Jie Gao, Rick Luettich University of North Carolina at Chapel Hill Jason Fleming
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Transcript of Jie Gao, Rick Luettich University of North Carolina at Chapel Hill Jason Fleming
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Development and Initial Evaluation of A Generalized Asymmetric Tropical Cyclone Vortex Model in ADCIRC
Jie Gao, Rick LuettichUniversity of North Carolina at Chapel Hill
Jason FlemingSeahorse Coastal Consulting
ADCIRC Users Group Meeting, USACE Vicksburg, MS, April 29, 2013
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Introduction
NW NE
SW SE
Storm forward motion
Schematic cross section of a hurricane wind field
Goal: use tropical cyclone storm parameters provided in NHC ATCF Best Track or Forecast Advisories to generate dynamically consistent pressure and wind fields for storm surge predictions.
Storm Parameterslon, lat of center of eye VmaxR64 , R50 , R34 in 4 storm quadrantsPc - ATCF BT only
Pn , Rmax - estimated separately
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Holland (1980) Wind Model (ADCIRC: NWS=8)
๐ (๐ )=๐๐+ (๐๐โ๐๐ )๐โ๐ด /๐ ๐ต
Hyperbolic hurricane pressure profile (Schloemer 1954):
(1)
Substitute into the gradient wind equations, the vortex wind velocity is:
(2)
Hurricane Isabel of 2003 showing the circular, symmetric eye associated with annular hurricanes at Sept 13 2013 1710Z.
The Holland Wind Model produces a symmetric hurricane vortex with the spatially constant Rmax.
๐ ๐๐๐ฅ
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๐ ๐ (๐ )=โ๐๐๐๐ฅ2 ๐(1โ ( ๐ ๐๐๐ฅ /๐ )๐ต ) (๐ ๐๐๐ฅ /๐ )๐ต+( ๐๐2 )
2
โ( ๐๐2 )
Substitute Eqs. (3) & (4) into Eqs. (1) & (2) - final Holland equations:
๐ (๐ )=๐๐+ (๐๐โ๐๐ )๐โ(๐ ๐๐๐ฅ /๐ ) ๐ต
(6)
(5)
Derive relationships for scaling parameters A, B
โข Assume V=Vmax @ r =Rmax (dV/dr = 0 @ r =Rmax)โข Assume << Vmax = cyclostrophic wind balance @ r =Rmax โข Setting dV/dr = 0 from Eq. (2) after dropping Corriolis terms:
๐ต=๐๐๐๐ฅ2 ๐๐ /(๐๐โ๐๐ ) (4)
(3)
Holland (1980) Wind Model (ADCIRC: NWS=8)
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๐ ๐ (๐ )=โ๐๐๐๐ฅ2 ๐(1โ ( ๐ ๐๐๐ฅ /๐ )๐ต ) (๐ ๐๐๐ฅ /๐ )๐ต+( ๐๐2 )
2
โ( ๐๐2 )
Substitute Eqs. (3) & (4) into Eqs. (1) & (2) - final Holland equations:
๐ (๐ )=๐๐+ (๐๐โ๐๐ )๐โ(๐ ๐๐๐ฅ /๐ ) ๐ต
(6)
(5)
Derive relationships for scaling parameters A, B
โข Assume V=Vmax @ r =Rmax (dV/dr = 0 @ r =Rmax)โข Assume << Vmax = cyclostrophic wind balance @ r =Rmax โข Setting dV/dr = 0 from Eq. (2) after dropping Corriolis terms:
๐ต=๐๐๐๐ฅ2 ๐๐ /(๐๐โ๐๐ ) (4)
(3)
Holland (1980) Wind Model (ADCIRC: NWS=8)
Holland โBโ
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โข Holland Equations (4), (5), (6)
โข Use either R64 , R50 , or R34 distance to strongest wind isotach (64kt, 50kt, 34kt) to solve for a different Rmax in each storm quadrant (NE, NW, SW, SE)
Asymmetric Holland Wind Model (ADCIRC: NWS=19)
Hurricane Bob of 1991 was extremely asymmetrical, having uneven distribution of the wind radii at Aug 19 1991 1226Z.
The asymmetrical characteristic of a hurricane can be addressed in AHW with spatially varying Rmax.
๐ ๐๐๐ฅ (๐ )
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๐ ๐ (๐ )=โ๐๐๐๐ฅ2 ๐(1โ ( ๐ ๐๐๐ฅ /๐ )๐ต ) (๐ ๐๐๐ฅ /๐ )๐ต+( ๐๐2 )
2
โ( ๐๐2 )
Substitute Eqs. (3) & (4) into Eqs. (1) & (2) - final Holland equations:
๐ (๐ )=๐๐+ (๐๐โ๐๐ )๐โ(๐ ๐๐๐ฅ /๐ ) ๐ต
(6)
(5)
Derive relationships for scaling parameters A, B
โข Assume V=Vmax @ r =Rmax (dV/dr = 0 @ r =Rmax)โข Assume << Vmax = cyclostrophic wind balance @ r =Rmax โข Setting dV/dr = 0 from Eq. (2) after dropping Corriolis terms:
๐ต=๐๐๐๐ฅ2 ๐๐ /(๐๐โ๐๐ ) (4)
(3)
Holland (1980) Wind Model (ADCIRC: NWS=8)
Holland โBโ
e.g., Vg=64 ktr=R64
Solve forRmax
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โข Holland Equations (4), (5), (6)
โข Use either R64 , R50 , or R34 distance to strongest wind isotach (64kt, 50kt, 34kt) to solve for a different Rmax in each storm quadrant (NE, NW, SW, SE)
โข Interpolate Rmax around storm Rmax (ฮธ)
Asymmetric Holland Wind Model (ADCIRC: NWS=19)
Hurricane Bob of 1991 was extremely asymmetrical, having uneven distribution of the wind radii at Aug 19 1991 1226Z.
The asymmetrical characteristic of a hurricane can be addressed in AHW with spatially varying Rmax.
๐ ๐๐๐ฅ (๐ )
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โข Holland Equations (4), (5), (6)
โข Use either R64 , R50 , or R34 distance to strongest wind isotach (64kt, 50kt, 34kt) to solve for a different Rmax in each storm quadrant (NE, NW, SW, SE)
โข Interpolate Rmax around storm Rmax (ฮธ)
Asymmetric Holland Wind Model (ADCIRC: NWS=19)
Hurricane Bob of 1991 was extremely asymmetrical, having uneven distribution of the wind radii at Aug 19 1991 1226Z.
The asymmetrical characteristic of a hurricane can be addressed in AHW with spatially varying Rmax.
๐ ๐๐๐ฅ (๐ )
๐ ๐ (๐ ,๐ )=โ๐๐๐๐ฅ2 ๐(1โ (๐ ๐๐๐ฅ /๐ )๐ต) (๐ ๐๐๐ฅ /๐ )๐ต+( ๐๐2 )
2
โ( ๐๐2 )๐ (๐ ,๐ )=๐๐+(๐๐โ๐๐ )๐โ( ๐ ๐๐๐ฅ /๐ )๐ต
(6)
(5)
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Problems with Asymmetric Holland Model (AHM) โข Inconsistency between Rmax ,Vmax and full gradient wind velocity, Vg , Eq. (6)
when Rmax โฎโฎ Vmaxโข In some cases unable to compute Rmax โข B is constant in space Eq. (4)
โข Only uses single (strongest) isotach in each quadrant
Asymmetric Holland Wind Model (ADCIRC: NWS=19)
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Generalized Asymmetric Wind Model (GAM)
โข Start again with the initial pressure and gradient wind equations from Holland (1980)
โข Do not assume cyclostropic balance dVg/dr = 0 @ r =Rmax
๐=1+๐๐๐๐ฅโ ๐ ๐๐๐ฅ ๐ /๐ต (๐๐๐๐ฅ
2 +๐๐๐๐ฅ๐ ๐๐๐ฅ ๐ )
๐ต=(๐๐๐๐ฅ2 +๐๐๐๐ฅ๐ ๐๐๐ฅ ๐ )๐๐๐ /๐ (๐๐โ๐๐ )
๐ ๐ (๐ ,๐ )=โ (๐๐๐๐ฅ2 +๐๐๐๐ฅ๐ ๐๐๐ฅ ๐ )๐๐ (1โ (๐ ๐๐๐ฅ /๐ )๐ต) (๐ ๐๐๐ฅ /๐ )๐ต+( ๐๐2 )
2
โ( ๐๐2 )
๐ (๐ ,๐ )=๐๐+(๐๐โ๐๐ )๐โ๐ (๐ ๐๐๐ฅ / ๐ )๐ต
(10)
(9)
(8)
(7)
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Comparison of Wind Formulations
๐ (๐ ,๐ )=๐๐+(๐๐โ๐๐ )๐โ ( ๐ ๐๐๐ฅ /๐ )๐ต(5)
๐ ๐ (๐ ,๐ )=โ๐๐๐๐ฅ2 ๐(1โ (๐ ๐๐๐ฅ /๐ )๐ต) (๐ ๐๐๐ฅ /๐ )๐ต+( ๐๐2 )
2
โ( ๐๐2 ) (6)
๐ต=๐๐๐๐ฅ2 ๐๐ /(๐๐โ ๐๐ ) (4)
๐ (๐ ,๐ )=๐๐+(๐๐โ๐๐ )๐โ๐ (๐ ๐๐๐ฅ / ๐ )๐ต (7)
๐ ๐ (๐ ,๐ )=โ (๐๐๐๐ฅ2 +๐๐๐๐ฅ๐ ๐๐๐ฅ ๐ )๐๐ (1โ (๐ ๐๐๐ฅ /๐ )๐ต) (๐ ๐๐๐ฅ /๐ )๐ต+( ๐๐2 )
2
โ( ๐๐2 )(8)
๐ (๐)=1+๐๐๐๐ฅโ ๐ ๐๐๐ฅ ๐ /๐ต (๐๐๐๐ฅ
2 +๐๐๐๐ฅ ๐ ๐๐๐ฅ ๐ )
๐ต(๐)=(๐๐๐๐ฅ2 +๐๐๐๐ฅ ๐ ๐๐๐ฅ ๐ )๐๐๐ /๐ (๐๐โ ๐๐ ) (9)
(10)
AHM NWS=19
GAM
Holland B
Wind
Pressure
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โข Re-calculate B and ฯ using the latest Rmax in each quadrant
B , ฯ
โข Use brute-force marching to solve for Rmax in each quadrant
Rmax
โข Guess initial values without considering coriolis force
B0 , ฯ0
converge ?
โข Spatially interpolate Rmax, B, and ฯ at each ADCIRC node.
Spatial Interpolation
โข Procedures
Implementation of GAM
โข Calculate dynamic wind and pressure fields
Vg(r, ฮธ), P(r, ฮธ)
โข Storm center locations, Vmax, Pn, Pc, multiple Isotachs and their radii, etc
Inputs
ASWIP ADCIRC
Fort.22
Output
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Weighted Composite Wind Field
NE
Isot 34
Isot 50
Isot 64
Composite
SE SW NW
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Weighted Composite Wind Field
NE
Isot 34
Isot 50
Isot 64
Composite
SE SW NW
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Weighted Composite Wind Field
NE
Isot 34
Isot 50
Isot 64
Composite
SE SW NW
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AHM (NWS = 19) only uses the highest isotach in each quadrant to generate its wind/pressure field.
GAM uses a linear weighting of parameter sets computed from all available isotachs in each quadrant.
Weighted Composite Wind Field in GAM
R64 R50 R34
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Weighted Composite Wind Field
NE
Isot 34
Isot 50
Isot 64
Composite
SE SW NW
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Comparison of Spatial Wind Fields (Strong Wind)
GAMAHM NWS=19
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Comparison of Spatial Wind Fields (Weak Wind)
GAMAHM NWS=19
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โข A new โGeneralized Asymmetric vortex Model" is implemented in ASWIP / ADCIRC, that solves the full gradient wind equation, and utilizes all available isotachs to generate composite wind fields.
โข The new formulation allows the model to (i) faithfully represent weaker and larger storms and (ii) to exactly fit multiple wind isotachs that are typically specified in each storm quadrant in either forecast or best track input.
โข Because GAM is still a parametric model, it lacks complexity when compared to re-analysis H*Wind. Does best available job of representing available ATCF BT / forecast parameters.
Conclusions
NWS = 19 GAM H*Wind
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Thank you!
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NWS = 19 NWS = 20 H*Wind
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Comparison of Spatial Wind Fields (Strong Wind) Cont.
AHM NWS=19 GAM
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Comparison of Spatial Wind Fields (Weak Wind) Cont.AHM
NWS=19 GAM