AQCHEM_NOTES - 13 January 2010

Solver Stability

   Several problems in the aqueous chemistry routine were uncovered in the
   application of the CMAQv4.7 multipollutant model.  In some instances,
   sporadic abnormally high sulfate concentrations were simulated (>400 ug/m3);
   in general, the noted abnormalities were episodic and variable. The aqueous
   chemistry subroutine in the multipollutant model includes new reactions with
   the hydroxyl radical to convert mercury (Hg) covalence states and to produce
   “cloud SOA” (Carlton et al., (2008)). These reaction rate constants are very
   fast ~ 1.E10 (L/mol/sec) compared to other reactions in the CMAQ aqueous
   mechanism, (e.g., ~1.E4 for S(IV) oxidation by H2O2). The stiffness resulting
   from coupling of faster and slower processes can lead to numerical
   instabilities in the forward Euler solver (i.e., the solver employed by
   aqchem.F for oxidation reactions).

   Several changes have been made to address the deficiencies in the aqueous
   chemistry solver. More precision was added to select variables to improve the
   accuracy of the calculations. Tests demonstrated that mass was not being
   conserved for species produced via aqueous phase oxidation reactions during
   the last chemistry integration step. This issue is only important
   episodically, when the maximum number of iterations (100) in the solver is
   reached (in which case the timestep for the final iteration is expanded to
   the remainder of the cloud lifetime. A design change was implemented so that
   now, after reaching 100 iterations, the solver will continue to integrate
   using a minimum 1 second timestep for the remainder of the cloud lifetime.
   Mass is conserved in the later part of the cloud lifetime, as total mass
   available is a limit for the oxidized amount. With this change, the mass
   conservation problems were eliminated.

   Considering that the aqueous chemistry routine was designed to predict
   sulfate and not stiff OH-reacting mechanisms, a further design change was
   implemented. Previously, OH reactions of glyoxal and methylglyoxal and Hg
   (for the multipollutant model) controlled the time step of oxidation
   reactions. Now only the sulfur reactions affect dt. In CMAQ’s gas phase, OH
   is assumed to be in pseudo-steady state, and it is not a transported species.
   This is because hydroxyl radical reactions tend to be catalytic (e.g.,
   consumption and production). In the aqueous phase chemistry, OH is absorbed
   by cloud water and in an open cloud model (i.e., the design approach
   currently employed), absorbed species (e.g., OH) would be replenished via
   gas-to-cloud partitioning. However, due to operator splitting, aqueous and
   gas-phase chemistry are not solved simultaneously. To account for this and
   other uncertainties in predicted OH aqueous phase concentrations (e.g.,
   neglect of production reactions (H2O2 + hv -> 2 OH) not currently implemented
   in aqchem), a steady-state assumption for OH is adopted in the aqueous
   chemistry routine.

   References:

    Carlton, A.G., B.J. Turpin, K.E. Altieri, S.P. Seitzinger, R. Mathur,
       S.J. Roselle, and R.J. Weber, CMAQ Model Performance Enhanced When
       In-Cloud Secondary Organic Aerosol is Included:  Comparison of Organic
       Carbon Predictions with Measurements, Environ. Sci. Technol., 42(23),
       8798-8802, 2008.