1. 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 Image source: http://www.gsfc.nasa.gov/gsfc/earth/terra/co.htm 4 th GEOS-Chem Scientific Meeting. April, 2009Mauricio Santillana- Harvard University Concentration Carbon Monoxide (CO) in 2000 at 15,000 ft.

2. How does GEOS-Chem work? http://celebrating200years.noaa.gov/breakthroughs/climate_model/ 4 th 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)

3. However, do we need to solve all equations in all grid boxes? Model reduction idea: Solve full equations only where most needed… Reasonable idea? Higher concentrations NO 4 th GEOS-Chem Scientific Meeting. April, 2009Mauricio Santillana- Harvard University Image credits: R.V. Martin (Dalhousie U.) 2 Observations

4. Examples: Isoprene and PAN Boxes where production or loss rate of NO > 10^2 mol/cm^3 sec P. Le Sager & M. Santillana 4 th GEOS-Chem Scientific Meeting. April, 2009Mauricio Santillana- Harvard University ActiveInactive July 8, 2004. 00Hrs GMT

5. Where are things happening? All species Percentage of species where production or loss rate > 10^2 mol/cm^3 sec P. Le Sager & M. Santillana 4 th GEOS-Chem Scientific Meeting. April, 2009Mauricio Santillana- Harvard University July 8, 2004. 00Hrs GMT

6. Where are things happening? All species Idea: 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. 4 th GEOS-Chem Scientific Meeting. April, 2009Mauricio Santillana- Harvard University Why 10 threshold? Example: OHTypical concentration = 10 mol / cm Life time = 1 sec. 2 6 3 Negligible!

7. 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) 4 th GEOS-Chem Scientific Meeting. April, 2009Mauricio Santillana- Harvard University

8. RMS error CPU time Chemistry only Threshold Fast/Slow= 10^2 mol/cm^3 sec RMS error= 1.8 % CPU time= 53 % (Savings 47%) 4 th GEOS-Chem Scientific Meeting. April, 2009Mauricio Santillana- Harvard University Sensitivity to inactivity threshold value 10 2 3 4 5

9. 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 4 th GEOS-Chem Scientific Meeting. April, 2009Mauricio Santillana- Harvard University Approx. 30% Overall savings, 48% savings in Chemistry

10. Preliminary results: NOx (1 week run) Simulation date: July 8, 2004. 00Hrs GMT 4 th GEOS-Chem Scientific Meeting. April, 2009Mauricio Santillana- Harvard University

11. Preliminary results: OH (1 week run) Simulation date: July 8, 2004. 00Hrs GMT 4 th GEOS-Chem Scientific Meeting. April, 2009Mauricio Santillana- Harvard University

12. Future work: – 1 month running right now, – Goal: 1 year. – Implement spatial extrapolation (Rastigeyev, Y., M.P. Brenner, and D.J. Jacob, PNAS, 2007) 4 th GEOS-Chem Scientific Meeting. April, 2009Mauricio Santillana- Harvard University Thank you Questions? Contact: msantill@fas.harvard.edu