Setup of 4D VAR inverse modelling system for atmospheric CH 4 using the TM5 adjoint model

1. Setup of 4D VAR inverse modelling systemfor atmospheric CH4using 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): Linearisation of non-linear model adjoint model: transpose of TLM

3. TM5 adjoint model forward model: TM5 is linear - slopes - limits: off - offline chemistry tangent linear model (TLM): Linearisation of non-linear model 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) adjoint model: transpose of TLM

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

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

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

7. 4D VAR data assimilation system

8. gradient test example for 3 days integration 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 - (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) emission inventory used to create synthetic observations -> "true emissions" Artificial increase of CH4 emissions over Germany by 30 % -> a priori emissions 4D VAR inversion

11. 4DVAR inversion using synthetic observations (global grid 6x4) 4D VAR inversion returns inventory very close to "true emission inventory' emission inventory used to create synthetic observations -> "true emissions" Artificial increase of CH4 emissions over Germany by 30 % -> a priori emissions 4D VAR inversion

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

13. 4DVAR inversion using synthetic observations (European zoom 3x2) 4D VAR inversion returns inventory very close to "true emission inventory' emission inventory used to create synthetic observations -> "true emissions" Artificial increase of CH4 emissions over Germany by 30 % -> a priori emissions 4D VAR inversion

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

15. 4DVAR inversion using synthetic observations (European zoom 1x1) 4D VAR inversion returns inventory very close to "true emission inventory' emission inventory used to create synthetic observations -> "true emissions" Artificial increase of CH4 emissions over Germany by 30 % -> a priori emissions 4D VAR inversion

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

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

18. conclusions • 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"

19. next steps • 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)