Elements of atmospheric chemistry modelling Prof. Michel Bourqui Office BH

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

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

(Wikipedia)

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

Historic evolution of internet (Wikipedia)

IPCC 2001, Technical summary

parameterise non-resolved and/or sub-grid processes using resolved quantities 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 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

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: 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 Paleo-climatologie (global scale, thousands-millions of years):

Examples of typical models used for different purposes: (cont’d) 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 Weather and regional pollution (regional, days – weeks):

Examples of typical models used for different purposes: (cont’d) 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 Climate and stratospheric chemistry (global, weeks - years):

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) Atmospheric layers (e.g. boundary layer, troposphere, stratosphere, mesosphere, thermosphere) Radiation Ocean Chemistry Aerosols Surface processes.etc… The required processes:

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

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

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

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

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

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

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

4) The Grid The Horizontal Grid (b) SPECTRAL GRID Physical spaceSpectral space (Lon, Lat) or (x, y)( k x, k y ) lat lon 2D Fourier transform kyky kxkx … …

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

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

Chemical rates k = k (Temperature, Pressure) …are stored as constants as Arhenius function parameters or as specific functions Chemical data required in the chemistry model: 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:

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: CH 4 + OH → CH 3 + H 2 O Typical lifetime of CH 4 :  CH4 = 1 / ( k [OH] ) = 10.2 years O(1D) + M → O + M Typical lifetime of O( 1 D):  O(1D) = 1 / ( k [M] ) = 2 · s  Time step necessary to resolve all the chemical reactions ?

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

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 ) + … Methods for solving chemical ODEs

3) The GEAR solver (semi-implicit): ODEs are turned into PDEs by partial derivation: dX/dt = - k X Y + … 4) The Family approach: Methods for solving chemical ODEs (cont’d)  d 2 X / dt dX = - k Y + … and the PDEs are solved using jacobian matrix inversion… large matrices!!! 1.Production / Loss is calculated for each species 2.Concentrations within a family are summed over 3.The family concentration is advanced in time (e.g. with a forward Euler scheme) 4.Individual species are re-partitionned

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

An example of use of atmospheric – chemistry models: The WMO Ozone Assessment Report 2002 The full report is available freely at

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

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

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

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