Applications of

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• Applications of
• Ensemble Variance and Co-variance
• in SCIPUFF
• Binbin Zhou1 and Jeff McQueen2
• 1. Science Application
  International Corp (SAIC)
• 2. Environmental modeling
  Center (EMC) NCEP
• Predictability Meeting,
  EMC/NCEP, Feb. 27, 2007

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• Second-order closure integrated PUFF (SCIPUFF)
• - A hazardous material dispersion model
  developed by Titans ARAP Group
• - Second-order closure turbulence scheme
  Gaussian puff dispersion model
• - 2nd-order closure -More accurate than
  K-closure (1st-order) turbulence scheme
• - Lagrangian trajectory
• A collection of 3-D, time-dependent
  Gaussian puffs released from certain location
• - Mesoscale model (s) SCIPUFF coupled
• A Mesoscale model (MM5, WRF) provides
  background fields for dispersion
• - Has been incorporated in Defense Threat
  Reduction Agencys (DTRA)
• Hazard Prediction and Assessment
  Capability (HPAC) software

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Example MM5 and WRF plumes near Torino
Olympics Blue HAPC uncertainties w/constant
large scale variances Courtesy Pat Hayes
DTRA-NGC
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• Puff trajectories are most influenced by local
  winds
• - PBL/SBL is determined by local scale
  factors
• Turbulence dispersion occurs within
  PBL/SBL
• Complexities in terrains, buildings,
  local winds, stabilities, surfaces, etc
• - Uncertainties exist in PBL and SBL
  prediction fields from the background
• model
• - Can estimate such uncertainties
• (1) Using experience formulations to
  estimate error variance growth
• (2) Using variance info from an ensemble
  forecast system

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• Experience formulations (SCIPUFF V. 2, Tech
  Report, 2006)
• Error growth is assumed as an increase in
  variance

Where is normalized error variance.
t is a time scale for error growth, t 1.53
days. When t ? t,
are climatological variances
and covariance
6
1.0
t 1.5 days
0.5
t 3.0 days
t
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• Var, CoV from ensemble systems (SREF, GENS)
• - Ensemble mean wind Var/CoV of winds
  are provided to SCIPUFF
• ? ensemble puff distributions
• - UUE, VVE and UVE at various forecast
  times can be input into SCIPUFF
• - UUE, VVE can be directly from spread 2,
  but UVE cant be done easily, so using
• Ensemble product generator
• (1) Co-variance
• (2) Co-efficient
• where u and v are at same grid point
  grid scale covariance, um and vm are mean of u
  and v components

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• Large scale variance (SLE)
• - In addition to UUE, VVE and UVE, so called
  large scale variances
• UUL, VVL, UVL are also contributed to
  meteorological uncertainty
• - UUE,VVE, UVE represent the outer variability
  on small grid cells.
• - UUL, VVL, UVL represent the variances on
  large grid scale?
• I am still not clear yet.
• - How to compute UUL, VVL, UVL? Still not
  known
• - Some tentative methods suggested by PSU
  recently
• UUE, VVE, UVE are computed at single grid
  point ( i )
• UUL, VVL, UVL are computed at two different
  points ( I, j )

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UUL, VVL, UVL continue

• Easy to be done by ensemble product generator,
  but will be very
• computing expensive.
• - Question
• How far away the two grid points ( I, j )
  ?
• - Answer
• Not solved yet

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• Vision of variance/Co-variance beyond
• SCIPUFF
• Ensemble Var/CoV mimic Turbulence Var/Cov

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Turbulence Ensemble
Variance
Variance
Self relation
Spread 2
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Turbulence Co-variance ? fluxes
? Sensible heat flux?
? Latent heat flux?
Ensemble Co-variance ? fluxes ?
?Ensemble sensible heat flux?
?Ensemble latent heat flux?
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Turbulent kinetic energy (TKE)
The relationship between TKE and other
coo-variances can be derived from Navier-Stokes
equations
Generated from mean flow (shear production)
Generated/dissipated from buoyancy (fluxes)
depending on atmospheric. stability
Viscous dissipation (into the surface)
Turbulence transport upward/downward
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Ensemble kinetic energy (EKE)
Question Could/How EKE be related to those
ensemble variances and co-variances like
TKE? Answer Dont know yet. From its form,
EKE also can be derived from Navier-Stokes
equation too! (Difference TKE only takes
account of vertical, EKE may also consider
horizontal) Following for sure TKE takes
energy from mean flow / buoyancy (large eddy) and
is dissipated into small eddies, so TKE increases
at day and decreases at night (decay). But EKE
is always increasing with time. TKE exists in
the real world, EKE only exists in ensemble
forecast systems The examples of EKE and other
ensemble variance and co-variance