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

O R I G I N A L P A P E R

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

North-Western Pacific basin, the percentage of intensity

reduc-tion 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

track error improvement indicate that ambient environ-ment 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; Emanuel1986; Holland1997; Chen and Yau2003; Mandal

et al 2007; Hill and Lackmann2009; 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

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
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: chanhkq@vnu.edu.vn; chanh.kieu@noaa.gov

1 The NHC official reports of the track and intensity errors can be found at: http://www.nhc.noaa.gov/verification/verify5.shtml DOI 10.1007/s00703-013-0278-0

future 50 % improvement of the track forecast skill in a TC

dynamical model2could 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

under-goes 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 Weber2000; Kwon et al.2002; Kieu and Zhang2009;

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 Bosart2002; Kieu and Zhang

2010; Pattnaik and Krishnamurti2007; 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

ide-alized assumption that is not achievable with TC dynamical

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 Pre-diction (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 Section2

describes the input data, model configuration, experiment setups, and methodology for separating the intensity uncertainties caused by the erroneous tracks Section3

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 inter-active, 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 experi-ments include (a) the modified Kain-Fritsch and Betts-Miller-Janjic cumulus parameterization scheme for the 36-and 12-km resolution domains; (b) the Yonsei University and Mellor-Yamada-Janjic planetary boundary layer (PBL)

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.

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

micro-physics 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

con-ditions 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 archive3is 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

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 rela-tively 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 VMAXerrors are 5.5, 7.5, and 9.5 m s-1, respectively

2.3 Methodology

To isolate part of the intensity errors associated with erroneous storm environment from those caused by inad-equate TC initialization or unrealistic model parameter-izations, 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 simula-tions can produce good tracks; some simulasimula-tions 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

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

3 Available at: http://www.aoml.noaa.gov/hrd/hurdat/Data_Storm.html 4 Available at: http://www.usno.navy.mil/JTWC

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 Table1 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

poten-tially 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

parame-terization, 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 Tables1and2, 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

par-ticular model configuration because each simulation has its

own model physics combination; and (2) it helps

ran-domize 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

embedded in the best ambient environment possible, it should be mentioned that a potential wrong ambient envi-ronment 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 improve-ment of the intensity errors between the good track simu-lations and the general reference simusimu-lations 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 Figure2 shows the absolute mean 1-, 2-, and 3-day VMAX errors for the NATB baseline experiment from 2007–2010 (see Table1for 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 imperfec-tion 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 3shows the average difference of the maximum 10-m wind and minimum sea level pressure

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.

between the FNL analysis and the best track observation at

the initial time for all cases listed in Table1 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

dif-ference 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

Table1 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 rela-tive 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 % sig-nificance 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 insuffi-cient vortex initialization and potential model errors asso-ciated 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

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 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

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

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 Table1) These stringent criteria reduce the number of

good track cases to only 20 cases (Table1) 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

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

Table 2 List of the TCs during

the 2007–2010 seasons in the

North-Western Pacific basin

that are used in the WPAB

experiment

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

Tropical cyclone Total number of

simulations in the WPAB experiment

Number of good track simulations in the WPAG subset

Number of good track simulations in the sensitivity analysis

(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 PMINerror 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

experi-ments 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

initial-ization causes significant impacts to the VMAXerrors for the

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 VMAXerrors 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 con-vincing decrease as seen in the NATG experiments, the 2-and 3-day VMAXerrors decrease from 10.6 and 12.1 m s-1

in the WPAB sample to 9.1 and 9.8 m s-1in the WPAG sample, which correspond to 15 and 19 % decrease in the

VMAX errors, respectively This is noteworthy as it indi-cates 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

(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

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

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

indi-cates 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

hur-ricane 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

sug-gests 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 VMAXerrors

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

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 storm-following 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 environ-ment for the TC moveenviron-ment 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

(b)

Fig 4 Similar to Fig 3 but for the WPAC basin

7 Reports of numerous NCEP Hurricane WRF (HWRF) model

real-time performance are available at: http://www.emc.ncep.noaa.gov/

HWRF/weeklies

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 VMAXerrors 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

depen-dence 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

inten-sity skill associated with such improvement of track

fore-cast 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

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 poten-tially 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, simula-tions 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 influ-ences such that the relative improvement between the gen-eral 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 Labora-tory (CISL) at the National Center for Atmospheric Research (NCAR).

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