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∞. J = ∫ 4 π I λ ,T A λ ,T QY λ ,T d λ. 0. Air Quality Modeling. ∂C/ ∂t = - ∂(uC)/ ∂x - ∂(vC)/ ∂y - ∂(wC)/ ∂z. kr = Ar(300/T)Bexp(Cr/T). dx = (R e cos φ )d λ e. Zac Adelman and Craig Mattocks Carolina Environmental Program. Outline. Why model air pollution?

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Air Quality Modeling

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air quality modeling

J = ∫4πIλ,T Aλ,T QYλ,T dλ


Air Quality Modeling

∂C/ ∂t = - ∂(uC)/ ∂x - ∂(vC)/ ∂y - ∂(wC)/ ∂z

kr = Ar(300/T)Bexp(Cr/T)

dx = (Recosφ)dλe

Zac Adelman and Craig MattocksCarolina Environmental Program

  • Why model air pollution?
  • Air quality modeling system components
    • Meteorology
    • Emissions
    • Chemistry and transport
  • Technical and operational details
  • Problems in air quality modeling
  • Application examples
  • Future directions in atmospheric modeling

Gas Chemistry:

Aqueous Chemistry:

O3 + NO  NO2 + O2

SO2(g) SO2 (aq)

O + O2 + M  O3 + M

Aerosol Processes:

Condensation & Deposition

Evaporation & Sublimation

Nucleation & Coagulation

Advection Diffusion

Boundary Conditions

Biogenic Emissions

Anthropogenic Emissions

Geogenic Emissions

Adapted from Mackenzie and Mackenzie, “Our Changing Planet”, Prentice Hall, New Jersey, 1995.



why model air pollution
Why model air pollution?
  • Air pollution models are frameworks that integrate our understanding of individual processes with atmospheric measurements
  • Air pollution systems are non-linear
    • Need to establish the link between emissions sources and ambient concentrations
air quality modeling components
Air Quality Modeling Components
  • Meteorology modeling
  • Emissions processing
  • Initial/boundary conditions processing
  • Photolysis rate processing
  • Chemistry and transport modeling
wrf arw basics
WRF-ARW Basics
  • Fundamentals of Numerical Weather Prediction
    • Real vs. artificial atmosphere
    • Map projections
    • Horizontal grid staggering
    • Vertical coordinate systems
  • Definitions & Acronyms
  • Flavors of WRF
    • ARW core
    • NMM core
  • Other Numerical Weather Prediction Models
    • MM5
    • ARPS
    • Global Icosahedral
  • WRF Model Governing Equations
    • Vertical coordinate and grid discretization
    • Time integration
    • Microphysics
  • Current Defects of WRF
real vs artificial atmosphere
Real vs. Artificial Atmosphere

True analytical solutions are unknown!

Numerical models are discrete approximations of a continuous fluid.

map projections
Map Projections

Example of a regional high resolution grid (projection of a spherical surface onto a 2D plane) nested within a global (lat,lon) grid with spherical coordinates

x = r cos  y = r 

Differences in map projections require caution when dealing with flow of information across grid boundaries.

WRF offers polar stereographic, Lambert conformal, Mercator and rotated Lat-Lon map projections.

arakawa a grid
Arakawa “A” Grid
  • Unstaggered grid - all variables defined everywhere.
  • Poor performance, first grid geometry employed in NWP models.
  • Noisy - large errors, short waves propagate energy in wrong direction, additional smoothing required.
  • Poorest at geostrophic adjustment - wave energy trapped, heights remain too high.
  • Can use a 2x larger time step than staggered grids.
arakawa b grid
Arakawa “B” Grid
  • Staggered, velocity at corners.
  • Preferred at coarse resolution.
  • Superior for poorly resolved inertia-gravity waves.
  • Good for geostrophy, Rossby waves: collocation of velocity points.
  • Bad for gravity waves: computational checkerboard mode.
  • Used by MM5 model.
arakawa c grid
Arakawa “C” Grid
  • Staggered, mass at center, normal velocity, fluxes at grid cell faces, vorticity at corners.
  • Preferred at fine resolution.
  • Superior for gravity waves.
  • Good for well resolved inertia-gravity waves.
  • Simulates Kelvin waves (shoulder on boundary) well.
  • Bad for poorly resolved waves: Rossby waves (computational checkerboard mode) and inertia-gravity waves due to averaging the Coriolis force.
  • Used by WRF-ARW, ARPS, CMAQ models.
arakawa d grid
Arakawa “D” Grid
  • Staggered, mass at center, tangential velocity along grid faces.
  • Poorest performance, worst dispersion properties, rarely used.
  • Noisy - large errors, short waves propagate energy in wrong direction.
arakawa e grid
Arakawa “E” Grid
  • Semi-staggered grid.
  • Equivalent to superposition of 2 C-grids, then rotated 45 degrees.
  • Center set to translated (lat,lon) = (0,0) to prevent distortion near edges, poles.
  • Developed for Eta step-mountain coordinate to enhance blocking, overcome PGF errors caused by sigma coordinates.
  • Controls the cascade of energy toward smaller scales.
  • Used by WRF-NMM and Eta models.
definitions acronyms
Definitions & Acronyms
  • WRF: Weather Research & Forecasting numerical weather prediction model
  • ARW: Advanced Research WRF [nee Eulerian Model (EM)] core
  • NMM: Nonhydrostatic Mesoscale Model core
  • WRF-SI: Standard Initialization (4 components) - prepares real atmospheric data for input to WRF
  • WRF-VAR: Variational 3D/4D data assimilation system (not used for this class)
  • IDV: Integrated Data Viewer - Java application for interactive visualization of WRF model output
flavors of wrf arw
Flavors of WRF (ARW)
  • ARW solver (research - NCAR, Boulder, Colorado)
    • Fully compressible, nonhydrostatic equations with hydrostatic option
    • Arakawa-C horizontal grid staggering
    • Mass-based terrain following vertical coordinate
      • Vertical grid spacing can vary with height
      • Top is a constant pressure surface
    • Scalar-conserving flux form for prognostic model variables
    • 2nd to 6th-order advection options in horizontal &vertical
    • One-way, two-way and movable nest options
    • Runge-Kutta 2nd & 3rd-order time integration options
    • Time-splitting
      • Large time step for advection
      • Small time step for acoustic and internal gravity waves
      • Small step horizontally explicit, vertically implicit
      • Divergence damping for suppressing sound waves
    • Full physics options for land surface, PBL, radiation, microphysics and cumulus parameterization
    • WRF-chem under development:
flavors of wrf nmm
Flavors of WRF (NMM)
  • NMM solver (operational - NCEP, Camp Springs, Maryland)
    • Fully compressible, nonhydrostatic equations with reduced hydrostatic option
    • Arakawa-E horizontal grid staggering, rotated latitude-longitude
    • Hybrid sigma-pressure vertical coordinate
    • Conservative, positive definite, flux-corrected scheme used for horizontal and vertical advection of TKE and water species
    • 2nd-order spatial that conserves a number of 1st-order and quadratic quantities, including energy and enstrophy
    • One-way, two-way and movable nesting options
    • Time-integration schemes: forward-backward for horizontally propagating fast waves, implicit for vertically propagating sound waves, Adams-Bashforth for horizontal advection and Coriolis force, and Crank-Nicholson for vertical advection
    • Divergence damping & E subgrid coupling for suppressing sound waves
    • Full physics options for land surface, PBL, radiation, microphysics (only Ferrier scheme) and cumulus parameterization
    • Note: Many ARW core options are not yet implemented! Nesting still under development
    • NMM core will be used for HWRF (hurricane version of WRF), operational in summer of 2007
other nwp models mm5
Other NWP Models (MM5)
  • MM5 (research - PSU/NCAR, Boulder, Colorado)
    • Progenitor of WRF-ARW, mature NWP model with extensive configuration options
    • Support terminated, no future enhancements by NCAR’s MMM division
    • Nonhydrostatic and hydrostatic frameworks
    • Arakawa-B horizontal grid staggering
    • Terrain following sigma vertical coordinate
    • Unsophisticated advective transport schemes cause dispersion, dissipation, poor mass conservation, lack of shape preservation
    • Outdated Leapfrog time integration scheme
    • One-way and two-way (including movable) nesting options
    • 4-dimensional data assimilation via nudging (Newtonian relaxation), 3D-VAR, and adjoint model
    • Full physics options for land surface, PBL, radiation, microphysics and cumulus parameterization
other nwp models arps
Other NWP Models (ARPS)
  • ARPS (research - CAPS/OU, Norman, Oklahoma)
    • Advanced Regional Prediction System
    • Sophisticated NWP model with capabilities similar to WRF
    • Primarily used for tornado simulations at ultra-high (25 meter) resolutions and assimilation of experimental radar data at mesoscale
    • Elegant, source code, easy to read/understand/modify, ideal for research projects, very helpful scientists at CAPS
    • Arakawa-C horizontal grid staggering
    • Currently lacks full mass conservation and Runge-Kutta time integration scheme
    • ARPS Data Assimilation System (ADAS) under active development/enhancement (MPI version soon), faster & more flexible than WRF-SI, employed in LEAD NSF cyber-infrastructure project
    • wrf2arps and arps2wrf data set conversion programs available
wrf model governing equations eulerian flux form
WRF Model Governing Equations(Eulerian Flux Form)


∂U/∂t + (∇ · Vu) − ∂(pφη)/∂x + ∂(pφx)/∂η = FU

∂V/∂t + (∇ · Vv) − ∂(pφη)/∂y + ∂(pφy)/∂η = FV

∂W/∂t + (∇ · Vw) − g(∂p/∂η − μ) = FW

Potential Temperature:

Diagnostic Hydrostatic (inverse density a):

∂Θ/∂t + (∇ · Vθ) = FΘ

∂φ/∂η = -μ



μ = column mass

V = μv = (U,V,W)

Ω = μ d(η)/dt

Θ = μθ

∂μ/∂t + (∇ · V) = 0

Geopotential Height:

∂φ/∂t + μ−1[(V · ∇φ) − gW] = 0


Runge-Kutta Time Integration

Φ∗ = Φt + t/3 R(Φt )

Φ∗∗ = Φt + t/2 R(Φ∗)

Φt+t = Φt + t R(Φ∗∗)

“2.5” Order Scheme

Linear: 3rd order

Non-linear: 2nd order

Square Wave Advection Tests:

runge kutta time step constraint
Runge-Kutta Time Step Constraint
  • RK3 is limited by the advective Courant number (ut/x) and the user’s choice of advection schemes (2nd through 6th order)
  • The maximum stable Courant numbers for advection in the RK3 scheme are almost double those in the leapfrog time-integration scheme

Maximum Courant number for 1D advection in RK3

  • Includes explicitly resolved water vapor, cloud and precipitation processes
  • Model accommodates any number of mixing-ratio variables
  • Four-dimensional arrays with 3 spatial indices and one species index
  • Memory (size of 4th dimension) is allocated depending on the scheme
  • Carried out at the end of the time-step as an adjustment process, does not provide tendencies
  • Rationale: condensation adjustment should be at the end of the time step to guarantee that the final saturation balance is accurate for the updated temperature and moisture
  • Latent heating forcing for potential temperature during dynamical sub-steps (saving the microphysical heating as an approximation for the next time step)
  • Sedimentation process is accounted for, a smaller time step is allowed to calculate vertical flux of precipitation to prevent instability
  • Saturation adjustment is also included
wrf microphysics options
WRF Microphysics Options
  • Mixed-phase processes are those that result from the interaction of ice and water particles (e.g. riming that produces graupel or hail)
  • For grid sizes ≤ 10 km, where updrafts may be resolved, mixed-phase schemes should be used, particularly in convective or icing situations
  • For coarser grids the added expense of these schemes is not worth it because riming is not likely to be resolved
current defects of wrf
Current Defects of WRF
  • Serious deficiencies in PBL parameterizations and land surface models produce biases/errors in the predicted surface and 2-meter temperatures, and PBL height. WRF cannot maintain shallow stable layers.
  • 3D/4D Variational data assimilation and Ensemble Kalman Filtering (EnKF) still under development, EnKF available to community from NCAR as part of the Data Assimilation Research Testbed (DART).
  • Not clear yet what to do in “convective no-man’s land” – convective parameterizations valid only at horizontal scales > 10 km, but needed to trigger convection at 5-10 km scales.
  • Multi-species microphysics schemes with more accurate particle size distributions and multiple moments should be developed to rectify errors in the prediction of convective cells.
  • Heat and momentum exchange coefficients need to be improved for high-wind conditions in order to forecast hurricane intensity. Wind wave and sea spray coupling should also be implemented. Movable, vortex-following 2-way interactive nested grid capability has recently been incorporated into the WRF framework.
  • Upper atmospheric processes (gravity wave drag and stratospheric physics) need to be improved for coupling with global models.
emissions processing
Emissions Processing





  • Emissions Processing Steps

AQM-ready Emissions:

emissions terminology
Emissions Terminology
  • Inventory: estimate of pollutant emissions at a given spatial unit
  • Model Grid: 3-d representation of the earths surface based on discrete and uniform spatial units, i.e. grid cells
  • Speciation: conversion of inventory pollutant species to model pollutant species
  • Gridding: conversion of inventory spatial units to model grid cells
  • Temporalization: conversion of inventory temporal units to those requires by an air quality model
emissions terminology1
Emissions Terminology
  • Plume rise: calculation of the vertical distribution of emissions from point sources and the subsequent allocation of the emissions to the model layers
  • Spatial surrogate: GIS-based estimate of the fraction of a grid cell covered by a particular land-use category (e.g. population or rural housing)
  • Profiles: emissions distributions in space, time, or to chemical species
  • Cross-referencing: relating profiles to specific emissions sources
area sources
Area sources
  • Most basic inventory unit
  • Country/province/municipality wide estimate
  • Requires spatial surrogates to map to a model grid
  • Examples
    • Construction and agricultural emissions
    • Road dust
    • Fires
mobile sources
Mobile sources
  • On-road: Estimate by road way and vehicle type
    • Requires emissions factors for local vehicles and activities/speeds for local roads
    • Gridding by road way distribution or links
    • Can use local meteorology to adjust emissions factors for temperature and humidity
    • Examples: Heavy-duty diesel trucks on primary highways, light-duty gasoline cars on rural roads
  • Non-road: Area-like estimates
    • Examples: Construction and mining vehicles, recreational vehicles (boats, ATV’s),
point sources
Point sources
  • Emissions at specific latitude-longitude coordinates
  • Often elevated sources that require stack parameters (e.g. stack height, exit gas velocities, exit gas temperatures, etc.)
  • Can use annual, daily, or hourly emissions estimates
  • Examples:
    • Electricity generating units (EGU’s)
    • Smelters
    • Wildfires
biogenic sources
Biogenic sources
  • Estimates of emissions from vegetation and soils
  • Uses gridded land-use data and emissions factors by vegetation type
  • Uses local meteorology to calculate emissions based on photosynthetically active radiation (PAR) and to adjust for temperatures
  • Examples:
    • VOC emissions from specific tree species
    • Soil NO
gridded sources
Gridded sources
  • Pre-gridded emissions from global databases
  • Normalize to the model grid to combine with other sources
  • Can encompass any of the emissions categories
  • Top-down vs. bottom-up emissions estimate
emissions processing1
Emissions Processing
  • Purpose: convert emissions data to formats required by air quality model
  • Primary functions
    • Import data into system
    • Spatial allocation (gridding)
    • Chemical allocation (speciation)
    • Temporal allocation
    • Merge
    • Quality assurance
emissions processing steps
Data Import

Inventory categories






ASCII or gridded binary

Country/state/county estimates

Annual estimates

Pollutants include bulk VOC and PM2.5

Spatial Allocation

Inventory spatial units  model grid

Requires spatial surrogates

Emissions Processing Steps

EI  Grid Cell Mapping

emissions processing steps1
Chemical Allocation

Tons  Moles

Converts inventory pollutants to air quality model species

Model-dependent speciation profiles

NOx  NO + NO2

VOC  PAR, OLE, etc.

PM2.5  NO3, SO4, etc.

Temporal allocation

Inventory units  hourly emissions

Requires temporal profiles

Emissions Processing Steps




emissions processing steps2

Combine all intermediate steps to create AQM-ready emissions

Combine individual source categories



Output file naming

Quality Assurance

Report base inventory values and changes at each processing step

Customize reporting

e.g. by state and SCC, by SCC and temporal profiles, by grid cell and surrogate I.D.

Means to determine why a result occurred

Emissions Processing Steps
other emissions processing steps
Plume Rise

Allocate elevated emissions sources to vertical model layers

Compute layer fractions

Require meteorology to calculate plume buoyancy

Stationary point, fires, in-flight aircraft


Grow and/or control inventories for future year modeling

Source-based projection information

Other Emissions Processing Steps
emissions processing paradigms











Emissions Processing Paradigms
  • Linear
    • Sequential steps that follow a particular order
    • Requires completing one step before completing the next
  • Parallel
    • Flexible sequence with steps in any order



initial and boundary conditions
Initial and Boundary Conditions
  • Initial conditions define the chemical conditions at the start of a simulation
    • Defined using vertical profiles of clean background concentrations
  • Boundary conditions define the chemical conditions on the horizontal faces of the modeling domain
    • Static and dynamic boundaries are possible
  • Initial conditions decay exponentially with simulation time; boundary conditions on the upwind boundary continue to affect predictions through an entire simulation.
initial boundary condition processing
Initial/Boundary Condition Processing
  • Processing requires generating IC/BC estimates on a model-grid
  • Nested simulations extract BC’s from a parent grid
  • Multi-day simulations extract IC’s from the last hour of the previous day
photolysis rate processing

J = ∫4πIλ,T Aλ,T QYλ,T dλ


Photolysis Rate Processing
  • Photolysis: Chemical dissociation caused by the absorption of solar radiation
  • Photolysis rate: rate of reaction for pollutants that undergo photolysis
  • Processing calculates clear sky photolysis rates at different latitudes and altitudes
  • Air quality models adjust rates with cloud cover estimates from meteorology
what are air quality models
What are air quality models?
  • Statistical models: describe concentrations in the future as a statistical function of current chemical and/or meteorological conditions
  • Chemistry-transport models (CTM): based on fundamental descriptions of physical and chemical processes in the atmosphere
how do ctms work
How do CTMs work?
  • Air Quality Model processes
    • Dynamical/thermodynamical: meteorology, land surface conditions (soil, water)
    • Transport: emissions, advection, diffusion, dry deposition, sedimentation
    • Gas phase chemistry: photochemistry, phase changes
    • Radiative: optical depth, visibility, energy transfer
    • Aerosol/clouds: nucleation, coagulation, heterogeneous chemistry, aqueous chemistry
overlay 3 d boxes on a grid
Lagrangian/Trajectory Models

Moves relative to the coordinate

Different locations at different times

Only emissions enter the cell

No material leaves the cell

Overlay 3-D boxes on a grid
overlay 3 d boxes on a grid1
Eulerian Models

Fixed relative to the coordinate

All locations at all times

Materials move through all cell faces*

Overlay 3-D boxes on a grid
conceptual approach to ctms
Conceptual approach to CTMs
  • Extend the 2-D box model to three dimensions














Basic Continuity Equation (flux in 1 direction):

∆C ∆x∆y∆z = u1C1∆y∆z∆t – u2C2∆y∆z∆t

Divide by ∆t and volume: ∂C/∂t = - ∂(uC)/ ∂x

u = wind vector

Ci = concentration of species i

expanded continuity equation
Expanded Continuity Equation







Expanded Continuity Equation Derivation:

Expand to flux three dimensions:

∂C/∂t = - ∂(uC)/ ∂x - ∂(vC)/ ∂y - ∂(wC)/ ∂z

= - ∙ (vC) (flux divergence form)

Add additional production and loss terms:

∂C/∂t + ∙ (vC) = D 2 C + R + E - S








u,v,w = wind vectors

E = emissions

S = loss processes

Ri = Chemical formation of species I

D = Molecular diffusion coefficient


Aqueous Chemistry:

Gas Chemistry:

Aerosol Processes:



Rnuc + Rc/e + Rdp/s + Rds/e + Rhr

Diffusion: D 2 C

Advection: - ∙ (vC)

Boundary Conditions




R = Rate

chem=chemical production/loss hr=heterogeneous reactions nuc=nucleation c/ev=condensation/evaporation dp/s=depositional growth/sublimation ds/e=dissolution/evaporation wash=washout dep=deposition emis=emissions

full continuity equations
Full Continuity Equations
  • Gas Continuity Equation

∂C/∂t + ∙ (vC) = D 2 C + Rchemg + Remisg + Rdepg+ Rwashg + Rnucg + Rc/eg + Rdp/sg + Rds/eg + Rhrg

  • Particle Continuity Equation (number)

∂n/∂t + ∙ (vn) = D 2n + Remisn + Rdepn+ Rsedn + Rnucn

+ Rwashn + Rcoagn

  • Particle Continuity Equation (volume concentration)

∂V/∂t + ∙ (vV) = D 2V + Remisv + Rdepv+ Rsedv + Rnucv

+ Rwashv + Rcoagv+ Rc/ev + Rdp/sv + Rds/ev

+ Regv + Rqgv + Rhrv

ctm coordinate systems
CTM Coordinate Systems
  • Convert all motion equations from Cartesian to spherical coordinates
  • Horizontal grids typically on the order of 1 to 36 km
  • Recent applications extending to 500m and 108 km
  • Lambert conformal, polar stereographic, and Mercator are the most common modeling projections

dx = (Recosφ)dλe dy = Red φ

ctm coordinate systems1

pa – pa,top

σ =

pa, surf - pa,top

CTM Coordinate Systems
  • Vertical grids extend from the surface to 10 km
  • Altitude coordinate: layers are defined as surfaces of constant height with variable pressure
  • Pressure coordinate: layers are defined as surfaces of constant pressure with variable height
  • Sigma-pressure coordinate: layers defined as surfaces of constant σ, where


boundary layer processes
Boundary layer more difficult to model because of greater turbulence and larger emissions forcing terms than in free troposphere; land surface interactions and planetary boundary layer (PBL) dynamics dominate

Surface temperature and soil moisture affect energy and moisture flux; affect mixing heights, winds, and pollutant concentrations

Boundary Layer Processes
modeled cloud processes
Radiative transfer: reflecting, scattering, and trapping heat

Atmospheric component of the hydrologic cycle

Wet deposition of gases and particles

Medium for aqueous phase chemistry

Vertical transport/convective mixing

Energy balance: temperature effects and photolysis rates

Aerosol Processes

Modeled cloud processes

Aerosol particle


Gas Phase

Water Droplet

pA pA(a) A(a) A(r)

B(a) B(r)

pC pC(a) C(a) C(r)


New aerosol particle

energy radiative effects

Optical depth

scattering and absorption between top of atmosphere and altitude x

Photolysis rates

Radiative transfer

J = ∫4πIλ,T Aλ,T QYλ,T dλ


Energy/Radiative Effects

dI/dx = σbIB - σext I

σ = extinction coefficient

I = visible radiance




Fs (-μ,Θ)


Multiple scattering


Single scattering



4πI = actinic flux A = absorption cross section QY = quantum yield

gas phase chemistry
Thousands of different organic and inorganic gases react to form smog and PM

Gas phase chemistry is a “stiff” system

Parameterized chemistry mechanisms represent the system with a few surrogate organic pollutants

Surrogates based on molecular or atomic structures of pollutants

Carbon bond lumping

Propane = 3 PAR:


1-Butene = 2 PAR + 1 OLE:


averaged reaction rates

Molecular lumping

Surrogates represent similarly reactive species

Explicit or averaged reaction rates

Gas Phase Chemistry
gas phase chemistry1
Important Inorganic Reactions

NO + O3 NO2 + O2

NO2 + hv  NO + O (λ<420 nm)

O + O2 + M  O3 + M

O3 + hv  O2 + O(1D) (λ<310 nm)

O3 + hv  O2 + O3P (λ>310 nm)

O(1D) + H2O  2OH

OH + O3  HO2 + O2


HONO + hv  OH + NO (λ<400 nm)

NO2 + OH  HNO3

HNO3 + hv  NO2 + OH (λ<335 nm)

Important Organic Reactions

(methane example)

OH + CH4  H2O + CH3∙

CH3∙ + O2  CH3O2∙

CH3O2∙ + NO  NO2 + CH3O∙

CH3O∙ + O2  HO2 + HCHO

CH3O2∙ + HO2  O2 + CH3O2H

CH3O2H + hv  CH3O∙ (λ<360 nm)

CH3O2H + OH  H2O + CH3O2∙

Gas Phase Chemistry
gas phase chemistry2
Gas Phase Chemistry

Key reaction sequence for smog

ROG∙ + NO  NO2 + ROG∙∙

NO + O3  NO2 + O2

NO2 + hv  NO + O

O + O2 + M  O3 + M

gas phase chemistry3

J = ∫4πIλ,T Aλ,T QYλ,T dλ


Gas Phase Chemistry
  • Kinetics

aA + bB  eE + fF Rate = kr[A]a[B]b

Rate constant calculations

d[A]t/dt = -kF[A]t = -kS[A]t[B]0 = -kT[A]t[B]0[C]0

1st order: A  D + E kF = -(1/t)ln [A]t/[A]0

2nd order: A + B  D + E kS = -(1/[B]0t)ln [A]t/[A]0

3rd order: A + B + C  D + E kT = -(1/[B]0[C]0t)ln [A]t/[A]0

Arrhenius equation for temperature dependence

kr = Ar(300/T)Bexp(Cr/T)

Troe equation for temperature and pressure dependence

kr = {(k∞,T k0,T [M])/(k∞,T+k0,T[M])}Fc[1+(logk0[M]/k∞)^2]^-1

Photolysis rate equation

aqueous chemistry
Aqueous Chemistry
  • Gases equilibrate with the aqueous phase by Henry’s law:

[A(aq)] = HApA

  • Dissolved gases react in solution to form new compounds
  • Sequence: droplet formation  gases dissolve in droplet  chemical reactions  evaporation
aerosol dynamics
Aerosol Dynamics
  • Size distribution: ratio of # aerosols in a diameter range to the size of the range; discrete function of the number of particles

Ni= ni∆Dp

  • Number distribution: continuous function of the diameter of the particles

N = ∫ nN(Dp)dDp

  • Aerosol moments: properties of the distributions (e.g. mean, variance)


aerosol dynamics1
Aerosol Dynamics
  • Mass transfer solutions to transport mass between gas/aqueous/solid phases
  • Solve gravitational settling, diffusion, and advection for moving particles around
  • 4 classes of nucleation for particle formation:
    • Homogenous  Homomolecular
    • Homogenous  Heteromolecular
    • Heterogenous  Homomolecular
    • Heterogenous  Heteromolecular
ctm setup and configuration
CTM Setup and Configuration
  • All CTM’s are free and open source
  • Compile on UNIX/Linux with Fortran
  • Script interfaces for compiling and running
  • Begin with download, installation, and compilation
  • Set up computing environment
    • I/O directories
    • Check for processor availability and disk space
ctm setup and configuration1
CTM Setup and Configuration
  • CTM’s are at the end of a long sequence of preprocessing steps
    • Prepare meteorology inputs with research and forecast met models
    • Prepare emissions inputs with specialized emissions processors
    • Prepare initial and boundary condition inputs with preprocessors packaged with CTM
    • Generate clear sky photolysis rates with a preprocessor packaged with CTM
ctm process schematic



Model Ready





Wet Dep

2-D/3-D Met







Dry Dep


Input File







Input File





Clear Sky

J Rates

CTM Process Schematic
modeling conventions
Modeling Conventions
  • Establish base case model performance
  • Simulate sensitivities off the base case
  • Select episodes or time periods that illustrate the problem being addressed
    • O3 episodes
    • PM episodes
    • High flow regimes/transport scenarios
    • Annual episodes for one-atmosphere modeling
one atmosphere approach
One Atmosphere Approach
  • Changing paradigm from multiple models that address individual process to a single unified model
  • Conceptually more realistic: all atmospheric processes are coupled
  • In practice very difficult because of confounding errors

“Right answer for the wrong reasons”

what is the right answer for ctms
What is the right answer for CTMs?
  • Evaluation techniques
    • Comparisons to ambient measurements
    • Sanity checks
    • Looking for known trends (diurnal/seasonal patterns, chemical signatures (ratios)
  • Comparison to measurements
    • Paired in space and time
    • Compare predicted vs observed maximums
    • Paired in space but not in time
    • Statistical metrics include paired/unpaired peak prediction accuracy, mean normalized bias, mean error
problems in air quality modeling
Problems in air quality modeling
  • Inconsistencies in spatial scales and speciation when comparing models to measurements
  • Incomplete measurement database (PBL, radiation budget, short lived pollutants, observations aloft)
  • Huge uncertainties in all input data

Garbage in = Garbage out

problems in air quality modeling1
Problems in air quality modeling
  • Met and chemistry models are tuned for certain conditions
    • Meteorology models generally don’t work well under stagnant, low flow conditions
    • Chemistry models break down at night and during background ambient conditions
  • Incomplete science
    • For various reasons, some important atmospheric processes are either not represented at all or are using crude approximations
significant ctm studies
Significant CTM Studies
  • Regional Ozone Model: early 1980’s, first regional scale model, early studies on regional transport
  • Regional Acid Deposition Model: mid 1980’s, 1st multi-pollutant model, predecessor to current modeling systems
  • National Acid Precipitation Assessment (NAPAP): 1980’s, established links between S emissions in the Midwest to acid rain in the Northeast; first modeling studies of emissions trading programs
significant ctm studies1
Significant CTM Studies
  • Ozone Transport Assessment Group (OTAG): mid 1990’s, established multi-scale problem of ozone, relationships between 1-hr vs. 8-hr ozone standard and transport, prevailing regional conditions for poor air quality, weekday-weekend trends in air quality
model application examples
Model Application Examples

Regional Ozone Sensitivities - NCDAQ

Combined Area, Mobile, Point Reductions

Base June, 1996

Combined Area, Mobile, Point Reductions

Across the board Area, Mobile Reductions

model application examples1
Model Application Examples
  • Intercontinental transport of pollutants
model application examples2
Model Application Examples
  • Continental one atmosphere modeling
  • 1 day, 24-hour average ozone
  • Observations overlaid on plot
model application examples3
Model Application Examples
  • Continental one atmosphere modeling

Summer, 2002 Sulfate

Winter, 2002 Nitrate

future directions
Future Directions
  • Quantify model uncertainties
  • Expand the ability of the models to represent and integrate all atmospheric processes
  • 2-way coupling between global, regional, and neighborhood scale models
  • Source apportionment technologies
  • Couple with other media/disciplines (water,soil,risk, economics)
  • Community/open source development