Making of a supermodel

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Making of a supermodel

• Amir Hakami

ENVE 5103 November 14, 2007
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Applications of air quality models

• How air quality models are utilized beyond the
  streamlined regulatory framework?
• Examples of applications
• Inverse modeling of emissions using satellite
  observations
• Models as policy support tools
• High-order analysis
• Cross-boundary pollution transport
• Some other potential applications
• Future directions in modeling

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Air quality management system
Air quality models can contain more information
than we usually use (i.e. sensitivity
coefficients).
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Sensitivity analysis

• What is the response to possible changes in
  inputs?
• Were mainly concerned with emissions, but also
• Uncertain parameters such as deposition
  velocities, rate constants, turbulence
  parameterization, etc
• Initial conditions ? practical significance in
  air quality forecasting
• In essence every modeling practice is sensitivity
  analysis because were ultimately interested in
  being able to characterize/predict the response.
• Formal sensitivity analysis gaining more
  momentum, in part owing to significant advance in
  computational resources.
• What if vs. How to questions?

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Local sensitivity coefficients
First-order sensitivities provide information
about slopes of the response surface, not
curvatures (nonlinearities).
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Forward vs. backward sensitivity analysis
Inputs/Sources
Outputs/Receptors

• Adjoint analysis is efficient for calculating
  sensitivities of a small number of outputs with
  respect to a large number of inputs. Forward
  analysis is efficient for the opposite case.
• Complementary methods (Source-based vs.
  Receptor-based), each suitable for specific types
  of problems.

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Model, forward, and adjoint formulations

• Forward model

• Forward sensitivity or DDM (Dunket et al., 1984)

• Backward/adjoint sensitivity (Sandu et al., 2005)

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High-order sensitivity analysis
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The question of nonlinearity

• Resulting mainly from the chemistry, but also
  from aerosol thermodynamics and dynamics
• Our analysis of air pollution control often
  presumes linearity
• First-order approximation
• Not an entirely bad assumption!
• By knowing second-order sensitivities
  (curvatures) in addition to first-order ones
  (slopes), we can explain the nonlinear behaviour

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Nonlinearity ozone isopleth

• Best example of nonlinearity in atmospheric
  response

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Nonlinearity sensitivity characterization
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HDDM formulation
High-order DDM or HDDM (Hakami et al., 2003)
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Presence of nonlinearities -daytime
2nd order DDM
1st order DDM
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Presence of nonlinearities - nighttime
2nd order DDM
1st order DDM
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Time- and location-dependent isopleths
Ozone isopleth, peak location
High-order coefficients can be used in a Taylor
expansion for creating isopleths (Hakami et al.,
2004)
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Time evolution of isopleths
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Improved projections
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Projection errors
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Adjoin sensitivity analysis of ozone nonattainment
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Adjoint formulation

• Target-based, receptor-oriented method Depends
  on the definition of a cost function ( J ) for
  which sensitivity calculations are carried out.
• Adjoint equations are integrated backward in
  time. At each location and time adjoint variables
  are gradients (sensitivities) of the cost
  function with respect to concentrations.

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General context (an example from the US)

• Ozone nonattainment One of the major air quality
  issues facing the U.S. and the World
• During 2004, 474 counties in the US, with 160
  million inhabitants, were in some degree of
  non-attainment with respect to the 8-hour NAAQS
  standard for ozone (80ppb).
• Because of sufficiently long lifetime of ozone
  and its precursors interstate transport plays an
  important role.
• CAIR (Clean Air Interstate Rule) for ozone and
  PM2.5.
• 28 eastern states in the US.
• Regulates NOx emissions from power plants only.
• Calls for cap-and-trade programs at the
  discretion of the states.
• Objective Development of a robust method for
  analysis of multi-state ozone nonattainment and
  long-range transport of ozone.

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Application details

• Adjoint version of STEM-2k1.
• Modeling domain covers continental US.
• 97x62x21 computational grid with 60 km horizontal
  grid resolution.
• Month of July and part of August 2004 (ICARTT
  campaign).
• 2001 NEI emission inventory.

Model performance statistics (40 ppb cut-point)
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Nonattainment (NA) analysis

• Cost function calculated only for concentrations
  above the threshold.
• Quadratic cost function to emphasize higher
  concentrations.

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Spatially-resolved NA sensitivities

• Total non-attainment sensitivities amount to
  335.
• Of the total, NOx, biogenic VOCs, and
  anthropogenic VOCs, account for 66, 21, and 13
  percent, respectively.
• Negative NOx sensitivities in metropolitan
  areas.

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Interstate transport state ranks
State ranks in NOx emissions, NA, and NA
sensitivity

• There is not a solid correlation between the
  first measure of responsibility (emissions) for
  the NA and scientifically more robust estimates
  (NA sensitivities) at the state level.

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Adjoint analysis as a policy support tool
Cost
Benefit
Effectiveness

• Nondiscriminatory emission trading (as proposed
  in CAIR) between the states with significantly
  differing contribution potentials (NA
  sensitivities) may compromise benefits from the
  reduction in the nationwide cap in the US (Hakami
  et al., 2006).

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Target-based analysis
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Potential applications

• Different applications depending on the
  definition of the cost function.
• As a receptor-based method, adjoint analysis is
  particularly powerful for policy applications
• Nonattainment analysis
• Most common uses in data assimilation and inverse
  modelling
• Lets look at few other examples (Hakami et al.,
  2007)

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Potential applications population exposure
Sensitivity to NOx emissions
Metric distribution
(Plots are normalized to the total metric)
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Potential applications - vegetation Stress
Sensitivity to NOx emissions
Metric distribution
(Plots are normalized to the total metric)
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Potential applications - temperature dependence
Population exposure
Vegetation stress
NB This only includes the effects through
chemistry.
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Satellite-based inverse modeling of emissions
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Application details

• An adjoint of gas-phase CMAQ is developed.
• SCIAMACHY tropospheric NO2 column densities used
  as observations.
• 3-day simulation (6/20/2005-6/22/2005).
• 36 km horizontal resolution (45x46), 23 vertical
  layers.
• 3-D time-independent, emission scaling factors
  (47610 variables to adjust).
• Time-dependent boundary conditions from GEOS-Chem
  global model (ozone, NO, NO2, PAN, HNO3).
• Lightning Emissions added to CMAQ.
• Why satellites? Why inverse modeling? And, what
  is inverse modeling?

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Adjoint formulation

• Cost function is defined to measure model misfits
  and deviation from a priori estimates
• Gradients of the cost function with respect to
  the control variables are calculated during
  backward calculations.
• The cost function is minimized iteratively using
  the calculated gradient.
• Here, we solve for emission scaling factors
• CMAQ grid cells are interpolated horizontally and
  vertically to produce concentrations that
  correspond to SCIAMACHY averaging kernel.

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SCIAMACHY vs. CMAQ
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Scaling factors

• Unrealistically large needs to be vastly
  improved

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Emerging areas of research (at Carleton and
elsewhere)
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At home

• Inverse modeling of satellite observations
  (Dalhousie, Caltech, JPL)
• The lightning question (Dalhousie).
• Forecasting (Waterloo, EC)
• Multi-pollutant non-attainment analysis
• Cross-border and intercontinental transport
• PM and mortality in Denver (CU, CSU)
• Adjoint for aerosols (GaTech)
• Control strategy optimization
• Climate change and air quality (JPL, UCLA)

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Elsewhere

• Aerosol parameterization
• Particularly secondary organic aerosols
• Inverse modeling
• One-atmosphere modeling
• Online dynamic/chemistry modeling
• Forecasting
• Ensemble forecasting
• Air quality and climate change
• Sub-grid representation
• Integration of space-borne observations in air
  quality applications
• Geo-synchronous satellites
• And

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Acknowledgements

• Thanks to
• John Seinfeld and Daven Henze (Caltech)
• Ted Russell, Talat Odman, Yongtao Hu, and
  Michelle Bergin (Georgia Tech)
• Adrian Sandu and Kumaresh Singh (Virginia Tech)
• Greg Carmichael, Tianfeng Chai, and Youhua Tang
  (University of Iowa)
• Daewon Byun (University of Houston)
• Dan Cohan (Rice University)
• Qinbin Li (JPL)

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Questions? Comments?
Thank you!!