1. GEOS-Chem Adjoint: construction and long-term maintainability A. Sandu, K. Singh: Virginia Tech D. Henze: Caltech K. Bowman: JPL

2. April 11, 2007 Adjoints enable sensitivity analysis and information feedback loops between GEOS-Chem and observations Optimal analysis state Chemical kinetics Aerosols GEOS-Chem Transport Meteorology Emissions Observations 4D-Var Data Assimilation Targeted Observ. Improved: forecasts science field experiment design models emission estimates Improved: forecasts science field experiment design models emission estimates

3. April 11, 2007 The sensitivity can be obtained either via the direct chain rule (TLM/DDM) or via its transpose (ADJ) TLM (DDM) = source-oriented approach ADJ = receptor-oriented approach

4. April 11, 2007 Adjoint variables describe areas of influence where changes in conc. impact the receptor (observations) 48 hrs areas of influence for a hypothetical TES sequence of observations

5. April 11, 2007 Adjoints can provide the sensitivities of ozone observations with respect to NOx emissions 1 week sensitivities of TES O3 w.r.t. athropogenic and lightning NOx emissions

6. April 11, 2007 Data assimilation combines multiple sources of information to estimate concentrations, emissions, etc Model (encapsulating knowledge on the physics, chemistry, thermodynamics, etc) Background (encapsulating best a-priori knowledge of the state) Observations (encapsulating new information about reality) Optimization uses gradients obtained via adjoint modeling

7. April 11, 2007 Assimilation of ICARTT data adjusts O 3 predictions considerably at 4pm EDT on July 20, 2004 Observations: circles, color coded by O 3 mixing ratio Surface O 3 (forecast)Surface O 3 (analysis) [Chai et al., 2006]

8. April 11, 2007 Assimilation of ozonesonde data and of DC-8 lidar observations for July 20, 2004 [Chai et al., 2006]

9. April 11, 2007 Targeted observations are deployed to areas where they provide maximum of information (criterion based on SVs) [Liao and Sandu, 2005] Verification: Korea, ground O 3 0 GMT, Mar/4/2001 O3O3 NO 2 HCHO

10. April 11, 2007 Construction of GEOS-Chem Adjoint is non-trivial Optimal analysis state Chemical Kinetics (KPP) Transport (continuous) Emissions Data Assimilation Targeted Observ. Improved: forecasts science field experiment design models emission estimates Improved: forecasts science field experiment design models emission estimates Aerosols (TAMC) GEOS-Chem Observation Operators (av. Kernels, intp.)

11. April 11, 2007 KPP automatically generates simulation and direct/adjoint sensitivity code for chemistry #INCLUDE atoms #DEFVAR O = O; O1D = O; O3 = O + O + O; NO = N + O; NO2 = N + O + O; #DEFFIX O2 = O + O; M = ignore; #EQUATIONS { Small Stratospheric } O2 + hv = 2O : 2.6E-10*S; O + O2 = O3 : 8.0E-17; O3 + hv = O + O2 : 6.1E-04*S; O + O3 = 2O2 : 1.5E-15; O3 + hv = O1D + O2 : 1.0E-03*S; O1D + M = O + M : 7.1E-11; O1D + O3 = 2O2 : 1.2E-10; NO + O3 = NO2 + O2 : 6.0E-15; NO2 + O = NO + O2 : 1.0E-11; NO2 + hv = NO + O : 1.2E-02*S; SUBROUTINE FunVar ( V, F, RCT, DV ) INCLUDE 'small.h' REAL*8 V(NVAR), F(NFIX) REAL*8 RCT(NREACT), DV(NVAR) C A - rate for each equation REAL*8 A(NREACT) C Computation of equation rates A(1) = RCT(1)*F(2) A(2) = RCT(2)*V(2)*F(2) A(3) = RCT(3)*V(3) A(4) = RCT(4)*V(2)*V(3) A(5) = RCT(5)*V(3) A(6) = RCT(6)*V(1)*F(1) A(7) = RCT(7)*V(1)*V(3) A(8) = RCT(8)*V(3)*V(4) A(9) = RCT(9)*V(2)*V(5) A(10) = RCT(10)*V(5) C Aggregate function DV(1) = A(5)-A(6)-A(7) DV(2) = 2*A(1)-A(2)+A(3)-A(4)+A(6)-&A(9)+A(10) DV(3) = A(2)-A(3)-A(4)-A(5)-A(7)-A(8) DV(4) = -A(8)+A(9)+A(10) DV(5) = A(8)-A(9)-A(10) END K P [Damian et.al., 1996; Sandu et.al., 2002] Chemical mechanism Simulation code

12. April 11, 2007 KPP has been tested in GEOS-Chem (Henze)

13. April 11, 2007 GEOS-Chem Adjoint History Offline aerosol (D. Henze, Caltech, 2005) TAF (M. Kopacz, Harvard, 2005) Full chemistry (D. Henze, Caltech) Wed. 1:45 v6-02-05, GEOS-3 met, gas-phase, aerosols Tagged CO, CO2 (M. Kopacz, Harvard) Thur. 12:15 Black Carbon (Q. Li, JPL) Wed. 2:30 Goal: develop a standardized GEOS-Chem adjoint model (VT, JPL, Harvard, Caltech, Toronto …)

14. April 11, 2007 Towards a standardized GEOS-Chem adjoint model Adjoints to use GEOS-4/GEOS-5 met Update from GEOS-Chem v6 to v7 Adjoints of different convection models Better integrate Kpp with GEOS-Chem. Develop ability to read the same chemical input files directly. Observation operators for specific satellites (TES, MOPPITT, OMI) Different adjoints for different processes (continuous/discrete, full/simplified). See algorithmic issues. Checkpoints: how often? After each process? Optimal log storage size? Optimization procedures Parallelization of adjoint over MPI

15. April 11, 2007 Keeping the 4D-Var/adjoint up-to-date when GEOS- Chem is continuously evolving Community can help: Encapsulate each science process, and have it communicate with the model through interfaces. Derivatives should not depend on global variables or on I/O. (e.g., deposition) Avoid large nonlinearities and points of non-differentiability in the forward model if at all possible (e.g., limiters) Allow simplified versions of science processes that will result in simplified adjoints (e.g., simplified advection adjoint) Prepare for automatic adjoint code generation: Implementation should allow the use of automatic differentiation without other code transformations. (Which AD engine of choice? TAMC, TAF, OpenAD? Full F90 support?) KPP for the automatic implementation of the direct/adjoint chemistry

16. April 11, 2007 Illustration of the adjoint calculation of sensitivities backward in time, starting from the observations

17. April 11, 2007 Adjoint sensitivity analysis of non-attainment metrics can help guide policy decisions Estimated contributions by state to violating U.S. ozone NAAQS in July 2004 [Hakami et al., 2005]