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®