Transcript Diabatic Digital Filter Initialization For Tropical Cyclone Model Forecasting Chi-Sann Liou

Diabatic Digital Filter Initialization For
Tropical Cyclone Model Forecasting
Chi-Sann Liou
Naval Research Laboratory
(JHT sponsored project)
Unbalanced Initial Conditions
Շ=0
Շ=1h
Շ=3h
Շ=0
Շ=1h
Շ=3h
1000
1000
1000
Unbalanced Initial Conditions
SLP
850 W
Static Initialization:
(nonlinear
normal
initialization)

Governing equation :
Normal modes :
 j
t
Balance condition :
x

 iMx  N, N  nonlinear forcing (adiabatic only)
t
 i j j  R j ,
 j
t
 0 for  j  c
Method : iterations to find  j
( n 1)

R j (n)
i j
,  j
( n)
j
( n 1)
j
(n)
 i j
 j ( n )
Dynamic Initialization:
Balance condition: high frequency tendency=0 at initial time
Method: damp or filter out high frequency components through back and
forth time integrations
Advantage: diabatic forcing is included in getting balance conditions
Disadvantage: cost more
t
Digital Filter
• A very selective low pass filter
• Using truncated inverse Fourier transform to remove
high frequency components from input signals
In Frequency F  F * H(  ), H(  )  1,   
out
in
c
Domain:
 0,   c
In Physical
~
Time Domain: f k 


i t
(
h

f
),
h
(
t
)

H
(

)
*
e
d
 n k n

n 
N
sin( nωc Δt )
  (hn  f k n ), hn 
nπ
n N
Dynamic Initialization with Digital Filtering
Adiabatic:
Diabatic:
DIAB1
t=0
-N
N
ADIA
t=0
Digital Filtering
(forecast)
-N
N
Digital Filtering
DIAB2
t=0
Digital Filtering
(forecast)
-N
N
Digital Filtering
(forecast)
Issues related to Diabatic Digital Filtering
• Asymmetry in back and forth integrations
• Lateral boundary conditions
• Surface boundary conditions
• Diffusion
• Moving grids
• Cost of the extra time integration
===> Shorten the back and forth time integrations
Use a efficient window in the inverse Fourier transform
Cutoff Period = 2 hours
Response Functions with Windows
Hamming
Lanczos
Kaiser
Dolph-Chebyshev
Riesz
Initialization with Digital Filtering
Initial Conditions After DDF Initialization
Շ=0
Շ=1h
Շ=3h
1000
1000
1000
Շ=0
Շ=1h
1000
Շ=3h
1000
1000
DDF Impact on COAMPS®
Track Forecast:
• depend on how unbalanced
initial conditions are
• larger improvements shown
in later forecast periods
(15 72h forecasts with OI analysis)
Implement Diabatic Digital Filter Initialization To HWRF
• Routines to compute weights of digital filtering
• Routines to apply the weights to prognostic variables
• Routines to control the initialization time integration
1. prepare a FORTRAN-90 module that includes all new
routines for DDF initialization
2. add new arrays and namelist variables for DDF to the NMM
registry file
3. write a driver routine to control time integration in different
phases of the initialization integration
4. integrate the DDF time integration controller into HWRF
forecast model.
Goal: Minimize HWRF code changes ==> single point interface
Minimize resource requirement ==> all local work arrays
Implement Diabatic Digital Filter Initialization To HWRF
HWRF Main Program (WRF.F)
WRF_INIT
WRF_RUN
WRF_FINALIZE
Call ddf_init (head_grid)
Call Integrate (head_grid)
ddf_init.F:
• allocate and initialize inner meshes
• allocate work arrays
• compute weights
• use ESMF clock utilities to control
DDF integrations
• call ddf_integrate and ddf_interface
(recursive calls in handling nest grid integration)
• deallocate work arrays
Summary
• With the Dolph-Chebyshev window and 2-h cutoff
period, diabatic digital filtering (DDF) can effectively
remove unbalanced initial conditions of a tropical
cyclone
• Adiabatic digital filtering only marginally improves
initial conditions for tropical cyclone forecast
• Modification to initial conditions by DDF depends
upon the degree of unbalance in the initial conditions
• DDF improves track forecast of COAMPS®
• DDF has been implemented to a test version of
HWRF and is currently under test