DSpace at VNU: A study of the connection between tropical cyclone track and intensity errors in the WRF model

Meteorol Atmos Phys (2013) 122:55–64
DOI 10.1007/s00703-013-0278-0

ORIGINAL PAPER

A study of the connection between tropical cyclone track
and intensity errors in the WRF model
Du Duc Tien • Thanh Ngo-Duc • Hoang Thi Mai
Chanh Kieu

•

Received: 27 December 2012 / Accepted: 20 August 2013 / Published online: 4 September 2013
Ó Springer-Verlag Wien 2013

Abstract This study examines the dependence of the
tropical cyclone (TC) intensity errors on the track errors
in the Weather Research and Forecasting (WRF-ARW)
model. By using the National Centers for Environmental
Prediction global final analysis as the initial and boundary
conditions for cloud-resolving simulations of TC cases
that have small track errors, it is found that the 2- and
3-day intensity errors in the North Atlantic basin can be
reduced to 15 and 19 % when the track errors decrease to
55 and 76 %, respectively, whereas the 1-day intensity
error shows no significant reduction despite more than
30 % decrease of the 1-day track error. For the NorthWestern Pacific basin, the percentage of intensity reduction is somewhat similar with the 2- and 3-day intensity
errors improved by about 15 and 19 %, respectively. This
suggests that future improvement of the TC track forecast
skill in the WRF-ARW model will be beneficial to the
intensity forecast. However, the substantially smaller

percentages of intensity improvement than those of the
Responsible editor: M. Kaplan.
D. D. Tien
Research and Development Division, National Center
for Hydro-Meteorological Forecasting, Hanoi, Vietnam
T. Ngo-Duc
Department of Meteorology, Hanoi College of Science,
Vietnam National University, Hanoi 10000, Vietnam
H. T. Mai Á C. Kieu
Laboratory for Weather and Climate Forecasting, Hanoi College
of Science, Vietnam National University, Hanoi 10000, Vietnam
C. Kieu (&)
I. M. Systems Group at NOAA/NWS/NCEP/EMC,
College Park, MD 20740, USA
e-mail: ;

track error improvement indicate that ambient environment tends to play a less important role in determining
the TC intensity as compared to other factors related to
the vortex initialization or physics representations in the
WRF-ARW model.

1 Introduction
Despite a steady improvement in the tropical cyclone (TC)
track forecast skill over the last few decades, progress in
TC intensity forecast skill has been slow to date with
marginal improvements mostly observed at the 48 and 72 h
forecast times (DeMaria et al. 2007; National Hurricane
Center (NHC)1). Such a stagnation of the intensity forecast
skill is intriguing as various observational analyses as well
as theoretical and modeling studies have shown that TC

development is rather sensitive to several environmental
factors such as sea surface temperature (SST), vertical
wind shear, topography, cold air intrusion, or tropical
waves activities (Gray 1968; George and Gray 1976;
Emanuel 1986; Holland 1997; Chen and Yau 2003; Mandal
et al. 2007; Hill and Lackmann 2009; Wang 2009; Zhan
et al. 2012). With the continuous decrease of the track
errors at all forecast lead times, one may expect some
advance in the intensity forecast skill. According to the
NHC official report, the mean 3-day maximum surface
wind (VMAX) forecast error for the North Atlantic (NATL)
basin has been, nevertheless, constant around 9.5 m s-1
since 1990. A question of the linkage between the TC track
and intensity forecast skill thus remains elusive. This
question is of significance as it is desirable to know if a
1

The NHC official reports of the track and intensity errors can be
found at: />
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56

future 50 % improvement of the track forecast skill in a TC
dynamical model2 could help reduce its intensity forecast
errors inherently.
Generally speaking, TC intensity forecast errors in a
dynamical model can be attributed to three main factors: (1)
a poor initial vortex representation of TCs; (2) inadequate

representations of the TC physical processes; and (3) wrong
ambient environment due to erroneous track forecasts (see
e.g., Knaff et al. 2003; Bender et al. 2007; DeMaria et al.
2007; Gall et al. 2012). Of the three, the first two factors
appear to be the most dominant as previous studies have
demonstrated that a poorly initialized vortex often undergoes some unrealistic spin-up or sometimes dissipates
quickly before it could develop more consistent dynamics
(see, e.g., Bender et al. 1993; Kurihara et al. 1993; Davidson
and Weber 2000; Kwon et al. 2002; Kieu and Zhang 2009;
Nguyen and Chen 2011). Likewise, the TC vortex can
readily drift away from the true development if deficient
physical parameterizations are utilized. As shown in many
studies, model errors associated with such inadequate
parameterizations of various physical processes could lead
to very different TC strength, even with the same initial
condition (see, e.g., Liu et al. 1997; Braun and Tao 2000;
Shen et al. 2000; Davis and Bosart 2002; Kieu and Zhang
2010; Pattnaik and Krishnamurti 2007; Osuri et al. 2011).
While much of recent efforts in improving the TC
intensity forecast have focused on the first two factors, the
influence of the ambient environment on the intensity
forecast errors in TC dynamical models has so far received
the least attention as it is difficult to isolate the intensity
errors related specifically to erroneous track forecasts from
the other factors under realistic environment conditions. By
investigating different combinations of the best track
datasets and the global forecasting system (GFS) forecasts/
analyses during the 2002–2009 hurricane seasons with a
statistical-dynamical model, DeMaria (2010) demonstrated
that forecast errors in the Logistic Regression Model

(LGEM; DeMaria et al. 2007) could be improved by more
than 15 % at 3 days and 35 % at 5 days by reducing
forecast track error to zero. Assuming a linear relationship
of the track and intensity errors, DeMaria suggested that a
50 % reduction in track errors could correspond to a 17 %
reduction in the intensity errors. This result is significant as
it indicates that future improvement of the track forecast
skill can be beneficial for the intensity forecast skill.
However, DeMaria’s direct use of the post-analysis best
track as an input for the statistical model is a highly idealized assumption that is not achievable with TC dynamical
2

In this study, a TC dynamical model is understood as a numerical
forecasting model that is based on a set of the full physics primitive
equations. These dynamical models are different from statistical (or
statistical-dynamical) forecasting models that rely on statistical
regression or empirical relationships.

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D. D. Tien et al.

models. This is because the real atmosphere always
exhibits some degree of uncertainties that prevent the TC
models from forecasting TC tracks perfectly.
In this study, we wish to address the connection between
the track and intensity errors in the Weather Research and
Forecasting (WRF-ARW, V3.2, Skamarock et al. 2005)
model, using the National Centers for Environmental Prediction (NCEP) global final analysis (FNL) dataset (US
National Centers for Environmental Prediction). The

objective is to examine how much intensity error reduction
the WRF-ARW model could achieve if its TC track errors
are reduced as much as possible. This question is tackled
by analyzing the intensity errors for a set of TCs whose
simulated tracks could fit most closely with the best track
analyses. Separate experiments are conducted for the
NATL basin and the Western North Pacific (WPAC) basin
to explore the degree to which the intensity errors are
related to the track errors for different basins.
The rest of the paper is organized as follows. Section 2
describes the input data, model configuration, experiment
setups, and methodology for separating the intensity
uncertainties caused by the erroneous tracks. Section 3
presents the main results and some discussions are given in
the final concluding section.

2 Experiment description
2.1 Model
The model chosen in this study is a non-hydrostatic version
of the Weather Research and Forecasting (WRF-ARW)
model (V3.2), which is configured with a two-way interactive, movable, multi-nested (36/12/4 km) grid. Due to
the large demand of computational resources and data
storage, the nested-grid domains are limited to 31 r levels
in the vertical direction, and the (x, y) dimensions of
155 9 155, 151 9 151, and 151 9 151 grid points for the
36-, 12-, and 4-km domain, respectively. The outermost
domain covers an area of *5,600 km 9 5,600 km, and
the 4-km innermost domain spans an area of
600 km 9 600 km around storm centers and is configured
to follow storm centers automatically, using the tracking

algorithm provided in the WRF model (see Fig. 1). Note
that both the intermediate and the innermost domain move
with storm centers, and so the model domains change with
storms and model integration. The model lateral boundary
conditions are updated every 6 h.
A set of physical parameterizations used in all experiments include (a) the modified Kain-Fritsch and BettsMiller-Janjic cumulus parameterization scheme for the 36and 12-km resolution domains; (b) the Yonsei University
and Mellor-Yamada-Janjic planetary boundary layer (PBL)


TC track and intensity errors in the WRF model

57

data from the Joint Typhoon Warning Center (JTWC)
center is used for verification purposes.4 While there are
some inconsistencies between different best track datasets
for different basins, these above two datasets are of relatively high quality that could provide both the observed TC
track and intensity reliably. As a reference to examine the
intensity errors, the official 10-m wind errors released by
the NHC for the NATL basin in the 2010 season is used for
comparisons. These official 1-, 2-, and 3-day VMAX errors
are 5.5, 7.5, and 9.5 m s-1, respectively.
2.3 Methodology

Fig. 1 Illustration of the model domain configurations for simulation
of Typhoon Megi (2010) valid at 0000 UTC 17 Oct 2010. Note that
the outermost domain is fixed in time, whereas the intermediate
(dashed box) and innermost domains (solid box) follow Megi centers
every 3 h. Initial position of the outermost domain is configured to be
at the center of Megi valid at the initial time. Solid contours denote

the sea level pressure (every 2 hPa) within the innermost domain at
the initial time

parameterization with the Monin–Obukhov surface layer
scheme; (c) the Rapid Radiative Transfer Model (RRTM)
scheme for the longwave radiation and the Goddard and
Dudhia scheme for the shortwave radiation; and (d) the Lin
et al., WSM3, and WSM6 scheme for the cloud microphysics. There is no cumulus parameterization for the 4-km
resolution domain.
2.2 Data
The model initial and boundary conditions data for all
simulations are taken from the FNL analysis with the
1° 9 1° resolution such that the best environmental conditions are maintained for the entire simulated period. For
the best track data needed for evaluating the TC track and
intensity errors, the official HURDAT data archive3 is used
for all experiments in the NATL basin. This best track
dataset is well calibrated and contains necessary TC
information such as latitudes and longitudes of TC centers,
the maximum surface wind (VMAX), or the minimum sea
level pressure (PMIN). In the WPAC basin, the best track
3

Available at: />
To isolate part of the intensity errors associated with
erroneous storm environment from those caused by inadequate TC initialization or unrealistic model parameterizations, the FNL dataset is used as initial and boundary
conditions for all WRF high-resolution simulations such
that good track simulations can be maximized. The
necessity of using the FNL dataset should be emphasized
because it is difficult to obtain a track forecast that fits well
with observation if real-time products such as the GFS

forecasts are used. While the current freely accessible FNL
data have fairly low resolution, this dataset to some extent
represents well the true atmosphere that is often considered
adequate for providing acceptable initial and lateral
boundary conditions for higher-resolution simulations. A
recent study of Mohanty et al. (2010) showed that the FNL
data indeed provide better TC tracks than use of either GFS
or Indian Global Forecast products.
To establish first a climatology of the TC track and
intensity errors with the model configuration described in
Sect. 2.1, two baseline experiments during the 2007–2010
TC seasons, one for the WPAC basin (WPAB) and the
other for the North Atlantic basin (NATB), are conducted.
Because the 1° 9 1° FNL data does not reflect fully the
true atmosphere, it is anticipated that not all TC simulations can produce good tracks; some simulations have large
track errors, while the other may have smaller track errors
at some lead times. After the baseline experiments with the
corresponding intensity errors are achieved, a subset of
TCs for which its simulated tracks fit closely with the best
track analysis is then singled out so that the intensity errors
associated with this subset can be calculated and compared
to the baseline errors. To be more specific for selecting
good track simulations, a track is classified as ‘‘a good
track’’ if it meets all three conditions: (1) the 1-day track
error is \30 km; (2) the 2-day error \50 km; and (3) the
3-day error \70 km. These thresholds are quite significant,
but acceptable as they are much smaller than the current
official track forecast errors, which are 82, 148, and
4

Available at: />
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58

189 km for the 1-, 2-, and 3-day lead times, respectively.
The good-track criteria are applied separately for the
NATL basin (NATG) and the WPAC basin (WPAG).
In principle, one could impose the criteria for track
selection as strictly as possible, so that the simulated tracks
best fit with observed tracks. However, our trials with
different values of track error thresholds showed that a too
strict filter would result in a very small sample size. For
example, imposing a 3-day track error in the NATL basin
smaller than 10 km would give a sample with only 2 out of
90 cases listed in Table 1. As such, the above thresholds
are chosen to compromise between the fit of the simulated
tracks and the sample size. Note also that it is necessary to
apply all of these above criteria for the 1-, 2-, and 3-day
track errors simultaneously such that any alteration to the
near-storm environment caused by the storms with potentially large track errors at a given lead time can be
minimized.
The TC cycles chosen in this study are based on two
criteria (1) the life cycle5 of any TC has to be at least
3 days so that the simulated 3-day track and intensity errors
can be verified; and (2) two consecutive cycles for one TC
must be at least 1 day apart to reduce the serial correlation
(Aberson and DeMaria 1994). For each simulation, an
ensemble of 21 members with different combinations of

the planetary boundary, microphysics, cumulus parameterization, and radiation schemes are employed such that
the member with the smallest 3-day track error can be
captured. Note that because TC tracks are influenced
greatly by model deficiencies as well as the quality of the
initial or boundary condition, there are many storms that do
not possess any good track simulation during their entire
life cycle. As seen in Tables 1 and 2, the largest percentage
of the good track cases for both the NATL and WPAC
basin that can be obtained with our set of simulations is
only *32 % of the total number of simulations. Since the
connection between the intensity and the track forecast
skill could vary among different ocean basins, two sets of
TCs in the NATL and WPAC basin during the 2007–2010
hurricane seasons are examined separately. Our ensemble
approach has two main advantages as compared to the use
of a single specific model configuration: (1) it removes the
systematic bias of model errors associated with one particular model configuration because each simulation has its
own model physics combination; and (2) it helps randomize the model characteristics so that the climatology of
the track/intensity is best represented, given the limited
number of storms.
Although the above criteria for selecting the good track
simulations could help to single out the storms that are
5

A life cycle of a TC is defined in this study as the beginning and the
ending of its record in the best track dataset.

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D. D. Tien et al.

embedded in the best ambient environment possible, it
should be mentioned that a potential wrong ambient environment may still develop within the WRF model due to its
inherent model errors even for perfect track simulations.
There is no exclusive way to prevent such model bias
development, unless the model is perfect. Recent studies
with the use of an ensemble of multiple physics for TC
forecasts appear to show that such multi-physics ensemble
could help alleviate the problem of model errors (see e.g.,
Meng and Zhang 2007; Kieu et al. 2012). This type of
multiple-physics ensemble approach, however, reduces the
capability to capture the good tracks, as different ensemble
members tend to have different storm movements. In this
study, no attempt has been made to exclude such model
errors as the main focus here is on the relative improvement of the intensity errors between the good track simulations and the general reference simulations. In this study,
the impacts of the model errors are assumed to be the same
among all experiments. More detailed analysis of this
multiple physics ensemble approach will be presented in
our upcoming study.
While the FNL dataset is considered as one of the best
possible representations of the large-scale atmosphere
among the reanalysis datasets, it is worth noting that the
FNL dataset does not accurately represent TC structure at
the mesoscale and below (cf. Fig. 3). Since the main goal
of this study is to examine the relative improvement of the
intensity errors between good track cases and the baseline
track simulations, we do not however attempt to correct the
initial vortex representation in any of our experiments.

3 Results

Figure 2 shows the absolute mean 1-, 2-, and 3-day VMAX
errors for the NATB baseline experiment from 2007–2010
(see Table 1 for the list of TCs and the corresponding total
number of simulations for each TC). One notices first that
the intensity errors in the NATB experiment are fairly
large, especially the 1-day error that could reach 10 m s-1.
Such large-intensity errors in the NATB experiment are
expected due to several sources of uncertainties in NATB
including inadequate representation of the initial vortex,
sub-optimal choices of model physics, erroneous simulated
tracks, low-grade model configurations, and the imperfection of the NCEP FNL analysis dataset. Of these, poor
vortex initialization appears to be the most dominant factor
in causing the large 1-day error. This can be seen in almost
all simulations, in which incipient vortices interpolated
directly from the FNL analysis are typically about 20 %
weaker than the observed intensity (in terms of VMAX). To
show this point, Fig. 3 shows the average difference of the
maximum 10-m wind and minimum sea level pressure


TC track and intensity errors in the WRF model
Table 1 List of the TCs during
the 2007–2010 seasons in the
North Atlantic basin that are
used in the NATB experiment

The criteria of the 1-, 2-, and
3-day absolute track errors for
the NATG subset are,
respectively, B30, 50, and

70 km (in the third column),
and B20, 35, and 50 km for the
sensitivity analysis with higher
criteria for selecting good tracks
(last column)

Tropical cyclone

59

Total number of
simulations in the
NATB experiment

Number of good
track simulations
in the NATG subset

Number of good track
simulations in the
sensitivity analysis

Dean (2007)

5

2

1

Felix (2007)

2

0

0

Noel (2007)

3

1

0

Erin (2007)

1

0

0

Gabrielle (2007)

1

0

0

Ingrid (2007)

2

1

1

Karen (2007)
Bertha (2008)

1
8

1
1

1
1

Cristobal (2008)

2

0

0

Omar (2008)

1

0

0

Fay (2008)

4

2

0

Gustav (2008)

6

4

2

Hanna (2008)

7

3

1

Ike (2008)

9

1

1

Bill (2009)

6

4

2

Fred (2009)

2

0

0

Ida (2009)

3

1

0

Alex (2010)

2

2

2

Igor (2010)

10

4

4

Colin (2010)

1

1

1

Earl (2010)

8

3

2

6
90

1
32

1
20

Danielle (2010)
Total

between the FNL analysis and the best track observation at
the initial time for all cases listed in Table 1. One can see
that the difference is relatively small when TCs are weak,
but increases rapidly for strong-intensity phases. This is
especially serious in the WPAC basin in which the difference between FNL analysis and best track is as large as
35 m s-1 in some cases. Apparently, such large incipient
difference has significant influence on TC development,
which explains the large 1-day intensity errors seen in
Fig. 2.
Similar to intensity errors, the track errors in the NATB
experiment are still significant despite the use of the FNL
analysis with the 1-, 2-, and 3-day mean errors of roughly

45, 112, and 298 km. Such significant track errors are
anticipated because the inherent errors of the WRF model
may result in imperfect storm development, causing the
storms to drift away from the real atmosphere, no matter
how well the boundary conditions are represented in the
FNL analysis. In addition, lack of vortex representation in
the FNL dataset could also influence the simulated tracks.
As the good-track simulations are sorted out (see
Table 1 for the specific good track selections), the mean
VMAX errors show some noticeable improvement. Except
for the 1-day error that shows no significant change, the 2-

and 3-day VMAX errors are reduced from 12.7 and
12.9 m s-1 in the NATB experiment to *10.8, and
10.4 m s-1 in the NATG sample at 90 % significance,6
respectively (Fig. 2, solid lines). Comparison of the relative ratios of the track and intensity errors between NATB
and NATG samples shows that the 55 and 76 % reduction
of the 2-, and 3-day track errors correspond to a reduction
of *15 and 19 % in the intensity errors at the 90 % significance level. This indicates that a large portion of the
intensity errors are not determined simply by the storm
track, but attributed more to other factors such as initial
condition or model physics. Note that the impact of the
inferior vortex representation or inadequate model physics
exists in both the baseline and the good track sample (see
Fig. 3), because there is no simple way to isolate these
factors in the two samples. The fact that both the insufficient vortex initialization and potential model errors associated with the physics representation are included in both
the NATL and NATG samples indicates that any intensity
error reduction in the NATG sample should therefore be

6

Statistical significance is evaluated by using the non-parametric
hypothesis test.

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60
Table 2 List of the TCs during
the 2007–2010 seasons in the
North-Western Pacific basin
that are used in the WPAB
experiment

D. D. Tien et al.

Tropical cyclone

Number of good track
simulations in the
sensitivity analysis

1

1

Sepat (2007)

4

2

1

Fitow (2007)

5

0

0

Hagibis (2007)

3

2

1

Man-Yi (2007)

3

2

1

Mitag (2007)

4

2

1

Krosa (2007)
Lekima (2007)

3
2

2
2

1
1

0

Nari (2007)

2

1

1

Wipha (2007)

2

1

1

Fengshen (2008)

5

0

0

Fung-Wong (2008)

2

1

0

Halong (2008)

2

0

0

Jangmi (2008)

4

1

1

Higos (2008)

3

1

0

Hagupit (2008)

4

0

0

Nakri (2008)

2

1

1

Maysak (2008)

1

1

0

14

3

1

Morakot (2009)

3

0

0

Vamco (2009)

2

2

1

Ketsana (2009)
Megi (2010)

3
8

0
1

0
0

Chaba (2010)

4

3

2

Conson (2010)

3

0

0

Chanthu (2010)

3

1

0

92

30

16

Total

considered as a direct consequence of the smaller track
errors in the NATG sample.
To further examine the dependence of the intensity
errors on the track errors, a stricter set of criteria for
selecting good tracks is tested in which a simulated track is
now considered as a good track if its 1-, 2-, and 3-day
absolute track errors are smaller than or equal to 20, 35,
and 50 km. This corresponds to 56, 68, and 83 % reduction
of the track errors relative to the NATB mean track errors
(see Table 1). These stringent criteria reduce the number of
good track cases to only 20 cases (Table 1). As seen in
Fig. 2, the intensity errors corresponding to this new track
filter do not, however, seem to decrease any further in spite
of the better track selection. Of course, the sample size of

20 cases is too small to have any definite result for this
situation, but one can notice at least that further reduction
of the track errors does not help reduce intensity errors at
any lead time at the 90 % level. A limit seems to exist :
even the perfect tracks could not help reduce the intensity
errors further in the NATL basin.

123

Number of good track
simulations in the
WPAG subset

Usagi (2007)

Parma (2009)

The criteria of the 1-, 2-, and
3-day absolute track errors for
the good track selection in the
WPAG subset and in the
sensitivity analysis are similar
to those in Table 1

Total number of
simulations in the
WPAB experiment

In terms of PMIN errors, a similar behavior to VMAX
errors is observed; the 2- and 3-day PMIN errors decrease

from 15.5 and 16.9 hPa in the NATB sample to *13.5 and
15.1 hPa in the NATG sample. This corresponds to 15 and
11 % decrease of the 2-, and 3-day errors, respectively
(Fig. 2b). Note, however, that the percentage of PMIN error
reduction does not seem to match with that of the VMAX
errors due to uncertainty in the minimum sea level pressure
calculation in the WRF model. This is because the sea level
pressure is a diagnostic variable that is determined by
several prognostic variables including geopotential height,
pressure, temperature, and water vapor mixing ratio. Thus,
the resulting improvement of the PMIN errors should be
degraded as these errors are the sum of the relative errors
from other prognostic variables. In addition, there is also
significant uncertainty in the observations of PMIN in the
best track, which may contribute further to the fluctuations
in the statistics as well. These explain the slightly smaller
improvement of PMIN as compared to VMAX. When a
stricter set of criteria for good track selection are applied


TC track and intensity errors in the WRF model

NATB

NATG

Sensitivity

61

(a)

(b)

Fig. 2 a The absolute errors of the simulated maximum 10-m wind
(VMAX, columns, unit: m s-1) for the NATB experiment (dark gray),
the NATG subset with the 1-, 2-, and 3-day absolute track errors B30,
50, and 70 km (medium gray), and the sensitivity sample with the 1-,
2-, and 3-day track errors B20, 35, and 50 km (light gray); b similar
to a but for the absolute minimum sea level pressure errors (PMIN,
unit hPa). Superimposed are the corresponding track errors (lines) for
the NATB experiment (circle), the NATG sample (square), and the
sensitivity test (diamond). The error bars denote the 90 % confidence
intervals, and the percentages of the improvement are provided next
to the x-axis

(diamond line in Fig. 2b), the percentage of reduction is
also nearly unchanged as observed for the VMAX errors.
Again, the change in the 1-day PMIN error is not significant
in both the NATG sample and the sensitivity sample when
stronger criteria for track selection are applied.
Unlike the NATL basin, VMAX errors in the WPAC
basin include several features not evident in the NATL
basin cases. First, the VMAX errors in the WPAB experiments are higher than those in NATB at all times (Fig. 4a).
In particular, the 1-day VMAX error is considerably larger
than the corresponding error in the NATL basin due to
much weaker incipient vortices initialized from the FNL
analysis in the WPAC basin (cf. Fig. 3). On average,
WPAC initial vortices are 30–35 % weaker than the
observed intensity. There are some cases for which the

strength of the initial vortices is not even half of the
observed storms (e.g., Typhoon Sepat initialized at 0000
UTC 16 August 2007 or Typhoon Nari initialized at 0000
UTC 14 September 2008). This insufficient vortex initialization causes significant impacts to the VMAX errors for the

Fig. 3 Mean initial difference of the maximum 10 m wind for the
baseline sample (dark shaded) and the good track sample (dark
striped), and the minimum sea level pressure for the baseline sample
(gray) and the good track sample (gray striped) between the FNL
analysis and the best track data for the North Atlantic basin and
North-Western Pacific (lower panel). The average difference is
calculated from all storms listed in Tables 1 and 2, and is stratified
according to the storm initial intensity. The numbers next to the x-axis
denote the number of cases for each bin

first 24 h in the WPAB basin as compared to the NATL
basin.
Despite the inferior vortex initialization, it is of interest
to notice that the 2- and 3-day VMAX errors show slightly
more improvement after the bad track simulations in the
WPAB sample are eliminated (i.e., the WPAG sample).
Although the 1-day VMAX error does not show any convincing decrease as seen in the NATG experiments, the 2and 3-day VMAX errors decrease from 10.6 and 12.1 m s-1
in the WPAB sample to 9.1 and 9.8 m s-1 in the WPAG
sample, which correspond to 15 and 19 % decrease in the
VMAX errors, respectively. This is noteworthy as it indicates that the better TC tracks in WPAC tend to help
improve the intensity forecast as efficiently as in the NATL
basin. Recent studies by Kehoe et al. (2007) show that most
of the large track error cases in WPAC are associated to
some degree with the subtropical high system that tends to
steer storms into an inimical environment. As a result, it is

expected that improvement in the track forecast could lead
to more noteworthy changes in the intensity errors in this
basin.
With the 1-, 2-, and 3-day track errors in the WPAB
experiment of *58, 131, and 315 km, it is seen that

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62

similar to the NATL basin the percentages of the intensity
error reduction are much smaller than those for track
errors. The fact that both the NATL and WPAC basin
exhibit similar smaller intensity error reduction despite
more than 50 % improvement of the track accuracy indicates again that a large portion of the intensity errors is
determined by other factors such as model initialization or
model physics. In particular, the model physics tends to
play a major role in determining the predictability of the
TC intensity at the times longer than 3 days as this is the
factor that controls not only the physics of TCs, but also the
characteristics of the ambient environment that the TCs are
embedded in. There appears to be growing evidence of the
important role of model physics at long ranges beyond
3 days. For example, real-time experiments with the hurricane WRF model conducted at NCEP7 showed that
intensity errors from different models with and without
vortex initialization appear to be comparable after 2 days
into integration regardless of the vortex initial strength.
This implies that the impacts of vortex initialization tend to
be most influential for the first 36–48 h. Of course, such

initial impacts could vary from case to case, but this suggests that the roles of model physics should be more
important at the longer range.
Of further significance is that although there is virtually
no additional decrease of the intensity errors in the NATL
basin when higher criteria for selecting good tracks are
applied in the sensitivity analysis (the diamond solid line in
Fig. 2a), there seems to be some extra decrease of the
VMAX errors when these higher criteria are used in the
WPAC basin (Fig. 4a). This is seen most clearly in terms
of the PMIN errors for which we notice that the smaller
track errors in the sensitivity analysis could help reduce the
3-day PMIN errors up to 21 % (Fig. 4b). This result is
consistent with the larger improvement of the VMAX errors
in the WPAG sample as compared to the NATB sample,
and demonstrates that TC intensity in the WPAC basin
appears to be more sensitive to the track errors. Therefore,
any significant improvement in the track forecast skill is
likely more beneficial to the intensity forecasts in WPAC
than in the NATL basin.

4 Discussions and conclusions
In this study, the dependence of the tropical cyclone (TC)
intensity errors on the track errors in the WRF-ARW model
has been investigated. Two baseline experiments during the
2007–2010 TC seasons in the North Atlantic (NATL) and
7

Reports of numerous NCEP Hurricane WRF (HWRF) model realtime performance are available at: />HWRF/weeklies.

123

D. D. Tien et al.

WPAB

WPAG

Sensitivity

(a)

(b)

Fig. 4 Similar to Fig. 3 but for the WPAC basin

North-Western Pacific (WPAC) basin were first conducted
to establish the climatology of the track and intensity errors
for the WRF-ARW model, using a triple-nested stormfollowing high-resolution configuration with the NCEP
final analysis (FNL) as the initial and boundary conditions.
Examination of the maximum 10-m wind (VMAX) and the
minimum sea level pressure (PMIN) errors in the NATL and
WPAC basins showed that the 1-day intensity error is
substantial in both basins due mostly to inadequate vortex
representation inherited in the FNL dataset. This issue is
more apparent in the WPAC basin where both the coverage
and quality of in situ observation data are low. Despite the
significant intensity errors, the overall track errors in both
WPAC and NATL basins are, however, comparable to the
current official best track errors, indicating the importance
of the FNL dataset in providing proper steering environment for the TC movement through the lateral boundary

conditions.
By using a random physics ensemble approach to
remove the model errors related to bias in model physics
parameterization, it was found that the 2- and 3-day
intensity errors can be reduced significantly as compared to
the baseline experiments for both the WPAC and NATL
basin after the large track error simulations were sorted out
by selecting only simulations with 1-, 2-, and 3-day track
errors smaller than 30, 50, and 70 km. In terms of VMAX,
the 2-, and 3-day errors for the good-track simulations are
improved by 15 and 19 % for the NATL basin, whereas the
1-day intensity error shows no significant reduction. Such


TC track and intensity errors in the WRF model

intensity improvement is, however, much smaller than the
track improvement for the corresponding times, which are
55 and 76 %, respectively. This indicates that a large
portion of TC intensity uncertainty is determined by other
factors such as vortex initialization or the internal TC
physics that is not well represented in the WRF model.
For the WPAC basin, it was found that the reduction of
the intensity errors after eliminating bad track simulations
is somewhat similar to that in the NATL basin; the 2- and
3-day VMAX errors decrease by about 15 and 19 % when
the large track error simulations are excluded. The VMAX
errors appear to decrease even further when the higher
criteria for good track selection are applied, while the same
criteria for good track selection could not help improve the

intensity errors in the NATL basin. Such intensity
improvement in WPAC indicates that ambient environment
tends to play an important role in the TC intensity forecast
in this area. Thus, future improvement in the track forecast
skill is expected to be favorable to the intensity skill in both
the WPAC and the NATL basin.
Given the results obtained so far with the WRF-ARW
model, a lingering question is why there has been little
improvement in the intensity forecast skill for the last
30 years despite a remarkable progress in the track forecast
skill. Note that the official intensity forecast skill is not
simply derived from dynamical models, but typically from
a statistical-dynamical model or subjective guidance that
involves some empirical constraints. So, it is not possible
to apply the results obtained with a dynamical model
directly to the official skill. However, the intimate dependence of the official forecasts on the dynamical models
suggests that several issues related to the dynamical models
could help explain the stagnation of the intensity forecast
skill. First, with the 3-day official track error reduced from
450 km to *250 km during the last 30 years, our results
suggest that the corresponding improvement in the intensity skill associated with such improvement of track forecast skill may have been at most a few percent. These
intensity improvements are perhaps too small and could
have been blurred by the growing complexity of the
operational TC models. Furthermore, various inherent
uncertainties in the current TC models could have blocked
the slight progress in the intensity errors associated with
better track forecasts. As seen from the good-track samples
in both the WPAC and NATL basins, 70 % reduction of
the track errors could only deliver about 15 % reduction of
the intensity errors even with the help of the NCEP FNL

dataset. Thus, the intensity forecast skill would not
improve much, unless there was some significant progress
in TC model physics.
Second, our conclusions obtained with the WRF model
are strictly limited to the track and intensity simulations
rather than the true track and intensity forecasts due to the

63

use of the NCEP FNL analysis data. As mentioned in Sect. 2,
this final analysis dataset is essential to obtain as many good
track simulations as possible within our computational
resource. With about 90 TCs and 35 cases with good track
simulations in each basin, it is clear that our results may not
be entirely conclusive and should be therefore considered
only as an upper limit for evaluating the track-intensity
connection in the WRF model. In addition, there is potentially some considerable difference in the error statistics
between strong versus weak storms that our study could not
explain due to the small sample size. In particular, simulations with strong storms could possess larger intensity errors
due to much larger initial intensity difference. In this study,
we have however not performed any stratification of storm
statistics because the total number of cases after imposing
the criteria for selecting the good track cases was too small
(*35 cases totally for each basin). Our implicit assumption
was that the samples of both reference and the good-track
simulations are sufficiently homogenous for all range of
storm initial intensity, model physics, and boundary influences such that the relative improvement between the general statistics and the good-track statistics can be realized.
Roles of model vortex initialization and assimilation of
additional sources of observation to enhance the storm
environment will be examined in our upcoming study.

Acknowledgments We would like to thank Buck Sampson at Naval
Research Laboratory-Monterey for his various valuable suggestions
and corrections. We would like also to extend our thanks to the two
anonymous reviewers for their very constructive comments and
suggestions, which helped improve the manuscript greatly. This
research was supported by the Vietnam Ministry of Science and
Technology Foundation DT.NCCB-DHUD.2011-G10. The FNL data
for this study are from the Research Data Archive (RDA) which is
maintained by the Computational and Information Systems Laboratory (CISL) at the National Center for Atmospheric Research
(NCAR).

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