This document discusses uncertainty in dispersion models used for air quality predictions. It notes that uncertainties should be routinely tracked for policy decisions, as in climate models. However, uncertainties are not commonly assessed for atmospheric pollution dispersion models. It recommends propagating uncertainties through parametric sampling and sensitivity analysis to determine influential parameters. Global sensitivity methods can evaluate model complexity and parameter importance. Closing the modeling loop through refinement informed by sensitivity analysis could help reduce prediction uncertainties.

1. School of something
FACULTY OF OTHER
The treatment of uncertainty in
dispersion models
Alison S. Tomlin
Energy and Resources Research Institute
SPEME, Faculty of Engineering

2. Why track uncertainties?
• In climate modelling the current expectation is that
uncertainties will be tracked within model predictions.
• Phrases such as “high confidence”, “likely”, “more likely
than not” etc. are presented along side mean predictions
and confidence limits.
• This is critical since such predictions are to be used in
decision making and policy formulation.
• Urban air quality models are also used to help form policy
on pollution mitigation strategies.
• So why are uncertainties in such model predictions not
routinely traced??

3. Hierarchy of model complexity
Direct numerical
simulation with
detailed chemistry.
Computationally expensive
Detailedchemicalandphysical
representations
Large Eddy
Simulation
Reynolds
Averaged CFD
+ Lagrangian
Semi-empirical
e.g. Gaussian, or
network models

4. Types of model uncertainty
Structural uncertainty:
➢ Missing physical/chemical processes within the model.
➢ Over simplification of processes to save compute power.
e.g. reduced chemistry, averaged turbulence representations.
➢ Influence of grid resolution.
Parametric uncertainty:
➢ Complex models contain large numbers of parameters
that are all uncertain.
e.g. kinetic reaction rates, roughness lengths, mixing
timescales, emissions, flux rates etc.

5. Propagating Uncertainties
➢ Parametric uncertainties can be propagated through
sampling methods using multiple model runs.
➢ Structural uncertainty more difficult to assess:
the “Unknown unknowns” dilemma.
➢ Neither approach commonly used in atmospheric pollution
dispersion models!

6. Can we learn from other
communities?
Climate Change community tests for structural uncertainties
via the inter-comparison of models and observations.

7. Could perform sensitivity
analysis of model components

8. Examples of process
sensitivity analysis

9. Model inter-comparison for
dispersion models?
➢ A few examples of inter-comparisons between models of
the same type e.g. Gaussian based, different RANS
models.
➢ Few exercises that compare models of different structure to
assess their fitness for purpose.
What does fit for purpose mean?
• Within parametric uncertainties model overlaps with error
bars of measured data.
• Model can be extrapolated to new conditions (not easy for
over-fitted models) i.e. predictive.
• Other criteria? Doesn’t have to be physically realistic.

10. Evaluation of complex models
• Need to evaluate if models are fit for purpose.
• Comparison of model with experimental or field data for
simple to complex scenarios.
MUST INCLUDE
• how much confidence we can place in simulations.
• If lack of agreement then how do we find contributing
causes?
• Sensitivity and uncertainty analysis help to answer these
questions:
- need strong feedback loop between model
evaluation and methods for model improvement.

11. Sensitivity and uncertainty
analysis
• Uncertainty analysis (UA)
estimates the overall predictive
uncertainty of a model given the
state/or lack of knowledge about its
input parameters.
• UA puts error bars on predictions.
Sensitivity analysis (SA) determines
how much each input parameter
contributes to the output uncertainty
(usually variance).
Parameter Si, x=2.2 m
Structure function coeff. C0 0.7976
Mixing time-scale coeff. α 0.1853
Σ Si 0.9843

12. How can uncertainties be
traced?
• The most consistent ways to trace uncertainties are
1. To run several models with potentially different structures and
parameterisations.
2. To run each model using an ensemble or random sample of input
parameters in order to generate a distribution of predicted target
outputs.
Parameter 1
Parameter2
Estimated maxEstimated min

13. Scatter plots for urban RANS dispersion
model
The examples show possible nonlinearities and large scatter –
obscuring overall sensitivity to parameter.
Wind direction° (input) Wind direction° (input)
Verticalvelocityinstreet(output)
Rooflevelturbulence(output)

14. High Dimensional Model
Representations (HDMR)
• Developed to provide detailed mapping of the input variable space to
selected outputs – a meta-model.
• Output is expressed as a finite hierarchical function expansion:
• Meta-model built using quasi random sample and approximation of
component functions by orthonormal polynomials.
• Used to generate partial variances and therefore sensitivity indices
• Si then ranked to give parameter importance.
)x,...,x,xx,xf)(xfff n21
nji
jiij
n
i
ii  

1
12...n
1
0 (f...)()(x

15. Component functions for
previous example
Wind direction°
Verticalvelocityinstreet
Rooflevelturbulence
Wind direction°
Verticalvelocity
Wind direction°Surface roughness length

16. Closing the loop
• High ranked parameters could then be re-estimated using ab
initio modelling studies or simple experiments which help to
isolate their effects.
• If the parameter can be re-estimated with better certainty
then the error bars of the prediction are reduced.
• In some cases, even within the error bars, there is no
overlap between experimental and modelled outputs.
suggests structural problems with the model
• For this reason comparisons of model vs observations
should include error bars on BOTH!

17. Example: York street canyon
simulation of [NO2]
Signal
controlled
intersection
TKE, wind
vectors for
θref=90° to
canyon
axis

18. Complex model couplings
Traffic micro-simulation
model
Vehicle Characteristics
Traffic Network
Information
Instantaneous
emissions model
Vehicle
speeds
Vehicle acceleration
CFD flow model
(MISKAM k-ε)
Meteorology Building
layouts
Emissions
Flow and turbulence
Dispersion model
Pollution concentrations

19. Parameter set varied in global
sensitivity study
Model parameters (26 in total):
➢velocity structure function coefficient co
➢mixing time-scale coefficient α
➢surface roughness z0 for inlet, surface and wall
➢temperature dependant rate parameters for NO/NO2/O3 reactions,
photolysis rate parameters for JO3 and JNO2
➢wind direction θref
➢temperature
➢background [O3]
➢NO:NOx ratio
➢traffic demand
Model
parametrisation
Physical/meteorological
Traffic
emissions

20. Sample sensitivity results
(θref= 110-130): average over 6 in-canyon
road-side locations: mean [NO2]
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
Averagesensitivityindex
Off-Peak
Peak

21. Summary of findings
• Based on the assumed uncertainties in input
parameters the predicted roadside increments in
[NO2] can vary by around a factor of 2.
• Using the HDMR approach the influence of
traffic related parameters e.g. demand, primary
NO2 fraction, can be assessed within the overall
data scatter.
• For sites away from the traffic queue the wind
direction is the single most important parameter
affecting predicted NO2.
• Model parameters such as surface roughness lengths are influential.
• Chemical parameters (for NO+O3) are important for sites near the
junction.
• Background O3 appears not to be too influential for this site.

22. Conclusions
• Propagating uncertainties within pollution dispersion models needs to
become more routine.
➢ Doesn’t come without a computational cost.
•Uncertainties can be significant e.g. causing a factor of 2 variability in
predicted concentrations.
•Using global sensitivity/meta-modelling approaches it is still possible to
trace the influence of controllable parameters e.g. traffic demand on
target outputs using component functions.
•Wind speed and direction are key parameters causing variability and yet
we have very few truly urban met stations.
We can learn from other communities!

23. HDMR software with graphical
user interface freely available
Main author: Tilo Ziehn

24. Example
• Need to be able to model formation of secondary pollutants such as NO2
in order to test the impact of emission reduction strategies.
• Computational fluid dynamics (CFD) models becoming more common in
pollution and emergency response management.
• Different turbulence closure schemes in use:
Reynolds Averaged Navier Stokes (RANS), Large Eddy Simulation
(LES).
• Also different dispersion schemes:
Lagrangian particle, stochastic fields, eddy diffusivity.
• Urgent need to evaluate where different approaches are “fit for purpose”
and the impacts of parametrisations of turbulence, mixing and kinetics.

25. Convergence with sample size
0.00E+00
1.00E+11
2.00E+11
3.00E+11
4.00E+11
5.00E+11
6.00E+11
7.00E+11
8.00E+11
9.00E+11
0 20 40 60 80 100 120
NO2concentration(moleculescm-3)
Sample size in Sobol sequence
Mean Variance
64 samples enough to
give accurate estimates
of mean and variance of
predicted [NO2]
What we want to know is which of the 26 input
parameters contribute most to this predictive variance
due to their estimated uncertainties i.e.
what are the global sensitivities for each parameter?