model reduction algorithms in atmospheric pollution transport simulations by mauricio santillana in...
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Model reduction algorithms in atmospheric pollution transport simulations
by Mauricio Santillana
In collaboration with: Daniel Jacob, Philippe Le Sager, Michael Brenner, Scott Norris, and Yevgenii Rastigeyev
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4th GEOS-Chem Scientific Meeting. April, 2009Mauricio Santillana- Harvard University
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How does GEOS-Chem work?
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4th GEOS-Chem Scientific Meeting. April, 2009Mauricio Santillana- Harvard University
• In Every grid box in Earth’s Atmosphere (3D), All chemical species are solved…• Focus: Standard tropospheric ozone-NOx-VOC-aerosol simulation (111 species being solved)
However, do we need to solve all equations in all grid boxes?
Model reduction idea: Solve full equations only where most needed… Reasonable idea?
Higherconcentrations NO
4th GEOS-Chem Scientific Meeting. April, 2009Mauricio Santillana- Harvard University
Image credits: R.V. Martin (Dalhousie U.)
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Observations
Examples: Isoprene and PAN
Boxes where production or loss rate of NO > 10^2 mol/cm^3 sec
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4th GEOS-Chem Scientific Meeting. April, 2009Mauricio Santillana- Harvard UniversityActiveInactive
July 8, 2004. 00Hrs GMT
Where are things happening? All species
Percentage of species where production or loss rate > 10^2 mol/cm^3 sec
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4th GEOS-Chem Scientific Meeting. April, 2009Mauricio Santillana- Harvard University
July 8, 2004. 00Hrs GMT
Where are things happening? All speciesIdea:• Divide domain in active/inactive regions (for each chemical species).• Solve for species that are active in each box.• Use a computationally cheaper method to calculate concentration for inactive species.
4th GEOS-Chem Scientific Meeting. April, 2009Mauricio Santillana- Harvard University
Why 10 threshold?
Example: OH Typical concentration = 10 mol / cmLife time = 1 sec.
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Negligible!
What do we do in inactive regions?Two Ideas:
2. Spatial exponential-decay extrapolation (In progress)
• Assume spatial exponential decay from essential regions
• Calculate concentration of species in non-essential regions at each time step using a distance function to the chemical boundary layer
• Ignore all mechanisms such as: transport, chemistry, deep convection, in non-essential regions
1. Alternative ODE solver(Preliminary results)
• Calculate concentration of species in inactive regions at each time step using an explicit ODE.
• Decouples equations.• Cheaper than implicit!
Explicit solver (analytic expression)
4th GEOS-Chem Scientific Meeting. April, 2009Mauricio Santillana- Harvard University
RMS error
CPU time
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Threshold Fast/Slow= 10^2 mol/cm^3 secRMS error= 1.8 %
CPU time= 53 % (Savings 47%)
4th GEOS-Chem Scientific Meeting. April, 2009Mauricio Santillana- Harvard University
Sensitivity to inactivity threshold value
10
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Preliminary results GEOS-Chem:(Using a new solver to implement active/inactive selection)
Threshold active/inactive= 10^2 mol/cm^3 sec
Original algorithm
New algorithm
4th GEOS-Chem Scientific Meeting. April, 2009Mauricio Santillana- Harvard University
Approx.30% Overall savings, 48% savings in Chemistry
Preliminary results: NOx (1 week run)
Simulation date: July 8, 2004. 00Hrs GMT4th GEOS-Chem Scientific Meeting. April, 2009Mauricio Santillana- Harvard University
Preliminary results: OH (1 week run)
Simulation date: July 8, 2004. 00Hrs GMT4th GEOS-Chem Scientific Meeting. April, 2009Mauricio Santillana- Harvard University
• Future work: – 1 month running right now,– Goal: 1 year.– Implement spatial extrapolation (Rastigeyev, Y., M.P. Brenner,
and D.J. Jacob, PNAS, 2007)
4th GEOS-Chem Scientific Meeting. April, 2009Mauricio Santillana- Harvard University
Thank you
Questions?
Contact: [email protected]