1. Setup of 4D VAR inverse modelling system for atmospheric CH 4 using the TM5 adjoint model Peter Bergamaschi Climate Change Unit Institute for Environment and Sustainability(IES) Joint Research Center Ispra, Italy Maarten Krol Institute for Marine and Atmospheric Research Utrecht, Netherlands

2. adjoint model forward model: tangent linear model (TLM): adjoint model: Linearisation of non-linear model transpose of TLM

3. TM5 adjoint model forward model: tangent linear model (TLM): adjoint model: TM5 is linear - slopes - limits: off - offline chemistry TM5 represents already tangent linear model TM5 adjoint: manual coding - transpose of each model operator - revert order of operators - provide passive, but required variables correctly (air mass) Linearisation of non-linear model transpose of TLM

4. adjoint model - applications efficient way to calculate full Jacobian matrix, if: number (obs) << number (parameters) 3-D back trajectories Systems with many observations AND many parameters: Minimization of cost function: 4D-VAR adjoint model Analytical solution of inverse problem Iterative approximation: for VERY complex systems (e.g. numerical weather prediction)

5. cost function parametersobservations Model prediction: Observation operator H observations Initial mixing ratio emission gradient of cost function

6. minimization [Bouttier and Courtier, 1999] dimension parameter space: TM5: ~1 E4 - 1 E5 (ECMWF(T511) : ~1 E 7 ) Minimisation algorithms: - M1QN3 [Gilbert, Lemarechal, 1995] - ECMWF conjugate gradient

7. 4D VAR data assimilation system

8. gradient test alpha DJ1 DJ2 t 1-t 0.01000000000000 -704.73790893311582-2078.99670025996011 2.95002819332835 -1.95002819332835 0.00100000000000 -70.47379089331153 -84.21637937355342 1.19500282737800 -0.19500282737800 0.00010000000000 -7.04737908933116 -7.18480503077902 1.01950029077560 -0.01950029077560 0.00001000000000 -0.70473790893312 -0.70611217403768 1.00195003715161 -0.00195003715161 0.00000100000000 -0.07047379089331 -0.07048753401415 1.00019501038134 -0.00019501038134 0.00000010000000 -0.00704737908933 -0.00704751656733 1.00001950767696 -0.00001950767696 0.00000001000000 -0.00070473790893 -0.00070473926218 1.00000192020693 -0.00000192020693 0.00000000100000 -0.00007047379089 -0.00007047377832 0.99999982162240 0.00000017837760 0.00000000010000 -0.00000704737909 -0.00000704734254 0.99999481310498 0.00000518689502 example for 3 days integration - (1-t) is reaching ~ 1E-7 -> proof for correct coding of adjoint - slight deterioration for longer integration times (1E-4 for 45 days integration), due to numerical effects

9. test of 4DVAR system using synthetic observations Create synthetic observations: - station data - total columns "brute force inversion" (-> test of 4DVAR system performance rather than realistic simulation with expected real data) - Assume global availabiltity of column data, uncertainty 0.1 ppb - Assume very high uncertainty for emissions (emission x 1 E4)

10. 4DVAR inversion using synthetic observations (global grid 6x4) Artificial increase of CH 4 emissions over Germany by 30 % -> a priori emissions 4D VAR inversion emission inventory used to create synthetic observations -> "true emissions"

11. 4DVAR inversion using synthetic observations (global grid 6x4) Artificial increase of CH 4 emissions over Germany by 30 % -> a priori emissions 4D VAR inversion emission inventory used to create synthetic observations -> "true emissions" 4D VAR inversion returns inventory very close to "true emission inventory'

12. 4DVAR inversion - analysis increments (global grid 6x4) 4D VAR inversion artificial increase a priori - SYNOBS a priori - a posteriori

13. 4DVAR inversion using synthetic observations (European zoom 3x2) emission inventory used to create synthetic observations -> "true emissions" Artificial increase of CH 4 emissions over Germany by 30 % -> a priori emissions 4D VAR inversion 4D VAR inversion returns inventory very close to "true emission inventory'

14. 4DVAR inversion - analysis increments (European zoom 3x2) 4D VAR inversion artificial increase a priori - a posteriori a priori - SYNOBS

15. 4DVAR inversion using synthetic observations (European zoom 1x1) emission inventory used to create synthetic observations -> "true emissions" Artificial increase of CH 4 emissions over Germany by 30 % -> a priori emissions 4D VAR inversion 4D VAR inversion returns inventory very close to "true emission inventory'

16. 4DVAR inversion - analysis increments (European zoom 1x1) 4D VAR inversion artificial increase a priori - SYNOBS a priori - a posteriori

17. minimisation algorithm (M1QN3) Good convergence within ~20 - ~100 iterations Convergence dependent on: - preconditioning - parameter set - observations - length of assimilation period

18. Conclusions demonstration for correct coding of TM5 adjoint (gradient test) setup of 4DVAR system for flexible incorporation various types of observational data (monitoring stations, satellite measurements) test of 4DVAR system using synthetic observations -> recovery of "true emissions" conclusions

19. Next steps finalisation of 4DVAR framework (many details still to be improved) further tests with synthetic observations (test of system performance, test of sampling strategies) minimisation algorithms / preconditioning parameter covariances (correlations) a posteriori uncertainty reduction estimates ……. real observations longer assimilation periods (-> meteo preprocessing) next steps