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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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