1. ATMOSPHERIC CHEMISTRY MODELS Daniel J
ATMOSPHERIC CHEMISTRY MODELS Daniel J. Jacob Harvard University

2. OBJECTIVE OF ATMOSPHERIC CHEMISTRY MODELS: QUANTIFY THE CONCENTRATIONS AND FLUXES OF ATMOSPHERIC SPECIES IN TIME AND SPACE
Lightning
MEASURES OF ATMOSPHERIC CONCENTRATIONS:
Number density ni (x, t ) [molecules cm-3]
Mixing ratio (mole fraction) Ci (x, t) [mol/mol]
Volcanoes
Fires
Land
biosphere
Human
activity
physics
chemistry
biology
Ocean

3. CONTINUITY EQUATION: FOUNDATION OF ATMOSPHERIC CHEMISTRY MODELS
accumulation
advection
diffusion
chemistry, emissions, deposition
temporal change in concentration in elemental volume
Mass flux divergence
in elemental volume
(flux in – flux out)
U = wind vector
D = molecular diffusion
coefficient
Production and loss rates in elemental volume
Molecular diffusion is negligible relative to advection on scales > 1 cm
Equation is given here in Eulerian form (fixed frame of reference); Lagrangian form (frame of reference moving with air) will be discussed later

4. CONTINUITY EQUATION CANNOT BE SOLVED EXACTLY
…because transport is turbulent (stochastic high-frequency fluctuations);
…because we do not have perfect information on transport (even time-averaged), emissions, chemistry, deposition;
…because the scales of variability range from 10-3 to 107 m.
Solution requires a model: simplified representation of complex system.
Design model; make assumptions needed
to simplify problem (computational resources,
physical clarity)
Define problem of interest
Evaluate model with relevant observations
model development loop;
Improve model, characterize its error
Apply model:
make hypotheses, predictions

5. DISCRETIZATION OF CONTINUITY EQUATION IN SPACE: PARTITION ATMOSPHERIC DOMAIN INTO GRIDBOXES
Solve continuity equation for individual gridboxes
Full chemistry/aerosol models can presently afford gridboxes
In global models, this implies a horizontal resolution of km in horizontal and ~ 1 km in vertical

6. DISCRETIZATION OF THE CONTINUITY EQUATION IN TIME: OPERATOR SPLITTING
Split the continuity equation into contributions from different processes:
… and integrate each process separately over discrete time steps:
where
(similar forms for the other operators)

7. THE TRANSPORT OPERATOR: parameterization of turbulence
Consider 1-dimensional transport with wind u:
Both u and ni have turbulent fluctuations over time interval Dt:
Fluctuating component
<u’> = 0
Time-averaged
component
Time-averaged flux <uni> has a turbulent component:
Mean advective
flux
Turbulent flux
(covariance of u’ and n’)
Parameterize turbulent flux as diffusion process (diffusion coefficient K):
and replace in 3-D continuity equation. This is 1st-order closure for turbulence

8. TURBULENT COMPONENT DOMINATES VERTICAL FLUX IN LOWER ATMOSPHERE
Example: CO2 flux observations at Harvard Forest, Massachusetts
small large
vertical
wind w T
CO2

9. THE TRANSPORT OPERATOR: parameterization of convection
Convective cloud
( km)
Convection is subgrid scale in global models and must be treated as a vertical mass exchange separate from transport by grid-scale winds.
Need info on convective mass fluxes from the model meteorological driver.
detrainment
Model
vertical
levels
downdraft
updraft
entrainment
Model grid scale

10. THE CHEMICAL OPERATOR: consider system of n interacting species
Solve system of n coupled ordinary differential equations for species
System is typically “stiff” (lifetimes range over many orders of magnitude)
Aimplicit solution method is necessary.
Simplest method: backward Euler. Transform into system of m algebraic equations with m unknowns
Solve e.g. by Newton’s method. Backward Euler is stable, mass-conserving, flexible (can use other constraints such as steady-state, chemical family closure, etc… in lieu of Dn/Dt). Unfortunately it is expensive (inversion of nxn matrix at each time step). Use it in 0-D calculations!
Most 3-D models use the Gear method, which is a higher-order implicit solution

11. DEPOSITION PROCESSES: dry deposition
Dry deposition describes uptake at Earth’s surface by chemical reaction, absorption, or collision (aerosols):
concentration in lowest model level
Deposition flux = Vd n1
“deposition velocity” (cm s-1)
Use “resistance-in-series” model for dry deposition Vd = 1 / (Ra + Rc)
Lowest model level (z1) n1
“Aerodynamic” resistance to turbulent transport: Ra = z/K (units: s cm-1) no
SURFACE
Surface resistance Rc to uptake

12. DEPOSITION PROCESSES: wet deposition
Soluble gases (KH > 104 M atm-1), aerosols are efficiently scavenged by clouds and precipitation:
nucleation
diffusion
(gases, aerosols)
impaction
large and small
aerosol particles
Our ability to model wet scavenging is limited mostly by the quality of the precipitation data:
where it rains
subgrid extent of precipitation, wet convection
Also need better understanding of ice processes

13. LAGRANGIAN vs. EULERIAN MODELING APPROACHES
Eulerian research models use assemblages of boxes exchanging mass to resolve spatial structure
Lagrangian research models use assemblages of traveling puffs not exchanging mass, and sum over all puff trajectories to resolve spatial structure
ni(x,to+Dt)
ni(x,to)

14. HOW CAN WE USE ATMOSPHERIC OBSERVATIONS TO IMPROVE MODELS?
ISSUES:
Observed variables (e.g., concentrations) may be different from the state variables for which we want to improve our knowledge (e.g., emissions)
Observations may not be in the right places, or may be subject to errors that reduce the information they contain.
Trivial example: let us improve our estimate of variable x by making a direct measurement
Before we make the measurement, we have an a priori estimate
xa ± sa for its value
The measurement indicates a value xm ± sm
What is our best estimate of x after the measurement? Minimize a cost function
(least-squares)
Our new best estimate is
with error

15. INVERSE MODELING: GENERALIZATION OF CONCEPT
Consider a state vector x, observation vector y which is linear function of x:
K is a Jacobian matrix from our atmospheric chemistry model (termed the forward model). If model is not linear, linearize it about a ref. point
e is the observational error vector
Let Sa, Se be the error covariance matrices on the a priori xa and on the observations y: then the best estimate of x after the observations is
with error covariance matrix
Chemical data assimilation follows the same principle with x = y (optimize gridded field of y from observations of y). Method is then called Kalman filter. In advanced data assimilation, one wishes to optimize y(to) from multiple observations at t [to, to+Dt] in a non-linear model; this requires local linearization at t with a tangent linear (or adjoint) model.

16. SOME APPLICATIONS USING THE GEOS-CHEM GLOBAL 3-D MODEL OF TROPOSPHERIC CHEMISTRY (
Meteorological input fields from NASA/DAO assimilated data, 1988-present; 1ox1o to 4ox5o horizontal resolution, vertical levels
Ozone-NOx-CO-hydrocarbon chemistry, aerosols, CH4, CO2: up to 80 interacting species depending on application
Applied to a wide range of problems, e.g.,
Testing of atmospheric transport with chemical tracers
Long-range transport of pollution
Support of aircraft missions
Satellite retrievals
Inversion of sources

17. METHYL IODIDE: TRACER OF MARINE CONVECTION IN GLOBAL ATMOSPHERIC MODELS Loss by photolysis (~4 days), relatively uniform ocean source, large aircraft data base [D.R. Blake, UCI]
Observations
Model
(GEOS-CHEM)
MCI: 0.40 (obs)
0.22 (mod)
MCI: 0.16 (obs)
0.14 (mod)
Define Marine Convection Index (MCI) as ratio of upper tropospheric (8-12 km)
to lower tropospheric (0-2.5 km) CH3I concentrations
MCI over Pacific ranges from 0.11 (Easter Island dry season) to 0.40 (observations over tropical Pacific)
GEOS-CHEM reproduces observed MCI with little global bias (+11%) but poor correlation (r2 = 0.15, n=11)
Bell et al. [2002]

18. LONG-RANGE TRANSPORT OF POLLUTION: SURFACE OZONE ENHANCEMENTS CAUSED BY ANTHROPOGENIC EMISSIONS FROM DIFFERENT CONTINENTS
GEOS-CHEM
model, July 1997
North America
Europe
Asia
Li et al. [2001]
Li et al. [2002]

19. COLUMN MEASUREMENT OF AN ABSORBING GAS USING SOLAR BACKSCATTER
absorption
Backscattered
intensity IB l1 l2
wavelength
l1, l2
Slant optical depth
ATMOSPHERE
Slant column
Scattering by
Earth surface
and by atmosphere
EARTH SURFACE

20. AIR MASS FACTOR (AMF) CONVERTS SLANT COLUMN WS TO VERTICAL COLUMN W
“Geometric AMF” (AMFG) for non-scattering atmosphere: q
EARTH SURFACE

21. IN SCATTERING ATMOSPHERE, AMF CALCULATION REQUIRES MODEL INFORMATION ON THE SHAPE OF THE VERTICAL PROFILE:
RADIATIVE TRANSFER MODEL
ATMOSPHERIC CHEMISTRY MODEL z IB Io
dt(z)
EARTH SURFACE
number density n(z)
Scattering weight
Shape factor
Palmer et al.
[2001]

22. ATMOSPHERIC COLUMNS OF NO2 AND FORMALDEHYDE (HCHO) MEASURED BY SOLAR BACKSCATTER FROM GOME ALLOW MAPPING OF NOx AND HYDROCARBON EMISSIONS
… but model info is needed for the vertical distributions of NO2 and HCHO
GOME SATELLITE
INSTRUMENT
Tropospheric NO2 column ~ ENOx
Tropospheric HCHO column ~ ENMHC
~ 2 km
hn (420 nm)
BOUNDARY
LAYER
hn (340 nm)
NO2 NO
HCHO CO OH
hours
O3, RO2
hours
NMHC
1 day
HNO3
Emission
Deposition
Emission
NITROGEN OXIDES (NOx)
NON-METHANE HYDROCARBONS

23. CAN WE USE GOME TO ESTIMATE NOx EMISSIONS. TEST IN U. S
CAN WE USE GOME TO ESTIMATE NOx EMISSIONS? TEST IN U.S. WHERE GOOD A PRIORI EXISTS
Comparison of GOME retrieval (July 1996) to GEOS-CHEM model fields
using EPA emission inventory for NOx
GOME
GEOS-CHEM
(EPA emissions)
BIAS = +3%
R = 0.79
Martin et al. [2002]

24. GOME RETRIEVAL OF TROPOSPHERIC NO2 vs. GEOS-CHEM SIMULATION (July 1996)
Martin et al. [2002]
GEIA emissions
scaled to 1996

25. FORMALDEHYDE COLUMNS FROM GOME: July 1996 means
Palmer et al. [2001]
BIOGENIC ISOPRENE IS THE MAIN SOURCE OF HCHO IN U.S. IN SUMMER

26. GOME GEIA (IGAC inventory) BEIS2 COMPARE TO…
MAPPING OF ISOPRENE EMISSIONS FOR JULY 1996 BY SCALING OF GOME FORMALDEHYDE COLUMNS [Palmer et al., 2002]
GOME
COMPARE TO…
GEIA (IGAC inventory)
BEIS2

27. QUANTITATIVE PREDICTIONS
PROGRESS IN ATMOSPHERIC CHEMISTRY REQUIRES INTEGRATION OF MEASUREMENTS AND MODELS
SATELLITE OBSERVATIONS
Global and continuous but
few species, low resolution
Source/sink
inventories
3-D CHEMICAL
TRACER MODELS
SURFACE OBSERVATIONS
high resolution but spatially limited
Assimilated
meteorological
data
AIRCRAFT OBSERVATIONS
High resolution, targeted flights
provide critical snapshots
for model testing
Chemical
and aerosol
processes
QUANTITATIVE PREDICTIONS

28. NASA TRACE-P aircraft mission over western Pacific(Mar-Apr 2001)
Satellite data
in near-real time:
MOPITT
TOMS
SEAWIFS
AVHRR
LIS
Stratospheric
intrusions
FLIGHT
PLANNING
Long-range transport from
Europe, N. America, Africa
ASIAN
OUTFLOW
3D chemical model
forecasts:
- ECHAM
- GEOS-CHEM
- Iowa/Kyushu
- Meso-NH
-LaRC/U. Wisconsin
Boundary layer
chemical/aerosol
processing
DC-8
P-3
PACIFIC
Emissions
Fossil fuel
Biomass burning
Biosphere, dust
ASIA
PACIFIC

29. FURTHER READING
Jacob, D.J., Introduction to Atmospheric Chemistry, Princeton University Press, 1999
Basic treatment of model design
Brasseur, G.P. et al. (eds), Atmospheric Chemistry and Global Change, Oxford University Press, 1999
Chap. 12 (“Modeling”) is concise and excellent
Seinfeld, J.H., and S. Pandis, Atmospheric Chemistry and Physics, Wiley, 1996
Excellent insights into modeling principles
Jacobson, M.Z., Fundamentals of Atmospheric Modeling, Cambridge University Press, 1999
Excellent presentations of modeling techniques