Elements of atmospheric
chemistry modelling
Prof. Michel Bourqui
Office BH 815
398 5450
[email protected]
http://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
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
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
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
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
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…
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
pressure
The Vertical Grid
Fixed pressure grid
Terrain following grid
4) The Grid
The Horizontal Grid
(Guffie and Henderson-Sellers)
4) The Grid
The Horizontal Grid
(b) SPECTRAL GRID
2D Fourier transform
Physical space
Spectral space
(Lon, Lat) or (x, y)
( kx , ky )
1 2 3 4…
ky
lat
lon
1 2 3 4 5 6 …
kx
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]
Trimolecular reactions
A + B + M → C + D + M
d[A] / dt = - k [A] [B] [M]
Photolysis reactions
A + h → B + C
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 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
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
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 ) + …
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:
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
to the radiation scheme
Spatial distribution of
chemicals + winds
Advection of chemicals
New spatial distribution
of chemicals
Chemistry solver
temperature
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
The Ozone depletion due to CFCs
Ozone column observations
(ground-based, WMO 1998)
(DU)
CFC scenario (A1), tropospheric concentration,
(WMO 1998)
(DU)
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 815
398 5450
[email protected]
http://www.meteo.mcgill.ca/bourqui/
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