Carbon Cycle: Definition of the problem. Inez Fung

Transcription

1 Carbon Cycle: Definition of the problem Inez Fung

2 Mean Meridional Circulation + Convection June July August pressure Dec Jan Feb Intertropical Convergence Zone (ITCZ): v=0: barrier to interhemispheric transport Convection: rapid turbulent mixing 90 90

3 C Atm Carbon Model + I ( C ) = + z 0 P = Atm _transport+ mixing ourcesins Chem Prod = FF + La nduse + (F F ) + ( F F ) oa ao "well nown" extrapolation of sparseobs ba ab

4 Atm Carbon Models C + I (C ) = Atm _transport+ mixing z = 0 ourcesins Kalnay Eq T(t b i+ 1 ) = M[T(t a i )] ycha Lecture 2 x Φ (x ) G( u ) i+ 1 = i +

5 An Atm Carbon Cycle Model C + I (C ) = z = 0 Atm _transport+ mixing ourcesins = FF + LandUse + (F F ) + ( F F oa ao ba ab What we ve got: ources/ins nown approximately or not well constrained C obs (actually mixing ratios X obs ) biweely, 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(αt); )

6 An Atm Carbon Cycle Model C + I (C ) = z = 0 Atm _transport+ mixing ourcesins = FF + LandUse + (F F ) + ( F F oa ao ba ab ) Why: Closing the carbon budget: a challenging scientific problem Where to put new measurements {design optimal observing networ} eed to predict future evolution of CO 2 and climate (global warming) Policy: how to manage carbon (reduce sources versus enhance sins){how to avoid dangerous future climate} Policy: monitor protocol compliance

7 The Data: CO2 in the lower troposphere Fung: C obs, X Kalnay: obs.. y o ; ycha: Z or Y In situ: tower, continuous Flas: 2m, twice weely >400m Tall Tower: 11, 30, 76, 122, 244 and 396 m; Continuous Other obs (Doney lecture Thursday Miller lecture Friday) secular trend - gradient easonal cycle Interannual variations

8 ot-so-confusing Terminology C + I (C ) = Atm _transport+ mixing z = 0 ourcesins = F F + LandUse + ( Foa F ao ) + ( F ba Fab ) "well nown" extrapolation of sparse obs ources = fluxes into atm ins = fluxes out of atm : Fluxes = forcing term = ources ins

9 C The Priors: + I (C ) = z = 0 = F F + LandUse + ( Foa F ao ) + ( F ba Fab ) "well nown" Atm _transport+ mixing ourcesins extrapolation of sparse obs

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

11 2-Box Model Applied to the Carbon Cycle τ M M = ( ) 2 Consider the case = 6 PgC/yr; = 0 τ = 1 yr Χ column M M = 3 PgC Χ Recall 1 PgC 0.5 ppmv if mixed in entire atm. 1 PgC 1 ppmv if mixed in a hemisphere. sfc column Χ = sfc 3 ppmv s Guess (3D model) surface gradient 1.5x column mean gradient Χ = 4.5 ppmv M M

12 Pressure (mb) Atmospheric CO 2 distribution as simulated by CAR CCM: Fossil fuel combustion (6 PgC/y) urface Zonal mean P Eq Latitude P

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

14 2-Box Model Applied to the Carbon Cycle Inverse problem τ Model: M M = ( ) 2 Given: sfc sfc ( Χ Χ ) = 2.5 column column Χ obs obs ( Χ ) = 1.7 ppmv M M = 1.7 PgC M M Invert model = 2 = 3.4 PgC/yr τ (sources sin s ) (sources sin s ) = 3.4 PgC/ yr (6 PgC/yr sin s ) (0 sin s ) = 3.4 PgC/yr sins sin s = 2.6 PgC/yr ppmv Obs Carbon Budget ins +ins = 3 PgC/yr

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

16 ow what? increase the number of sin terms: Land, Ocn, Land, ocn (or more see David Baer exercise) Generalize: in = in + in L O X = L = Ψ in + Ψ in "basis function" L L forward _ model(in ) L X = Ψ X, etc; do same for sources L L src / sin L L L X = forward_model( rc / in ) X = Ψ X src / sin Variational Approach: Find Ψ = Ψ rc / in stn 2 stn,obs X stn Ψ Ψ,prior 2 2 σstn src / sin σ,prior X = H( X ) = H( Ψ X ) (apply Observations Operator) stn to minimize (X ) ( ) J = +, where 2