linear combination of response to each source or sink Divide surface into basis regions pecify unitary source (e.g. 1 PgC/year) each year from each region imulate atm CO 2 basis response with atm general circulation model Reconstruct fluxes and concentrations: unknown μ k = 30 EQ P W 60 W 0 60 E 120 E 180 ) s (x, y) k ) s (x, y) ) k ) s k (x, y) μ k kregions c(x, y,z) = μ k kregions c k (x, y,z,t) c ) k (x, y,z)

17 Ex II: (tep 2) Bayesian Inversion: perfect circulation model Inversion: eek the optimal source/sink combination {μ k } to match atmospheric CO 2 data: minimize [C obs (stn) μ k c ) k (stn)] 2 J = kregions + stn kregions [μ k μ k prior ] 2 [ k prior ] 2 stn 2 Obs. etwork mainly remote marine locations Trying to infer information over land Undetermined; non-unique solutions; prior estimates of source/sinks as additional constraints

18 Ex IIa: Posterior from many perfect circulation models μ k prior ± k prior Model m: {μ posterior mk ± posterior mk } X Mean,std_dev (μ posterior mk ) Mean ( posterior mk ) Little innovation in tropics, Africa Great innovation in. Ocean Gurney et al. ature 2005

19 What next? Anticipating satellite data eparating transport, initial conditions & surface fluxes Kalnay ychka x b i+1 = M(x a i ) Analysis at time i => forecast at time i+1 x b i+1 = (x i ) + G(u i ) x 0 0 x prior transport initial conditions Fluxes, parameters J(x) = 1 { 2 (x 0 0 x prior ) T B 1 (x 0 0 x prior ) + [ y o H(x) ] T R 1 [ y o H(x) ] Deviation of initial conditions from prior 4D Variational methods: adjust initial conditions to better match future data +(u u prior ) T P 1 (u u prior )} Deviation of fluxes from prior Deviation of x from observations

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