This document discusses atmospheric chemistry models and their use in quantifying atmospheric concentrations and fluxes. Global 3D models divide the atmosphere into grid boxes and use the continuity equation to track species concentrations over time, accounting for transport, chemistry, emissions and deposition. Transport is parameterized using turbulence and convection schemes. Chemistry is solved using operator splitting and implicit methods. Models are evaluated and improved using atmospheric observations from satellites, aircraft and surface sites through data assimilation techniques like inverse modeling. Examples are given of various applications of the GEOS-CHEM global model.

1. ATMOSPHERIC CHEMISTRY MODELS Daniel J. Jacob Harvard University http://www-as.harvard.edu/chemistry/trop

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

3. CONTINUITY EQUATION: FOUNDATION OF ATMOSPHERIC CHEMISTRY MODELS 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 advection diffusion chemistry, emissions, deposition accumulation 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 10 7 m. Solution requires a model : simplified representation of complex system. Define problem of interest Design model; make assumptions needed to simplify problem (computational resources, physical clarity) Evaluate model with relevant observations model development loop; Apply model: make hypotheses, predictions Improve model, characterize its error

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 10 5 -10 6 gridboxes In global models, this implies a horizontal resolution of 100-500 km in horizontal and ~ 1 km in vertical

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

7. THE TRANSPORT OPERATOR: parameterization of turbulence Consider 1-dimensional transport with wind u: Both u and n i have turbulent fluctuations over time interval  t : Time-averaged component Fluctuating component < u’> = 0 Time-averaged flux < un i > 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 1 st -order closure for turbulence

8. TURBULENT COMPONENT DOMINATES VERTICAL FLUX IN LOWER ATMOSPHERE vertical wind w T CO 2 small large Example: CO 2 flux observations at Harvard Forest, Massachusetts

9. THE TRANSPORT OPERATOR: parameterization of convection Convective cloud (0.1-100 km) Model grid scale Model vertical levels updraft entrainment downdraft detrainment 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.

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)  implicit 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  n  t  Unfortunately it is expensive (inversion of n x n 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): Lowest model level ( z 1 ) n 1 “ Aerodynamic” resistance to turbulent transport: R a = z/ K (units: s cm -1 ) Surface resistance R c to uptake n o Deposition flux = V d n 1 “ deposition velocity” (cm s -1 ) concentration in lowest model level Use “resistance-in-series” model for dry deposition V d = 1 / ( R a + R c ) SURFACE

12. DEPOSITION PROCESSES: wet deposition Soluble gases ( K H > 10 4 M atm -1 ), aerosols are efficiently scavenged by clouds and precipitation: nucleation impaction diffusion (gases, aerosols) 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 large and small aerosol particles

13. 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 LAGRANGIAN vs. EULERIAN MODELING APPROACHES n i (x,t o ) n i (x,t o  t 

14. HOW CAN WE USE ATMOSPHERIC OBSERVATIONS TO IMPROVE MODELS? 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 x a ±  a for its value The measurement indicates a value x m ±  m What is our best estimate of x after the measurement? Minimize a cost function (least-squares) Our new best estimate is with error ISSUES:

15. INVERSE MODELING: GENERALIZATION OF CONCEPT 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( t o ) from multiple observations at t [ t o , t o +  t ] in a non-linear model; this requires local linearization at t with a tangent linear (or adjoint ) model. 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  is the observational error vector Let S a , S   be the error covariance matrices on the a priori x a and on the observations y: then the best estimate of x after the observations is with error covariance matrix

16. SOME APPLICATIONS USING THE GEOS-CHEM GLOBAL 3-D MODEL OF TROPOSPHERIC CHEMISTRY (http://www-as.harvard.edu/chemistry/trop/geos) Meteorological input fields from NASA/DAO assimilated data, 1988-present; 1 o x1 o to 4 o x5 o horizontal resolution, 20-48 vertical levels Ozone-NO x -CO-hydrocarbon chemistry, aerosols, CH 4 , CO 2 : 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) Define Marine Convection Index (MCI) as ratio of upper tropospheric (8-12 km) to lower tropospheric (0-2.5 km) CH 3 I 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 (r 2 = 0.15, n=11) Bell et al. [2002] MCI: 0.40 (obs) 0.22 (mod) MCI: 0.16 (obs) 0.14 (mod)

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 EARTH SURFACE Scattering by Earth surface and by atmosphere ATMOSPHERE absorption wavelength     Slant optical depth Backscattered intensity I B Slant column    

20. AIR MASS FACTOR (AMF) CONVERTS SLANT COLUMN  S TO VERTICAL COLUMN  “ Geometric AMF” (AMF G ) for non-scattering atmosphere: EARTH SURFACE 

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

22. ATMOSPHERIC COLUMNS OF NO 2 AND FORMALDEHYDE (HCHO) MEASURED BY SOLAR BACKSCATTER FROM GOME ALLOW MAPPING OF NO x AND HYDROCARBON EMISSIONS Emission NO h  (420 nm)  O 3 , RO 2 NO 2 HNO 3 1 day NITROGEN OXIDES (NO x ) NON-METHANE HYDROCARBONS Emission NMHC OH HCHO h  (340 nm)  hours CO hours BOUNDARY LAYER ~ 2 km Tropospheric NO 2 column ~ E NOx Tropospheric HCHO column ~ E NMHC Deposition GOME SATELLITE INSTRUMENT … but model info is needed for the vertical distributions of NO 2 and HCHO

23. CAN WE USE GOME TO ESTIMATE NO x 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 NO x GOME GEOS-CHEM (EPA emissions) BIAS = +3% R = 0.79 Martin et al. [2002]

24. GOME RETRIEVAL OF TROPOSPHERIC NO 2 vs. GEOS-CHEM SIMULATION (July 1996) GEIA emissions scaled to 1996 Martin et al. [2002]

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

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

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

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