# Presentation: 344037

## An ATD Model that Incorporates Uncertainty  

- R. Ian Sykes
- Titan Research & Technology Div., Titan Corp.
- 50 Washington Road
- Princeton NJ
**OFCM Panel Session on Uncertainty in ATD Models**
**9****th**** Annual George Mason University Conference **
**on Transport and Dispersion Modeling**
- July 19, 2005

## Methods for Estimating Uncertainty

- Explicit methods
- compute a representative collection of possible results, e.g.
- Monte Carlo
- Large Eddy Simulation
*generally straightforward, but computationally expensive*
- Statistical Methods
- compute statistics directly, e.g.
- PDF
- Statistical moments
*generally computationally efficient, but difficult to formulate*

## SCIPUFF ATD Model

- SCIPUFF uses simplest statistical method
- develop conservation equation for first two moments
- i.e., concentration mean and fluctuation variance
- use simple 2-parameter pdf to estimate probability
- implement in Lagrangian puff model
- Start with scalar diffusion equation
- where ***u*** is the turbulent (random) velocity

## Ensemble Statistics

- Define ensemble average
- not trivial in unsteady, inhomogeneous atmosphere
- Use classical techniques to develop equations for mean,   , and variance,
- Turbulent concentration fluctuations
- driven by velocity fluctuations
- determined largely by dissipation rate
- modeled in terms of turbulence spectrum

## Sources of Uncertainty

- Meteorology
- wind field
- turbulent boundary layer fluctuations
- mesoscale fluctuations
- uncertainty (forecast or analysis/interpolation)
- thermodynamics
- temperature
- humidity
- boundary layer
- stability
- mixed layer depth
- turbulence intensity

## More Sources of Uncertainty

- Landcover
- roughness / canopy
- terrain
- Physical processes
- liquids
- liquid droplet/pool evaporation
- liquid absorption / desorption
- particles
- gravitational settling
- dry deposition
- Source characteristics, etc., etc.

## SCIPUFF Uncertainty

- Generally limited to windfield
- expected to be significant and irreducible
- can also describe source location uncertainty via initial conditions
- Need estimates for
- turbulence intensity,             etc.
- turbulence correlation scales	, 
- Boundary layer turbulence (reasonably) well understood
- idealized shear- and buoyancy-driven layers
- investigating use of mesoscale model TKE for more general cases
- Mesoscale and Forecast Uncertainty poorly understood

## Large Scale Variations

- Large Scale means larger than PBL scale
- important for assessing long range dispersion
- also required for forecast/analysis uncertainty
- Ensemble forecasts
- explicit calculation of an ensemble provides a direct measure of velocity statistics
- limited sample gives velocity variances
- may be able to estimate Lagrangian autocorrelation timescale
- Subgrid fluctuations
- depends on subgrid terrain / landcover
- energy cascade from larger scales
- Smagorinsky model unlikely to be adequate for dispersion

## Role of Ensemble Modeling

- Ensemble methodology is generally applicable
- can describe any quantifiable uncertainty
- requires explicit description of random distribution of input / model parameters
- relatively expensive
- difficult to ensure complete coverage of all possible conditions
- Combined ensemble / statistical approach
- use statistical techniques to model limited range of uncertainty within larger ensemble
- e.g. use SCIPUFF to represent range of conditions within a set of sub-ensembles

## MM5 Dispersion EnsembleWarner et al (JAM, 2002)

## Ensemble Statistics

- One-point correlations are straightforward
- mean:
- variance:
- Length / Time Correlation scale is more difficult
- investigate Lagrangian autocorrelation

## Probability of exceeding 107kg-s/m3

- SCIPUFF Statistical
- Prediction

- MM5 Explicit
- Ensemble

## Concluding Remarks

- Many sources of uncertainty in atmospheric dispersion predictions
- sensitivity studies are needed to quantify/prioritize other uncertainties
- Meteorological uncertainty is known to be important
- ensemble modeling promises characterization of large (resolved) scale uncertainty
- subgrid mesoscale/synoptic requires research
- SCIPUFF modeling approach
- provides an efficient treatment of a major component of uncertainty
- can be combined with explicit approaches for more generality