Regional Inversion

of continuous atmospheric CO2 measurements

A first attempt !

P. , P. , P. , P. , and P.

Philippe Peylin , [peylin@lsce.saclay.cea.fr]Peter Rayner ,Philippe Bousquet , Philippe Ciais,Philippe Heinrich,F. hourdin

Outline

• Measurements over Europes

• Requirements for regional inversions

• Time resolution in an inversion ?

• LMDz transport model :- direct approach- retro-plume approach

• European set up : primarily results

The European observing system :

AEROCARB database : http://www.aerocarb.cnrs-gif.fr/database.html

Flasks In-situAircraft Aircraft (project)

Aircraft measurements - Orleans, France

Free troposphere

CO2 concentrations for all flights

PBL

Continuous measurements At Mace Head

How to use such information ?

How to assimilate continental sites ?

• Transport models are to be improved : - Higher resolution in time and space

- Parameterization of PBL

Mesoscale models : boundary problems !Nested models : computing time !Global with zoom : LMDz model

• Data selection in models : - position in space and time properly represented

• Prior land fluxes should be improved : - Fossil fuel- Diurnal cycle of biospheric fluxes

• Inverse procedure need to be updated :- Spatial resolution of fluxes : pixel ?- Time resolution : identical for fluxes / obs ?

Monthly mean24 hr

Monthly meanFlask timing

Con

cent

ratio

ns (p

pm)

Diurnal rectification effect : Selection of model output according

to flask data timing (TM3)

[ ppm

][ p

pm ]

CO2 - fossils

Spatial position of Schauinsland station in mesoscale model REMO

REMO 30mREMO 130mObservations

DAYS(Chevillard, 2001)

Data selection

A 2GtC/yr Sink over Europe, consistent with all Observations (kaminsky et al.)

Spatial resolution of fluxes

Few large regions All pixels?

Compromise needed OR all pixel + correlations

• Aggregation error

• Estimation error

Time discretisation

• Estimation of flux X ={xi, i=1,n}with a temporal distribution xi

• Observations Y = {yi, i =1, m}with same errors R

• None Bayesien

Question : Should we average data at the time-resolution of the fluxes we solve for ?

- Annual flux : Monthly data ?- Monthly flux : Daily data ?- Satellite : assimilate individual shot ?

Little derivation :

mYYm

ii /

1

11

m

iix

with error mR /

m

i RYXH iiXJ

1

2

21

..)(

mRYXH

XJ/.

2

21 .)(

0)(

dXXdJ

HYX 1

~

mHdYXd

i .1~

1

i i

i ii

H

HYX

)().(~

22

i i

i

i HH

dYXd

)(

~2

2

Same weight for all data

Data weight proportional to Hi

Averaged dataY

All data{yi, i =1, m}

Hi = Transport o Flux-distribution {xi}

High values of Hi correspond to “ low mixing by transport ”

and / or“Peak of the flux time-distribution”

Error estimates

12

2 ~)( PXdXJd

mHR

mH

RPi i /.

~2

2

2

2

1

i iHRP 2

2

2 )(~

m

ii

m

ii HmH

1

22

1

)(/

We can show

21~~ PP

Uncertainties are always smaller with all individual data

month

Con

cent

ratio

n (p

pmv)

Temperate N. Amer. (3rd yr)

Annual response function sampled each monthTime pattern : total respiration (SiB2)

Pulse of 1GtC / year

5

10

15

20

25

Days

Con

cent

ratio

n (p

pmv)

Monthly response function sampled each dayTime pattern : flat

Pulse of 1GtC / month Western Europe (July pulse)

0

10

20

30

40

-10

Summary of time discretisation ?

• Need some caution when using data at higher time resolution than that of the fluxes

• Individual terms Hi need to be compared !

• Annual flux / Monthly data is not adapted

• Monthly flux / daily data ??

• Solution is probably : solve fluxes at the resolution of the data + time-correlation(equivalent to the “spatial aggregation problem”)

LMDz transport model• GCM from the LMD laboratory (Paris)

• Nudged with ECMWF

• Global with possible zoom- 0.5 x 0.5 degree in zoom- 4 x 4 degree at the lowest

• 19 vertical levels

• Backward mode possiblegrid zoomed over Europe

Inverse Transport : “retro-plume” approachFrederic Hourdin

Direct approach :

dtxdcJ

..

J: measure = mean CO2 per kg of airC: concentration of CO2 (kg / kg air): density of air : distribution of the measure : spatial and temporal domain

C is govern by :01.

zck

zcdragV

tc

With - surface flux : =

- C = Ci at t0

zck

Inverse approach : Rewrite measure using the advection/diffusion equation like in lagrange multipliers

dtxdzck

zcdragV

tcdtxdcJ 1.... *c

c*: distribution to be determined

• integration by parts

• c* that satisfy

• 0 =

zck

zcdragV

tc *

** 1.

zck

*

Using :

We obtain :

Sti dtdydxcxdccJ *

0* ...

Contribution fromInitial conditions

Flux contribution

Retro-plume approach

• Simply run transport backward in time (need to save all mass flux in a forward run)

• C* is the sensitivity to both surface fluxes / initial conditions in ppmv / kgC

Direct mode / Inverse mode

Source variable Sample c* according to distribution

Emission according To selected data

Selection of data J

Example of retro-plumes

Day 1 Day 2

Day 4 Day 8

Schauinsland station in November 1998

Mace Head retro-plume Day 4

longitude

Day 4

European Inversion,

using continuous data,

with high temporal/spatial

flux resolution,

for a short period (campaign)

Only a first attempt !

methodological experiment

• Data : 2 sites Mace Head / Schauinsland Daily average values• Period : Campaign type experiment

one month : November 1998• Regions :

- Pixels for Western Europe- Rest of the world with large regions (18)

• Time resolution of fluxes :- Daily for pixels- monthly for the other large regions

• Priors Pixels Large regions

Flux: Bousquet et al. Bousquet et al. Error: 100 % of mean 1GtC + correlations (0.8)

• Special treatment for initial conditions

Map of regions + 2 sites

Mace Head Schauinsland

November November

Treatment of initial conditions

• Add additional unknowns corresponding to initial conditions

• Reduce the size of initial condition problem by projecting on main directions in the data space using SVD.

Cinit = H x Pprior (60 x 50000) (50000)

(SVD decomposition)

U . W . VT x Pprior

H’ x P’ (60 x 60) (60)

Solve for P’ with :- prior value from global simulation (using bousquet et al. fluxes)- error corresponding to 3 ppm

Fit to the data

Model components : MHD

Europe Pixels

Other big regions

Initial conditions

days

posteriorprior

ppm

v

-4

8

-4

8

-4

8

Model components : SCH

Initial conditions

days

posteriorprior

ppm

v

-4

8

-4

8

-4

8

Europe Pixels

Other big regions

Summary

• Regional CO2 flux estimates require complete and permanent monitoring of CO2

• Transport models have to be improved over the continents !

• Selection of the data (time and space) is crucial

• Inverse scheme : - High spatial resolution with correlations - Temporal resolution of fluxes adapted to the resolution of the data

• Initial conditions seem to be important for campaign based inversions (10 day !)

• => Need for other constraints : O2/N2, C14, C13, O18, Radon, …

AEROCARB project: European Inversion

Model REMO-D DEHM HANK LMDZ TM3Horiz.Resolution

0.5 x 0.5° 150 x 150km(N. hemis)50 x 50 km(Europe)

270 x 270km90 x 90 km

3.75° x 2.5° 3.5° x 3.5°

Vert.Resolutionlowest(nb layers)

60 m(20)

80 m(24)

100m(24)

150 m(19)

150 m(19)

Domain Euro+sib N. Hemis N. Hemis Globe GlobeWind forcing 6h ECMWF at

B.C.30h restore alldomain

Full nudgingECMWF (12h)

Full nudgingU,V, T, P (6h)NCEP

Nudging U,V(6h)ECMWF

6h ECMWF

- 5 models- European domain for regional models- Boundary from global model (TM3)- Use continuous data over Euro-Siberia (12 sites)- Account for “diurnal rectifier” / selection (during aircraft profiles)• Monthly inversion first

• Daily inversion in a second step

Days

Con

cent

ratio

n (p

pmv)

Monthly response function sampled each dayTime pattern : flat

Pulse of 1GtC / month Western Europe (January pulse)

month

Con

cent

ratio

n (p

pmv)

Annual response function sampled each monthTime pattern : total respiration (SiB2)

Pulse of 1GtC / year Boreal N. Amer. (3rd yr)

Conclusions Regional CO2 flux estimates require a complete and permanent monitoring of “regional”

air using atmospheric data (flask & continuous sites, towers, airplane, …)---> Monitoring of air is essential to estimate European carbon budget.

 Currently data limited inversions are becoming model limited inversion as we intend to assimilate continental measurements----> Transport models have to be improved over the continents.

 There is only one carbon cycle. There is no reason to assimilate only atmospheric data.----> A global carbon assimilation system should be developed

Addressing these issues should allow to provide Kyoto relevant estimates of European carbon budget within the next decade.