Reprint 564
Probability Forecasts of High Winds and Related Warnings
Associated with Tropical Cyclones in Hong Kong
C.C. Lam & S.C. Tai
International Symposium on Tropical Weather and Climate,
Guangzhou, China, 7-11 November 2004
Probability Forecasts of High Winds and Related Warnings
Associated with Tropical Cyclones in Hong Kong
Queenie C.C. Lam and S.C. Tai
Hong Kong Observatory
Email: [email protected]
Abstract
To assist forecasters in formulating forecasts and warning strategies in tropical
cyclone situations, a methodology using a combination of statistical and NWP
techniques has been developed to predict the probability of occurrence of strong or
gale force winds in Hong Kong. The tropical cyclone forecast intensity and
positions relative to Hong Kong are first determined based on observations and model
ensemble forecasts compiled from ECMWF, JMA, NCEP and UKMO global models.
Using the statistical relationship between the TC intensity, distance of the TC from
Hong Kong and local climatological wind data, the probability of occurrence of
strong and gale force winds in the Harbour of Hong Kong is then derived. The
uncertainties in TC forecast positions are also taken into account in the probability
forecast.
This paper presents the methodology of estimating the probability of strong or
gale force winds in Hong Kong under TC situations. Forecast verification and
calibration results for 1999-2003 and a case illustration on the use of probability
forecast of TC signal show that the probability forecast tool provides useful objective
guidance for forecasters' reference. Limitations and future possible enhancements in
the probability forecast tool are discussed.
1.
Introduction
On average, six tropical cyclones affect Hong Kong each year. To mitigate the
impact of tropical cyclones, Hong Kong operates a graded Tropical Cyclone Warning
Signal System to warn the public of the threat of winds associated with a tropical
cyclone. The System consists of five numbers representing increasing levels of local
wind strength. The Tropical Cyclone Signal No. 1 is issued whenever a tropical
cyclone is within 800 km of Hong Kong and may affect the territory later. Signals
No. 3 and No. 8 warn the public of strong and gale/storm force winds in the city
respectively. Signal No. 9 signifies increasing gale or storm force winds, while No.
10 warns of hurricane force winds (Lam, 2000).
1
In view of the stringent building codes in Hong Kong, home is generally
considered the safest place for people to take refuge from a tropical cyclone. When
Signal No. 8 is issued, the Hong Kong Observatory advises the public to stay home or
return home. Practically all activities in the city move towards shutdown. All
schools, government offices, banks, the stock market, and courts are closed. Most
public transport services will start to cease operation. When Signal No. 9 goes up,
even the underground train will stop. With Signal No. 10, the city grinds to a
complete halt to prepare for the onslaught of a full-fledged typhoon.
The TC warning signals issued by the HKO are based on the forecast wind
strengths within the Victoria Harbour (the ‘Harbour’) of Hong Kong. Based on
climatological wind data associated with TCs, probability of the occurrence of strong
and gale force winds within the Harbour can be derived statistically, given that the
position of a TC relative to Hong Kong and intensity of the TC are known. Using
this statistical relationship and based on the subjective TC forecast track with its
uncertainties, the probability of the occurrence of strong or gale force winds within
the Harbour due to an approaching TC can be derived.
Operational numerical weather prediction (NWP) models have matured in the
past decade and become indispensable in weather forecasting. Studies have shown
that the statistical evaluation of a large number of forecasts produced by a model
ensemble, either using a single model started from different initial conditions or a set
of independent numerical models, is in general superior in quality to the forecasts of
individual numerical models (Zhang and Krishnamurti, 1997; Elsberry and Carr, 2000;
Aberson, 2001; Weber, 2003).
The HKO began to experiment with multi-model ensemble method based on the
equally weighted average of the forecast tropical cyclone positions of ECMWF, JMA
and UKMO global models in 1999 (Lee and Wong, 2002). NCEP global model was
added to the ensemble in 2002. Model ensemble forecast track has been serving as
the basis for forecasters to work out the operational TC warning track ever since.
The HKO has developed a methodology using a combination of statistical and
NWP techniques to predict the probability of occurrence of strong or gale force winds
within the Harbour of Hong Kong. The methodology for generating probability
forecast of high winds and verification results are detailed in the following sections.
2
2.
Methodology
2.1 Statistical model for the occurrence of high winds
Based on climatological data from 1968-2001, there were 143 tropical cyclones
necessitating the issuance the Signal No.3 or above. Of these, 115 caused strong
winds and 32 of them caused gales in the Harbour. They were used to calculate the
probability occurrence of strong winds or gales. The number of typhoons (Ts),
severe tropical storms (STSs), tropical storms (TSs) and tropical depressions (TDs)
passing each 1 degree-latitude and 1 degree-longitude box within 15-25 N, 106-123 E
during the period were counted from their hourly positions linearly interpolated from
the 6-hourly HKO's best track positions. For each category of TC, the ratio of the
number of TCs passing the 1-degree box and causing strong winds (gales) or above in
the Harbour to the total number of TCs passing the box was calculated as the
probability of occurrence of strong winds (gales) in the Harbour. Maps of
probability isopleths for the occurrence of strong winds or gales were then constructed
and smoothed at 10 percent intervals for each TC category. Amongst the 32 tropical
cyclones, there were 19 Ts, 11 STSs and 2 TSs that triggered gales in the Harbour.
These two TSs, Faye in 1992 and Cam in 1999, either passed directly over or very
close to Hong Kong. As the number of cases with gales caused by TS is too small,
the corresponding probability map was not constructed. Only the gale probability
maps for T and STS were constructed.
2.2 Dynamic model for TC track forecast
Numerical model guidance has shown to be increasingly more reliable in TC
track forecast in the past decade (Lam, 2001). The equally weighted multi-model
ensemble method was put into operation at HKO in 2002 in view of its superiority
over the forecasts of individual models and conventional methods like climatology
and persistence. The forecast TC positions of the ECMWF, JMA and NCEP models
are determined from the surface prognoses as the point of minimum mean seal-level
pressure which is identified by overlapping parabolic interpolation (Manning and
Haagenson, 1992). The resolutions of the ECMWF, JMA and NCEP prognostic data
received by HKO are 2.5 degrees, 1.25 degrees and 1.0 degree respectively. The
forecast TC positions of the UKMO global model are extracted from the TC guidance
of UKMO received via the GTS. These positions are identified by the point of
maximum relative vorticity at the 850-hPa level (Heming and Radford, 1998).
3
A Tropical Cyclone Information Processing System (TIPS) was developed at the
HKO to derive and display the model ensemble TC track on-the-fly to facilitate the
formulation of TC warning track and forecast strategies. Forecast tracks from
individual models or from different operational centres can be displayed in TIPS upon
forecasters' selection. Figure 1 shows a sample layout of the TIPS in the case of
Typhoon Aere in August 2004. Forecasters will apply an objective method to
identify and correct persistent bias for model ensemble forecasts when they formulate
the TC warning track (Lam and Ma, 2004). Table 1 shows the verification results of
model ensemble forecasts, individual model forecasts together with HKO's official
forecasts for TCs over the area of responsibility of HKO for TC warning for shipping
(10-30 N, 105-125 E) in 2001-2003. The skill of model ensemble forecast translated
into a noticeable improvement in HKO’s official TC forecast (Figure 2). HKO's
warning track and intensity forecasts at 24-hour intervals up to 72 hours ahead are
interpolated at hourly intervals for the calculation of probabilities of strong winds and
gales in the Harbour.
2.3 Estimation of uncertainties in track forecast
To account for the uncertainty of TC forecast positions in the calculation of
probability forecast of high winds, two types of perturbation schemes are used to
derive perturbed TC tracks. One scheme is static and the other is dynamic.
A statistical model for error distributions for 24- and 48-hour forecast positions
was derived using forecast position errors for HKO’s TC warning track from 1999 to
2002 with a sample size of 621 and 438 respectively. The HKO extended TC track
forecast to 72 hours in 2003. The sample size of 72-hour position error distribution
is too small to be directly used in the statistical model. A factor of 1.3 of 48-hour
position error, which is estimated based on 2003 dataset, is therefore taken as the
72-hour position error. The latitudinal and longitudinal position errors are used to
form the perturbation field in this statistical perturbation scheme.
In the dynamical perturbation scheme, deviations of the TC forecast positions of
all available individual models from the model ensemble forecast position in
latitudinal and longitudinal directions are used to form the perturbation field.
Individual models other than those members of the model ensemble, such as HKO's
Operational Regional Spectral Model and JMA's Typhoon Model, are also used to
determine the model spread.
4
2.4 Probability forecast of strong and gale force winds
For each perturbation scheme, a bivariate Guassian distribution (Wilks, 1995) is
adopted to fit the perturbation field and obtain the probability density function for the
occurrence of TC. 25 perturbed tracks are constructed within 85 % of the bivariate
Gaussian distribution for position uncertainties. A schematic diagram showing the
method of construction is given in Figure 3. The number of perturbed tracks and the
85th percentile are chosen to optimize the computational time. Figure 4(a) and (b)
show the perturbed tracks passing within the 85th percentile probability ellipses using
dynamical and statistical perturbation schemes respectively in the case of Typhoon
Dujuan in September 2003.
The probability of the occurrence of strong (gale) winds in the Harbour is then
generated at hourly intervals based on the perturbed tracks, probability density
function of TC occurrence, as well as the probability map of strong (gale) winds as
described in section 2(a). At time t, the probability is calculated as follows :
(t ) = ∑ P I (W | r k ) P
25
P
where
P (W r )
I
k
k =1
(r (t ))
k
= probability of strong or gale winds given the location of TC
at r on the kth perturbed track and intensity category I.
W denotes strong or gale force winds.
P (r
k
(t ) ) = probability of the TC at location r and time t on the kth
perturbed track.
Probability forecasts generated up to 72 hours with a 3-hourly update are
displayed in the form of a time series and a table based on HKO's TC warning track
for forecasters' reference (Figure 5). Probabilities of the occurrence of strong and
gale force winds during the whole event of TC regardless of the time of occurrence,
the total event probability, are also derived.
P (total _ event) = Max{P (t )}
t =1,..., 72
In addition, probabilities of TC coming within 300 km, 500 km and 800 km
range of Hong Kong, as well as making landfall are generated at hourly intervals
based on the probability density function.
5
In the probability calculation, uncertainties in intensity forecast are not catered
for in the current configuration. Hourly intensity values in terms of maximum
sustained winds are interpolated from 72-hour forecasts at 24-hour intervals from TC
warning for shipping. As the probability maps are constructed for four TC
categories, viz. TD, TS, STS and T, probability forecast of strong/gale force winds
may drop or increase sharply when forecast intensity changes from one TC category
to another. To avoid rapid drop of probability forecast of high winds when the TC is
about to make landfall within the next 24 hours, the intensity values are kept
unchanged until the TC makes landfall.
3.
Verification and calibration
3.1 Verification methods
Verifications of forecast probability based on statistical perturbation scheme and
dynamical perturbation scheme were carried out, using datasets of TCs in 1999-2003
and 2002-2003 respectively. The latter verification dataset started from 2002 after
the adoption of multi-model ensemble method in TC forecasting. Probability
forecasts were stratified into three categories, namely 0-33 % for low probability;
34-66 % for medium probability and 67-100 % for high probability. Two methods
of verification were employed :
(i)
The Brier score, a common performance indicator for probabilistic forecasts,
was calculated for each 3-hourly forecast period. The Brier score is
essentially the mean-squared error of the probability forecasts and it ranges
from 0 to 1 (Wilks, 1995). Less accurate forecasts receive higher Brier
scores. If probability forecasts always give 50 %, then the Brier score will
be 0.25.
(ii) The percentage of cases where strong or gale force winds actually occurred
during an interval of 3 hours (T+0 to T+3 hours, T+4 to T+6 hours,…,etc.)
was counted for each forecast probability category, and compared with the
maximum of hourly forecast probability during the 3-hour time slot.
Verifications were only performed for cases with TC warning positions
falling within 800 km of Hong Kong and non-zero forecast probability so as
to avoid over-estimation of hit rate for the “Low” probability category.
6
3.2 Verification results of statistical perturbation scheme
Categorical verification results for probability forecast of strong and gale force
winds are shown in Figure 6 and Table 2. Some observations are as follows :
(i) The Brier scores were generally below 0.18 for all forecast hours, in respect
of probability forecasts of both strong and gale force winds.
(ii) Forecast of "Low" probability (0-33 %) in general matched well with the
actual occurrence of strong and gale force winds.
(iii) The performance of forecasts of "Medium" probability (34-66 %) and
"High" probability (67-100 %) was comparatively less satisfactory. In the
case of strong winds, forecasts of "High" or "Medium" probability were
generally over-estimated up to around T+39 hours and T+48 hours
respectively. Conclusions could not be meaningfully drawn for longer
forecast hours in view of its small sample size.
(iv) For gale force winds, forecast of "Low" probability agreed reasonably well
with the actual occurrence. Forecast of "Medium" probability was
generally over-estimated. The sample size was too small for making
remarks on the forecast of “High” probability.
With an attempt to improving the overall performance of probability forecasts,
calibration of the probability forecast, P, was applied by using an empirical formula:
Pcalibrated
=
P
γ
With this gamma correction factor, the calibrated forecast probability will always lie
within the range of 0-100 % regardless of the value of γ. The optimal values of γ for
strong and gale force winds were derived by minimizing the total error of the
probability forecasts :
Total Error =
24
3
k
i
∑∑
(Pki – ACPi)2
where ACPi = mid value of the "Low" (0-0.33), "Medium" (0.34-0.66) or "High"
(0.67-1.00) category, i.e, 0.17, 0.50 and 0.83 respectively for the
three categories.
Pki = forecast probability for the kth 3-hourly time slot and the ith
category (Low, Medium or High).
In this study, the value of γ was found to be 1.9 for strong winds, but there was no
optimal value for gales .
7
Comparison of the calibrated probability forecast with the percentage of actual
occurrence for strong winds is shown in Figure 7. There was significant
improvement for the "Medium" probability forecast up to around T+48 hours.
However, the "High" probability forecast was still over-estimated up to around T+21
hours.
3.3 Verification results of dynamical perturbation scheme
Verification results for probability forecast of strong winds are shown in Figure 8
and Table 2. It is noted that :
(i) The Brier scores were generally below 0.2 for all forecast hours.
(ii) Forecast of ”Low” and ”Medium” probability for strong winds matched
rather well with the percentage of actual occurrence up to T+48 hours.
(iii) Forecast of ”High” probability for strong winds was satisfactory up to
T+21 hours, but then it became over-estimated by one category from T+21
to T+39 hours.
The sample size for verifications of probability forecast of strong winds beyond
T+48 hours in the case of “Low” and “Medium” probability, and beyond T+39 hours
for “High” probability category, as well as gale force winds for the entire forecast
range was too small for any meaningful remarks to be drawn. Calibration could be
tested for the dynamical perturbation scheme when more data are accumulated in the
future.
4.
Probability forecast of Signal No.3 and No.8
For application to operational TC warnings, once the warning track is decided,
probability forecasts of strong winds and gales in the Harbour are generated
automatically in support of decision making for the issuance of TC signal No.3 and
No.8 respectively. In 2004, the HKO started providing public transport operators
with probability forecast of signal change when local signal No. 3 or above is in force
on a trial basis, to facilitate their planning for the suspension and resumption of
transport services.
The Signal No. 3 (No.8) is normally issued within a certain lead time before the
earliest expected occurrence of Force 6 (Force 8) in the Harbour area. The method
described in the previous section is taken one step further with the incorporation of
operational practices to generate probability forecast of Signal No.3 and No.8, as
8
described below.
To make automatic generation of signal probabilities possible for decision
support, a set of parameters for lead times and rules is incorporated into the algorithm.
Firstly, when strong (gale) winds are expected within 6 hours, Signal No.3 (No.8) will
have to be issued as soon as possible. Secondly, the lead time of 6 hours for issuing
Signal No.8 should take higher priority as No.8 has greater impact on the community.
Therefore, it is desirable to have the No.3 issued at least 6 hours before issuing the
No.8, and it implies that the No.3 will have to be issued as soon as possible when gale
force winds are expected in less than 12 hours. Based on the above criteria and
assumptions, the probability forecast for No.3 for the time period (T, T+3 hours) will
be :
(i) Max (hourly probability of strong winds between max (current hour, T) and
T+9 hours); or
(ii) Max (hourly probability of gales between max (current hour, T) and T+15
hours),
whichever is larger.
Probability forecasts of No.3 and No.8 are displayed in the form of a table with a
time slot of 3 hours up to 72 hours ahead (Figure 9). Forecasts based on dynamical
perturbation scheme, statistical perturbation scheme (with and without calibration),
and HKO's warning track (i.e. no perturbation) are generated to provide the scientific
basis for formulating TC warning strategies by forecasters.
5.
Use of probability forecast of TC signals - a case illustration for Typhoon
Dujuan in 2003
The application of probability forecast to TC signal assessment is illustrated in
the case of T. Dujuan (0313) in a step-by-step approach. The HKO's best analyzed
track for Dujuan is given in Figure 10. The Standby Signal No.1 was issued in the
evening of 1 September. The chance of Signal No.3 was assessed using the
probability forecast tool for every 3 to 6 hours subsequently. The categorical
probability forecast was taken as the highest one from the model spread perturbation
method, and statistical perturbation method with and without calibration. The
chance provided by the probability forecast tool for Signal No.3 was medium before 9
a.m. on 2 September, turning to high in the late morning on the same day. As
Dujuan was a fast-moving TC, the time between the onset of strong and gale force
winds would be expected to be rather close. The probability forecast tool indicated
that the Signal No.3 could be issued as early as around 9:00 a.m. In reality, the
9
Signal No.3 was issued at 10:40 a.m.
After the issuance of Signal No.3, the chance for the issuance of Signal No.8 was
assessed. The probability forecast tool suggested the chance for Signal No.8 was
high in the early afternoon and the No.8 should be considered at around 2 p.m.
Dujuan moved quickly towards Hong Kong from the east and the HKO issued the
Signal No.8 at 2:20 p.m. when Dujuan was about 230 km to the east of Hong Kong.
Local winds were strong northwesterlies in the afternoon, reaching gale force towards
the evening.
Dujuan was forecast to come within several tens of kilometres of Hong Kong and
other methods had to be applied when assessing the probability of No.9 or No.10 after
the issuance of Signal No.8. Monitoring the Doppler radar velocity field, local
automatic weather station data and TC short-term movement was useful for assessing
higher signals. The HKO issued the Increasing Gale or Storm Signal No. 9 at 8:10
p.m. on 2 September. On that night, Dujuan skirted 30 km to the north of the HKO
Headquarters. Local winds, in particular those over the northern part of the New
Territories, strengthened from gale to storm force. Winds at Lau Fau Shan even
reached hurricane force for a short period of time. Gale to storm force winds were
also recorded in other parts of the territory, including the Harbour.
Strong to gale southerly winds prevailed over the territory when Dujuan moved to
the west of Hong Kong. The signal No. 9 was replaced by the Signal No. 8 at 10:10
p.m. the same night. In assessing the chance for cancellation of Signal No.8, the
probability forecast tool was used. The time at which winds would have a 50 %
chance of falling below gales was taken here as an indicator of a high chance for
cancellation of Signal No.8. Real-time verification of the probability forecast in the
first few hours was used in assessing the reliability of different methods. In the
assessment made before the midnight of 2 September, the chance for replacing No.8
by No. 3 was medium before 2 a.m. on 3 September while the chance was high
between 2 a.m. and 5 a.m. Shortly after midnight, the chance for replacing No.8 by
No.3 suggested by the probability forecast tool was revised based on an updated
forecast TC track to occur a bit earlier. In the actual situation, Dujuan weakened
rapidly over Guangdong overnight and local winds abated generally.
The
replacement of Signal No. 8 by Signal No.3 was made at 1:30 a.m. on 3 September.
The probability forecast tool suggested the chance of cancellation of Signal No.3 was
high between 5 a.m. to 8 a.m. on the same day. The time at which strong winds
would have a 50 % chance of moderating was around 7 a.m. Local winds weakened
substantially in the small hours. The Signal No.3 was cancelled at 3:20 a.m.
10
Unfortunately, winds strengthened again at around 4 a.m. It was not until 7 a.m. that
strong winds ceased to blow in the Harbour.
If the probability forecast tool
guidance was available at the time, the decision maker could then have more objective
guidance for determining the cancellation time of Signal No. 3.
The probability forecast tool was shown to be useful for the issuance and
cancellation of Signal No.3 and No.8 in the case of Dujuan.
6.
Discussions and concluding remarks
Probability forecasts of strong and gale force winds in Hong Kong up to 72 hours
ahead are automatically generated at the HKO when a TC enters into the area of
responsibility for warning for shipping. A composite method of using statistical and
dynamical model-based techniques is developed to assist forecasters in formulating
forecasts and warning strategies in TC situations. In the calculation of probability
forecast, the uncertainties in TC forecast positions are estimated by past statistical
position error distribution or spread of individual models from model ensemble.
Probability forecasts generated by using statistical perturbation method are calibrated
by using a gamma correction factor. Calibrations are currently applied to forecasts
generated from statistical perturbation scheme only. They will be applied to
forecasts based on dynamical perturbation scheme when more data from model
ensemble is accumulated in the future.
Verifications are carried out for the statistical and dynamical perturbation
schemes, using dataset of 1999-2003 and 2002-2003 respectively. Salient points of
observations are summarized as follows :
(i)
A Brier score of less than 0.2 was achieved for all forecast hours, showing
that the probability forecast tool possess skills with both statistical and
dynamical perturbation schemes.
(ii) Forecasts of “Low” probability for strong winds and gales generally
matched well with the actual occurrence.
(iii) Significant improvement for calibrated “Medium” probability forecast for
strong winds was found based on statistical perturbation scheme.
Improvement in “High” probability forecast was less significant and a
general over-estimation was still found up to around T+21 hours.
(iv) The performance of dynamical perturbation scheme for strong winds was
in general satisfactory up to T+48 hours judging from the categorized
comparison results against the actual occurrence.
11
(v)
More samples are required for verifying the performance for gale winds,
for both the statistical and dynamical perturbation schemes.
With the incorporation of guidelines and practices in operational TC warning,
probability forecasts of strong and gale force winds within the Harbour are utilized to
generate probability forecasts of TC Signal No.3 and No.8 in Hong Kong. The case
illustration of Typhoon Dujuan in this paper demonstrated the good potential of the
probability forecast tool in facilitating the formulation of warning strategies by
forecasters.
In utilizing the probability forecast tool, forecasters have to take note of the
following limitations of the tool :
(i)
Uncertainties in intensity forecast have not been catered in the current
configuration.
Hourly intensity values in terms of maximum
sustained winds are just interpolated from 72-hour forecasts at 24-hour
intervals from the TC warning for shipping.
(ii)
As the probability maps are constructed for four TC categories, viz. TD,
TS, STS and T, probability forecast of strong/gale force winds may
drop or increase sharply when forecast intensity changes from one TC
category to another. The intensity stratification in generating
probability maps may not be fine enough.
(iii)
The statistically derived probability maps for the occurrence of gales in
the Harbour in the case of TS and the occurrence of storm or hurricane
force winds in the cases of STS and T are not available due to small
sample size problem.
(iv)
The effect of TC size has not been taken into account in the
construction of probability maps, again due to sample size problem.
Large TCs tend to trigger strong winds/gales in the region of lower
nominal probability in the isopleth map and vice versa for small TCs.
The arrival or presence of northeast monsoon during the approach of a
(v)
TC could result in onset of gales in the Harbour earlier than given by
the probability forecast tool.
In view of the ever-increasing remote-sensing data for initialization of TC vortex
and ever-improving model performance, incorporation of mesoscale model forecasts
of wind structure of TC or wind forecasts for specific locations will be a promising
way to enhance the probability forecast tool. In addition, incorporation of strike
probabilities generated from dynamical ensemble prediction systems (EPSs) with at
least several tens of members may add values to the dynamical perturbation scheme
12
which is currently based on a few deterministic model forecasts.
Acknowledgements
The authors would like to thank Mr. C.Y. Lam, Dr. M.C. Wong and Mrs. Hilda
Lam for their valuable comments. Thanks are also extended to Mr. Simon Ching for
his programming effort and active participation in the discussions together with Mr.
W.C. Woo; Dr. T.C. Lee and Messrs M.S Wong and C.F. Ma for deriving the statistical
probability of strong and gale force winds given the location and intensity of an
approaching TC.
13
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14
Bull. Amer. Meteor. Soc., 78, 2785-2795.
15
Table 1 Mean forecast position errors of model ensemble, its individual members
and HKO's warning track for TCs over 10-30 N, 105-125 E in 2001-2003. Number
of forecasts in brackets.
24-hour forecast
ECMWF
2001
165 (33)
2002
126 (21)
2003
158 (29)
Overall
150 (83)
JMA
129 (68)
97 (41)
153 (61)
126 (170)
NCEP
147 (56)
147 (56)
UKMO
127 (74)
122 (42)
137 (62)
129 (178)
Ensemble
97 (38)
109 (51)
103 (89)
HKO
135 (176)
119 (86)
151 (129)
135 (391)
48-hour forecast
ECMWF
2001
247 (23)
2002
189 (13)
2003
255 (19)
Overall
230 (55)
JMA
228 (43)
152 (27)
253 (41)
211 (111)
NCEP
239 (39)
239 (39)
UKMO
209 (48)
186 (26)
247 (43)
214 (117)
Ensemble
165 (22)
192 (34)
179 (56)
HKO
233 (122)
212 (56)
239 (88)
228 (266)
(iii) 72-hour forecast
ECMWF
2001
261 (40)
2002
260 (7)
2003
382 (11)
Overall
301 (58)
JMA
312 (34)
298 (14)
389 (24)
333 (72)
NCEP
325 (22)
325 (22)
UKMO
322 (42)
310 (13)
403 (23)
345 (108)
Ensemble
297 (4)
260 (15)
279 (19)
HKO
321 (38)
321 (38)
(i)
(ii)
16
Table 2 Brier scores of probability forecasts of strong and gale force winds in the
Harbour with dynamic perturbation scheme and statistical perturbation scheme with
and without calibration. The period of verification dataset for statistical perturbation
scheme is 1999-2003 while that for dynamical perturbation scheme is 2002-2003.
Forecast hour
0-3
3-6
6-9
9-12
12-15
15-18
18-21
21-24
24-27
27-30
30-33
33-36
36-39
39-42
42-45
45-48
48-51
51-54
54-57
57-60
60-63
63-66
66-69
69-72
3-72
Strong
(statistical/not
calibrated)
0.14 (275)
0.14 (285)
0.16 (296)
0.17 (313)
0.16 (328)
0.16 (347)
0.16 (352)
0.16 (358)
0.12 (274)
0.13 (276)
0.14 (276)
0.14 (279)
0.15 (275)
0.16 (273)
0.16 (267)
0.16 (255)
0.11 (14)
0.09 (14)
0.08 (14)
0.06 (14)
0.05 (14)
0.02 (14)
0.01 (14)
0.01 (14)
0.22 (411)
Brier scores (Number of samples)
Gale
Strong
Strong
(statistical/not
(statistical/
(dynamical/not
calibrated)
calibrated)
calibrated)
0.18 (66)
0.12 (275)
0.13 (79)
0.13 (83)
0.12 (285)
0.12 (87)
0.08 (107)
0.14 (296)
0.16 (87)
0.10 (118)
0.15 (313)
0.18 (87)
0.10 (129)
0.15 (328)
0.18 (85)
0.07 (154)
0.15 (347)
0.19 (85)
0.05 (173)
0.15 (352)
0.19 (82)
0.04 (174)
0.15 (358)
0.23 (73)
0.04 (151)
0.11 (274)
0.21 (57)
0.05 (162)
0.12 (276)
0.19 (55)
0.05 (164)
0.14 (276)
0.20 (53)
0.04 (169)
0.14 (279)
0.19 (52)
0.05 (170)
0.15 (275)
0.18 (50)
0.05 (166)
0.16 (273)
0.18 (47)
0.03 (148)
0.16 (267)
0.18 (44)
0.03 (130)
0.15 (255)
0.16 (41)
0.01 (12)
0.16 (14)
0.10 (14)
0.01 (12)
0.14 (14)
0.07 (14)
0.01 (13)
0.11 (14)
0.06 (13)
0.00 (12)
0.08 (14)
0.06 (11)
0.00 (11)
0.05 (14)
0.05 (9)
0.00 (9)
0.00 (14)
0.03 (7)
0.00 (7)
0.00 (14)
0.02 (7)
0.00 (5)
0.00 (14)
0.01 (4)
0.15 (264)
0.29 (411)
0.26 (99)
17
Fig.1 Display of forecast tracks of model ensemble and individual members on the
Tropical Cyclone Information Prediction System (TIPS) in the case of Typhoon Aere
(0417).
Fig.2 Performance of HKO's official TC track forecast in terms of error ratio with
respect to climatology-persistence method from 1975 to 2003 over the area of 10-30
N, 105-125 E.
18
Fig.3 A schematic diagram showing the construction of 25 perturbed tracks evenly
distributed within 85 % of the bivariate Gaussian distribution for position
uncertainties (ellipse in thick black). Samples of perturbed tracks are drawn in blue
lines. They are generated by fitting points with the same number to a cubic spline.
19
(a)
(b)
Fig.4 Perturbed tracks passing within the 85th percentile probability ellipses using (a)
dynamical and (b) statistical perturbation schemes respectively in the case of Typhoon
Dujuan in September 2003.
20
(a)
(b)
Fig 5 Probability forecasts of listed events shown in (a) a time series (strong and gale
force winds in blue and green bars respectively); and (b) a tabular form.
21
(a)
(b)
Fig.6 Percentage of actual occurrence of (a) strong winds and (b) gales in Hong Kong for
cases with ‘High’ (red), ‘Medium’ (green) and ‘Low’ (blue) probability forecasts based on
statistical perturbation scheme. HKO's warning tracks with TC positions within 800 km
of Hong Kong in 1999-2003 were used.
22
Fig.7 Same as Fig.6(a) but with calibration using a gamma correction factor of 1.9.
Fig.8 Same as Fig.6(a) but with probability forecasts based on dynamical perturbation
scheme and the period of verification dataset is 2002-2003.
23
Fig.9 Probability forecasts of Signal No.3 and No.8 shown in a tabular form at
3-hourly intervals (Low : 0-33 % in purple; Medium : 34-66 % in yellow; High :
67-100 % in pink).
Fig.10 HKO's best analyzed track for Typhoon Dujuan in 2003.
24