1. Models of atmospheric chemistry
The concept of model
Atmospheric structure and dynamics
Chemical processes in the atmosphere
Model equations and numerical approaches
Formulation of radiative, chemical , and aerosol rates
Numerical methods for chemical systems
Numerical methods for advection
Parameterization of subgrid-scale processes
Surface fluxes
Atmospheric observations and model evaluation
Inverse methods for atmospheric chemistry
Appendix E: Brief mathematical review
Available at
Password is ‘ctm’

2. Models solve the continuity equation for atmospheric species
Eulerian flux form:
Eulerian advective form:
Lagrangian form:
Brasseur and Jacob, 4.2

3. Eulerian models partition atmospheric domain into gridboxes
This discretizes the continuity equation in space
Solve continuity equation for individual gridboxes
Present computational limit -107 gridboxes
In global models, this implies a horizontal resolution of ~ 1o (~100 km) in horizontal and ~ 1 km in vertical
Chemical Transport Models (CTMs) use external meteorological data as input
General Circulation Models (GCMs) compute their own meteorological fields
Brasseur and Jacob, 4.8

4. Lagrangian models track transport of points in model domain (no grid!)
Transport large number of points with trajectories from input meteorological data base (U) over time steps Dt
Points have mixing ratio or mass but no volume
Determine local concentrations in a given volume by the statistics of points within that volume or by interpolation
position
to+Dt
PROS over Eulerian models:
stable for any wind speed
no error from spatial averaging
easily track air parcel histories
easy to parallelize
CONS:
need very large # points for statistics
inhomogeneous representation of domain
individual trajectories do not mix
nonlinear chemistry is problematic
UDt
position to
Brasseur and Jacob, 4.11

5. Lagrangian receptor-oriented modeling
Run Lagrangian model backward from receptor location,
with points released at receptor location only
flow backward in time
Efficient quantification of source influence distribution on receptor (“footprint”)

6. Question
The Eulerian form of the continuity equation is a first-order PDE in four dimensions. What are suitable boundary conditions for each of these dimensions in a global model?

7. Atmospheric turbulence
Reynolds number Re = UL/ >> 104 down to mm scale
Turbulence occurs on all scales down to mm where molecular diffusion takes over
Typical observations
of horizontal wind in PBL
Brasseur and Jacob, 8.2

8. Summer daytime observations at Harvard Forest, MA
vertical
wind w T
CO2
Brasseur and Jacob,

9. Turbulent kinetic energy cascade
wavenumber
“Big whirls have little whirls,
Which feed on their velocity.
And little whirls have lesser whirls
And so on to viscosity”
Lewis Fry Richardson

10. Turbulent diffusion parameterization
California fire plumes, Oct 2004
Industrial plumes
Brasseur and Jacob, 8.4.1

11. Deep convection
Organized but subgrid (except in cloud-resolving model with ~1 km resolution)
Requires non-local parameterization
Convective cloud
( km)
detrainment
Model
vertical
levels
downdraft
Large-scale
subsidence
updraft
entrainment
Model grid scale
Brasseur and Jacob, 8.7

12. Questions
1. Deep convection is almost always initiated from the boundary layer (lowest ~2 km of atmosphere), never from the free troposphere above. Why? 2. Aircraft vertical profiles downwind of deep convective events often show a "C-shaped" profile for surface air pollutants with high concentrations in the boundary layer and upper troposphere, and low concentrations in the middle troposphere. Why? 3. Could such a shape be simulated with an eddy diffusion parameterization for deep covenction?