Further Developments and Applications for the Adjoint of CMAQ

1. Further Developments and Applications for the Adjoint of CMAQ Amir Hakami, Kumaresh Singh, Adrian Sandu, John Seinfeld (Carleton, Caltech, Va Tech) 6th Annual CMAS Conference Chapel Hill October 1, 2007

2. Overview • Brief introduction to adjoint sensitivity analysis • Implementation details • Current status • KPP integration • Forward (DDM/TLM) implementation • Process-by-process validation • Computational performance • Potential applications • Future developments CMAS Conference Oct 1, 2007

3. Forward vs. BackwardSensitivity Analysis Inputs/Sources Outputs/Receptors • Adjoint analysis is efficient for calculating sensitivities of a small number of outputs with respect to a large number of inputs. Forward analysis is efficient for the opposite case. • Complementary methods (Source-based vs. Receptor-based), each suitable for specific types of problems. CMAS Conference Oct 1, 2007

4. DDM/TLM and adjoint formulations • Forward model • Tangent linear model (TLM/DDM) • Adjoint model CMAS Conference Oct 1, 2007

5. Current status of CMAQ-ADJ • Developed in collaboration between Caltech and Va Tech • Developed for version 4.5 • Pretty hard to keep up with CMAS releases! • Only gas-phase processes • Only uniform grid – no nesting • Only sequential simulation • Discrete adjoint with the exception of HADV • Availability: • Va Tech version: • http://www.cs.vt.edu/~asandu/Software/CMAQ_ADJ/CMAQ_ADJ.html • Caltech/Carleton: to be released soon • More details: Hakami et al. (2007), ES&T (in press) CMAS Conference Oct 1, 2007

6. KPP integration: work-precision diagram • Chemistry independent with 5 Rosenbrock and 4 Runge-Kutta solvers CMAS Conference Oct 1, 2007

7. DDM implementation • More accurate than DDM-3D implementation CMAS Conference Oct 1, 2007

8. Backward simulation scheme CMAS Conference Oct 1, 2007

9. Chemistry • Chemistry-only simulations • Seminormalized sensitivity of ozone to initial NO CMAS Conference Oct 1, 2007

10. Vertical diffusion • Chemistry + vertical diffusion • Seminormalized sensitivity of ozone to NO emissions CMAS Conference Oct 1, 2007

11. Horizontal advection BF (+100%) BF (-10%) Adjoint DDM • Sensitivity of ozone in 20st column cross section to initial ozone in 20th column • Only HADV in x direction • Hence, continuous approach for HADV • Bott exhibits better behavior CMAS Conference Oct 1, 2007

12. A side note: what to validate? • As developers, should we only validate our numerical routines for concentrations? • In light of increased attention paid to model sensitivities, it appears that validation efforts should include sensitivity information as well as concentrations • Even if not performing formal sensitivity analysis, we are routinely using (finite) differences. • It is imperative to make sure that our numerical routines do not produce response surfaces that are overly fractured/discontinuous. CMAS Conference Oct 1, 2007

13. HDIFF (top) and VADV CMAS Conference Oct 1, 2007

14. Full model validation NO emissions Initial ozone CMAS Conference Oct 1, 2007

15. Computational efficiency 1- Values are normalized to forward simulation with EBI solver. 2- Values are normalized to the forward simulation with the same solver. 3- Values include the time required for concentration integrations. CMAS Conference Oct 1, 2007

16. Potential applications (environmental exposure) • Different applications depending on the definition of the cost function. • As a receptor-based method, adjoint analysis is particularly powerful for policy applications • Nonattainment analysis (Hakami et al., 2006) • Most common uses in data assimilation and inverse modeling • Let’s look at few other examples CMAS Conference Oct 1, 2007

17. Potential applications – population exposure Population exposure metric: Sensitivity to NOx emissions Metric distribution (Plots are normalized to the total metric) CMAS Conference Oct 1, 2007

18. Potential applications - vegetation Stress Vegetation damage (W126) metric: Metric distribution Sensitivity to NOx emissions (Plots are normalized to the total metric) CMAS Conference Oct 1, 2007

19. Potential applications - temperature dependence Population exposure Vegetation stress NB: This only includes the effects through chemistry. CMAS Conference Oct 1, 2007

20. Future research plans • Further development of the adjoint of CMAQ: • Clouds, aqueous, and aerosol processes. • Aerosol thermodynamics will be a significant challenge. • Parallelization. • Backward nesting. • Coupling with GEOS-Chem in backward mode. • That would give us a regional-to-global forward and backward sensitivity analysis platform CMAS Conference Oct 1, 2007

21. Summary and conclusions • KPP integration with CMAQ provides users with good combination of accuracy and efficiency. • Both DDM and adjoint implementations show very good level of accuracy and computational efficiency. • Receptor-oriented nature of the adjoint method makes it ideal for policy applications and target-based analysis. • Problems with PPM advection adjoint indicates the need for the development community to validate sensitivities (differences) in addition to concentrations. CMAS Conference Oct 1, 2007

22. Acknowledgements • Thanks to • Daewon Byun, Soontae Kim, and Qinbin Li • Funding Agencies: NSF and NASA CMAS Conference Oct 1, 2007

23. Questions? Comments? Thank you!! CMAS Conference Oct 1, 2007

24. Adjoint analysis • Target-based, receptor-oriented method: Depends on the definition of a cost function ( J ) for which sensitivity calculations are carried out. • Adjoint equations are integrated backward in time. At each location and time adjoint variables are gradients of the cost function with respect to state vector (concentrations). CMAS Conference Oct 1, 2007