Rahul A' Zaveri, Richard C' Easter, Jerome D' Fast

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An Efficient Algorithm for Dynamic Gas-Particle
Partitioning In MOSAIC

• Rahul A. Zaveri, Richard C. Easter, Jerome D.
  Fast
• Pacific Northwest National Laboratory, Richland,
  WA
• Leonard K. Peters
• Battelle, Columbus, OH

International Aerosol Modeling Algorithms
Conference University of California,
Davis December 6, 2007
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MOSAIC Model for Simulating Aerosol Interactions
and Chemistry

• Treats key gas aerosol components
• Comprehensive gas chemistry
• Accurate particle thermodynamics
• Dynamic gas-particle partitioning
• Sectional or modal framework
• Computationally efficient
• Implemented in WRF-chem

Zaveri, R.A., R.C. Easter, J.D. Fast, and L.K.
Peters, Model for Simulating Aerosol
Interactions and Chemistry (MOSAIC), JGR, in
review, 2007.
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Thermodynamics Module in MOSAIC
Accurate and Efficient

• Activity Coefficients MTEM
• Equilibrium Phase State MESA
• Solid-Liquid Equilibrium
• Water Content
• Kelvin Effect

MTEM Multicomponent Taylor Expansion
Method MESA Multicomponent Equilibrium Solver
for Aerosols
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Dynamic Gas-Particle Partitioning
Aerosol-Phase Gas-Phase

• Sources of Stiffness
• Implicit non-linear ODEs
• Time scales for bins vary over 3-4 orders of
  magnitude
• Very short time scales for H ions in
  near-neutral aqueous solutions
• Very short time scales for relatively minor
  species evaporating from the solid phase

Numerical solvers for such systems are prone to
producing oscillating and/or inaccurate solutions
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Mass Transfer Module ASTEM (Adaptive Step
Time-split Euler Method)
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ASTEM Algorithm
Time-split the overall solution into two parts
over hASTEM (5 min)

• Part 1. Condense non-volatile species H2SO4 (
  some NH3)
• Analytical solution over all bins (exponential
  decay)

• Call MESA to update the particle phase states for
  all bins

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ASTEM Algorithm
Part 2. Condense/evaporate semi-volatile species
HNO3, HCl, NH3
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ASTEM Algorithm
Master equation

• Three parameters to be determined
• Gas-Solid fluxes
• Saturation ratios
• Time step h

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Gas-Solid Fluxes
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Saturation Ratios
Saturation Ratios
Everything is known except
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The Million Dollar Question

• Sun and Wexler (1998)
• coupled condensation of acids and NH3
• Does not allow for gradual changes in pH
• Pilinis et al. (2000)
• Artificial restriction on H.
• Does it give the correct solution, though??
• Jacobson (2005)
• Dynamic mass transfer only for acids
• Need to call thermodynamics module again for NH3
  equilibrium

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New Approach

• Function of
• mass transfer coefficients,
• equilibrium constants,
• gas-phase concentrations
• aqueous-phase molalities
• Evolves smoothly and accurately
• Reaches the correct equilibrium value

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Adaptive Time Stepping Scheme
The last parameter that remains to be determined
is the time step h
An adaptive time-stepping scheme is developed
that ensures mass conservation and smooth
solution.
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ASTEM Recap

• Time split non-volatile and semi-volatile species
• Explicit Euler for gas-solid ODEs
• Semi-implicit Euler for gas-liquid ODEs with
  dynamic pH
• Adaptive time stepping scheme

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Monodisperse Test Cases Low RH (30)
Time (h)
Time (h)
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Monodisperse Test Cases High RH (85)
Time (h)
Time (h)
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Monodisperse Test Cases Moderate RH (55)
Time (h)
Time (h)
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Monodisperse Test Case Variable RH (30 to 70)
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Polydisperse Test Case Low RH (30)
Dry Particle Diameter, Dp (mm)
Dry Particle Diameter, Dp (mm)
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Polydisperse Test Case Low RH (30)
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Polydisperse Test Case High RH (85)
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Polydisperse Test Case High RH (85)
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Computational Efficiency on 3.0 GHz Intel Xeon
Proc.
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Computational Efficiency on 3.0 GHz Intel Xeon
Proc.
SCAQS 1987 Case 3-day simulation
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Summary

• MOSAIC is mass conserving and produces highly
  accurate, smooth, efficient, and robust solutions
  to the dynamic gas-particle mass transfer
  problem.
• The overall accuracy of MOSAIC has been
  independently verified against the benchmark
  version of the code that uses the LSODES solver
  and against the benchmark AIM2 model at
  equilibrium.
• Overall efficiency of MOSAIC is comparable to
  ISORROPIA on a per bin basis for a typical 3-D
  model time step of 5 min. At the same time,
  MOSAIC shows much higher accuracy than ISORROPIA,
  especially at low and moderate RH

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Acknowledgements

• Dr. Anthony Wexler for helpful discussions on
  gas-particle mass transfer solvers and the AIM2
  web-based models.
• Dr. Athanasios Nenes, Georgia Tech, for his
  efforts in the intercomparison of MOSAIC and
  ISORROPIA.
• DOEs Atmospheric Science Program and NASA Earth
  Science Enterprise for funding major portions of
  this work.

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