HYbrid Single-Particle Lagrangian Integrated Trajectory Model Roland R. Draxler

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HYbrid Single-Particle Lagrangian Integrated
Trajectory ModelRoland R. Draxler

• HISTORY
• 1.0 (1979) rawinsonde data with day/night
  (on/off) mixing
• 2.0 (1983) rawinsonde data with continuous
  mixing
• 3.0 (1987) meteorological model gridded fields
• 4.x (1996) multiple meteorology with hybrid
  particle-puff
• 4.0 (8/98) switch from NCAR to postscript
  graphics
• 4.1 (7/99) isotropic turbulence options
• 4.2 (12/99) revised terrain sigma use of
  polynomial
• 4.3 (3/00) revised vertical auto-correlation for
  dispersion
• 4.4 (4/01) dynamic array allocation and lat-lon
  meteo
• 4.5 (9/02) integrated ensemble and matrix
  options
• 4.6 (6/03) non-homogeneous turbulence correction
• 4.7 (1/04) added velocity variance and TKE
  options

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Overview of Model Features

• Predictor-corrector advection scheme
• Linear spatial temporal interpolation of
  meteorology from external sources
• Vertical mixing based upon SL similarity, BL Ri,
  or TKE
• Horizontal mixing based upon velocity
  deformation, SL similarity, or TKE
• Puff and Particle dispersion computed from
  velocity variances
• Concentrations from particles-in-cell, or Puffs
  with Top-Hat or Gaussian distributions
• Multiple simultaneous meteorology and / or
  concentration grids

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Eulerian Dispersion Models

• Advection-Diffusion Equation
• Solve for local derivative
• at all grid points
• Dispersion a function of concentration gradients
• Handles many sources
• complex chemistry
• Artificial diffusion can be a problem for point
  sources

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Lagrangian Dispersion Models

• Solve for total derivative
• along the trajectory
• Computation required only at nearby grid points
• Concentrations for point sources handled
  correctly
• Implicit linearity
• Concentration at a receptor the sum from all
  sources
• Solution for too many sources can be inefficient

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Relationship of Trajectory to Height
FieldAnimation Example

• July 12-13, 1979
• 700 hPa height field
• Snapshots 4x / day
• Trajectory follows height
• Isobaric calculation
• Parcel release at 3 km
• Represents advection of point integrated in space
  and time!

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Equations for the Trajectory Computation

• Position computed from average velocity at the
  initial position (P) and first-guess position
  (P')
• P(tdt) P(t) 0.5 V(P,t) V(P',tdt) dt
• P'(tdt) P(t) V(P,t) dt
• The integration time step is variable Vmax dt lt
  0.75
• The meteorological data remain on its native
  horizontal coordinate system
• Meteorological data are interpolated to an
  internal terrain-following (s) vertical
  coordinate system
• s (Ztop - Zmsl) / (Ztop - Zgl)
•  

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Example Trajectory Graphic from HYSPLIT

• Postscript output format
• Labels describe
• Starting time
• Starting location
• Starting height
• Meteorological data
• Vertical Projection
• Shown by time
• Height or pressure

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Example of Numerical Trajectory Error

• The numerical accuracy of the computation can be
  estimated by running a forward and then backward
  trajectory to the origin point
• The numerical integration errors will be much
  smaller than the data representation errors

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Example of Meteorological Data Errors

• The largest source of error is the representation
  of variables by discrete data points
• A qualitative measure of the error can be
  determined by running trajectories using
  meteorological data from different sources
• Trajectories have been computed using data from
  ECMWF, NOAA, and MM5 (108and 36-km)
• Differences between trajectories are much greater
  than the numerical error

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Ensemble Estimates of Trajectory Error

• Each member of the trajectory ensemble is
  calculated by offsetting the meteorological data
  by a fixed grid factor
• The default offset is one meteorological grid
  point in the horizontal and 0.01 sigma units in
  the vertical
• The results in 27 members for all-possible
  offsets in X, Y, Z

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Trajectory Representation of a Plume

• A single trajectory cannot properly represent the
  growth of a pollutant cloud when the wind field
  varies in space and height
• The simulation must be conducted using many
  pollutant particles
• New trajectories are started every 4-h at 10,
  100, and 200 m AGL to represent the boundary
  layer transport

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Dispersive 2500 Particle Plume Simulation

• Particle a point mass of contaminant. A fixed
  number is released with mean and random motion.
• Puff a 3-D cylinder with a growing
  concentration distribution in the vertical and
  horizontal. Puffs may split if they become too
  large.
• Hybrid a circular 2-D object (planar mass,
  having zero depth), in which the horizontal
  contaminant has a puff distribution and in the
  vertical functions as a particle.

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Particle and Puff Distribution after 24-hRandom
Particles (left) and Mean Puff Positions (right)

• dsh/dt 20.5 su
• su (Kx / TL)0.5

• X(tdt)Xmean(tdt)U'(tdt) dt
• U'(tdt)R(dt) U'(t)U" (1-R(dt)2 )0.5
• R(dt)exp(-dt/TLx)
• U s x Gaussian Random Number
• sh2 (Xi-Xm)2

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Particle Positions with Dispersion

• Initial release 1000 particles
• Each advection step computed with mean wind and
  turbulence
• Position results after 24 hrs
• Horizontal distribution primarily due
  differential advection
• Effects of horizontal and vertical wind shear as
  particles mix to different levels

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Computation of Air Concentration

• Each particle is assigned a pollutant mass
• Concentration is simply the mass sum / volume
• Volume may be defined as the
• concentration grid cell for particles
• the volumetric distribution of the puff

• 3D particle dC q (dx dy dz)-1
• Hybrid Top-Hat dC q (pi r2 dz)-1
• Hybrid Gaussian dC q (2 pi s2 dz)1 exp(-x2 /
  2s2)
• Puff Top Hat dC q (pi r2 dzp)-1
• Puff Gaussian dC q (2 pi s2 dzp)1 exp(-x2 /
  2s2)

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Concentrations Resulting from a Single Particle

• Concentration Grid defined at 50 km resolution
• Air concentration unit mass / volume
• Concentration depends on particles residence
  time in cell
• A single particle (or trajectory) cannot
  represent the complex plume

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Concentrations Resulting from the Release of 1000
Particles and 50-km Grid

• Results shown after 24 hours
• 50 km concentration grid size
• The internal plume structure is is not well
  resolved due to the large concentration cell size

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Concentrations Resulting from the Release of 1000
Particles and 25-km Grid

• Shown after 24 hours
• 25 km concentration cell size
• Smaller cell sizes shows more structure
• Horizontal distribution appears to be noisy
• Needs more particles
• Suggests use of puff approach
• Faster to model growth of particle distribution
  (puff)

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Why Puff Dispersion?

• Simulation models the growth of the particle
  distribution (standard deviation)
• Requires fewer particles (puffs)
• Growth uses the same turbulence parameters
• Hybrid method suggested default
• Fewer puffs required for horizontal distribution
• Vertical shears captured more accurately by
  particles

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Turbulence Options

•  Standard Diffusivity / Deformation
• Kz k wh z (1 - z/Zi)
• Kh 2-0.5 (c d)2 du/dy dv/dx
•  Velocity Variances for Short-Range
• w2 3.0 u2 (1 z/zi)3/2
• u2 4.0 u2 (1 z/zi)3/2
• v2 4.5 u2 (1 z/zi)3/2
• Turbulent Kinetic Energy
• E 0.5 (u2 v2 w2)
• w2 0.52 E, u2 0.70 E, v2 0.78 E
• u2 v2 0.36 w2

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Horizontal Distribution for a Single Puff

• Top-Hat Distribution
• Uniform over 1.54 sigma
• Mean Gaussian

• Gaussian Distribution
• Shown over 3 sigma
• Mean Top Hat

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Horizontal Distribution for 500 Puffs

• Left side using the Top-Hat
• Central region identical to the Gaussian
• Sharp transition at the edges

• Right side using the Gaussian
• Central region identical to Top-Hat
• Smooth transition at the edges

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Example 24-h Average Air ConcentrationsUsing 500
top-hat particle-puffs

• Actual grid cell values

• Standard display output
• Uses grid smoothing to produce cleaner contours

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Ensemble ConcentrationsProbability of Exceeding
10-12

• NCEP/NCAR
• ECMWF ERA40
• MM5 (108, 36, 12, 4 km)

• Internal grid shift
• 27 member ensemble
• Using 36-km MM5

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Ensemble Calculation Example from ANATEX

• Plot shows 90th percentile model concentration
  contours for a 24h period several days after the
  tracer release
• Within a contour, 10 of the members predict a
  higher concentration and outside of the contour
  90 of the members predict a lower concentration
• Locations for the measured values are indicated
  by X and the corresponding value

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Local Scale VerificationWashington D.C. -
Metropolitan Tracer Experiment

• Tracer releases
• Rockville, Mt. Vernon, Lorton
• every 36-h at 2 locations
• Sampling
• 3 locations at 8-h
• 93 locations monthly
• Duration all 1984
• Meteorology
• ECMWF ERA-40 (shown)
• MM5 4-km (incomplete)
• Nocturnal intensives
• Plume measurements
• Tethersonde data

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Regional Scale VerificationIdaho Forest Fires
August 2000

• Daily particle snapshot positions at 1800 UTC
• Squares represent TOMS satellite aerosol index
  value
• Continuous particle release to correspond with
  with major forest fire location
• Particles line up with air mass boundaries

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Continental Scale VerificationChina Dust Storm
April 2001

• Emissions using integrated PM10 module
• Friction velocity over desert land-use grid cells
  exceeds threshold velocity
• Daily particle snapshot positions at 0600 UTC
• Colored squares show TOMS aerosol index value

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China April 2001 Dust Storm PM10 Concentrations

• Predicted concentrations over the US 10 to 18
  days after the event started
• Slight over-prediction at most sites due to
  no-deposition during simulation
• Arrival times match measured times
• Measurements are 24h averages taken every 3rd day

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China 2002 Dust Storm PM10

• March 2002 event not global like the April 2001
  dust storm
• Hourly PM10 measurements shown in Seoul, Korea
• Excellent match with time of onset and peak
  concentrations
• Measured duration much greater, probably due to
  particle re-suspension
• As in other cases, model predicts emission
  locations and amount

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Quantitative VerificationStatistics for Several
Long-Range Experiments

• Experiment Model R FB FMS KS RANK
•   ACURATE May 2002 0.25 -0.05 18.73 79 1.43
• Dec 2002 0.25 0.48 18.01 79 1.21
•   ANATEX1 Dec 2002 0.34 0.29 35.09 59 1.73
• Dec 2003 0.44 0.18 32.84 59 1.85
•   ANATEX2 Dec 2002 0.18 0.16 34.06 56 1.73
• Dec 2003 0.18 0.19 33.97 56 1.72
•   ANATEX3 Dec 2002 0.14 0.12 21.01 50 1.67
• Dec 2003 0.17 0.0 20.70 56 1.73
•   CAPTEX Dec 2002 0.00 -0.12 16.78 71 1.40
• Dec 2003 0.02 -0.27 17.07 71 1.33
•   INEL74 Apr 2001 0.00 0.13 7.97 92 0.48
• Dec 2002 0.00 1.39 7.27 92 0.46
• OKC80 Dec 2002 0.08 -0.66 27.60 34 1.52
• Dec 2003 0.43 -0.87 35.01 43 1.67
•   ETEX Apr 2001 0.48 0.33 57.27 68 1.96
• Dec 2003 0.45 0.78 47.69 68 1.61
•  

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Averaged Verification Statistics
Temporally Averaged Verification Statistics for
Long-Range Experimental Data   Experi
Experiment Model R FB FMS KS RANK   ACURATE
May 2002 0.90 -0.06 100.0 58 3.20 Dec
2002 0.86 0.47 100.0 78 2.73  ANATEX1 Dec
2002 0.85 0.26 100.0 18 3.41 Dec
2003 0.85 0.14 100.0 23 3.43  ANATEX2 Dec
2002 0.56 0.13 100.0 26 2.98 Dec
2003 0.48 0.16 100.0 26 2.89  ANATEX3 Dec
2002 0.25 0.05 98.67 48 2.54 Dec
2003 0.20 -.06 98.67 46 2.54  CAPTEX Dec
2002 0.80 -0.17 94.87 17 3.33 Dec
2003 0.76 -0.31 94.87 19 3.18  INEL74 Apr
2001 0.13 1.39 100.0 89 1.43 Dec
2002 0.35 1.41 100.0 98 1.44  OKC80 Dec
2002 0.96 -0.64 80.0 18 3.21 Dec
2003 0.83 -0.85 90.0 20 2.97  ETEX Apr
2001 0.51 0.23 84.89 20 2.79 Dec
2003 0.59 0.65 82.55 20 2.65  
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Summary

• Point source pollutant transport and dispersion
  calculations are very sensitive to
  source-receptor geometry and the meteorological
  data driving the calculation
• Event based verification includes all the above
  limitations of temporal and spatial resolution
• Future systems should incorporate automated
  verification linked with satellite observations
  of smoke from fires and dust storms