Using Observations to Improve
Hurricane Initialization
X. Zou
Department of Meteorology
Florida State University
February 14, 2007
Outline
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Hurricane Initialization
(Vortex bogusing schemes)
Hurricane Observations
(Potential applications)
A 4D-Var Approach
(Vortex bogusing and/or data assimilation)
Numerical Results
(Hurricane forecast impact)
Hurricane Initialization Using Bogus Vortex
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Why is bogus vortex needed?
How is vortex bogussing done?
What is the forecast impact?
Bogus Vortex
An artificial initial vortex which is conceptually correct and is
specified based on a few available observational parameters,
an empirical structure of a model variable and dynamic and
thermodynamic constraints
Vortex Bogussing
Creation of a bogus vortex
Conditions for Bogus Vortex Specification
1. The structure of the vortex should be dynamically and
thermodynamically consistent
Wind and mass fields in balance
Coherent moisture field
2. Size and intensity of the real TC should be represented
Real storms evolving in different environmental
conditions possess unique size and intensity
3. The bogus vortex is compatible with the resolution and
physics of the prediction model
Prevent false spinup
Why is a bogus vortex needed?
 Observations within and around hurricanes could be
either insufficient or problematic
Radiosonde observations are not over oceans.
Rain contamination with QuikSCAT surface winds
Cloud contamination with satellite radiances
 Initial vortices in model initial conditions are often too
weak and misplaced
 Having an initial vortex at correct location with
realistic intensities and structures is important for
hurricane track and intensity forecasts
How is vortex bogussing done?
 Specify a bogus vortex of a single variable
Rankine vortex --- tangential wind
Fujita’s vortex --- sea-level pressure
Holland’s vortex --- seal-level pressure
 Generate a dynamically and thermodynamically
consistent initial vortex of all model variables
Traditional method: Simplified dynamical constraints
An Early Method Used at NCEP
Mukut B. Mathur. 1991: The National Meteorological
Center's Quasi-Lagrangian Model for Hurricane
Prediction. Monthly Weather Review, 119, 1419-1447.
bogus
1) Specify an empirical surface pressure field psfc
with observed
> pressure at the vortex center (pc)
> pressure of the outermost closed isobar (pout at r=Rout)
> pressure of the hurricane environment  p 
2) Derive vortex fields of other model variables
> surface wind speed using the gradient wind relation (GWR)
>3D wind speed from surface wind using empirical vertical
structure functions
>3D geopotential from 3D wind speed using GWR
>3D wind vector from geopotential using GWR with variable f
>virtual temperature from geopotential using the hydrostatic eq.
>relative humidity (RH) by a linear interpolation assuming a
saturated vortex center and a lower value of RH at Rout
An Early Method Used at NCEP
bogus
1) Specify an empirical surface pressure field psfc
with observed
2) Derive vortex fields of other model variables
3) Merge vortex fields with the gridded large-scale analysis
X  wXvortex  (1  w)Xanalysis
where
  r 
, r  Rout
 cos 

w    2 R
0,
r  Rout

NCEP analysis
Hurricane Gilbert (1988)
at 1200 UTC 14 September
Large-scale analysis:
 The maximum wind is located
far from the center (>300 km)
 Little evidence of a warm core
Prescribed bogus vortex
Figure 1 from Mathur (1991)
Prescribed bogus vortex:
• Strongest cyclonic winds close to
the center
• A warm core with a large warm
temperature anomaly in the
middle and upper troposphere
Potential temperature (solid line, unit: K)
Normal component of wind velocity (dashed
line, unit: m/s)
48-h forecast without bogus vortex
Hurricane Gilbert (1988)
at 1200 UTC 16 September
The 48-h forecast with bogus
vortex is characterized by
48-h forecast with bogus vortex
Figure
2 from
Figure
2 from
MathurMathur
(1991)
(1991)
 Stronger wind
 Warmer temperature
 Deeper hurricane
A GFDL Method
Yoshio Kurihara, Morris A. Bender and Rebecca J. Ross,
1993: An Initialization Scheme of Hurricane Models by
Vortex Specification. Monthly Weather Review, 121, 20302045.
Morris A. Bender, Rebecca J. Ross, Robert E. Tuleya and
Yoshio Kurihara. 1993: Improvements in Tropical Cyclone
Track and Intensity Forecasts Using the GFDL Initialization
System. Monthly Weather Review, 121, 2046-2061.
The task of GFDL vortex initialization is completed by adding
hE  hsv  IC
(IC) = (GA) - (vortex in GA) + (specified bogus vortex)
Environmental field hE
hsv
Main procedures
 Obtain the environmental fields by removing often poorly
analyzed tropical cyclone vortex from the large-scale analysis
 Specify a symmetric vortex tangential wind field
 Generate a symmetric vortex of all variables using an
axisymmetric hurricane prediction model, with a nudging
term imposing the specified tangential wind field
 Obtain an asymmetric component of wind from integrating
a simplified barotropic vorticity equation initialized by the
symmetric tangential wind
(Capture the asymmetric structure of TCs due to the planetary vorticity
advection by the symmetric flow within the vortex)
 Readjust mass fields to a state of balance to the asymmetric
wind using divergence equation
Improved Hurricane Track Forecast
(include seven cases of Atlanta storms)
Figure 6 from Kurihara et al. (1993)
Hurricane Observations
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Radiances
TOMS ozone
GPS RO
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Radar data
Dropsonde
QuikSCAT
Challenges and potential applications
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Information
Radiances
hydrometeor, temperature
TOMS ozone
tropopause height
GPS RO
high-vertical-resolution profile of
atmospheric refractvity
Radar data
high resolution radial wind and
refractivity
Dropsonde
atmospheric vertical profiles
QuikSCAT
surface wind
85V Tbs for Hurricane Bonnie
at 00 UTC 24 Aug 1998
Model simulated (30km)
SSM/I obs. (18 km)
18 km
The maximum difference of Tb at 85GHz within Hurricane Bonnie >100 K.
The difference of maximum Tb at 85GHz within Hurricane Bonnie >40 K.
RTM Improvements
The RTM includes effects of absorption, emission, scatter, and
multi-scattering (Liu, 1998).
In the original version, the ice particles and air had been assumed a
homogeneous mixture with the dielectric constant of the ice
particle and the volume of the mixture considered as a solid sphere
with the mass of the ice particle.
In the modified version, the Maxwell-Garnett mixing formula is
used for the calculation of the dielectric constant for ice particles.
In the modified version, the values of the intercept parameter N0
of the drop size distribution and the density ρ of the hydrometeor
are made more consistent with the values of these parameters in
the explicit moisture schemes.

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6 km
6 km
Tb at 85 GHz for
Hurricane Bonnie
(8/25 00 UTC, 1998)
18 km
Reisner scheme 1
Reisner scheme 2
6 km
6 km
SSM/I
The maximum Tb difference < 20 K
Goddard scheme
Schultz scheme
Hurricane Erin observed by TOMS ozone
on 15UTC 12 September 2001
SLP
Tropical depression
6 Sept. 2001
Tropical storm
8 Sept. 2001
Hurricane category 3
10 Sept. 2001
GHT340K
TOMS ozone
Scatter plot for TOMS O3 and geopotential at 340 K
(All data within 650-km radial distance for all 12
chosen hurricanes are included)
Radial mean GHT340K (gpm)
Bonnie(1998)
Aug.22-24,26
Alberto(2000)
Aug. 12,13
Isaac(2000)
Sept. 22-25,27
Erin(2001)
Sept. 6,8,10
Felix(2001)
Sept. 9-11
Lili(2002)
Sept. 26,27,29
Isidore(2002)
Sept. 19,20
Fabian(2003)
Aug. 30, Sept
1-3
Isabel (2003)
Sept. 6,9,11,12
Radial mean TOMS ozone (DU)
Case-dependent radial mean TOMS O3 versus GHT340K profiles
Radial mean GHT340K (gpm)
Radial mean TOMS ozone (DU)
Case-dependent radial mean TOMS O3 versus GHT340K
with daily means subtracted from both fields
A linear regression model for hurricane
initialization using TOMS ozone


model
model


340K
340K  51.30  O3  O3  1.92
STDE=176m (~1-2%)
Hurricane Erin on September 10, 2001
TOMS ozone
Large-scale analysis
NCEP
 340
K
O3
Geopotential field at 340K
with O3 data incorporated
Model
NCEP
 340




K
340 K
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Challenges
Radiances
large model/observation difference
TOMS ozone
not directly linked to model variables
GPS RO
too little data within a hurricane
Radar data
too high resolution with limited coverage
Dropsonde
not available above flight levels and
within extreme weathers
QuikSCAT
rain contamination
A 4D-Var Approach for Bogusing Vortex
and/or Data assimilation
Advantages:
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 Indirect remote-sensing observations can be assimilated
simultaneously while generating bogus vortex
 The best dynamic and thermodynamic constraint --hurricane forecast model --- is imposed within bogus
vortex.
 Diabatic effect is included
A 4D-Var Vortex Bogus Scheme
Procedures:
1. Specify a bogus SLP.
2. Generate fields of all model variables
describing an initial vortex by fitting
a hurricane forecast model to the bogus SLP.
Key features:
(i) A bogus SLP field can be specified based on TPC
(tropical prediction center) observed parameters.
(ii) A 4D-Var assimilation window as short as 15-30
minutes is sufficient for this vortex initialization.
Specification of a Bogus SLP
Fujita’s Formula:
pbogus (r)  pout 
( pout  pc )

1  r 2 / 2R02
R0  0.38R34kt  3.8

1
2
,
r  Rout
(linear regression model)
where
pc --- Central SLP

 p --- Pressure of the outermost closed isobar
out
Rout --- Radius of the outermost closed isobar
R35kt --- Radius of the 35kt wind
Four observed
TPC parameters
Fujita’s SLP Radial Profiles
Sensitivity studies suggest:
..
Differences in the size of real hurricanes are appreciable.
Hurricane track and intensity forecasts are sensitive to
specified size of initial vortex.
TPC Observed
(known)
Input to Fujita’s
formula
Rmax
R35kt
R50kt
R64kt
Linear regression model?
R0
Hurricane forecast modelderived R0, Rmax,R35kt, …..
Size Specification for Initial Vortex
17 cases:
Felix (1995)-1
Opal (1995)-1
Fran (1996)-3
Erika (1997)-1
Bonnie (1998)-9
Floyd (1999)-2
R0  0.38R34kt  3.8
needed for vortex
size specification
A TPC parameter
Numerical Results: Impact on Hurricane Forecast
1. Applying a 4D-Var vortex bogusing to the prediction of
Hurricane Bonnie (1998) and Hurricane Alberto (2000)
2. Assimilation of microwave radiance for the prediction of
Hurricane Bonnie (1998)
Hurricane Bonnie (1998)

Initializing Hurricane Bonnie
at 12 UTC August 23, 1998
R34kt  255 km
R0  0.38R34kt  3.8
R0  93 km

Hurricane Bonnie (1998)
Hurricane initialization time: 12 UTC, 23 August 1998
TPC observed parameters:
Pc = 958 hPa, Rmax=25 km,
Vmax=100kt, R34kt=255 km,
Numerical Experiments:
EH
Holland
EF1
Fujita
R0= 25 km=Rmax
EF2
Fujita
R0= 93 km
Model: MM5 at 18-km resolution
Linear regression model
Radial profiles
Large-scale analysis
Radial profile of the bogus SLP
1000
EH
EF1
EF2
958
958
958
Wind Increments at 850 hPa after 4D-Var BDA
Wind increments at 850 mb after
BDA with R0=34 km
u’
v’
East-west cross sections of the difference
between EF2 and analysis at 6-h interval

0
1
East
420km
30min
Time
West
420km
Pressure
Perturbation
-40
-18
4 hPa
Temperature
-4
8
20K
East-west cross sections of the divergence
increments after hurricane initialization
0-30 min
 7 10 4 S1
7 10 4 S1
30-60 min
 5 10 4 S1
5 10 4 S1
At t0, hydrostatic balance dominates.
Upper-level convergence
Less denser air
Warming
Adiabatic warming
Bogusing
- pp
Low-level divergence
At tR, dynamic balance dominates.
Upper-level divergence
Warming
Latent heat
Low
Low-level convergence
East-west cross sections of the difference between
EF2 and large-scale analysis of mixing ratio

0
1
East
420km
West
420km
0-30 min
30-60 min
 5  10 3 g/kg
5  10 3 g/kg
30min
60min
Time
Track
Central pressure
Track error
Maximum wind speed
Hurricane Alberto (12-14 Aug., 2000)
Assimilation of Satellite Radiance
• Initialization time: 1200 UTC 23 August 1998 (Hurricane Bonnie)
• Forecast model: COAMPS
• Resolution: 30 km horizontal grid spacing, 30 vertical levels
• Experiments:
CNTRL – Control forecast using COAPS analysis
ETB
– with SSM/I observations and a non-diagonal B
ETBN – with SSM/I observations and a diagonal B
qi
Height (km)
Height (km)
qc
qs
qr
Background Error Covariance
Shown as a correlation matrix and
a profile of standard deviation
Height (km)
qg
Height (km)
Hydrometeor std. (g/kg))
Singular Values of B
Most variances are accounted
for by the first few singular
vectors for hydrometeor
variables.
B Matrix and Its Approximation
qr Largest Singular Value
Height (km)
qr Full Matrix
1 x 107
kg/kg
Height (km)
Height (km)
The general structure of the full B matrix is captured by the
largest singular vector.
qi
Inverse Background
Covariance Matrices
qs
qr
Height (km)
Height (km)
Height (km)
qc
qg
Height (km)
Multiplied by 1 x 10-5 kg/kg
Tb at 19 GHz (12 UTC, 23 August 1998)
Obs..
SSM/I
without Tb assim.
CNTRL
with Tb assim.
ETB
Tb at 85 GHz (12 UTC, 23 August 1998)
Obs..
SSM/I
without Tb assim.
CNTRL
with Tb assim.
ETB
ETB – non-diagonal B
ETBD – diagonal B
Difference (K)
Height (m)
Initial condition of qr after Tb Assimilation
qr cross sections (unit: g/kg)
24 h Forecast
(initial time: 1200 UTC 08/23/98)
Intensity
Track
Conclusions
 There are a lot of available hurricane observations whose
applications to hurricane initialization represent a challenge
and have great potential.
 The 4D-Var approach is an effective method for hurricane
initialization, which allows forecast model constraint and
hurricane observations be incorporated simultaneously.
 Model simulated Tb at lower frequency 19 GHz, 37 GHz
and 22 GHz (sensitive to liquid precipitation and water
vapor) matched the observations much better than Tb at
85V (sensitive to precipitating ice concentrations).
 Some forecast improvement was seen in the minimum
central SLP and Tbs after the assimilation of Tb.
4D-Var hurricane initialization:
Zou, X., and Q. Xiao, 2000: Studies on the initialization and
simulation of a mature hurricane using a variational
bogus data assimilation scheme. J. Atm. Sci., 57, 836860.
Park, K., and X. Zou, 2004: Toward developing an
objective 4D-Var BDA scheme fo hurricane
initialization based on TPC observed parameters.
Mon. Wea. Rev., 132, 2054-2069.
Assimilation of satellite observations:
Zou, X., Q. Xiao, Alan E. Lipton, and George D. Modica,
2001: A numerical study of the effect of GOES
sounder cloud-cleared brightness temperatures on the
prediction of hurricane Felix. J. Appl. Meteor., 40, 34-55.
Amerault, C. and X. Zou, 2003: Preliminary steps in
assimilating SSM/I brightness temperatures in a
hurricane prediction scheme. J. Atmos. Oceanic
Technol., 20, 1154-1169.
Zou, X. and Y.-H. Wu, 2005: On the relationship between
TOMS ozone and hurricanes. J. Geoph. Res., 110,
No. D6, D06109 (paper no. 10.1029/2004JD005019).
Wu, Y.-H. and X. Zou, 2007: Impact of TOMS ozone on
hurricane track prediction. (to be submitted)