Elements of atmospheric chemistry modelling

Prof. Michel BourquiOffice BH 815398 5450michel.bourqui@mcgill.cahttp://www.meteo.mcgill.ca/bourqui/

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 equationsAtm/ocean dynamics: set of partial differential equations

For instance:

Sub-grid dynamics is parameterised by a diffusion termRadiation is parameterised using broad spectral bandsSub-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

pres

sure

4) The Grid

(Guffie and Henderson-Sellers)

The Horizontal Grid

4) The Grid

The Horizontal Grid

(b) SPECTRAL GRID

Physical space Spectral space

(Lon, Lat) or (x, y) ( kx , ky )

lat

lon

2D Fourier transform

ky

kx1 2 3 4 5 6 …1

2 3

4 …

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 sectionI = actinic flux

…are stored as ‘look-up tables’ of J ( , I )

Official data available at: http://jpldataeval.jpl.nasa.gov/download.html

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 ?

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)

d2X / 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 athttp://ozone.unep.org/Publications/6v_science%20assess%20panel.asp

CFC scenario (A1), tropospheric concentration, (WMO 1998)

(DU)

(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 BourquiOffice BH 815398 5450michel.bourqui@mcgill.cahttp://www.meteo.mcgill.ca/bourqui/