Transcript ppt file

Track Forecasting of 2001
Atlantic Tropical Cyclones
Using a Kilo-Member
Ensemble
8:30 AM April 30, 2002
Jonathan Vigh
Master’s Student
Colorado State University
Department of Atmospheric Science
Acknowledgments
Wayne Schubert, graduate advisor
 Mark DeMaria
 Scott Fulton
 Rick Taft
 Funding

– Significant Opportunities in Atmospheric
Research and Science (SOARS) Program,
fellowship
– American Meteorological Society, fellowship
What causes track error?
Inaccurate spatial and temporal sampling ->
analysis uncertainty
 Incomplete representation of physical processes
 Discretization and truncation error
 Atmosphere’s inherent chaotic nature

– Instability
– Nonlinear interactions between various spatial scales
(Leslie et al., 1998)
What is an ensemble?

A collection deterministic realizations
obtained by varying:
– Model (numerics, resolution, or physics)
– Perturbing model parameters
– Initial analysis fields
 Time of analysis
 Generation method (adjoint or 4DVAR methods)
 Stochastic or bred perturbations
Benefits of an ensemble
With many realizations over properly perturbed
initial conditions, the subspace of dynamical
pathways can be sampled
 Ensemble mean is generally more accurate than
a single deterministic forecast (Leith, 1974)
 Ensemble allows estimation of higher moment
statistics of the forecast

– Forecast uncertainty
– Bifurcation of dynamical pathways
– Probability density functions
MBAR: Multigrid Barotropic Model
Modified barotropic vorticity equation
Finite difference, multigrid methods (Fulton,
2001)
 3 Nested grids on a square 6000 km domain


h1 = 125 km, h2 = 63 km, h3 = 31 km

Efficient and accurate multigrid methods makes
a kilo-scale operational model feasible
– Accuracy comparable to LBAR in only 1/38 of the
computing time
– Each 120-hr track forecast takes ~2.5 seconds
– A 1980 member ensemble takes approximately 1.3
hours on a 1 GHz Intel PC
Perturbations in initial and
background fields
Operational MRF ensembles
 5 independent breeding cycles are used in
the analysis cycle to estimate subspace of
fastest growing analysis errors (Toth and
Kalnay, 1997)
 Adding and subtracting these vectors from
the analysis yields 10 + control initial and
background fields for MBAR
 00Z at 2 degree resolution

Perturbations to vertical averaging
Four deep layer vertical averages of wind
field simulate uncertainties in steering
layer depth
 Pressure weighted averages of following
layers (mb):

– Shallow
– Medium
– Deep
– Entire
(850 - 700)
(850 – 350)
(850 – 200)
(1000 – 100)
Perturbations to vertical
decomposition of vertical modes
In 2D barotropic vorticity models, ultra-long
Rossby waves experience excessive
retrogression (Wiin-Nielsen, 1959)
 Inclusion of inverse Rossby radius in the
prognostic equation can fix this
 Uncertainties in the vertical decomposition of the
tropical atmosphere are handled by perturbing
equivalent phase speed

– 50 ms-1
– 150 ms-1
– 300 ms-1
Perturbations to vortex
size/strength

Simulates uncertainties in the size and
strength of the vortex
– Weak or small TS (vmax = 15 ms-1)
– Weak or medium sized hurricane (wmax = 35
ms-1)
– Strong or large hurricane (vmax = 50 ms-1)

For a barotropic model, the size of the
outer circulation is important factor in the
track forecast
Perturbations to storm motion
vector
Simulates uncertainties in the initial storm
location and direction
 Motion vector added to wind field of bogus
vortex with exponentially decaying blending
radius

–
–
–
–
–
No motion perturbation
Fast and to right
Slow and to right
Fast and to left
Slow and to left
Cross-multiplication across the five
perturbation classes
11 initial and background fields (180)
 4 deep layer averages
(495)
 3 vertical decompositions
(660)
 3 vortex sizes/strengths
(660)
 5 motion vectors
(396)
--------------------------------------------1980 ensemble members
26 sub-ensembles

So what does the kilo-ensemble
look like?
Chantal
 Dean
 Erin
 Iris
 Michelle
 Olga

Chantal
August 17 and 18
Well handled by the ensemble
 A fairly weak storm embedded in trade
flow
 For first several days of forecast, a tight
envelope, indicating high confidence

Dean
August 23
Example of the challenges of recurvature
off the East Coast
 Total ensemble mean lagged behind
actual path
 Ensemble ‘swarm’ stretched out in the
direction of recurvature

Erin
September 3
A storm which weakened to a tropical
depression, then later strengthened to a
strong hurricane
 Ensemble mean successfully predicted
path, although significant cross-track
spread developed

Iris
October 5
Another example of a tight envelope early
on, suggesting high forecast confidence
 Ensemble spreads out at end, but actual
track still contained in envelope
 A minority of members experience
recurvature

Michelle
Storm tracked along edge and then
outside of envelope – an example of the
ensemble’s failure to accurately span all
dynamical pathways
 An example of rapid growth in ensemble
spread with time, suggesting low
confidence in ensemble mean forecast
 Ensemble mean caught in middle of
bifurcation -> large errors

Olga
Forecasts for 11/24/02 inaccurately
predict recurvature – large spread
develops
 Forecasts for 11/25/02 catch onto the
correct path. Large spread but ensemble
means are accurate
 Forecasts for 11/26/02 show an example
of one sub-ensemble correctly picking the
storm path

Average error of sub-ensembles based on vertical averaging
800
700
Average track error (nm)
600
500
CLP5
A5K0
ZTOT
400
SLY4
SLY5
SLY6
SLY7
300
200
100
0
0
12
24
36
48
60
72
Forecast period (hrs)
84
96
108
120
Average track error for sub-ensembles over ceqv
700
600
Forecast period (hrs)
500
CLP5
400
A5K0
ZTOT
SGM1 (50 m/s)
300
SGM2 (100 m/s)
SGM3 (300 m/s)
200
100
0
0
12
24
36
48
60
72
Average track error (nm)
84
96
108
120
Average track error of sub-ensembles based on vortex size/strength
700
600
Average track error (nm)
500
CLP5
400
A5K0
ZTOT
SVM1 (15 m/s)
SVM2 (30 m/s)
300
SVM3 (50 m/s)
200
100
0
0
12
24
36
48
60
72
Forecast period (hrs)
84
96
108
120
Average xbias of sub-ensembles based on vertical averaging
50
0
0
12
24
36
48
60
72
84
96
108
120
Average xbias (nm)
-50
-100
CLP5
A5K0
ZTOT
-150
SLY4
SLY5
SLY6
SLY7
-200
-250
-300
-350
Forecast period (hrs)
Average xbias over sub-ensembles based on ceqv
50
0
Average xbias (nm)
1
2
3
4
5
6
7
-50
8
9
10
11
CLP5
A5K0
ZTOT
SGM1 (50 m/s)
SGM2 (100 m/s)
SGM3 (300 m/s)
-100
-150
-200
Forecast period (hrs)
Average ybias over sub-ensembles based on ceqv
150
100
Average ybias (nm)
50
CLP5
0
A5K0
0
12
24
36
48
60
72
84
96
108
120
ZTOT
SGM1 (50 m/s)
SGM2 (100 m/s)
-50
SGM3 (300 m/s)
-100
-150
-200
Forecast period (hrs)
Average ybais of sub-ensembles based on vertical averaging
80
60
Average ybias (nm)
40
20
CLP5
A5K0
ZTOT
0
SLY4
1
2
3
4
5
6
7
8
9
10
11
SLY5
SLY6
SLY7
-20
-40
-60
-80
Forecast period (nm)
Average xbias over sub-ensembles based on vortex size/strength
50
0
0
12
24
36
48
60
72
84
96
108
120
-50
Average xbias (nm)
-100
-150
CLP5
A5K0
ZTOT
-200
SVM1 (15 m/s)
SVM2 (30 m/s)
-250
SVM3 (50 m/s)
-300
-350
-400
-450
Forecast period (hrs)
Average ybas of sub-ensembles based on vortex size/strength
100
50
Average ybias (nm)
0
0
12
24
36
48
60
72
84
96
108
120
CLP5
A5K0
ZTOT
-50
SVM1 (15 m/s)
SVM2 (30 m/s)
SVM3 (50 m/s)
-100
-150
-200
Forecast period (hrs)
Average spread across perturbation class
1800
1600
Total average spread (nm)
1400
1200
SBF
SGM
1000
SLY
SMV
800
SVM
ZTOT
600
400
200
0
12
24
36
48
60
72
Forecast time (hrs)
84
96
108
120
Conclusions
Swarm diagrams can lead to useful estimates of
forecast confidence
 Ensembles are useful for spotting bifurcations in
possible future tracks
 The ensemble mean isn’t more accurate than
control
 But great utility of ensembles is the estimation
of higher moments, such as forecast spread ->
estimates of forecast reliability

Future Work
Tune ensemble perturbation classes to reduce bias of
ensemble mean
 Tune ensemble spread to be the ‘right’ size
 Calculate probability density functions of storm location
from ensemble output
 Use fuzzy logic/adaptive weighting/neural network to
select more accurate custom sub-ensembles
 Automate for operational use, web output
 Create ensemble toolbox for forecasters allowing effect
of perturbations in parameters on the forecast track to
be easily seen and quantified

References





Fulton, S. R., 2001: An adaptive multigrid barotropic
cyclone track model. Mon. Wea. Rev., 129, 138-151.
Leith, C. E., 1974: Theoretical skill of Monte Carlo
forecasts. Mon. Wea. Rev., 102, 409-418.
Leslie, L. M., Abbey, R. F., and Holland, G. J., 1995:
Tropical Cyclone Track Predictability. Meteorol. Atmos.
Phys., 65, 223-231.
Toth, Z., and E. Kalnay, 1997: Ensemble forecasting at
NCEP and the breeding method. Mon. Wea. Rev., 125,
3207-3310.
Wiin-Nielsen, A., 1959: On barotropic and baroclinic
models, with special emphasis on ultra long waves. Mon.
Wea. Rev., 87, No. 5, 171-183.