dynamic initialization to improve tropical cyclone intensity and structure forecasts chi-sann liou...
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Dynamic Initialization to Improve Tropical Cyclone Intensity and Structure Forecasts
Chi-Sann Liou
Naval Research Laboratory, Monterey, CA
(JHT Project, Progress Report)
Unbalanced Initial Conditions of a TC Forecast
• Improper balance conditions included in analyzing TC circulation
• Diabatic Forcing: an important component in TC circulation balance
– Forecast model must be involved in getting balanced initial conditions
• Method of getting balanced initial conditions
– 4D Var, or
– 3D Var with a proper initialization procedure
SLP
850 W
Unbalanced Initial Conditions
Dynamic Initialization
• Must consider diabatic forcing in TC balance– Dynamic initialization (assuming unbalanced components are high frequency)
t=0
-N N
(forecast)
Digital Filtering
t=0
N
(forecast)
Extra Damping
– Traditional method versus Digital Filter
Digital Filter
• A very selective low pass filter
• Using truncated inverse Fourier transform to remove high frequency components from input signals
c
c
,
,
1)H(),H(*FF inout
0
In Frequency Domain:
In Physical Time Domain:
dethfhf tink
nnk *)()(),(
~H
nπ
tnωhfh
Δcnnk
N
Nnn
)sin(),(
Gibbs’ Phenomenon
deheh inn
tinN
Nnn
c
HH ,Unfortunately:
converges very slowly !!
2sin
2
,2
n
h
π
n
tωFor Δc H =>
Filter Response Function
c = 2/(6*3600) t = 240s
)(F)(F
)T(in
out
• Pass band: <p=-3dB
• Stop band: >s= -20dB
• Transition band: p >>s
• Stop band ripple: s= -20log()
= largest ripple Size
p s
cutoff
=>
Window Functions
• Apply a window function to improve convergence:
tinN
Nn
c cenπ
Δtnω
)sin(nWH
i.e.,
• Windows Tested:– Lanczos– Hamming– Riesz– Kaiser– Dolph-Chebyshev
(Fixed Windows)
(Adjustable Windows)
nπ
Δtnωh c
nn
)sin(W
Windows Tested
Lanczos:
Hamming:
Riesz:
Kaiser:
Dolph-Chebyshev:
NnNn
Nnwn
0,)1/(
)]1/(sin[
)12
2cos(46.054.0
N
nwn
2)1
(1
N
nwn
function Bessel :)(,)(
}])1
(1[{
0
0
212
0
xllNn
lwn
N
mn
mNn mxT
Nww
102
0
]cos)2
cos(21[)12(
1
T2N: Chebyshev polynomial,)12(
2,)12(2
),cosh21cosh( 1
0
Nn
Nm
Nx
nm
Hamming
Lanczos
Kaiser
Dolph-Chebyshev
Riesz
Response Functions with Windows
Dynamic Initialization with Digital Filtering
Adiabatic:
Diabatic:
t=0
-N N
(forecast)
Digital Filtering
ADIA
t=0
-N N
(forecast)
Digital Filtering
DIAB1
t=0
-N N
(forecast)
Digital Filtering
DIAB2Digital Filtering
Cost of Digital Filtering Initialization
• Compute filter weights
• Apply filtering
• Perform backward and forward initialization integration
===> 95% cost
Initialization integration cutoff frequency (period=c):
tc
2
N
• For tropical cyclone forecast: c = 2 hours
(For NWP forecast with Lanczos window : c= 6 hours)
Initialization with Digital Filtering
Tropical Cyclone Isabel (2003091012)
Analyzed Initialized
Initialization with Digital Filtering
Summary
• With the Dolph-Chebyshev window and 2-h cutoff period, diabatic digital filtering can effectively provide much better balanced initial conditions of a tropical cyclone
• Adiabatic digital filtering only marginally improves initial conditions for tropical cyclone forecast
• The type-2 diabatic digital filtering integration strategy makes very little difference in the results, but cost ¼ more in time integration
• Diabatic digital filtering initialization improves track forecast of COAMPS®