GEOS-Chem Adjoint Users Guide (Draft)

Transcription

1 GEOS-Chem Adjoint Users Guide (Draft) Daven K. Henze May 12, 2009 Contents 1 Getting started Obtaining run packages Obtaining source code The run script Benchmark simulations Downloading benchmark packages Running benchmark simulations Analyzing benchmark results Checklist for running code 9 3 Selecting the adjoint model operational mode Active variable selection Pre-processor includes Process specific flags Subroutines that get edited frequently SUBROUTINE SET ICS SUBROUTINE INIT WEIGHT SUBROUTINE RESCALE ADJOINT Directories and output files Directories Output files Essential output files Nonessential output files Sensitivity with respect to reaction rate coefficients 14 1

2 6.1 Adding new reactions Saving reaction rate sensitivities Validating code Global tests of a subset of the adjoint model Spot tests of full adjoint model Box model adjoint chemistry tests Generating forward and reverse code for GEOS-Chem with the Kinetic PreProcessor (KPP) KPP input files Post processing KPP generated code Interfacing KPP code with GEOS-Chem Implementing OpenMP Parallelization in KPP generated code Performing global benchmarks of new chemical solvers References 21 2

3 1 Getting started 1.1 Obtaining run packages Run packages are available from the GC-adjoint website. The package includes the following directories ADJvXX bench/tmp ADJvXX bench/adjtmp ADJvXX bench/run.v geos3 where XX is the current version number. The run script, input files, and benchmark results are in the run directory, ADJvXX run.v geos Obtaining source code To access the CVS repository, place the following lines in your.cshrc file (or bash equivalent) setenv CVS_RSH ssh setenv CVSROOT where name is your user name. To download the most current copy of the code, enter the following command cvs checkout dkh_gc_adj This will download a code directory dkh gc adj containing the source code. Place this in the run package, ADJvXX bench/dkh gc adj. Perhaps you already have a version of the source code. To determine the status of your existing code vs the current repository version, enter your local copy of the code directory and type cvs status or perhaps more useful, cvs status grep Status To determine the difference between your copy and the repository copy, type cvs diff -D now 3

4 The commands without arguments will apply to all files in the repository. To use them for only one specific file, for example adjoint mod.f, type: cvs diff -D now adjoint_mod.f Note: the -D takes the difference between your copy and the newest repository copy. Without the -D flag, you see the difference between your copy and the version that was in the repository as of the last time you checked out the code. To replace your local copy of adjoint mod.f with the newest version from the repository, cvs checkout adjoint_mod.f or to merge the contents from the repository with your own, cvs update adjoint_mod.f More information on CVS is at For now, please do not use the commit command. I will handle incorporating changes into the code repository. Please do not distribute copies of the code at this time; you may refer such requests to me. 1.3 The run script NOTE: The run script only seems to work if you use tcsh. My apologies to users of other shells. To use, you have to set several variables in the script, following the instructions therein. Change often (almost every run): X XSTOP RNAME Change rarely (only when migrating to a new filesystem): DSAVE DRUNDIR DPACK Unlikely to need to be changed from the defaults: DCODE DRUN 4

5 The frequently changed variables are X, XSTOP, and RNAME. Set RNAME to be a descriptive name of your current calculation (such as ADJv23_optimize_NH3_emissions). Set the start (or current) iteration number, X. Set XSTOP to the final iteration number. For example, if you ve already computed five iterations, then set X=6 and XSTOP=9 to compute three more. At each iteration, the current value of X is assigned to the variable N_CALC_STOP in inverse.f, the code is recompiled, the executable is moved to the run directory, and the program is executed. X = 0 is used for generating pseudo observations. For example, if X=0 and XSTOP =4: Computational flow for each iteration X=0 X=1 X=2 X=3 X=4 σ=1 σ=1+δσ read *.01 read *.01 read *.01 DO_GEOS_CHEM DO_GEOS_CHEM update σ update σ update σ make *obs* DO_ADJOINT DO_GEOS_CHEM read *.02 read *.02 write *.01 DO_ADJOINT update σ update σ write *.02 DO_GEOS_CHEM read *.03 DO_ADJOINT write *.03 Why is it necessary to recompile the code between each iteration? includes many initialization processes, LOGICAL, SAVE. IF ( FIRST ) THEN CALL INIT_ARRAYS FIRST =.FALSE. ENDIF. :: FIRST =.TRUE. update σ DO_GEOS_CHEM DO_ADJOINT write *.04 The forward model By recompiling the code between each iteration, these logical control switches get automatically reset to FIRST =.TRUE.. Doesn t this repeated reading / writing / optimizing take a lot of time? No, not with respect to the expense of the forward and backward model calculations. For sensitivity calculations, set X and XSTOP to 1 5

6 1.4 Benchmark simulations Downloading benchmark packages Download one of the benchmark packages from puck: ADJvXX bench opt geos3 ADJvXX bench opt geos3 lin ADJvXX bench opt geos4 ADJvXX bench fd geos3 ADJvXX bench fd geos3 short ADJvXX bench fd geos4 These packages contain the necessary inputs and the benchmark results Running benchmark simulations Setting input files You will need to make the following changes to the input files, as they depend upon your particular filesystem: Set DRUN and DSAVE in the run script, as dictated by your filesystem. Set data folder locations DATA_DIR GEOS_3_DIR and GEOS_4_DIR in input.geos. May have to change LZIP, depending on wether or not your met data is zipped. As of ADJv27, the TEMP_DIR directory setting here is no longer relevant, as this is overwritten by hardwired code in setup.f to allow for relative addressing of this directory. Set HDF locations in Makefile (for version ADJv28 and earlier) Setting source code When running the benchmark tests, you should checkout your own copy of the source code (see Sect. 1.2) and make the appropriate modifications to it to try the various benchmarks. The CVS repository contains the source code for the default test, ADJvXX bench opt geos3. No adjustment of source code necessary to run this test. The difference between the source code for the ADJvXX bench opt geos3 test and other tests are given in the file diff.adjvxx bench *.txt in the run directory. For example, in the package ADJvXX bench opt geos4, there is a file diff.adjvxx bench opt geos4.txt, which should look something like this: 6

7 Index: define.h =================================================================== RCS file: /Volumes/scratch/CVSrepos/dkh_gc_adj/define.h,v retrieving revision diff -r define.h 99,100c99,100 < #define GEOS_3 GEOS_3 <!#define GEOS_4 GEOS_4 --- >!#define GEOS_3 GEOS_3 > #define GEOS_4 GEOS_4 Therefore, to run the ADJvXX bench opt geos4 benchmark test, this file tells you to change line 99 and 100 of define.h to indicate use of GEOS 4 met fields. Running the tests like:./run > log.my_benchmark_test & Now you are ready to execute the run script, with a unix command If all goes well, the output should finish with: G E O S C H E M A D J O I N T E X I T E D N O R M A L L Y Note: for the finite difference tests, the simulation is aborted on purpose after the forward model evaluation at the 3rd iteration, in which case the logfile will end with: * * * E R R O R * * * G E O S C H E M A D J O I N T D I D N O T F I N I S H That s OK. Finishing the calculation here by computing the adjoint again would be a waste of time Analyzing benchmark results Optimization tests The optimization benchmark simulation attempts to optimize emissions of anthropogenic ammonia, ENH3_an, starting with domain wide exponential scaling 7

8 factors of ln(2.00) and pseudo observations that were generated with exponential scaling factors of The simulation is only 6h long and should start to converge after a few iterations. Output from my benchmark runs are in the directory../run.v geos3/optdata/. To quickly see how the cost function converges, grep OptData/cfn* The cost function should have reduced by more than an order of magnitude. Note: not all value of the cost function listed here correspond to accepted iterations of the optimization procedure. Some are function evaluations that correspond to the optimization performing searches in various directions before finding the optimal path towards a minimum. To see which values correspond to accepted iterations, grep iterate log To see the inverse modeling solution after the 6th iteration, look at the optimized scaling factors in the gctm.ics.06 file using gamap, IDL> gamap, file= gctm.ics.06, IJ-EMS-$, yrange=[-1,1] Check the value for EMSNH3a. Scaling factors should be close to 0.0 in locations where anthropogenic NH3 emissions are significant. The scaled emissions themselves are shown in the IJ-EM0-$ category. Finite difference tests The finite difference tests are domain wide comparisons of adjoint sensitivities of SO4 to NOx emissions over the course of a 1 week simulation with no transport. All other processes are included. In essence, this tests an ensemble of column models. To speed up the evaluation of this test, chemistry is only calculated in the LFD level. This simulation will run for 2 complete iterations, and then only the forward part of the 3rd iteration, afterwhich the logfile will state something like: Global validation test for values > MAX of global 2nd order ADJ / FD = MIN of global 2nd order ADJ / FD = Number of places where ratio off by = 88 That the min and max of the ADJ / FD ratio is much greater or less than 1.d0 may or may not be significant. In general, it shouldn t be off by more than x10, and the number of places where the ratio is off by more than 10% shouldn t be much more than 100. However, 8

9 to tell wether ADJ / FD rations that deviate from 1.0 are owing to errors in the adjoint code or to limitations of finite difference sensitivities, the results will have to be plotted. The key results are saved to the *save2* file. The contents can be analyzed using GAMAP. After loading a file and viewing some results, IDL> gamap, file= gctm.save generate a data set for a scatter plot of adjoint vs finite difference values using IDL> fd_stats and plot the results in MATLAB using >>fd_vs_adj Sample output is shown here: The IDL and MATLAB scripts for making these plots are here: More about setting up and designing your own finite difference validation tests is in Sect Checklist for running code Set folder locations in run and CMN ADJ, input.geos. Set HDF locations in Makefile (for version ADJv28 and earlier) All the standard forward model inputs need to be defined. Set the run script to the proper number of iterations Set ACTIVE_VARS in CMN ADJ Check pre-processor includes in CMN ADJ Check logical control flags and OBS_FREQ in CMN ADJ Set WEIGHT in INIT_WEIGHT (adjoint mod.f ). Check SET_ICS in inverse mod.f. 3 Selecting the adjoint model operational mode All of the following are defined in CMN ADJ. 9

10 3.1 Active variable selection ACTIVE_VARS is used to control what type of calculation is being performed by specifying the active variables. The following types of simulations are supported: TRACERS EMISSIONS FDTEST For optimization of tracer concentrations (i.e. initial conditions). For optimization of emissions. No optimization. Gradients compared to finite difference calculations. Currently this is set up to compare gradients with respect to emissions parameters. Note: this method of adding model functionality no longer preferred, see below. 3.2 Pre-processor includes Several pre-processor include statements in CMN ADJ also control the operational mode of the adjoint model. For future model development, this is the preferred technique, as opposed to defining more possible values for ACTIVE_VARS. These mainly affect when (and if) observations are read, when corresponding predictions are saved, and how the cost function is calculated. Current supported modes of operation: JACOBIAN PM_ATTAINMENT O3_ATTAINMENT IMPROVE_OBS CASTNET_OBS LOG_OPT NO2_SAT_OBS default For finite difference test or sensitivity calculations. For use, must also set ACTIVE_VARS = FDTEST. Cost function is model predictions only; no observations (pseudo or real) required. Set X=1 and XSTOP=2 in the run script. Note that this only calculates one column of the model Jacobian, not the full Jacobian matrix. For aerosol attainment sensitivities; no observations (pseudo or real) required. For ozone attainment sensitivities; no observations (pseudo or real) required. Assimilate aerosol observations from IMPROVE data files. Assimilate aerosol observations from CASTNET data files. Use log-scaling factors. Assimilate SCIAMACHY or GOME NO 2 data from KNMI hdf files. If none of these are defined, the default operation is for using pseudo observations. FD_GLOB Perform domain wide finite difference test. Goes with JACOBIAN and ACTIVE_VARS = FDTEST. MAK has defined other modes of operation? 10

11 3.3 Process specific flags Can turn on and off various processes, similar to the forward model flags in input.geos, using the logical flags in CMN ADJ. Invalid combinations of forward and backwards flags will be caught in the ARE_FLAGS_VALID subroutine in geos chem mod.f. For example, you can t have chemistry without dry deposition, as dry deposition rates are necessary for chemistry. Also, for turning chemistry on and off, use LADJ_CHEM flag in CMN ADJ rather than the LCHEM flag in input.geos. 4 Subroutines that get edited frequently 4.1 SUBROUTINE SET ICS This routine sets scaling factors at the beginning of the run. If FWD_RUN_TYPE = REFERENCE, then these are the scaling factors used to generate pseudo observations. If FWD_RUN_TYPE= PERTURBED, then these scaling factors are the initial guesses. For inverse model tests using pseudo observations, we usually set the initial guess of scaling factors to be some value other than one (or zero for LOG_OPT) and then try to converge to values of one (zero). For real data assimilation problems or attainment studies, we begin with our best estimate, i.e. scaling factors equal to one (zero), and converge to values that lead to best agreement with observations. 4.2 SUBROUTINE INIT WEIGHT This subroutine is used to specify the domain over which observations are included in the cost function for the JACOBIAN, ATTAINMENT, or pseudo observation model runs. 4.3 SUBROUTINE RESCALE ADJOINT This subroutine also regularizes the cost function via inclusion of a priori constraints. Parameters of note: REG_EMS REG_PARAM Uncertainty of the emissions A weighting factor (γ) that determines the overall weight of the a priori constraints 11

12 5 Directories and output files 5.1 Directories The adjoint code package ADJvXX [foo] contains the following directories dkh gc adj run.v geo3 adjtmp tmp run.v /optdata Code directory Run directory Adjoint temporary file directory (gctm.chk.*; gctm.obs.*; gctm.save.*; gctm.adj.*; aero.ave.*; satave.*; jsave.* ) Forward model temporary file directory (unzipped met fields) Results from each iteration (gctm.gdt.*; cfn.*; gctm.ics.*, fwd dat.*.tar; gctm.arr) 5.2 Output files See Sect. 5.1 for locations. All are binary bunch files unless otherwise noted. Note: files that don t have an iteration token in their name will be overwritten or removed at each iteration. Exceptions are aero.ave* and satave* files, which are lumped into fwd dat.*.tar files after each iteration, see the run script. 12

13 5.2.1 Essential output files adjtmp/gctm*.chk.* OptData/gctm.gdt.NN OptData/gctm.ics.NN OptData/cfn.NN Checkpoint files. Generated during the forward run; deleted after they are used in the backward run (although the L_DEL_CHECKPT flag in CMN ADJ allows you to not delete them if desired). See checkpt mod.f for more details on content. Gradients of active parameters at each iteration NN (IJ-GDE-$). These gradients are semi-normalized. To include fully-normalized gradients (IJ-GDEN$ for diagnostic purposes), set L_WRITE_GDEN =.TRUE. at the top of the rountine MAKE_GDT_FILE. Also included are emissions sensitivities, DEMISRR, DEMISRRB, DBIOFUEL, and DBURNEMI. Scaling factors at each iteration NN. The scaled emissions themselves at each iteration are also included in this file for diagnostic purposes. Hence, the a priori estimates of emissions will be found in gctm.ics.01, optimized emissions found in gctm.ics.10, etc. The scaling factors are IJ-EMS-$ and the emissions themselves are IJ-EM0-$. For attainment studies, emissions as a percentage in the US are IJ-EMP-$. Emissions from EMISRR, EMISRRB, BIOFUEL, and BURNEMI. Cost function at each iteration NN. ASCII 13

14 5.2.2 Nonessential output files adjtmp/satave.bpch adjtmp/gctm.adj.yyyymmdd.hhmmss Adjoint state variables (λ c ). Purely diagnostic; only written if LADJ_TRAJ = T (in CMN ADJ ) and ITS_TIME_FOR_OBS. The number of these files kept can be controlled using the REMOVE_ADJ_FILE routine (defunct, need to fix!) in adjoint mod.f and the N_ADJ_KEEP parameter in CMN ADJ. Can be saved as sensitivities with respect to concentrations or concentration scaling factors, see MAKE_ADJ_FILE in adjoint mod.f. adjtmp/gctm.obs.yyyymmdd.hhmmss Pseudo observation file. adjtmp/gctm.save.yyyymmdd.hhmmss Diagnostic file. Used for process specific finite difference tests. adjtmp/gctm.save2.yyyymmdd.hhmmss Diagnostic file. Used for process specific second order finite difference tests. Only generated if... adjtmp/aero.ave.yyyymmdd Aerosol data and corresponding model predictions. Generated when running with IMPROVE_OBS or PM_ATTAINMENT options. adjtmp/jsave.yyyymmdd Contributions to cost function. Generated when running with IMPROVE_OBS or ATTAINMENT options. Satellite data and corresponding model predictions for NO2_SAT_OBS. OptData/gctm.gdta.NN Gradients of all parameters at each iteration NN. Only generated if CALL MAKE_GDT_ALL_FILE in inverse.f. OptData/gctm.arr run.v geos3/fwd met run.v geos3/backwd met Integrated reaction rate constant sensitivities. Elements of the forward meteorology in the FD cell. Elements of the backward meteorology in FD cell. Should agree exactly with contents of FWD met. 6 Sensitivity with respect to reaction rate coefficients Currently, sensitivities with respect to the following reaction rate constants are included: 14

15 6.1 Adding new reactions To have the model calculate sensitivity with respect to additional rate constants, the following needs to be updated: Update the total number of active reaction rate constants, NCOEFF in gckpp adj Global.f90. NCOEFF is a the size of the vector JCOEFF, which holds the indicies of the active reaction rate constants. For the new active rate constants, make an entry in gckpp adj Util.f90 for JCOEFF. Define the value of JCOEFF(new index) to be the index of the reaction rate in the KPP generated reaction rate constant vector RCONST. This number can be found in the KPP input file gckpp adj.eqn on left side of each reaction definition. The corresponding SMVGEAR index is on the right side. Add an entry in the mapping array RCONST2RKPP for the new reaction in gckpp adj Util.f90. Make sure that the sensitivity with respect to this rate constant is actually being calculated in the subroutine ros_dadjint in gckpp adj Integrator.f90. The code contains the general formula for calculating discrete sensitivities with respect to reaction rate constants, see Appendix A of (Henze and Seinfeld, 2006). The general formula calculates all elements of (J p (t n, c n ) k i ) T u i and f T p (T i, C i ) u i. However, many of the elements of J p (t n, c n ) k i ) T (DJDR) and f T p (T i, C i ) (DFDR) are actually zero. Automatically exploiting such sparsity will be a future feature of KPP. Until then, we have to enter the non zero elements manually if we want only the sparse calculation. For example, if we would like to calculate the sensitivity of the cost function with respect to the rate constant for the reaction ALD 2 + NO 3 HNO 3 + MCO 3, we would find the following entry for this reaction in the KPP input file gckpp adj.eqn: {40} ALD2 + NO3 = HNO3 + MCO3: RKPP(JLOOP,54); If NCOEFF was previously 8, then we would set NCOEFF = 9 in gckpp adj Global.f90. gckpp adj Util.f90, in the subroutine INIT_KPP we would add the following lines: JCOEFF(9) = 40 RCONST2RRATE(40) = 54! ALD2 + NO3 --> HNO3 + MCO3 As mentioned above, in the routine ros_dadjint in gckpp adj Integrator.f90, these sensitivities can be calculated using the general formula, or one could implement the sparse formula: CASE(9)! f_r(y) * u j = ind_ald2 In 15

16 V_P(vpstart+icoeff,m) = DFDR(NVAR*(icoeff-1)+j)*U(istart+j-1,m) j = ind_no3 V_P(vpstart+icoeff,m) = V_P(vpstart+icoeff,m) + DFDR(NVAR*(icoeff-1)+j)*U(istart+j-1,m) j = ind_hno3 V_P(vpstart+icoeff,m) = V_P(vpstart+icoeff,m) + DFDR(NVAR*(icoeff-1)+j)*U(istart+j-1,m) j = ind_mco3 V_P(vpstart+icoeff,m) = V_P(vpstart+icoeff,m) + DFDR(NVAR*(icoeff-1)+j)*U(istart+j-1,m)! ( J_r x k )^T * u j = ind_ald2 V_P(vpstart+icoeff,m) = V_P(vpstart+icoeff,m) + DJDR(NVAR*(icoeff-1)+j)*U(istart+j-1,m) j = ind_no3 V_P(vpstart+icoeff,m) = V_P(vpstart+icoeff,m) + DJDR(NVAR*(icoeff-1)+j)*U(istart+j-1,m) j = ind_hno3 V_P(vpstart+icoeff,m) = V_P(vpstart+icoeff,m) + DJDR(NVAR*(icoeff-1)+j)*U(istart+j-1,m) j = ind_mco3 V_P(vpstart+icoeff,m) = V_P(vpstart+icoeff,m) + DJDR(NVAR*(icoeff-1)+j)*U(istart+j-1,m) 6.2 Saving reaction rate sensitivities The subroutine SAVE_INST_ARR can be used to print out reaction rate sensitivities in a particular cell at every time step. This routine also calls the routine MAKE_ARR_FILE which writes the integrated sensitivities globally to a binary punchfile, gctm.arr. 7 Validating code. The adjoint of GEOS-Chem is designed to be validated in several manners. 7.1 Global tests of a subset of the adjoint model By turning off multidirectional transport related processes, the adjoint model sensitivities can be compared to finite difference sensitivities on a global scale, see Fig. 1 and 3 of Henze and Seinfeld (2006). For example, to check the adjoint of the chemistry only in a single vertical level, set the following: in run: 16

17 X=1 XSTOP=3 in CMN ADJ : JACOBIAN FD_GLOB ACTIVE_VARS = FDTEST select a dependent species, NFD select a vertical level, LFD select a control parameter, EMSFD IFD and JFD don t matter as we re doing a domain wide test set the finite difference perturbation (δσ), FD_DIFF = 1.d-1 set the background values of σ to one, FD_PERT = 1.d0 and FD_BKGRND = 1.d0 Make sure that OBS_FREQ is set long enough so that the cost function is only evaluated once during the simulation. Set LADJ_TRAN =.FALSE. Set LAERO_THERM =.FALSE. in input.geos: Turn off convection ( LCONV = F ) Turn off turbulent mixing ( LTURB = F ) Turn off wet deposition ( LWETD = F ) Leave on dry deposition ( LDRYD = T ) Leave on transport ( LTRAN = T ), which will be overridden by LADJ_TRAN =.FALSE. in chemistry mod.f, only compute chemistry in certain cells by uncommenting lines such as:!if ( L == LFD ) THEN! print*, ONLY DO CHEM IN FD LEVEL!!!!. As of ADJv29, the following setting are triggered automatically setting ACTIVE_VARS = FDTEST and by defining FD_GLOB. For older versions, some of these changes will have to be implemented manually: in chemistry mod.f, reduce emissions (and corresponding adjoints) by an order of magnitude to avoid creating lots of very stiff systems: uncomment the following lines just prior to CALL INTEGRATE_ADJ. To only compute chemistry in the LFD level uncomment the lines: 17

18 !IF ( L == LFD ) THEN! print*, ONLY DO CHEM IN FD LEVEL!!!!! print*, REDUCE emissions! RCONST(231:242) = 0.1d0 * RCONST(231:242) replace ADJ_RRATE(JJLOOP,NREAC) = LAMBDA_P(ICOEFF,NJ,JJLOOP) with ADJ_RRATE(JJLOOP,NREAC) = 0.1d0 * LAMBDA_P(ICOEFF,NJ,JJLOOP) in SUBROUTINE GET_ADJ_RRATE in adjoint mod.f : In SUBROUTINE INIT_WEIGHT set WEIGHT(:,:,LFD,NFD) = 1d0 in inverse mod.f : Apply FD_DIFF globally in SET_ICS_FORFD The results of this test will be written to a *.save2.* file in adjtmp, which will contain one and two-sided finite difference gradients, adjoint gradients, and the ratio of the adjoint gradients to the finite difference gradients. See MAKE_SAVE_FILE_2 in checkpt mod.f for further details. 7.2 Spot tests of full adjoint model Alternatively, we can compare adjoint gradients to finite difference gradients for control parameters one location at a time, but with all model processes turned on. in run: X=1 XSTOP=2 in CMN ADJ : JACOBIAN Make sure that FD_GLOB is undefined. ACTIVE_VARS = FDTEST 18

19 select a dependent species, NFD select particular control parameter IFD JFD LFD and EMSFD set the finite difference perturbation (δσ), FD_DIFF = 1.d-1 set the background values of σ to one, FD_PERT = 1.d0 and FD_BKGRND = 1.d0 probably want to turn on additional diagnostic output, so set L_PRINTFD =.TRUE. Make sure that OBS_FREQ is set long enough so that the cost function is only evaluated once during the simulation. in input.geos: Turn on all desired processes. As of ADJv29, the following setting are triggered automatically setting by undefining FD_GLOB. For older versions, these changes will have to be implemented manually: in adjoint mod.f : In SUBROUTINE INIT_WEIGHT set WEIGHT(IFD,JFD,LFD,NFD) = 1d0 in inverse mod.f : Apply FD_DIFF only in the test cell SET_ICS_FORFD The adjoint and finite difference gradients and the ratio ADJ / FD will be written to standard output at the end of the run. The reported adjoint gradient is actually the average of the values at σ = 1 and σ = 1 + δσ. Since such tests involve the continuous adjoint of advection, the ratio ADJ / FD can not be expected to be unity. Benchmark tests are given in (Henze and Seinfeld, 2006). 7.3 Box model adjoint chemistry tests It can also be informative to check the performance of the chemistry adjoint calculations in a single cell, particularly when considering new reactions, or sensitivities with respect to additional reaction rates (see Sect. 6). Currently, the routine GCKPP_FD_DRIVER is set up to test sensitivities with respect to reaction rates, and it is straightforward to modify it to test sensitivities with respect to initial conditions. The following is a brief lists of things to consider with using this routine. Check the comments in the code itself for further details. 19

20 Select the desired location for testing chemistry by defining IFD,JFD, and LFD in CMN_ADJ. The routine is called from within chem adj.f. Comment out the standard call to GCKPP_DRIVER. Uncomment the call to GCKPP_FD_DRIVER. If you wish to analyze chemistry at some time other than NYMDb, NHMSb then use the code provided for calling the standard chemistry routine when the local time is within a desired range. Within the routine GCKPP_FD_DRIVER set the following: If GCKPP_DRIVER will have been called prior to calling GCKPP_FD_DRIVER, then call the initialization routine INIT_ADJ_ANTHROEMS. Otherwise, also call INIT_KPP and INIT_SMV2KPP. Control parameter to be tested, currently NNREAC. The internal step size (in 3 places!) Select either first or second order finite difference tests. Select the perturbation (δσ) size. The main results are written to standard out as a list of species names, adjoint and finite difference sensitivities. These comparisons are reported here for only the diagonal of the Jacobian. 8 Generating forward and reverse code for GEOS-Chem with the Kinetic PreProcessor (KPP) (Damian et al., 2002; Sandu et al., 2003; Daescu et al., 2003) 20

21 8.1 KPP input files 8.2 Post processing KPP generated code Interfacing KPP code with GEOS-Chem Implementing OpenMP Parallelization in KPP generated code 8.3 Performing global benchmarks of new chemical solvers References Daescu, D. N., A. Sandu, and G. R. Carmichael (2003), Direct and adjoint sensitivity analysis of chemical kinetic systems with KPP: II - numerical validation and applications, Atmos. Environ., 37 (36), Damian, V., A. Sandu, M. Damian, F. Potra, and G. R. Carmichael (2002), The kinetic preprocessor KPP - a software environment for solving chemical kinetics, Comput. Chem. Eng., 26 (11), Henze, D. K., and J. H. Seinfeld (2006), Development of the adjoint of GEOS-Chem, Atmos. Chem. Phys. Discuss., 6, 10,591 10,648. Sandu, A., D. N. Daescu, and G. R. Carmichael (2003), Direct and adjoint sensitivity analysis of chemical kinetic systems with KPP: Part I - theory and software tools, Atmos. Environ., 37 (36),