Chemistry Working Group: Difference between revisions
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Revision as of 16:00, 1 June 2017
Chemistry Working Group
All users interested in the GEOS-Chem chemistry scheme and associated processes (photolysis, heterogeneous, deposition) are encouraged to subscribe to the chemistry email list (click on the link in the contact information section below).
Contact information
Oxidants and Chemistry Working Group Co-Chairs | |
---|---|
Oxidants and Chemistry Working Group email list | geos-chem-oxidants [at] g.harvard.edu |
To subscribe to email list | Either
Or
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To unsubscribe from email list | Either
Or
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--Bob Y. (talk) 18:29, 21 August 2015 (UTC)
Current GEOS-Chem Chemistry Projects (please add yours!)
User Group | Description | Contact Person | Date Added |
---|---|---|---|
NIA / LaRC | Tropospheric ozone over East Asia: Ozonesonde observations and modeling analysis | Hongyu Liu | 5 May 2015 |
MIT | Exploring the impact of monoterpene and aromatic chemistry on ozone and OH reactivity | Will Porter | 12 April 2017 |
MIT | Simulating the global reactive carbon budget | Sarah Safieddine | 12 April 2017 |
University of York | Halogen chemistry | Tomas Sherwen | 12 April 2017 |
University of York | Isoprene over Borneo | Shani Garraway | 12 April 2017 |
University of York | Impacts of uncertainty in chemical kinetics | Ben Newsome | 12 April 2017 |
University of York | Impacts of resolution in GEOS-Chem | Ben Newsome | 12 April 2017 |
University of York | Updates to the kinetics of Criegee chemistry based on new chamber experiments | Mat Evans | 12 April 2017 |
University of Wollongong | Simulation of small (methyl, ethyl, propyl) alkyl nitrates in GEOS-Chem | Jenny Fisher | 12 April 2017 |
Harvard University | Halogen extension to include explicit phase partitioning and mass transfer | Sebastian D. Eastham | 12 April 2017 |
US EPA | Alkane chemistry and product yields as a function of temperature/pressure. | Barron H. Henderson | 4 May 2017 |
US EPA | Carbon and Nitrogen Balance and checking software. | Barron H. Henderson | 4 May 2017 |
US EPA | Update DSMACC for v11 GEOS-Chem Chemistry and Emissions to facilitate chemical experiments | Barron H. Henderson | 4 May 2017 |
FSU | Stratosphere-troposphere coupling, improvements to UCX & H2 chemistry | Chris Holmes | May 2017 |
FSU | Methane and methyl chloroform lifetimes | Chris Holmes | May 2017 |
FSU | Arctic halogen & ozone chemistry | Chris Holmes | May 2017 |
--Bob Y. 15:08, 25 April 2014 (EDT)
Current GEOS-Chem Chemistry Issues (please add yours!)
Carbon balance
Script for evaluating carbon balance
Barron Henderson wrote:
[I created] an evaluation script to preserve balances going forward as the mechanism evolves (e.g., as isoprene gets updated).
Currently, this done using an off-line script described in a linked note. The approach is pretty straight-forward, but could be expanded to check conservation of functional groups as suggested by Mat.
Longer term, the same technique would ideally be built-in to the standard KPP as an optional report. I discussed it with Michael Long and we both think that KPP has most of the capability for atom conservation (if not all). It may simply be a matter of defining the chemical formulas in the *.spc file.
--Melissa Sulprizio (talk) 21:06, 22 May 2017 (UTC)
Fixes for carbon creating reactions
These fixes will be included in v11-02c.
Sarah Safieddine wrote:
Colette, Barron, Mat and myself modified 13 previous "carbon creating" reactions to preserve carbon. The [table below] lists all the corrections for the reactions in globchem.dat V902 that we corrected, with all the details.
Reaction # in globchem.dat v9-02 | Unbalanced Reaction | Rate constant | Issue (R=Reactants, P=Products) |
Fix and corrected reaction (in green) |
---|---|---|---|---|
453 | R4O2 + NO → NO2 + 0.32ACET + 0.19MEK + 0.18MO2 + 0.27HO2 + 0.32ALD2 + 0.13RCHO + 0.05A3O2 + 0.18B3O2 + 0.32ETO2 | K* (1-YN) where YN is returned from fyrno3.f; K=2.7E-12 exp(350/T) (Xcarbn=4.5) | Creates carbon: R=4C P=4.26C | Replace 0.18B3O2 by 0.093B3O2 to achieve carbon closure (as suggested by Barron). R4O2 + NO → NO2 + 0.32ACET + 0.19MEK + 0.18MO2 + 0.27HO2 + 0.32ALD2 + 0.13RCHO + 0.05A3O2 + 0.093B3O2 + 0.32ETO2 |
453 | R4N1 + NO → 2NO2 + 0.39CH2O + 0.75ALD2 + 0.57RCHO + 0.3R4O2 | 2.7E-12 exp(350/T) | Creates carbon: R=4C, P=4.8C | Fix, as suggested by Matt: R4N1 + NO → 2NO2 + 0.570RCHO + 0.86ALD2 + 0.57CH2O |
453 | ATO2 + NO → 0.96NO2 + 0.96CH2O + 0.96MCO3 + 0.04R4N2 | 2.8E-12 exp(300/T) | Creates carbon: R=3C, P=3.04 | Fix as suggested by Mat: ditch the R4N2 channel ATO2 + NO → NO2 + CH2O + MCO3 |
803 | RIO2 → 2HO2 + CH2O + 0.5MGLY + 0.5GLYC + 0.5GLYX + 0.5GLYX + 0.5HAC + OH | 4.07E+08 exp(-7694/T) | Creates carbon: R=5C, P=7C There was a fix proposed on the isoprene scheme wiki page but still not enough |
Fix as suggested by Sarah: remove CH2O RIO2 → 2HO2 + 0.5MGLY + 0.5GLYC + 0.5GLYX + 0.5HAC + OH |
453 | ISNOOB + NO3 → R4N2 + GLYX + 2NO2 | 2.3E-12 | Creates carbon: R=5C, P=6C | Fix as suggested by Barron: Replace R4N2 by PROPNN ISNOOB + NO3 → PROPNN + GLYX + 2NO2 |
453 | ISNOOB+NO→0.94R4N2 +0.94GLYX +1.88NO2 | 2.6E-12 exp(380/T) | Creates carbon: R=5C, P=5.64C | Same as above ISNOOB + NO → 0.06R4N2 + '0.94PROPNN' + 0.94GLYX + 1.88NO2 |
453 | ISNOHOO + NO → 0.934R4N2 + 0.934HO2 + 0.919GLYX | 2.6E-12 exp(380/T) | Creates carbon: R=5C, P=5.574C | Fix by Barron: ISNOHOO + NO → 0.081R4N2 + 0.919PROPNN + 0.934HO2 + 0.919GLYX |
472 | MAN2 + HO2 → 0.075PROPNN + 0.075CO + 0.075HO2 + 0.075MGLY + 0.075CH2O + 0.075NO2 + 0.15OH + 0.85ISNP | 2.91E-13*exp(1300/T)[1-exp(-0.245*n)],n=4 | Creates carbon: R=4C, P=4.85C | Fix by both Mat and Barron: Replace ISNP with 0.85MAOP + 0.85NO2 MAN2 + HO2 → 0.075PROPNN + 0.075CO + 0.075HO2 + 0.075MGLY + 0.075CH2O + 0.075NO2 + 0.15OH + 0.85MAOP + 0.85NO2 |
719 | ATO2 + MCO3 → MEK + ACTA | 1.87E-13 exp(500/T) | Creates carbon: R=5C, P=6C | From the WIKI: replace MEK with MGLY ATO2 + MCO3 → MGLY + ACTA |
817 | Br + ALD2 → HBr + MCO3 + CO | 1.3E-11 exp(-360/T) | Creates carbon: R=2C, P=3C | Remove CO Following Parrella et al., Table 2a, reactions R7 to R10 (also for the 3 reactions below) Br + ALD2 → HBr + MCO3 |
818 | Br + ACET → HBr + ATO2 + CO | 1.66E-10exp(-7000/T) | Creates carbon: R=3C, P=4C | Remove CO, same as above Br + ACET → HBr + ATO2 |
819 | Br + C2H6 → HBr + ETO2 + CO | 2.36E-10 exp(-6411/T) | Creates carbon: R=2C, P=3C | Remove CO, same as above Br + C2H6 → HBr + ETO2 |
820 | Br + C3H8 → HBr + A3O2 + CO | 8.77E-11 exp(-4330/T) | Creates carbon: R=3C, P=4C | Remove CO, same as above Br + C3H8 → HBr + A3O2 |
--Melissa Sulprizio (talk) 20:51, 22 May 2017 (UTC)
Identification of carbon leaking reactions
Sarah Safieddine wrote:
76 other reactions leaked carbon, we enforced carbon conservation by tracking the lost carbon as CO2 (labeled as {CO2} in the document ROC_SI.docx, Table 2). This is the supplementary material for Safieddine, Heald and Henderson, 2017. It contains the corrections for both the carbon leaking and carbon creating reactions and all other information. The paper for reference can be found here: http://onlinelibrary.wiley.com/doi/10.1002/2017GL072602/abstract.
--Melissa Sulprizio (talk) 21:06, 22 May 2017 (UTC)
Fixes to correct ALK4 lumping issue
These fixes were included in v11-02a and approved on 12 May 2017.
Barron Henderson wrote:
I have a lumping-related issue that I know some of you are already aware of. There is a chemical carbon source (and secondary ETO2 source).
Right now, ALK4 (via R4O2) produces 4.26 moles carbon products per reaction. The ALK4 representation can be traced back to a paper by Frederick Lurmann. That paper refers to a report that I have been unable to obtain. In fact, Frederick Lurmann no longer has a copy. When we spoke, however, he confirmed my suspicion that ALK4 is based on a 70% butane and 30% pentane mixture. Our 4.26 carbon product appears to be based on two differences (typos?) from the paper that alter the yields.
If ALK4 emissions are introduced using a 4C assumption, then ALK4 chemistry is acting as a 7% carbon source. From a ozone reactivity standpoint, this is not a major issue. First, the speciation of VOC is highly uncertain and most of the atmosphere is NOx-limited. Even so, it represents another reason to revisit our lumped species.
I have extensive notes on what I interpret as happening. To the best of my knowledge, we need to make three modifications to R4O2 + NO. The first two are to make R4O2 correctly linked to Lurmann and the third is to correctly connect the mass emissions with the molar conservation.
- Increase MO2 stoichiometry from 0.18 to 0.19
- Increase RCHO stoichiometry from 0.13 to 0.14 (or A3O2 from 0.05 to 0.06 -- it is not clear to me when this was introduced).
- Modify the carbon count for ALK4 (i.e. the MolecRatio field in the GEOS-Chem species database) from 4 to 4.3.
Fixes 1 and 2—which can be applied to the KPP globchem.eqn file—will make the carbon conservation consistent with Lurmann's. Right now, it looks like there were a couple changes that could have been inadvertent (i.e., 0.18 instead of 0.19). If there was a reason for these changes, I have been unable to find it.
--Bob Yantosca (talk) 20:21, 31 January 2017 (UTC)
JPL Released 18th Rate Coefficient Evaluation
This update was included in v11-02a and approved on 12 May 2017.
JPL has released its 18th evaluation of chemical rate coefficients for atmospheric studies (Burkholder et al., 2015)." A new page (Updates in JPL Publication 15-10) is being created to compare rates between GEOS-Chem v10 and JPL Publication 15-10.
- J. B. Burkholder, S. P. Sander, J. Abbatt, J. R. Barker, R. E. Huie, C. E. Kolb, M. J. Kurylo, V. L. Orkin, D. M. Wilmouth, and P. H. Wine "Chemical Kinetics and Photochemical Data for Use in Atmospheric Studies, Evaluation No. 18," JPL Publication 15-10, Jet Propulsion Laboratory, Pasadena, 2015 http://jpldataeval.jpl.nasa.gov.
---B. Henderson 2016-05-03 15:25 (EDT)
Working Group Tele-con on the 2nd December 2011
Isoprene chemistry
I've created a page with some of the recent literature on isoprene chemistry. Please add more papers as they come along! ( MJE Leeds)
HO2 + CH2O
Scheme does not contain the HO2 + CH2O --> Adduct reaction (MJE Leeds)
Hermans, I., et al. (2005), Kinetics of alpha-hydroxy-alkylperoxyl radicals in oxidation processes. HO2 center dot-initiated oxidation of ketones/aldehydes near the tropopause, Journal of Physical Chemistry A, 109(19), 4303-4311.
According to this paper, this reaction is significant when Temperature is below 220K.
--J Mao. 15:00, 10 Aug 2009 (EDT)
Previous issues that have now been resolved
Centralizing chemistry time step
This update was tested in the 1-month benchmark simulation v9-01-02q and approved on 18 Oct 2011.
Please see the full discussion on the Centralized chemistry time step wiki page.
--Bob Y. 16:01, 4 November 2011 (EDT)
Acetone photolysis
This discussion has been moved to our FAST-J photolysis mechanism wiki page.
--Bob Y. 15:20, 20 May 2014 (EDT)
Issues that have been since rendered obsolete by newer code updates
Most of the issues described below pertained to the SMVGEAR chemical solver (which was replaced by FlexChem in v11-01) and/or the FAST-J photolysis mechanism (which was replaced by FAST-JX in v10-01).
NIT should be converted to molec/cm3 in calcrate.F
SMVGEAR was removed from GEOS-Chem v11-01 and higher versions. The code in calcrate.F will be replaced by the KPP master equation file.
In calcrate.F, we have:
! Nitrate effect; reduce the gamma on nitrate by a ! factor of 10 (lzh, 10/25/2011) IF ( N == 8 ) THEN TMP1 = State_Chm%Tracers(IX,IY,IZ,IDTSO4) + & State_Chm%Tracers(IX,IY,IZ,IDTNIT) TMP2 = State_Chm%tracers(IX,IY,IZ,IDTNIT) IF ( TMP1 .GT. 0.0 ) THEN XSTKCF = XSTKCF * ( 1.0e+0_fp - 0.9e+0_fp & *TMP2/TMP1 ) ENDIF ENDIF
Here NIT is added to SO4 but NIT is in different units than SO4. This unit difference can be traced to the definition of IDTRMB, which is only nonzero for species that are in the SMVGEAR mechanism. Since NIT is not a SMVGEAR species, IDTRMB = 0 for NIT and it is therefore skipped in the unit conversion from kg --> molec/cm3 in partition.F.
This issue was discovered during the implementation of FlexChem. In GEOS-Chem v11-01g and later versions, units of NIT are properly accounted for in routine HETN2O5 (found in gckpp_HetRates.F90).
--Melissa Sulprizio (talk) 20:25, 12 September 2016 (UTC)
--Bob Yantosca (talk) 20:27, 31 January 2017 (UTC)
rate of HNO4
SMVGEAR was removed from GEOS-Chem v11-01 and higher versions. The globchem.dat file is now replaced by the KPP master equation file.
Ellie Browne found a typo in the globchem.dat (GEOS-Chem v8-02-01 and beyond)
A 73 9.52E-05 3.2E+00 -10900 1 P 0.60 0. 0. 1.38E+15 1.4E+00 -10900 0 0.00 0. 0. HNO4 + M =1.000HO2 +1.000NO2 + +
This should be corrected as:
A 73 9.52E-05 3.4E+00 -10900 1 P 0.60 0. 0. 1.38E+15 1.1E+00 -10900 0 0.00 0. 0. HNO4 + M =1.000HO2 +1.000NO2 + +
The difference is within 2%.
--J Mao. 19:04, 30 Aug 2010 (EDT)
--Bob Yantosca (talk) 20:29, 31 January 2017 (UTC)
near-IR photolysis of HNO4
This update was added to GEOS-Chem v8-02-04.
SMVGEAR was removed from GEOS-Chem v11-01 and higher versions. The globchem.dat file is now replaced by the KPP master equation file. Also, FAST-JX has now replaced FAST-J photolysis.
1. Since FastJX already takes this into account with cross section data at 574nm, we do not need to redo this in calcrate.f. We can therefore comment out this entire IF block:
!--------------------------------------------------------------------- ! Prior to 10/27/09: ! FastJX has taken near-IR photolysis into account with ! cross section at 574nm, so we don't need to add 1e-5 anymore. ! According to Jimenez et al., "Quantum yields of OH, HO2 and ! NO3 in the UV photolysis of HO2NO2", PCCP, 2005, we also ! changed the branch ratio from 0.67(HO2)/0.33(OH) to 0.95/0.05 ! This will put most weight of near-IR photolysis on HO2 channel. ! (jmao, bmy, 10/27/09) ! !!============================================================== !! HARDWIRE addition of 1e-5 s-1 photolysis rate to !! HNO4 -> HO2+NO2 to account for HNO4 photolysis in near-IR -- !! see Roehl et al. 'Photodissociation of peroxynitric acid in !! the near-IR', 2002. (amf, bmy, 1/7/02) !! !! Add NCS index to NKHNO4 for SMVGEAR II (gcc, bmy, 4/1/03) !!============================================================== !IF ( NKHNO4(NCS) > 0 ) THEN ! ! ! Put J(HNO4) in correct spot for SMVGEAR II ! PHOTVAL = NKHNO4(NCS) - NRATES(NCS) ! NKN = NKNPHOTRT(PHOTVAL,NCS) ! ! DO KLOOP=1,KTLOOP ! RRATE(KLOOP,NKN)=RRATE(KLOOP,NKN) + 1d-5 ! ENDDO !ENDIF !---------------------------------------------------------------------
2. We need to change the branch ratio of HNO4 photolysis in ratj.d. Change these lines from:
13 HNO4 PHOTON OH NO3 0.00E+00 0.00 33.3 HO2NO2 14 HNO4 PHOTON HO2 NO2 0.00E+00 0.00 66.7 HO2NO2
to:
13 HNO4 PHOTON OH NO3 0.00E+00 0.00 5.0 HO2NO2 14 HNO4 PHOTON HO2 NO2 0.00E+00 0.00 95.0 HO2NO2
This is based on Jimenez et al. (Quantum yields of OH, HO2 and NO3 in the UV photolysis of HO2NO2, PHYSICAL CHEMISTRY CHEMICAL PHYSICS, 2005) shows that HO2 yield should be 0.95 and OH yield should be 0.05 for wavelength above 290nm.
This way all the near-IR photolysis will have most weight on HO2 channel(Stark et al., Overtone dissociation of peroxynitric acid (HO2NO2): Absorption cross sections and photolysis products, JOURNAL OF PHYSICAL CHEMISTRY A, 2008).
This update has now been added to the chemistry mechanism documentation file.
--J Mao. 11:00, 26 Oct 2009 (EDT)
--Bob Y. 16:08, 4 November 2011 (EDT)
yield of isoprene nitrates
This update was added to GEOS-Chem v8-03-02 as a post-release patch, and standardized in GEOS-Chem v9-01-01.
SMVGEAR was removed from GEOS-Chem v11-01 and higher versions. The globchem.dat file is now replaced by the KPP master equation file.
Fabien Paulot found a problem in current chemistry scheme. In GEOS-Chem v8-02-01 and beyond, isoprene nitrates are produced twice: one through channel A and one through 10% loss in channel B. This makes the loss of NOx larger than it should be (18.7% vs. 10%) and also reduces the yield of MVK/MACR/CH2O by about 13%.
A 453 2.70E-12 0.0E+00 350 1 B 0.00 0. 0. 5.00E+00 0.0E+00 0 0 0.00 0. 0. RIO2 + NO =0.900NO2 +0.900HO2 +0.340IALD +0.340MVK +0.220MACR +0.560CH2O + + A 453 2.70E-12 0.0E+00 350 1 A 0.00 0. 0. 5.00E+00 0.0E+00 0 0 0.00 0. 0. RIO2 + NO =1.000HNO3 + + +
So it should be corrected as (no channel A):
A 453 2.70E-12 0.0E+00 350 0 0 0.00 0. 0. RIO2 + NO =0.900NO2 +0.900HO2 +0.340IALD +0.340MVK +0.220MACR +0.560CH2O + + D 453 2.70E-12 0.0E+00 350 1 A 0.00 0. 0. 5.00E+00 0.0E+00 0 0 0.00 0. 0. RIO2 + NO =1.000HNO3 + + +
--J Mao. 18:04, 30 Aug 2010 (EDT)
--Bob Yantosca (talk) 20:31, 31 January 2017 (UTC)
Potential issue with reading restart.cspec file
This update was tested in the 1-month benchmark simulation v9-01-02c and approved on 21 Jul 2011.
The binary-punch format restart.cspec.YYYYMMDDhh file is slated to be replaced by a netCDF-format restart file, starting in GEOS-Chem v11-01 and higher versions. But during a transition period, you can still request binary-punch format output.
Jingqiu Mao discovered a mis-indexing problem when using the restart.cspec.YYYYMMDDhh file. Please see this wiki post for more information.
--Bob Y. 16:02, 4 November 2011 (EDT)
--Bob Yantosca (talk) 20:33, 31 January 2017 (UTC)
GLCO3, GLPAN bug in standard mechanism
This update was tested in the 1-month benchmark simulation v9-01-03a and approved on 08 Dec 2011.
SMVGEAR was removed from GEOS-Chem v11-01 and higher versions. The globchem.dat file is now replaced by the KPP master equation file.
Fabien Paulot wrote:
- I think there is a relatively serious bug in the standard chemistry. GLPAN and GLCO3 are set to inactive but their production and loss reactions are active. As a result they never reach equilibrium and this results in an artificial loss of NOx.
- If this is the only cause of the imbalance between sources and sinks of NOx in my simulations, this would account for ~5% of NOy losses. I don't see that problem in a simulation with a different chemistry that among other changes does not feature those reactions. So hopefully that's it.
- To fix the error, I made the following modifications in globchem.dat:
- I set GLPAN and GLCO3 rxns from active to dead. These rxns were causing an artificial loss of NOx.
- I have physically removed GLCO3, GLP, GLPAN, GPAN, ISNO3, MNO3, O2CH2OH, MVN2 and their associated reactions.
- I have made GLYX active. I'm not sure why it's not active by default.
- and to ratj.d:
- I deleted photolysis reactions for MNO3 and GLP, since these species have also now been deleted in globchem.dat
--Bob Y. 14:51, 10 November 2011 (EST)
--Melissa Payer 10:49, 15 December 2011 (EST)
--Bob Yantosca (talk) 20:35, 31 January 2017 (UTC)
Bug in routine ARSL1K
This update was tested in the 1-month benchmark simulation v9-01-03m and approved on 06 Jun 2012.
SMVGEAR was removed from GEOS-Chem v11-01 and higher versions. The ARSL1K routine was replaced by an equivalent function in KPP's rate law library.
A bug in routine ARSL1K became problematic in the implementation of Justin Parrella's tropospheric bromine chemistry mechanism for GEOS-Chem v9-01-03. In the bromine chemistry mechanism, a sticking coefficient of 0.0 is passed to the routine ARSL1K for non-sulfate, non-sea salt aerosol. The IF statement modified in GEOS-Chem v8-02-04 resulted in the reaction rate being set to the default value of 1.0d-3. A 1-month benchmark for July 2005 indicated that the simulated BrO was a little more than twice the expected zonal mean. Modifying the default value from 1.0d-3 to 1.0d-30 resulted in reasonable simulated BrO values.
Mat Evans wrote:
- I've re-run two 2 month simulation [using GEOS-Chem v9-01-02]. One with the error handling value of 1e-3 (standard) and one with it being 1e-30. There are 5127 time and space points where the model traps the problem and invokes the 1e-3 or 1e-30 value. There are 30*24*2*37*72*46 (roughly 200 million) time and space points when the error could have occurred so we are looking at a relatively infrequent event.
- The simulations show virtually no difference between the two simulations.
- mean and stddev ratio of all grid boxes with and without the fix are shown below
NOx 0.999996 0.000409291 Ox 1.00000 1.27233e-05 O3 1.00000 1.52284e-05 PAN 0.997849 0.0111997 CO 1.00000 4.21768e-06 ALK4 0.990514 0.0351941 ISOP 0.999979 0.0108033 H2O2 0.992067 0.0264659 DST1 1.00000 0.00000 HO2 0.999996 0.00309464 OH 1.00003 0.00767954
- So although there are some differences they are very minor. For completeness we should put this in as a bug fix (make the error value 1d-30 rather than 1d-3). But it is not a major problem.
--Melissa Payer 17:52, 14 May 2012 (EDT)
--Bob Yantosca (talk) 20:35, 31 January 2017 (UTC)
Documentation
- Updated chemical reactions that will be used in GEOS-Chem v8-02-04 and higher.
- Updated chemical reactions now used in GEOS-Chem v8-02-01 through GEOS-Chem v8-02-03.
- All typos have now been corrected in the present file.
- Format of FAST-J input file jv_spec.dat
--Bob Y. 15:41, 27 October 2009 (EDT)