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. Backward Sensitivity 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:
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
Forward Model
Adjoint Model
INIT (t=0)
DO (Synchronization steps)
DO (Advection steps)
V-DIFF
COUPLE
H-ADV
WRITE CHECKPOINT (Density)
V-ADV
H-DIFF
DECOUPLE
WRITE CHECKPOINT (CONC)
CHEM
NEXTIME (TSTEP)
END DO
WRITE CONC
INIT (t=tF)
FORCE-ADJ
NEXTIME (-TSTEP)
READ CHECKPOINT (CONC)
CHEM-ADJ
H-DIFF-ADJ
READ CHECKPOINT (Density)
V-ADV-ADJ
H-ADV-ADJ
V-DIFF-ADJ
WRITE ADJ
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
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
Adjoint
DDM
BF (+100%)
BF (-10%)
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
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14. Full model validation Initial ozone NO emissions
CMAS Conference Oct 1, 2007

15. Computational efficiency
Solver
Normalized computational times
Forward Model 1
DDM 2, 3
Adjoint 3
CMAQ-EBI
1.00 -
CMAQ-ROS3
2.10
CMAQ-SMVGEAR
3.69
KPP-ROS2
1.59
1.88
2.02
KPP-ROS3
1.08
1.96
KPP-ROS4
1.18
2.11
KPP-RODAS3
0.96
2.12
2.09
KPP-RODAS4
2.39
2.18
KPP-RADAU-2A
2.08
7.81
7.87
KPP-LOBATTO
2.66
7.93
7.25
KPP-GAUSS
8.13
5.41
KPP-RADAU-1A
1.99
7.60
7.96
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:
Metric distribution
Sensitivity to NOx emissions
(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. Further development of the adjoint of CMAQ:
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