Using TIGGE data to diagnose initial perturbations and
their growth for tropical cyclone ensemble forecasts
Seminar at Naval Postgraduate School
22 Sep. 2008
Munehiko Yamaguchi1, Sharanya S. Majumdar1,
Melinda S. Peng2, Carolyn A. Reynolds2, David S. Nolan1
1. Rosenstiel School of Marine and Atmospheric Science, University of Miami
2. Marine Meteorology Division, Naval Research Laboratory
Progress of TC track forecasts
Time series of annual average position errors in
Tropical Cyclone (TC) Track Forecasts by the Japan Meteorological Agency
(JMA) Global Spectral Model
- Western North Pacific from 1997 to 2007 (three-year running mean) -
The position error of 5 day forecasts in 2007 is
smaller than that of 3 day forecasts in 1997.
Enough room to improve TC track forecasts
Position errors of each TC Track Forecast
by JMA/GSM in 2007
Position errors are sorted in ascending order
Forecast time: 72 hours
Total number of forecast events: 102
Position error (km)
1000
800
600
400
200
0
average
Various approach to improve forecasts
Current
system
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assimilation
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User
•Reducing the errors of deterministic track forecasts is not
only the approach.
•Providing confidence information based on ensemble
forecasts is also one way to improve TC track forecasts.
•Yamaguchi et. al (2009) developed the Typhoon
Ensemble Prediction System (EPS) at the Japan
Meteorological Agency
and demonstrated that the
ensemble spread is an indicator of confidence of TC track
forecasts.
Confidence information provided by ensemble forecasts
Position Errors of Ensemble Mean
at 5-day forecasts (km)
Strong relationship between ensemble spread and position
error of ensemble mean track forecasts
3000
Number of
sample1： 149
2500
2000
1.The TC strength of L is included in
this verification
2. Ensemble mean tracks are defined
using more than 1 ensemble
member
1500
1000
500
0
0
4000
8000
12000
Ensemble spread of TC positions2
(ensemble spread accumulated from 0 to 120 hour
forecasts every 6 hours)
How to bring out forecast uncertainties
Ensemble spread is a variability (standard deviation) between the members
in the ensemble forecast.
Ensemble spread can be used as an indicator of confidence of forecast.
Dramatis Personae
Analysis field
Uncertainty of
Analysis field
Deterministic forecast
Forecast Uncertainty
Ensemble member
T=t0
T=t1
Some contradictions as seen among various EPSs
ECMWF
NCEP
Dolphin initiated at
00UTC 13 Dec. 2008
Sinlaku initiated at
12UTC 10 Sep. 2008
The recently established The Observing System
Research
The grey lines are ensemble
and Predictability Experiment (THORPEX)track
Interactive
predictions.
black line
Grand Global Ensemble (TIGGE) databaseThemakes
it is the best
track.
possible to conduct a systematic inter-comparison
of
black triangles are the
global model ensembles and investigate theThe
reason
whyat 120-h.
the
forecast positions
ensemble spread changes from one EPS to another.
Japan
Philippines
Taiwan
Specifications of ECMWF, NCEP and JMA EPS
Note that
The verifications in this study are
based on initial time 0000 UTC
unless otherwise noted because
the most of the airborne
observations were conducted
centered on 0000 UTC.
Verification results of JMA are
based on 1200 UTC because
JMA’s EPS is initiated only at
1200 UTC.
JMA’s EPS is the Medium-range
EPS, not the Typhoon EPS.
What I did
I compared the kinetic energy of ensemble initial perturbations for Typhoon Sinlaku, using
TIGGE data from ECMWF, NCEP and JMA* (Medium range EPS, not Typhoon EPS).
I calculated the following two elements through 10th to 19th of September 2008.
1. Vertical profile of the kinetic energy
2. Horizontal distribution of the kinetic energy
Calculation procedures:
1. Download u and v of initial ensemble fields at 1000, 925, 850, 700, 500, 300, 250
and 200 hPa through ECMWF’s TIGGE site.
2. Convert the latitude-longitude coordinate into the x-y coordinate centered on the
central position of Sinlaku.
3. Calculate ensemble perturbations (u’ and v’) of all ensemble members at each
vertical level.
4. Calculate kinetic energy defined as u’^2+v’^2 from the results of 3.
5. Calculate grid- and ensemble-averaged kinetic energy at each vertical level over the
2000km x 2000km domain and draw the vertical profile.
6. Calculate vertically- and ensemble-averaged kinetic energy over the 2000km x
2000km domain and draw the horizontal distribution.
Best track and intensity of Typhoon Sinlaku
Synopsis in a before-recurvature stage
Geopotential height (solid line) and stream function (dash line)
500 hPa
250 hPa
Sinlaku was located west of the Pacific High. The High is not
strong enough to interact with the typhoon, so the steering caused
by the Pacific High is weak. Sinlaku moved very slowly at that
time; less than 10 km h-1.
Synopsis in a during-recurvature stage
Geopotential height (solid line) and stream function (dash line)
500 hPa
250 hPa
Sinlaku was located in a confluent area induced by the westerly jet
and the southerly flow at the west edge of the Pacific
Synopsis in a after-recurvature stage
Geopotential height (solid line) and stream function (dash line)
500 hPa
250 hPa
Sinlaku was sandwiched by both features; it was located north of
the Pacific High and south of the westerly jet, being advected by
the confluent westerlies.
Vertical profile of KE in a before-recurvature stage
Vertically averaged horizontal distribution of KE in a before-recurvature stage
ECMWF
NCEP
JMA
Storm-relative coordinate with the domain of 2000 km x 2000km
2000km
2000km
Note that the scale of NCEP is 10 times as large as that for ECMWF and JMA
Comparison of kinetic energy of ensemble initial perturbations for Typhoon Sinlaku (2008)
15 Sep. 00Z
(during-recurv.)
18 Sep. 00Z
(after-recurv.)
JMA
Vertically averaged kinetic energy of
ensemble initial perturbations
ECMWF
NCEP
JMA
Storm-relative coordinate
2000km
10 Sep. 00Z
(before-recurv.)
Vertical profile of
kinetic energy of
ensemble initial
perturbations
NCEP
ECMWF
2000km
Temperature and specific humidity perturbation
I did the same verifications for temperature and
specific humidity perturbations.
Total energy = ½ {(u’2 + v’2)
! Kinetic energy
+ cpT’T’/Tr
! Available Potential energy
+ Lc Lc q’ q’/cp/Tr}
! Specific humidity energy
cp is the specific heat of dry air at constant pressure, T’ is a temperature
perturbation about the control analysis, and Tr = 300 K is a reference
temperature. Similarly, Lc is the latent heat of condensation and q’ is a
specific humidity perturbation.
Comparison of APE of ensemble initial perturbations for Typhoon Sinlaku (2008)
Vertical profile of
APE of ensemble
initial perturbations
Vertically averaged APE of
ensemble initial perturbations
ECMWF
NCEP
JMA
15 Sep. 00Z
(during-recurv.)
18 Sep. 00Z
(after-recurv.)
NCEP
2000km
10 Sep. 00Z
(before-recurv.)
Storm-relative coordinate
JMA
ECMWF
2000km
Comparison of SHE of ensemble initial perturbations for Typhoon Sinlaku (2008)
Vertical profile of
SHE of ensemble
initial perturbations
Vertically averaged SHE of
ensemble initial perturbations
NCEP
JMA
15 Sep. 00Z
(during-recurv.)
18 Sep. 00Z
(after-recurv.)
2000km
10 Sep. 00Z
(before-recurv.)
Storm-relative coordinate
JMA
NCEP
2000km
ECMWF’s perturbations
1. ECMWF perturbs wind and temperature and does not perturb specific humidity.
2. In the before-recurvature stage, the ECMWF wind perturbation has a peak at 700hPa on average and is largest in the near environment of the typhoon. Looking at
each ensemble member, the maximum amplitude is found to be 4.4 m s−1,
appearing about 700 km away from the typhoon center while the amplitude within
100 km from the typhoon center is only 1.6 m s−1 at most.
3. As the typhoon moves northward, the amplitude above 500-hPa becomes larger,
corresponding to the change in the area of highest amplitude from the typhoon
surroundings to the synoptic features north of the typhoon.
4. As with the wind perturbation, the temperature perturbation also has a peak in the
mid-troposphere (e.g., the maximum amplitude in the before-recurvature stage
is 2.6 K at 500-hPa and about 500 km away from the typhoon center, implying that
the perturbation has little influence on the warm core structure in the inner region).
5. The vertical profiles of the wind and temperature perturbations are quite similar to
those of perturbations seen in TEPS at JMA, that also uses singular vectors
targeted for TCs (Yamaguchi et al 2009).
NCEP’s perturbations
1. NCEP perturbs all components; wind, temperature and specific humidity.
2. The amplitude of the wind perturbation is larger than ECMWF, especially in the
upper troposphere. For example, it is 9.2 times as large as ECMWF at 200-hPa
in the before-recurvature stage; the amplitude averaged over the 2000 km ×
2000 km domain about the typhoon center is 3.4 m s−1. This trend is common in
the other stages.
3. In the before-recurvature stage, there are large amplitudes in the temperature and
specific humidity perturbations within about 300 km from the typhoon center.
Looking at each ensemble member, the maximum amplitude of temperature
(specific humidity) perturbation is found to be 2.1 K (1.8 g kg−1), which appear at
250-hPa (700-hPa). Considering that the temperature anomaly due to the warm
core structure in the non-perturbed field (not shown) is about 4.0 K at 250 hPa, the
temperature perturbation strengthens the warm core structure by about 50 %.
The specific humidity perturbation increases the moisture by 16 % at 700-hPa
with respect to the non-perturbed field.
JMA’s perturbations
1. JMA also perturbs all components; wind, temperature and specific humidity.
2. JMA’s perturbations are characterized by the large amplitude of the specific
humidity perturbation. For example, it is 3.7 times as large as NCEP at 925hPa in the before-recurvature stage; the amplitude averaged over the 2000 km
× 2000 km domain about the typhoon center is 1.25 g kg−1.
3. The perturbation area is not in the typhoon surroundings but mainly south of the
typhoon. This is because JMA uses moist singular vectors for creating the
perturbations and they are not targeted for each TC, but for the entire tropics.
That is why the amplitude south of the typhoon becomes smaller as the typhoon
moves north.
4. On the other hand, the amplitude of the wind perturbation is small. For example,
it is a quarter of ECMWF at 700-hPa in the before-recurvature stage; the
amplitude averaged over 2000 km × 2000 km domain about the typhoon center is
0.24 m s−1. This trend is common in the other stages.
How do the perturbations modify the symmetric
and asymmetric wind field of Typhoon?
Symmetric wind field
Tangential wind at 850-hPa (before recurvature stage)
ECMWF
NCEP
Black: CTL
Grey: Ensemble member
1.
The size of the typhoon (radial profile of the symmetric component of tangential wind) is similar among the
ensemble members in each EPS;
2.
The range of maximum tangential wind is less than 1 m s−1
3.
The radius of the maximum tangential wind does not change significantly;
4.
The differences between ECMWF and NCEP are much larger than the differences caused by the initial
perturbations in each ensemble.
5.
These trends are common in other stages.
Asymmetric wind field
Steering flow at 500-hPa (before recurvature stage)
The steering flow is defined here as the asymmetric flow at 500-hPa
averaged over 300 km from the typhoon center.
ECMWF
NCEP
Black: CTL
Grey: Ensemble member
1.
The ensemble members are dispersed around the non-perturbed member in both EPSs.
2.
The change in the steering flow of NCEP is larger than ECMWF; In the before-recurvature stage, it is 0.67 m s−1
for NCEP and 0.49 m s−1 for ECMWF on average.
3.
These trend are common in other stages, probably due to the relatively large amplitude of initial perturbations
Perturbation evolution for Sinlaku
Growth of kinetic energy of asymmetric wind component of ensemble perturbations
A 2-day time series of the kinetic energy of the storm-relative asymmetric component of
each wind perturbation at 500-hPa. The kinetic energy is calculated as the difference
between asymmetric wind components of the non-perturbed member (control analysis and
forecast) and each ensemble member to investigate how the steering flow of the ensemble
members is different from that of the non-perturbed member.
Before recurvature stage (00Z 10th Sep. 2008)
ECMWF
NCEP
Definition of
kinetic energy of asymmetric wind component
(uasym_i − uasym_c)2 + (vasym_i − vasym_c)2,
where (uasym_i, vasym_i) and (uasym_c, vasym_c) are the
asymmetric horizontal wind fields of the i’th
ensemble member and the control, respectively.
Ensemble member with the largest growth (ECMWF Ensemble member 44)
Before recurvature stage (00Z 10th Sep. 2008)
Track of EPS member with the largest growth (ECMWF)
Ensemble member 44
Ensemble member 43
Westernmost (left) and easternmost (right) course among
all EPS members
Growth of kinetic energy of asymmetric wind component of ensemble perturbations -2-
Before recurvature stage (00Z 13th Sep. 2008)
ECMWF
NCEP
Example of ECMWF ensembles
Example of NCEP ensembles
Relationship of spread of ensemble track forecasts between ECMWF and NCEP
2007
2008
r = 0.27
r = 0.56
r = 0.21
3 day forecasts
1 day forecasts
r = 0.26
Summary
1. Ensemble perturbations and their growth around a tropical cyclone are investigated
using the THORPEX Interactive Grand Global Ensemble (TIGGE).
2. Vertical and horizontal distributions of initial perturbations produced by the European
Centre for Medium-Range Weather Forecasts (ECMWF), the National Centers for
Environmental Prediction (NCEP) and the Japan Meteorological Agency (JMA) are
compared for Typhoon Sinlaku
3. The amplitudes and distributions of the perturbations are found to be different among
the 3 centers: before, during and after recurvature.
4. The growth rate of the asymmetric component of wind perturbations (that control the
steering flow) is much higher in the ECMWF ensemble than that of NCEP, usually
leading to a relatively large ensemble spread of tracks in ECMWF for forecasts beyond
3 days. Due to the relatively large amplitudes of their initial perturbations, NCEP
generally possesses a larger ensemble spread at forecast times of order 1 day.
Thank you for listening
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A sensitive analysis technique is needed to maximize the effect on a
numerical prediction and to minimize the cost of the observations.
©JAXA
©ＮＡＳＡ
Adaptive observations
©Vaisala
sensitive area
2nd year in RSMAS
Title:
On singular vector based sensitivity analysis for tropical
cyclones in a non-divergent barotropic framework
Motivation:
How sensitive are the fast-growing perturbations to the
intensity, size and asymmetry of the initial TC-like vortex?
How does the perturbations (sensitivity region) affect track
forecasts?
Methodology:
Using the SPECTRAL ELEMENT OCEAN MODEL (M.
Iskandarani et al. 1995), singular vectors are computed for
various initial conditions.
Thank you for listening
Acknowledgments
Sharanya S. Majumdar1
Melinda S. Peng2
Carolyn A. Reynolds2
David S. Nolan1
1. Rosenstiel School of Marine and Atmospheric Science, University of Miami
2. Marine Meteorology Division, Naval Research Laboratory
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