Transcript Holland (1980) Wind Model (ADCIRC: NWS=8)

Development and Initial Evaluation of A
Generalized Asymmetric Tropical
Cyclone Vortex Model in ADCIRC
Jie Gao, Rick Luettich
University of North Carolina at Chapel Hill
Jason Fleming
Seahorse Coastal Consulting
ADCIRC Users Group Meeting, USACE Vicksburg, MS, April 29, 2013
Introduction
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 Parameters
lon, lat of center of eye
Vmax
R64 , R50 , R34 in 4 storm quadrants
Pc - ATCF BT only
Storm forward motion
NW
SW
NE
SE
Pn , Rmax - estimated separately
Schematic cross section of a hurricane wind field
Holland (1980) Wind Model (ADCIRC: NWS=8)
Hurricane Isabel of 2003
showing the circular,
symmetric eye associated
with annular hurricanes
at Sept 13 2013 1710Z.
𝑅𝑚𝑎𝑥
The Holland Wind Model
produces a symmetric
hurricane vortex with the
spatially constant Rmax.
Hyperbolic hurricane pressure profile (Schloemer 1954):
𝑃 𝑟 = 𝑃𝑐 + 𝑃𝑛 − 𝑃𝑐 𝑒 −𝐴
𝑟𝐵
(1)
Substitute into the gradient wind equations, the vortex wind velocity is:
𝑉𝑔 𝑟 =
𝐴𝐵 𝑃𝑛 − 𝑃𝑐 𝑒 −𝐴
𝑟𝐵
𝜌𝑟 𝐵 +
𝑟𝑓
2
2
−
𝑟𝑓
2
(2)
Holland (1980) Wind Model (ADCIRC: NWS=8)
Derive relationships for scaling parameters A, B
• Assume V=Vmax @ r =Rmax
(dV/dr = 0 @ r =Rmax)
• Assume 𝑓Rmax<< Vmax = cyclostrophic wind balance @ r =Rmax
• Setting dV/dr = 0 from Eq. (2) after dropping Corriolis terms:
𝐴 = 𝑅𝑚𝑎𝑥 𝐵
(3)
2 𝜌𝑒 𝑃 − 𝑃
𝐵 = 𝑉𝑚𝑎𝑥
𝑛
𝑐
(4)
Substitute Eqs. (3) & (4) into Eqs. (1) & (2) - final Holland equations:
𝑃 𝑟 = 𝑃𝑐 + 𝑃𝑛 − 𝑃𝑐 𝑒 − 𝑅𝑚𝑎𝑥
𝑉𝑔 𝑟 =
2
𝑉𝑚𝑎𝑥
𝑒
1− 𝑅𝑚𝑎𝑥 𝑟 𝐵
𝑅𝑚𝑎𝑥 𝑟
𝐵
+
𝑟 𝐵
𝑟𝑓 2
2
(5)
−
𝑟𝑓
2
(6)
Holland (1980) Wind Model (ADCIRC: NWS=8)
Derive relationships for scaling parameters A, B
• Assume V=Vmax @ r =Rmax
(dV/dr = 0 @ r =Rmax)
• Assume 𝑓Rmax<< Vmax = cyclostrophic wind balance @ r =Rmax
• Setting dV/dr = 0 from Eq. (2) after dropping Corriolis terms:
𝐴 = 𝑅𝑚𝑎𝑥 𝐵
(3)
2 𝜌𝑒 𝑃 − 𝑃
𝐵 = 𝑉𝑚𝑎𝑥
𝑛
𝑐
Holland “B”
(4)
Substitute Eqs. (3) & (4) into Eqs. (1) & (2) - final Holland equations:
𝑃 𝑟 = 𝑃𝑐 + 𝑃𝑛 − 𝑃𝑐 𝑒 − 𝑅𝑚𝑎𝑥
𝑉𝑔 𝑟 =
2
𝑉𝑚𝑎𝑥
𝑒
1− 𝑅𝑚𝑎𝑥 𝑟 𝐵
𝑅𝑚𝑎𝑥 𝑟
𝐵
+
𝑟 𝐵
𝑟𝑓 2
2
(5)
−
𝑟𝑓
2
(6)
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.
𝑅𝑚𝑎𝑥 𝜃
The asymmetrical
characteristic of a hurricane
can be addressed in AHW
with spatially varying Rmax.
• Holland Equations (4), (5), (6)
• 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)
Holland (1980) Wind Model (ADCIRC: NWS=8)
Derive relationships for scaling parameters A, B
• Assume V=Vmax @ r =Rmax
(dV/dr = 0 @ r =Rmax)
• Assume 𝑓Rmax<< Vmax = cyclostrophic wind balance @ r =Rmax
• Setting dV/dr = 0 from Eq. (2) after dropping Corriolis terms:
𝐴 = 𝑅𝑚𝑎𝑥 𝐵
(3)
2 𝜌𝑒 𝑃 − 𝑃
𝐵 = 𝑉𝑚𝑎𝑥
𝑛
𝑐
Holland “B”
(4)
Substitute Eqs. (3) & (4) into Eqs. (1) & (2) - final Holland equations:
e.g.,
Vg=64 kt
r=R64
Solve for
Rmax
𝑃 𝑟 = 𝑃𝑐 + 𝑃𝑛 − 𝑃𝑐 𝑒 − 𝑅𝑚𝑎𝑥
𝑉𝑔 𝑟 =
2
𝑉𝑚𝑎𝑥
𝑒
1− 𝑅𝑚𝑎𝑥 𝑟 𝐵
𝑅𝑚𝑎𝑥 𝑟
𝐵
+
𝑟 𝐵
𝑟𝑓 2
2
(5)
−
𝑟𝑓
2
(6)
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.
𝑅𝑚𝑎𝑥 𝜃
The asymmetrical
characteristic of a hurricane
can be addressed in AHW
with spatially varying Rmax.
• Holland Equations (4), (5), (6)
• 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)
• Interpolate Rmax around storm  Rmax (θ)
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.
𝑅𝑚𝑎𝑥 𝜃
The asymmetrical
characteristic of a hurricane
can be addressed in AHW
with spatially varying Rmax.
• Holland Equations (4), (5), (6)
• 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)
• Interpolate Rmax around storm  Rmax (θ)
𝑃 𝑟, 𝜃 = 𝑃𝑐 + 𝑃𝑛 − 𝑃𝑐 𝑒 −
𝑉𝑔 𝑟, 𝜃 =
2
𝑉𝑚𝑎𝑥
𝑒
1− 𝑅𝑚𝑎𝑥 𝑟 𝐵
𝑅𝑚𝑎𝑥 𝑟
𝑅𝑚𝑎𝑥 𝑟 𝐵
𝐵
+
𝑟𝑓 2
2
(5)
−
𝑟𝑓
2
(6)
Asymmetric Holland Wind Model (ADCIRC: NWS=19)
Problems with Asymmetric Holland Model (AHM)
• Inconsistency between Rmax ,Vmax and full gradient wind velocity, Vg , Eq. (6)
when 𝑓 Rmax ≮≮ Vmax
• In some cases unable to compute Rmax
• B is constant in space Eq. (4)
• Only uses single (strongest) isotach in each quadrant
Generalized Asymmetric Wind Model (GAM)
• Start again with the initial pressure and gradient wind equations from
Holland (1980)
• Do not assume cyclostropic balance  dVg/dr = 0 @ r =Rmax
𝑃 𝑟, 𝜃 = 𝑃𝑐 + 𝑃𝑛 − 𝑃𝑐 𝑒 −𝜓 𝑅𝑚𝑎𝑥
𝑉𝑔 𝑟, 𝜃 =
2
𝑉𝑚𝑎𝑥
+ 𝑉𝑚𝑎𝑥 𝑅𝑚𝑎𝑥 𝑓 𝑒 𝜓
1− 𝑅𝑚𝑎𝑥 𝑟 𝐵
𝑟 𝐵
𝑅𝑚𝑎𝑥 𝑟
(7)
𝐵
+
𝑟𝑓 2
2
2
𝐵 = 𝑉𝑚𝑎𝑥
+ 𝑉𝑚𝑎𝑥 𝑅𝑚𝑎𝑥 𝑓 𝜌𝑒 𝜓 𝜓 𝑃𝑛 − 𝑃𝑐
2 +𝑉
𝜓 = 1 + 𝑉𝑚𝑎𝑥 𝑅𝑚𝑎𝑥 𝑓 𝐵 𝑉𝑚𝑎𝑥
𝑚𝑎𝑥 𝑅𝑚𝑎𝑥 𝑓
−
𝑟𝑓
2
(8)
(9)
(10)
Comparison of Wind Formulations
AHM
NWS=19
𝑃 𝑟, 𝜃 = 𝑃𝑐 + 𝑃𝑛 − 𝑃𝑐 𝑒 −
𝑉𝑔 𝑟, 𝜃 =
2
𝑉𝑚𝑎𝑥
𝑒
1− 𝑅𝑚𝑎𝑥 𝑟 𝐵
𝑅𝑚𝑎𝑥 𝑟 𝐵
𝑅𝑚𝑎𝑥 𝑟
𝐵
+
𝑟𝑓 2
2
−
𝑟𝑓
2
2 𝜌𝑒 𝑃 − 𝑃
𝐵 = 𝑉𝑚𝑎𝑥
𝑛
𝑐
𝑃 𝑟, 𝜃 = 𝑃𝑐 + 𝑃𝑛 − 𝑃𝑐 𝑒 −𝜓
2
𝑉𝑚𝑎𝑥
+ 𝑉𝑚𝑎𝑥 𝑅𝑚𝑎𝑥 𝑓 𝑒 𝜓
1− 𝑅𝑚𝑎𝑥 𝑟 𝐵
Pressure
(6)
Wind
(4) Holland B
GAM
𝑉𝑔 𝑟, 𝜃 =
(5)
𝑅𝑚𝑎𝑥 𝑟 𝐵
𝑅𝑚𝑎𝑥 𝑟
𝐵
(7)
+
𝑟𝑓 2
2
−
𝑟𝑓
2
(8)
2
𝐵(𝜃) = 𝑉𝑚𝑎𝑥
+ 𝑉𝑚𝑎𝑥 𝑅𝑚𝑎𝑥 𝑓 𝜌𝑒 𝜓 𝜓 𝑃𝑛 − 𝑃𝑐
(9)
2 +𝑉
𝜓(𝜃) = 1 + 𝑉𝑚𝑎𝑥 𝑅𝑚𝑎𝑥 𝑓 𝐵 𝑉𝑚𝑎𝑥
𝑚𝑎𝑥 𝑅𝑚𝑎𝑥 𝑓
(10)
Implementation of GAM
• Procedures
B0 , ψ0
• Guess initial
values without
considering
coriolis force
ASWIP
ADCIRC
B,ψ
Rmax
• Use brute-force
marching to
solve for Rmax in
each quadrant
• Re-calculate B
and ψ using the
latest Rmax in
each quadrant
Spatial
Interpolation
• Spatially
interpolate Rmax,
B, and ψ at each
ADCIRC node.
converge
?
Inputs
• Storm center
locations, Vmax,
Pn, Pc, multiple
Isotachs and
their radii, etc
Output
Fort.22
Vg(r, θ),
P(r, θ)
• Calculate
dynamic wind
and pressure
fields
Weighted Composite Wind Field
NE
Isot 34
Isot 50
Isot 64
Composite
SE
SW
NW
Weighted Composite Wind Field
NE
Isot 34
Isot 50
Isot 64
Composite
SE
SW
NW
Weighted Composite Wind Field
NE
Isot 34
Isot 50
Isot 64
Composite
SE
SW
NW
Weighted Composite Wind Field in GAM
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.
R64
R50
R34
Weighted Composite Wind Field
NE
Isot 34
Isot 50
Isot 64
Composite
SE
SW
NW
Comparison of Spatial Wind Fields (Strong Wind)
AHM
NWS=19
GAM
Comparison of Spatial Wind Fields (Weak Wind)
AHM
NWS=19
GAM
Conclusions
•
A new “Generalized 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.
•
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.
•
Because GAM is still a parametric model, it lacks complexity when compared to reanalysis H*Wind. Does best available job of representing available ATCF BT /
forecast parameters.
NWS = 19
GAM
H*Wind
Thank you!
NWS = 19
NWS = 20
H*Wind
Comparison of Spatial Wind Fields (Strong Wind) Cont.
AHM
NWS=19
GAM
Comparison of Spatial Wind Fields (Weak Wind) Cont.
AHM
NWS=19
GAM