Elements of atmospheric chemistry modelling

1. Elements of atmospheric chemistry modelling Prof. Michel Bourqui Office BH 815 398 5450 michel.bourqui@mcgill.ca http://www.meteo.mcgill.ca/bourqui/

2. Motivations for developing Atmospheric numerical models: • Putting together our knowledge and testing it against observations • Predicting tomorrow’s pollution, tomorrow’s UV strength, next century’s climate and ozone hole • Cleverly interpolating sparse observational data in the atmosphere

3. Evolution of computers: a few milestones • 1950: Programming languages (Fortran, C,…) • 1960: Graphics started • 1969: UNIX • 1971: First microprocessor • Until late 1970s: Punched cards for data • 1980s: PCs, start of internet • 1985: Windows • 1990s: Laptops • 1991: Linux

4. (Wikipedia)

5. Punched Cards (used until late 1970s) (Wikipedia)

6. Historic evolution of internet (Wikipedia)

7. IPCC 2001, Technical summary

8. However, numerical models do not resolve everything (yet)! In reality, they: • solve numerically the equations representing considered systems/processes at scales larger than the grid-scale For instance: Atm/ocean chemistry: set of ordinary differential equations Atm/ocean dynamics: set of partial differential equations • parameterise non-resolved and/or sub-grid processes using resolved quantities For instance: Sub-grid dynamics is parameterised by a diffusion term Radiation is parameterised using broad spectral bands Sub-grid clouds are parameterised using grid-scale winds

9. Running a comprehensive model is very expensive! Depending on the purpose, we use “simpler” models, where some processes are parameterised Examples of typical models used for different purposes: Paleo-climatologie (global scale, thousands-millions of years): • Simple atmospheric model of the troposphere (usually only a few layers in the vertical) • Simple oceanic model • Parameterisation of vegetation • Parameterisation of sea-ice • Carbon cycle (ocean, vegetation, atmosphere) • Parameterisation of solar activity

10. Examples of typical models used for different purposes: (cont’d) Weather and regional pollution (regional, days – weeks): • High-resolution, limited area atmospheric model of the troposphere (boundary conditions are required!) • Tropospheric chemistry • Parameterisation of cloud physics and chemistry • Simple parameterisation of ocean • Simple parameterisation of vegetation • Simple parameterisation of sea-ice • No solar variability

11. Examples of typical models used for different purposes: (cont’d) Climate and stratospheric chemistry (global, weeks - years): • Low-resolution, global atmospheric model of the troposphere and stratosphere • Stratospheric chemistry • Parameterisation of gravity wave breaking • Simple parameterisation of clouds • Simple parameterisation of ocean • Simple parameterisation of vegetation • Simple parameterisation of sea-ice • Parameterisation of solar cycles

12. To summarize, we use a hierarchy of models, depending on: The required spatiotemporal scales: • Coverage (e.g. Global, limited area, plume resolving) • Resolution (e.g. 500km, 50 km, 5km, a few meters) The required processes: • Atmospheric layers (e.g. boundary layer, troposphere, stratosphere, mesosphere, thermosphere) • Radiation • Ocean • Chemistry • Aerosols • Surface processes • .etc…

13. Basics of Atmospheric Models 1) The ‘Primitive Equations’ (+ chemical tracers)

14. 1) The ‘Primitive Equations’ (cont’d) (Guffie and Henderson-Sellers)

15. 2) The Boundary Conditions Ground: • Orography → friction • Vegetation → evapotranspiration, heat flux • Oceans, sea-ice → evaporation, heat flux • Emissions → sources/sinks of chemicals Lateral (for limited area models only): • Momentum • Energy • Mass and chemicals

16. 2) The Boundary Conditions (cont’d) Top: • Solar cycle • Atmospheric waves dampening to avoid reflection 3) The Initial Conditions (everywhere in the domain) • Momentum • Energy • Mass, chemical tracers Remark: Chaotic nature of the flow  weather forecasts require accurate initial conditions  climate simulations must be repeated for several initial conditions

17. 3) The Initial Conditions (required everywhere in the domain) • Momentum • Energy • Mass, chemical tracers • Remark: • Chaotic nature of the flow • weather forecast require accurate initial conditions …hence, the need for cleverly interpolated observational data • climate simulations must be repeated for different initial conditions …and must be statistically analysed

18. 4) The Grid The Vertical Grid pressure Terrain following grid Fixed pressure grid

19. 4) The Grid The Horizontal Grid (Guffie and Henderson-Sellers)

20. 4) The Grid The Horizontal Grid (b) SPECTRAL GRID 2D Fourier transform Physical space Spectral space (Lon, Lat) or (x, y) ( kx , ky ) ky 1 2 3 4 … lat kx lon 1 2 3 4 5 6 …

21. Basics of Photochemistry Models Unimolecular reactions A → B + C d[A] / dt = - k [A] Bimolecular reactions A + B → C + D d[A] / dt = - k [A] [B] A + B + M → C + D + M Trimolecular reactions d[A] / dt = - k [A] [B] [M] A + h → B + C Photolysis reactions d[A] / dt = - J [A] with J =  q  I d

22. Example: The Canadian Middle Atmosphere (CMAM) stratospheric model (Granpré et al., Atmo-Ocean 1997)

23. Chemical data required in the chemistry model: Chemical rates k = k (Temperature, Pressure) …are stored as constants as Arhenius function parameters or as specific functions Photolysis rates J =  q  I d where q = quantum yield  = cross section I = actinic flux …are stored as ‘look-up tables’ of J ( , I ) Official data available at: http://jpldataeval.jpl.nasa.gov/download.html

24. Solving the chemical reactions’ set of ODE: • The big difficulty: • the set of ODE is ‘stiff’, ie: • chemical lifetimes cover a very large range of time scales Example: CH4 + OH → CH3 + H2O Typical lifetime of CH4: CH4 = 1 / ( k [OH] ) = 10.2 years O(1D) + M → O + M Typical lifetime of O(1D): O(1D) = 1 / ( k [M] ) = 2 · 10-9 s  Time step necessary to resolve all the chemical reactions ?

25. Solving the chemical reactions’ set of ODE: In a chemistry model used to solve 3D atmospheric chemistry, it is not possible to have such small time steps!  Need integration schemes that are stable when time steps are larger than the smallest chemical lifetime Semi-implicit solvers: time Point to be predicted

26. Methods for solving chemical ODEs 1) The simplest solver (not semi-implicit): Forward Euler X (t) = X (t – t) + t · dX/dt and dX/dt = - k X (t - t ) Y (t - t ) + … 2) The simplest ‘implicit’ solver : Backward Euler X (t) = X (t – t) + t · dX/dt and dX/dt = - k X (t ) Y (t - t ) + …

27. Methods for solving chemical ODEs (cont’d) 3) The GEAR solver (semi-implicit): ODEs are turned into PDEs by partial derivation: dX/dt = - k X Y + …  d2X / dt dX = - k Y + … and the PDEs are solved using jacobian matrix inversion… large matrices!!! 4) The Family approach: • Production / Loss is calculated for each species • Concentrations within a family are summed over • The family concentration is advanced in time (e.g. with a forward Euler scheme) • Individual species are re-partitionned

28. Coupling Atmospheric and Chemistry models to the radiation scheme Atmospheric dynamics + physics solver Spatial distribution of chemicals + winds temperature Advection of chemicals New spatial distribution of chemicals Chemistry solver

29. An example of use of atmospheric – chemistry models: The WMO Ozone Assessment Report 2002 The full report is available freely at http://ozone.unep.org/Publications/6v_science%20assess%20panel.asp

30. The Ozone depletion due to CFCs Ozone column observations (ground-based, WMO 1998) (DU) CFC scenario (A1), tropospheric concentration, (WMO 1998) (DU)

31. 3D Chemistry-Climate Model Forecasts of Ozone Recovery (From Austin et al. 2003)

32. 3D Chemistry-Climate Model Forecasts of Ozone Recovery (From Austin et al. 2003)

33. References • A climate Modelling Primer, K. McGuffie and Henderson-Sellers, Ed. Wiley. • Fundamentals of Atmospheric Modeling, M. Z. Jacobson, Ed. Cambridge. Further Questions: Prof. Michel Bourqui Office BH 815 398 5450 michel.bourqui@mcgill.ca http://www.meteo.mcgill.ca/bourqui/