Inverse modelling of CO emissions

J.-F. Müller and T. Stavrakou

Belgian Institute for Space Aeronomy

Avenue Circulaire 3, 1180 Brussels

jfm@aeronomie.be

EVERGREEN International Workshop

19-20 January 2006, KNMI, De Bilt, The Netherlands

Outline

Carbon monoxide: sources and sinks

Inverse modeling of emissions using the adjoint model

State-of-the-art in CO inversion

The IMAGES model used in two inversion exercises constrained by:

a) 1997 CMDL data & GOME NO2 columns b) the 2000-2001 MOPITT CO columns

Big-region vs. grid-based inversion approach

Comparison to independent observations and past studies

Conclusions and outlook

Carbon monoxide: sources and sinks

COCO2 CH2O CH4

OH OH, hv OH

1100 570 360

85 30

deposition deposition

NMVOC (non-methane volatile organic compounds)

700100

50

200

80250

OH,O3

100340

deposition

SOA= Secondary

OrganicAerosols

CO2

(units: Tg C/year)

410

???

Inverse modelling of emissions

Cost function:

measures the bias between the model and the observations

J(f)=½Σi (Hi(f)-yi)T E-1(Hi(f)-yi) + ½ (f-fB)TB-1(f-fB)

Model operator acting on the

control parameters

observations

1st guess values of the control parameters

Matrix of errors on the observations

Matrix of errors on the control parameters

Vector of the control parameters

For what values of f is the cost function minimal?

The adjoint model

Gradient of the cost function

Calculation of new parameters f with a descent algorithm Minimum of J(f) ?

Observations

Forward CTM Integration from t0 to t

Transport

Chemistry

Cost function J(f)

Adjoint model Integration from t to t0

Adjoint transport

Adjoint chemistry

Adjoint cost function

Current informations

Control variables f

yes

no

Optimized control parameters

Inversion studiesInversion studies Model usedModel used Observations Observations usedused

Bergamaschi et al., 2000

TM2 CMDL 1993-1995

Pétron et al., 2002 IMAGES CMDL 1990-1996

Kasibhatla et al., 2002 GEOS-CHEM CMDL 1994-1996

Palmer et al., 2003 GEOS-CHEM TRACE-P 2001

Arellano et al., 2004 GEOS-CHEM MOPITT 2000

Pétron et al., 2004 MOZART MOPITT 2000-2001

Müller & Stavrakou, 2005

IMAGES + ADJOINT

CMDL 1997GOME NO2 col. 1997

Pétron et al., to be submitted

MOZART MOPITT 2000-2004

Stavrakou & Müller, submitted

IMAGES + ADJOINT

MOPITT 2000-2001

Inverting for CO emissions – State-of-the-art

Advantages from the use of the adjoint

The calculated derivatives are exact

The full (transport/chemistry) adjoint allows to take non-linearities into account, e.g. the non-linear relationship between CO concentrations and surface emissions

The emissions of different compounds can be optimized simultaneously, their chemical interactions being taken into account

The computational time to determine the model sensitivity does not depend on the number of control variables grid-based inversions can be addressed

BUT: the exact posterior error estimation is not possible within this framework

Instead, iterative approximations of the inverse Hessian can be used

The IMAGES model

Provides the global distribution of 60 chemical compounds at 5°x5° resolution and 25 vertical levels (Müller and Brasseur, 1995)

A priori anthropogenic emissions : 1997 EDGAR v3 inventory (Peters and Olivier, 2003)

Biomass burning emissions : GFED database (Van der Werf et al., 2003) or the POET inventory (Olivier et al., 2003)

Biogenic emissions for isoprene and monoterpenes from Guenther et al., 1995, and for CO from Müller and Brasseur, 1995

Model time step : 1 day, spin-up time : 4 months, 1 year simulation

A. Big-region inversion of the 1997 CO emissions

The inversion is constrained by:

NOAA/CMDL CO mixing ratios

Ground-based FTIR CO vertical column abundances

GOME tropospheric NO2 columns

Simultaneous optimization of the

total annual CO & NOx emissions

over large regions (39 flux parameters)

chemical feedbacks via the adjoint

constant seasonality of the sources

B is assumed diagonal

Müller and Stavrakou, ACP, 2005

Impact of emission changes on OH

Comparison to aircraft observations

Direct calculation of the Hessian matrix using finite differences on the adjoint model

Use of the inverse BFGS formula and the output of the minimization algorithm at each iteration

Use of the DFP update formula

Estimation of the posterior errors

B. Big-region vs. grid-based inversion for optimizing the 2000-01 CO&VOC emissions The inversion is constrained by the MOPITT daytime CO columns from

May 2000 to April 2001

The columns and averaging kernels are binned onto the IMAGES grid and monthly averaged total : ~ 6000 observations

Error on the column is assumed 50% of the observed value

« Big-region approach »: optimize the global CO fluxes over large regions as in case A (18 variables)

« Grid-based » inversion: optimize the fluxes emitted from every model grid cell by month ( ~30000 param.) seasonality and geographical

distribution varied source-specific correlations

among prior errors on the flux parameters B non-diagonal

In both cases,

distinguish between anthropogenic, biomass burning and biogenic emissions

Stavrakou and Müller, 2006, submitted

The error correlation setup

Anthropogenic emissions errors:

highly correlated within the same country

weakly correlated within large world zones

uncorrelated in any other case

constant temporal correlation

Vegetation fire and biogenic emissions:

spatial correlations decrease with geographical distance

they are further reduced when the fire or ecosystem type differ

temporal correlations

Optimization results

• Both solutions succeed in reducing the model/MOPITT bias over most regions

• Larger cost reduction in the grid-based case (4.6) as compared to the big-region setup (2.2)

Big-region setup Grid-based setup

MOPITT column

Anthropogenic emission updates

Optimized global anthropogenic emissions : 664 Tg CO/yr (+16%)

More significant increase over the eastern China in the grid-based (110%), compared to the big-region setup (80%)

Reduced South Asian emissions by ~40%

Small changes over America, Europe and Oceania

Big-region setup Grid-based setup

0

50

100

150

200

250

N.Am. S.Am. Africa Europe Far East S.Asia

A priori

Big-region

Grid-based

Anthropogenic emissions by region

Vegetation fire emission updates

Big-region setup

Grid-based setup

Seasonal variation

prior GFEDprior POETbig-region GFEDgrid-based GFEDgrid-based POET

Remarkable convergence of optimizations using either GFED or POET prior emissions

Important changes in seasonality of biomass burning emissions

Increased S. African emissions in September, reduction in June when using GFED

Biogenic emission updates Seasonal

variation

Global enhancement of biogenic VOC emissions (~ +15%)

Higher NMVOCs oxidation source by 10%

grid-based inversion

prior

big-region

grid-based

Comparison to independent data

(CMDL, FTIR, aircraft campaigns)

priorbig-regiongrid-based

2200

2400

2600

2800

3000

3200

Global annual in Tg CO

Bergamaschi et al.,2000

Pétron et al., 2002

Arellano et al., 2004

Müller&Stavrakou,2005

Stavrakou&Müller,2006

Comparison of our results to past inverse modelling studies

600

700

800

900

1000

Anthropogenic emissions

Conclusions and perspectives

Feasibility of the multi-compound inversion

Higher performance of grid-based inversion for reactive compounds

Importance of the error correlation setup for better constraining the large number of emission parameters in the grid-based framework

The posterior uncertainty analysis (using the DFP approximation) shows important error reductions for large-scale fluxes (e.g. Chinese anthropogenic emissions, African biomass burning), but small error reductions for individual grid cells

Large increases of anthropogenic emissions over Far East

Synergetic use of different datasets is required to better quantify emissions, in particular the CO production from the NMVOCs