J.-F. Müller and T. Stavrakou IASB-BIRA Avenue Circulaire 3, 1180 Brussels Seminar at Harvard University, June 2nd, 2006 Inverse modelling of emissions based on the adjoint model technique

Short introduction on carbon monoxide Adjoint-based inverse modeling: methodology The IMAGES model used in two inversion exercises constrained by:  A) 1997 CMDL data & GOME NO2 columns  B) the MOPITT CO columns Big-region vs. grid-based inversion approach Related work at IASB-BIRA: satellite retrievals of tropospheric gases, chemistry of terpenes Conclusions and perspectives Outline

COCO 2 CH 2 O CH 4 OHOH, hvOH deposition NMVOC (non-methane volatile organic compounds) OH,O deposition SOA= Secondary Organic Aerosols CO 2 (units: Tg C/year) 410 ?? ? Carbon monoxide: sources and sinks

Inversion methodology and setup The a priori emission distributions for a given species can be expressed as : where j runs over the base functions. The posterior flux estimate is given by where f is a vector of dimensionless control parameters to be optimized, so that the posterior fluxes are close enough to the prior bottom-up fluxes and the resulting abundances exhibit minimal deviation from the observed concentrations. The solution of this problem corresponds to the minimum of the cost function.

Cost function: measures the bias between the model and the observations J(f)=½Σ i (H i (f)-y i ) T E -1 (H i (f)-y i ) + ½ (f-f B ) T B -1 (f-f B ) 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? Inversion methodology and setup

Gradient of the cost function Calculation of new parameters f with a descent algorithm Minimum of J(f) ? Observations Forward CTM Integration from t 0 to t Transport Chemistry Cost function J(f) Adjoint model Integration from t to t 0 Adjoint transport Adjoint chemistry Adjoint cost function Checkpointing Control variables f yes no Optimized control parameters Minimizing the cost

Calculated derivatives are exact Non-linearities (chemical feedbacks) are taken into account The emissions of different compounds can be optimized simultaneously, their chemical interactions being taken into account Computational time not dependent on the number of control variables  grid-based inversions can be addressed High computational cost: calculation of derivatives requires 3 times more CPU time than a forward model run, and on the order of iterations are needed to attain convergence (reduction of gradient by a factor >1000) The exact estimation of posterior error is not possible within this framework; instead, iterative approximations of the inverse Hessian can be used Adjoint modelling: pros and cons

60 chemical compounds, 5°x5° resolution, 25 σ levels (Müller and Brasseur, 1995) Use monthly averaged meteorological fields from ECMWF analyses, impact of wind variability represented as horizontal diffusion Semi-lagrangian transport Anthropogenic emissions : 1997 EDGAR v3 Biomass burning emissions : GFED (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 Two main modes: (A) with or (B) without diurnal cycle calculations Mode B (Δt=1 day) uses info. on diurnal profiles of chemical species calculated in mode A (Δt=20 min) to correct the kinetic rate constants and photorates Inverse modeling: only in mode B (emission updates not expected to affect the diurnal behavior of chemical compounds) 16 months simulations, including spin-up of 4 months The IMAGES model

The inversion is constrained by: NOAA/CMDL CO mixing ratios Ground-based FTIR CO vertical column abundances GOME tropospheric NO 2 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 A. Big-region inversion of the 1997 CO emissions

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 posterior errors

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, JGR, in press B. Big-region vs. Grid-based inversion for optimizing CO&VOC emissions

Spatial correlations for anthrop. emissions E n = total emission of country n, σ En = standard error d i n = fraction emitted by the country n in the i th grid cell φ i = total flux emitted by the cell i E n = total emission of country n, σ En = standard error d i n = fraction emitted by the country n in the i th grid cell φ i = total flux emitted by the cell i = fraction of the flux emitted by the cell i and country n σ En / E n = 0.6, 0.35 for industrialized countries A nm = 1, when n=m, 0.3 if n,m belong to the same big region, 0 otherwise C ij nm = 0.7, 0.85 when n,m belong to the industrialized countries, 1 when i=j

Correlation setup for pyrogenic and biogenic emissions Spatial correlations : Based on the geographical distance d ij between the grid cells i and j Relative error on the flux : 0.7 for pyrogenic / 0.6 for biogenic Decorrelation length : 2000 km for pyrogenic / 6000 km for biogenic e i n : fraction of the flux emitted by the cell i and ecosystem n (n=2 for pyrogenic, 40 for biogenic emissions) C nm : 1 or 0.5 depending on whether the same or different ecosystems occupy the grid cells i and j Temporal correlations : linearly varying between 0 and 0.5 for pyrogenic emissions, between 0.7 and 0.9 for biogenic emissions

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 Optimization results

Evolution of the cost and its gradient throughout the minimization The gradient is 10 times smaller than its initial value after 6 iterations

The gradient is 100 times smaller than its initial value after 24 iterations

The gradient is 1000 times smaller than its initial value after 42 iterations

Anthropogenic emissions by region

Big-region setup Grid-based setup prior GFED prior POET big-region GFED grid-based GFED grid-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 Vegetation fire 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 Biogenic emission updatesSeasonal variation

prior big-region grid-based Comparison to independent data (CMDL, FTIR, aircraft campaigns) prior

Anthro- pogenic sources Tropical forest fires Savanna fires Extra- tropical fires Biogenic sources Photo- chemical source Total prior standard grid-based errors on control variables doubled errors on control variables halved decorrelation lengths doubled decorrelation lengths halved lower temporal anthropogenic correlations halved spatial correlations for anthrop. sources constant biog. fluxes Sensitivity inversions

Comparison of our results to past inverse modelling studies

East Asian anthropogenic emissions

After 6 iterations (grad./10) After 42 iterations (grad./1000) After 24 iterations (grad./100) Biogenic emissions error reduction

After 6 iterations (grad./10)After 24 iterations (grad./100) After 42 iterations (grad./1000) Anthropogenic emissions error reduction

Regions AnthropogenicPyrogenicBiogenic N. America S. America N. Africa S.Africa Europe Far East 1.71 Former S. U S. Asia Oceania Tropics (25 N-25 S) Extratropics Error reduction factors over large regions (estimated using the DFP-based update)

Sigma-pressure coordinate system, 40 levels Use of ECMWF analyses for convective fluxes, PBL diffusion clouds washout/rainout KPP as alternative chemical solver (not in adjoint model calculations - well for diurnal cycle calculations) MEGAN model for BVOC emissions Treatment of diurnal cycle NMVOC chemical mechanisms Optimize horizontal diffusion coefficients using adjoint technique and output using varying winds OR get rid of these coefficients and use varying winds done IMAGES model updates (in progress) in progressfuture

In collaboration with KNMI, determination of NO 2 tropospheric columns from satellites (AMFs, stratosphere from KNMI model) Retrieval of CH 2 O columns from GOME using IMAGES profiles Related work at IASB-BIRA : satellite retrievals (M. Van Roozendael et al.)

(Courtesy of I. De Smet & M. Van Roozendael) GOME-IMAGES CH 2 O :

State-of-the-art mechanism development for α-pinene, based on theoretical work of J. Peeters and co-workers (Uni. Leuven) Mechanism validation by simulations of laboratory experiments using a box model SOA parameterization based on original vapor pressure prediction method Reduced mechanism (~30 compounds) (work in progress) Future: ozonolysis of α-pinene and sesquiterpenes Related work at IASB-BIRA: chemistry of terpenes

Alpha-pinene + OH quasi-explicit mechanism : Peeters et al. (2001), Fantechi et al. (2002), Vereecken and Peeters (2004), Capouet et al. (2005) Very exotic chemistry (ring closure, isomeri- sations, peroxy radical decomposition, etc.) 800 species, 2400 reactions (ozonolysis included)

Capouet et al., 2005 Lamp spectra Model simulation of laboratory experiments

CO CH 2 O +OH Hermans et al., 2004; 2005 : +HO 2 CH 2 OHO 2 +NO HCOOH +HO 2 +hv Also for acetone and other carbonyls! J. Phys Chem. A (May 2005) Related work at IASB-BIRA : unexpected reaction sequences in the UT/LS

Feasibility of multi-compound and grid-based inversions Comparable results of big-region and grid-based approaches when averaged over large regions Importance of the error correlation setup for grid-based inversions -- further work needed to better quantify the correlations Posterior uncertainty analysis made possible by the DFP approximation, shows important error reductions for large-scale fluxes (e.g. Chinese anthropogenic emissions, African biomass burning), small error reductions for individual grid cells Synergetic use of different datasets is required to better quantify emissions, in particular the CO production from the NMVOCs CH 2 O from satellites promising in that perspective, but large differences between retrievals by different groups  intercomparisons are mandatory Also, large differences between inversion studies based on same data but different models Conclusions and perspectives