GEOS-Chem Adjoint: construction and long-term

maintainability

A. Sandu, K. Singh: Virginia TechD. Henze: CaltechK. Bowman: JPL

April 11, 2007

Adjoints enable sensitivity analysis and information feedback loops between GEOS-Chem and observations

Optimal analysis state

Chemical kinetics

Aerosols

GEOS-Chem

TransportMeteorology

Emissions

Observations4D-VarData

Assimilation

Targeted Observ.

Improved:• forecasts• science• field experiment design• models • emission estimates

Improved:• forecasts• science• field experiment design• models • emission estimates

April 11, 2007

The sensitivity can be obtained either via the direct chain rule (TLM/DDM) or via its transpose (ADJ)

00 y

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TLM (DDM) = source-oriented approach

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ADJ = receptor-oriented approach

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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

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

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)

,2,1,,,tosubject 11

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zyHRzyHyyByyymin 1T1T0

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Optimization uses gradients obtained via adjoint modeling

April 11, 2007

Assimilation of ICARTT data adjusts O3 predictions considerably at 4pm EDT on July 20, 2004

Observations: circles, color coded by O3 mixing ratio

Surface O3 (forecast)

Surface O3 (analysis)

[Chai et al., 2006]

April 11, 2007

Assimilation of ozonesonde data and of DC-8 lidar observations for July 20, 2004

[Chai et al., 2006]

April 11, 2007

Targeted observations are deployed to areas where they provide maximum of information

1

22max

2

kksT k

(criterion based on SVs)

[Liao and Sandu, 2005]

Verification:Korea, ground O3

0 GMT, Mar/4/2001

O3 NO2 HCHO

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

ObservationOperators

(av. Kernels, intp.)

April 11, 2007

KPP automatically generates simulation and

direct/adjoint sensitivity code for chemistry

#INCLUDE atoms

#DEFVARO = O; O1D = O; O3 = O + O + O; NO = N + O; NO2 = N + O + O;

#DEFFIXO2 = 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 P

[Damian et.al., 1996; Sandu et.al., 2002]

Chemical mechanism Simulation code

April 11, 2007

KPP has been tested in GEOS-Chem (Henze)

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 …)

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

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