ACPAtmospheric Chemistry and PhysicsACPAtmos. Chem. Phys.1680-7324Copernicus PublicationsGöttingen, Germany10.5194/acp-16-14925-2016Revisiting the steering principal of tropical cyclone motion in a numerical
experimentWuLiguangliguang@nuist.edu.cnhttps://orcid.org/0000-0002-0784-5853ChenXiaoyuKey Laboratory of Meteorological Disaster, Ministry of Education
(KLME), Pacific Typhoon Research Center (PTRC), Nanjing University of
Information Science & Technology, Nanjing, ChinaState Key Laboratory of Severe Weather, Chinese Academy of
Meteorological Sciences, Beijing, ChinaLiguang Wu (liguang@nuist.edu.cn)2December20161623149251493630April201610June201628October201610November2016This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://acp.copernicus.org/articles/16/14925/2016/acp-16-14925-2016.htmlThe full text article is available as a PDF file from https://acp.copernicus.org/articles/16/14925/2016/acp-16-14925-2016.pdf
The steering principle of tropical cyclone motion has been
applied to tropical cyclone forecasting and research for nearly 100 years. Two
fundamental questions remain unanswered. One is why the steering flow plays a
dominant role in tropical cyclone motion, and the other is when tropical
cyclone motion deviates considerably from the steering. A high-resolution
numerical experiment was conducted with the tropical cyclone in a typical
large-scale monsoon trough over the western North Pacific. The simulated
tropical cyclone experiences two eyewall replacement processes.
Based on the potential vorticity tendency (PVT) diagnostics, this study
demonstrates that the conventional steering, which is calculated over a
certain radius from the tropical cyclone center in the horizontal and a deep
pressure layer in the vertical, plays a dominant role in tropical cyclone
motion since the contributions from other processes are largely cancelled
out due to the coherent structure of tropical cyclone circulation. Resulting
from the asymmetric dynamics of the tropical cyclone inner core, the
trochoidal motion around the mean tropical cyclone track cannot be accounted
for by the conventional steering. The instantaneous tropical cyclone motion
can considerably deviate from the conventional steering that approximately
accounts for the combined effect of the contribution of the advection of the
symmetric potential vorticity component by the asymmetric flow and the
contribution from the advection of the wave-number-one potential vorticity
component by the symmetric flow.
Introduction
The environmental steering principle has been applied to tropical cyclone
track forecasting for nearly 100 years (Fujiwara and Sekiguchi, 1919; Bowie,
1922), which states that a tropical cyclone tends to follow the large-scale
flow in which it is embedded. Such a steering concept has been extended to
include the beta drift (also called secondary steering) that arises mainly
from the interaction between tropical cyclone circulation and the planetary
vorticity gradient (Holland, 1983; Chan, 1984; Chan and Williams, 1987;
Fiorino and Elsberry, 1989; Carr and Elsberry, 1990; Wang and Li, 1992; Wang
and Holland, 1996a). The steering flow is usually calculated over a certain
radius from the tropical cyclone center in the horizontal and a deep pressure
layer in the vertical (Dong and Neumann, 1986; Velden and Leslie, 1991; Franklin et al., 1996). For convenience,
here we call it the conventional steering flow. As a rule of thumb, the
conventional steering flow has been extensively used in tropical cyclone
track forecasting and understanding of tropical cyclone motion (e.g.,
Simpson, 1948; Riehl and Burgner, 1950; Chan and Gray, 1982; Fiorino and
Elsberry, 1989; Neumann, 1993; Wu and Emanuel, 1995a, b; Wang and Holland,
1996b, c; Wu et al., 2011a, b). Given complicated interactions between
tropical cyclone circulation and its environment, tropical cyclone motion
should not be like a leaf being steered only by the currents in the stream.
Therefore, two fundamental issues still remain regarding the steering
principle. First, why can the conventional steering play a dominant role in
tropical cyclone motion? Second, when may tropical cyclone motion deviate
considerably from the conventional steering?
The potential vorticity tendency (PVT) paradigm for tropical cyclone motion
was proposed by Wu and Wang (2000), in which a tropical cyclone tends to move
to the region of the PVT maximum. In other words, tropical cyclone motion is
completely determined by the azimuthal wave-number-one component of PVT, and
all of the factors that contribute to the azimuthal wave-number-one component
of PVT play a potential role in tropical cyclone motion. The contributions of
individual factors can be quantified through the PVT diagnosis, and the
steering effect is one of the factors (Wu and Wang, 2000). Wu and Wang (2000,
2001a) evaluated the PVT approach using the output of idealized numerical
experiments with a coarse spacing of 25 km and understood the vertical
coupling of tropical cyclone circulation under the influence of vertical wind
shear. Wu and Wang (2001b) found that convective heating can affect tropical
cyclone motion by the heating-induced flow and the positive PVT that is
directly generated by convective heating.
The PVT paradigm was further verified by Chan et al. (2002). The
observational analysis indicated that the potential vorticity advection
process is generally dominant in tropical cyclone motion without much change
in direction or speed, while the contribution by diabatic heating (DH) is usually
less important. An interesting finding of the study is that the contribution
of diabatic heating becomes important for irregular tropical cyclone motion,
suggesting that track oscillations as well as irregular track changes may be
explained by changes in the convection pattern. The PVT approach has been
used in understanding tropical cyclone motion in the presence of the effects
of land surface friction (FR), river deltas, coastal lines, mountains, islands,
cloud-radiative processes and sea surface pressure gradients (e.g., Wong and
Chan, 2006; Yu et al., 2007; Fovell
et al., 2010; Hsu et al., 2013; Wang et al., 2013; Choi et al., 2013).
As we know, the coarse resolution of the numerical experiment in Wu and
Wang (2000) was unable to resolve the eyewall structure and tropical cyclone
rainbands, which may affect tropical cyclone motion (Holland and Lander,
1993; Nolan et al., 2001; Oda et al., 2006; Hong and Chang, 2005). Under the
PVT paradigm, in this study we use the output from a high-resolution
numerical experiment to address the aforementioned two fundamental issues
that are important to understanding tropical cyclone motion. The numerical
experiment was conducted with the Advanced Research Weather Research and
Forecast (WRF) model. In particular, an initially symmetric baroclinic vortex
is embedded in the low-frequency atmospheric circulation of Typhoon
Matsa (2005) to simulate tropical cyclone motion in a realistic large-scale
environment. For simplicity, the present study focuses on the numerical
experiment without the influences of land surface and topography.
The output of the numerical experiment
The numerical experiment conducted with the WRF model (version 2.2) in this
study contains a coarsest domain centered at 30.0∘ N,
132.5∘ E and four two-way interactive domains. In order to better
simulate the tropical cyclone rainbands and eyewall structure, the horizontal
resolutions are 27, 9, 3, 1 and 1/3 km. The three innermost
domains move with the tropical cyclone (Fig. 1). The model consists of 40
vertical levels with a top at 50 hPa. The WRF single-moment three-class scheme
and the Kain–Fritsch cumulus parameterization scheme (Kain and Fritsch, 1993)
are used in the outermost domain. The WRF single-moment three-class scheme (Hong
and Lim, 2006) and no cumulus
parameterization scheme are used in the four inner domains. The other model
physics options are the Rapid Radiative Transfer Model (RRTM) longwave
radiation scheme (Mlaewe et al., 1997), the Dudhia shortwave radiation scheme
(Dudhia, 1989) and the Yonsei University scheme for planetary boundary layer
parameterization (Noh et al., 2003).
Model domains of the numerical experiment with the three innermost
domains moving with the storm, the initial 850 hPa wind (m s-1) field
(vectors) and the simulated tropical cyclone track (red).
The National Centers for Environmental Prediction (NCEP) Final (FNL)
Operational Global Analysis data with resolution of
1.0∘× 1.0∘ every 6 h were used for deriving the
large-scale background with a 20-day low-pass Lanczos filter (Duchon, 1979).
The low-frequency fields were taken from those of Typhoon Matsa (2005) from
00:00 UTC on 5 August to 00:00 UTC on 9 August 2005. At 00:00 UTC on 5 August, the
typhoon was located to the northeast of the island of Taiwan with a maximum
surface wind of 45 m s-1. During the following 3 days, Matsa moved
northwestward in the monsoon trough and made landfall on mainland China at
19:40 UTC on 5 August. The sea surface temperature is spatially uniform, being
29 ∘C. The analysis nudging for the wind components above the lower
boundary layer is used in the coarsest domain to maintain the large-scale
patterns with a nudging coefficient of 1.5 × 10-4 s-1.
A symmetric vortex is initially embedded at 25.4∘ N,
123.0∘ E (Matsa's center) in the background (Fig. 1). The vortex was
spun up for 18 h on an f plane without environmental flows to make it
relatively consistent with the WRF model dynamics and physics. Considering
several hours of the initial spin-up, here we focus only on the 72 h period
from 6 to 78 h with the output at 1 h intervals. The simulated tropical
cyclone takes a north-northwest track (Fig. 1), generally similar to that of
Typhoon Matsa (2005). The evolution of tropical cyclone intensity is shown in
Fig. 2. Although the sea level minimum pressure generally decreases with
time, the maximum wind speed shows considerable fluctuations.
Time series of tropical cyclone intensity: (a) sea level minimum
pressure (hPa) and (b) maximum wind speed at 10 m (m s-1).
Figure 3 shows the simulated wind and radar reflectivity fields at 700 hPa.
The vertical wind shear, which is calculated between 200 and 850 hPa over a
radius of 500 km from the tropical cyclone center, is also plotted in the
figure. The tropical cyclone center is defined as the geometric center of the
circle on which the azimuthal mean tangential wind speed reaches a maximum
(Wu et al., 2006). We use a variational method to determine the tropical
cyclone center each hour at each level. Different definitions of the tropical
cyclone center are also used, and it is found that fluctuations in tropical
cyclone translation do not depend on the specific definition of the tropical
cyclone center. At 24 h (Fig. 3a), the vertical wind shear is more than
10 m s-1. The eyewall is open to the southwest, and strong eyewall
convection occurs mainly on the downshear left side (Frank and Ritchie,
2001). The rainbands simulated in the innermost domain exhibit apparent
cellular structures (Houze, 2010), mostly on the eastern side. The eyewall
replacement cycle (ERC), which is important for tropical cyclone intensity
change (Wu et al., 2012; Huang et al., 2012), is simulated in this numerical
experiment. At 48 h (Fig. 3b), the vertical wind shear is weaker and the
tropical cyclone undergoes an ERC. At 72 h (Fig. 3c), the outer eyewall just
forms, while the inner one is breaking during the second ERC. Figure 3
suggests that the simulated tropical cyclone has a structure similar to a
typical observed one, especially in the inner-core region.
Simulated wind (vectors, m s-1), radar reflectivity (shading,
dBz) fields at 700 hPa, and the vertical wind shear (bold arrows in the
center) between 200 and 850 hPa after (a) 24, (b) 48
and (c) 72 h integration. The x and y axes indicate the
distance (km) relative to the storm center. The upper (lower) scale vector at
the right lower corner is for the 700 hPa wind (vertical wind shear).
Two eyewall replacement processes, which may affect tropical cyclone motion
(Oda et al., 2006; Hong and Chang, 2005), can be further shown in Fig. 4. The
evolution of the azimuthal mean component of the 700 hPa wind in the 9 km
domain indicates the eyewall replacement processes around 42 and 68 h.
During the first eyewall replacement, for example, the wind
starts to intensify outside the eyewall around 36 h, in agreement with
previous numerical studies (Wu et al., 2012; Huang et al., 2012). The radius
of maximum wind is located about 40 km after the 6 h spin-up and
decreases to about 30 km at 42 h. The lifetime maximum wind speed occurs at
60 h after the second eyewall replacement process (Fig. 2b). We also
conducted a similar sensitivity experiment without the sub-kilometer domain.
The tropical cyclone track in the experiment is generally similar to that in
the sub-kilometer simulation, but no eyewall replacement cycle can be
observed in the sensitivity experiment.
Evolution of the simulated azimuthal mean component (m s-1) of
the 700 hPa wind in the 9 km domain. The x axis and y axis indicate the
distance (km) from the storm center and the integration time (hours), respectively.
Dominant role of the conventional steering
The relationship between PVT and tropical cyclone motion can be written as
(Wu and Wang, 2000)
∂P1∂tf=∂P1∂tm-C×∇Ps,
where subscripts m and f indicate, respectively, the moving and fixed
reference frames, and C is the velocity of the reference frame that moves
with the tropical cyclone. In other words, C is the velocity of tropical
cyclone motion, which can vary in the vertical. P1 and Ps are the azimuthal wave-number-one and symmetric components of
potential vorticity with respect to the storm center. It can be seen that the
PVT generated in the fixed reference frame (the term on the left-hand side)
is provided for the development of the wave-number-one component (the first
term on the right-hand side) and for tropical cyclone motion (the second term
on the right-hand side). The first term on the right-hand side of Eq. (1) was
neglected in Wu and Wang (2000), but we retain it in this study. The term can
be calculated with the 2 h change of the wave-number-one component in the
frame that moves with the tropical cyclone center.
The PVT generated in the fixed reference frame can be calculated with the PVT
equation in p coordinates as
∂P∂t=-V×∇P-ω∂P∂p-g∇3×-QCpπq+∇θ×F,
where P, V and ω are potential vorticity, horizontal and vertical
components of the wind velocity, respectively. Equation (2) contains
horizontal advection (HA), vertical advection (VA), DH and FR terms on the right-hand side. Q,
θ, q and F are diabatic heating rate,
potential temperature, absolute vorticity and friction, while g,
cp and π are the gravitational acceleration, the specific
heat of dry air at constant pressure and the Exner function, respectively. ∇3
and ∇ denote the three- and two-dimensional gradient operators, respectively.
Time series of tropical cyclone speed (thick black), PVT speed
(blue) and conventional steering (red): (a) magnitude, (b) zonal component
and (c) meridional component.
Following Wu and Wang (2000), a least-squares method is used to estimate the
velocity of tropical cyclone motion (C) in Eq. (1). The translation
velocity is also calculated with the hourly positions of the tropical cyclone
center. For convenience, the tropical cyclone motion estimated with the PVT
diagnostic approach and that with the center position are referred to as the PVT
velocity and the tropical cyclone velocity, respectively, in the following
discussion. In the PVT approach, we find that the estimated tropical cyclone
motion is not very sensitive to the size of the calculation domain. As we
know, however, determination of the conventional steering flow for a given
tropical cyclone is not unique and depends on the size of the calculation
domain (Wang et al., 1998). Here we select the calculation domain to minimize
the difference between the tropical cyclone speed and the conventional
steering flow. After a series of tests, we find that such a minimum can be
reached when the 270 km radius is used. This is consistent with the analysis
of the airborne Doppler radar data in Marks et al. (1992) and Franklin et
al. (1996). The analysis indicated that tropical cyclone motion was best
correlated with the depth-mean flow averaged over the inner region within
3∘ latitudes. Note that the PVT, tropical cyclone and steering
velocities are calculated at each level, and then the depth-mean ones are
averaged over the layer between 850 and 300 hPa.
Figure 5a shows the time series of the magnitudes of the tropical cyclone
velocity (black), the PVT velocity (blue) and the conventional steering
(red). Note that the PVT velocity and the conventional steering are
instantaneous, whereas the tropical cyclone velocity is calculated based on
the 2 h difference of the center position. For consistency, a
three-point running mean is applied to the PVT speed and the conventional
steering. These magnitudes generally increase as the tropical cyclone takes a
north-northwest track. The mean speeds calculated from the PVT approach and
the center positions are 2.86 and 2.75 m s-1 over the 72 h period.
Compared to the tropical cyclone speed, the root-mean-square error (RMSE) of
the PVT speed is 0.22 m s-1, only accounting for 8 % of the
tropical cyclone speed.
Figure 5b and c further display the zonal and meridional components of the
tropical cyclone velocity (black), the PVT velocity (blue) and the
conventional steering (red). While the westward component fluctuates about
the mean zonal tropical cyclone (PVT) speed of -1.0 m s-1, the
northward component generally increases with time. Figure 5 clearly indicates
that the translation velocity of the tropical cyclone can be well estimated
with the PVT approach.
The environmental and secondary steering flows are indistinctly referred to
as the conventional steering flow in this study. The conventional steering shown
in Fig. 5 is averaged over the same radius (270 km) and the 850–300 hPa
layer, as used in the calculation of the PVT speed. The 72 h mean magnitudes
of the tropical cyclone velocity and the conventional steering are 2.86 and
2.87 m s-1, respectively, only with a difference of 6.7∘ in
the motion direction. We also calculated the RMSE of
the conventional steering averaged over various time periods with the
tropical cyclone speed (Fig. 6). The RMSE of the magnitude decreases with the
increasing average period, generally less than 9 % of the translation
speed of the tropical cyclone. The difference in direction also decreases
with the increasing average period within 9–11∘. Considering
uncertainties in determining tropical cyclone centers and calculating the
steering, we conclude that the conventional steering plays a dominant role in
tropical cyclone motion. However, Fig. 5 indicates that the instantaneous
tropical cyclone motion can considerably deviate from the conventional
steering. The conventional steering cannot account for the fluctuations in
tropical cyclone motion, which will be further discussed in Sect. 5.
Changes of the RMSEs of the speed (blue boxes, %) and direction
(black dots, ∘) of the conventional steering averaged over various
time periods.
Contributions of individual processes
The individual contributions of various terms in the PVT equation to tropical
cyclone motion can also be estimated with Eq. (1), as shown by Wu and Wang
(2000). In this study, the contribution of the FR term is
calculated as the residual of the PVT equation. Figure 7 shows the individual
contributions of the terms in the PVT equation to tropical cyclone motion.
While the contribution of the HA term plays a dominant role (Fig. 7c), the
figure exhibits considerable fluctuations, suggesting that the contributions
of the DH and VA terms tend to cancel each other (Fig. 7a and b). Here we
discuss the contribution of each term in the PVT equation to understand the
dominant role of the conventional steering in tropical cyclone motion.
Contributions of the horizontal advection (HA, black), vertical
advection (VA, blue), diabatic heating (DH, red) and friction (FR, purple)
terms in the PVT equation to tropical cyclone motion: (a) zonal component, (b)
meridional component and (c) magnitude.
Horizontal advection
As discussed in Wu and Wang (2001b), the HA term in the PVT equation can be
approximately written as V1×∇Ps-Vs×∇P1, where
Vs is the symmetric component of the tangential wind and V1
is the wave-number-one component of the asymmetric wind. The first term (HA1)
represents the advection of the symmetric potential vorticity component by
the asymmetric flow. The second term is the advection of the wave-number-one
potential vorticity component by the symmetric flow (HA2).
Time series of the conventional steering (thick black) and the
contributions of the HA (thick purple), HA1 (red) and HA2 (blue)
terms: (a) zonal component and (b) meridional component. Note that the
conventional steering is deducted from the contribution of the HA1 term.
The contribution of the HA1 term is literally the steering effect, but it is
not the conventional steering that is calculated as the velocity of the mean
wind averaged over 300–850 hPa within the radius of 270 km from the
tropical cyclone center in this study. Wu and Wang (2001a) pointed out that
the steering effect in the HA1 term is associated also with the gradient of
the symmetric potential vorticity component, which makes its contribution
confined to the inner region of tropical cyclones.
Figure 8 shows the contributions of the HA1 and HA2 terms, which exhibit
considerable fluctuations with time. The contribution of HA and the
conventional steering are also plotted. For clarity, the conventional
steering is removed from the contribution of HA1 (i.e., HA1′). The 72 h
mean difference between the contribution of HA1 and the conventional steering
is -1.25 m s-1 in the zonal component and 1.62 m s-1 in the
meridional component, suggesting that the contribution of the HA1 term is
considerably different from the conventional steering. In fact, the
contributions of the HA1 and HA2 terms are highly anticorrelated. The
correlations for the zonal and meridional components are -0.82 and -0.80,
respectively. The negative correlations suggest the cancellation between the
contributions of the HA1 and HA2 terms. As a result, the combined effect of
the HA1 and HA2 terms can actually account for the effect of the conventional
steering except the short-time fluctuations, as shown in Fig. 8. It is
interesting to note that the contributions of the HA1 and HA2 terms increase
in magnitude during the two eyewall replacement processes around 42 and
68 h, suggesting that the tropical cyclone motion considerably deviates from
the steering of the asymmetric flow during eyewall replacement. However, it
seems that the two eyewall replacement processes have little influence on the
tropical cyclone motion (Fig. 5a).
(a) HA1 (shaded, 10-10 m2 s-2 K kg-1) and
(b) HA2 (shaded, 10-10 m2 s-2 K kg-1) with the
wave-number-one and symmetric components of potential vorticity (contours,
10-6 m2 s-1 K kg-1) and winds (vectors, m s-1) at
700 hPa after 18 h of integration. The dashed circle indicates the
radius of maximum wind.
The cancellation between the contributions of the HA1 and HA2 terms arises
from the interaction between the symmetric and wave-number-one components of
the tropical cyclone circulation. As an example, Fig. 9a shows HA1 and the
wave-number-one components of potential vorticity (contours) and winds at
700 hPa after 18 h of integration. The positive (negative) anomalies of
potential vorticity are nearly collocated with the cyclonic (anticyclonic)
circulation. Since the potential vorticity in the inner core is generally
elevated, the advection of the symmetric potential vorticity component by the
flows between the cyclonic and anticyclonic circulations leads to the maximum
(minimum) HA1 in the exit (entrance) of the flows between the cyclonic and
anticyclonic circulation. On the other hand, the advection of the
wave-number-one component of potential vorticity by the symmetric cyclonic
flow leads to the maximum HA2 in the entrance and the minimum HA1 in the exit
(Fig. 9b). Although the contributions of the HA1 and HA2 terms can fluctuate
with a magnitude of about 4 m s-1 (Fig. 8), their combined effect
shows only small-amplitude fluctuations in the tropical cyclone motion. The
short-time fluctuations will be discussed in the next section.
The wave-number-one components of the 500 hPa vertical motion
(contours, m s-1), 700 hPa winds relative to the tropical cyclone
motion (vectors, m s-1) and 500 hPa heating rate (shaded,
10-4 K s-1) after 18 h of integration. The dashed circle
indicates the radius of maximum wind.
Contributions of diabatic heating and vertical advection
Some individual contributions in Fig. 7a and b are statistically correlated.
For example, the zonal contribution of the HA term is negatively correlated
with that of the DH term with a coefficient of -0.44, and the meridional
contribution of the HA term is negatively correlated with that of the VA
terms with a coefficient of -0.54. The correlation coefficients pass the
significance test at the 95 % confidence level. It is suggested that the
contributions of individual terms can partially cancel each other due to the
coherent structure of the tropical cyclone.
Time series of the contributions of diabatic heating at 700
(blue) and 400 hPa (red), and the contribution of diabatic heating (thick
black) averaged over the layer between 300 and 850 hPa.
We first discuss the contribution of the VA term. The VA contains two primary
terms: the advection of the symmetric component of potential vorticity by the
wave-number-one component of vertical motion (VA1) and wave-number-one
component of potential vorticity by the symmetric component of vertical
motion (VA2). Our examination indicates that the contribution of the VA term
is dominated by that of VA1. That is, the direction of the contribution of
the VA term is determined by the orientation of the wave-number-one component
of vertical motion. Figure 10 shows the wave-number-one components of the
500 hPa vertical motion, 700 hPa winds relative to tropical cyclone motion
and 500 hPa heating rate after 18 h of integration. We can see that the
upward (downward) motion generally occurs in the entrance (exit) region of
the 700 hPa winds. Bender (1997) found that vorticity stretching and
compression are closely associated with the vorticity advection due to the
relative flow (difference between the wave-number-one flow and the TC motion),
but Riemer (2016) recently argued that Bender's mechanism did not work in his
idealized experiment. We find that the contribution of the HA term is indeed
significantly correlated with those of the VA and DH terms, suggesting the
relationship between the vertical motion (diabatic heating) and the relative
flow.
The contribution of diabatic heating results mainly from
-qs×∇3h1, where
qs is the symmetric component of the absolute vorticity,
∇3 the three-dimensional gradient operator and h1 the
wave-number-one component of diabatic heating rate. Since the absolute
vorticity is dominated by the vertical component of relative vorticity and
diabatic heating rate reaches its maximum in the middle troposphere, it is
conceivable that the contribution of diabatic heating should cancel each
other in the low and upper troposphere. Figure 11 shows the contribution of
diabatic heating at 700 and 400 hPa. The correlation between 700 and
400 hPa is -0.68 in the zonal direction and -0.67 in the meridional
direction.
Small-amplitude oscillation of the tropical cyclone track with
respect to the 9 h running mean track: (a) 6–18 and (b) 59–69 h. The
x and y axes indicate the distance (km) relative to the 9 h running mean
track.
Distribution of potential vorticity (shaded, 10-6 m2 s-1 K kg-1)
and magnitude of wind (contour, m s-1) within the
inner-core region during the period of 13–18 h at 700 hPa. The dashed circle shows the
radius of maximum wind, with the tropical cyclone center indicating with
crosses.
Trochoidal motion
As shown in Fig. 5, the tropical cyclone motion exhibits considerable
fluctuations. In an instant, the steering can significantly deviate from the
tropical cyclone motion. At 60 h, for example, the zonal steering is
-0.55 m s-1, about one-third of the zonal motion of the tropical
cyclone (-1.42 m s-1); the meridional steering is 2.71 m s-1,
slower than the meridional motion of the tropical cyclone
(3.05 m s-1). The deviation from the tropical cyclone motion is
13.5∘ in the direction and 18 % in the magnitude.
Based on radar data and satellite images, many studies have documented the
oscillation of a tropical cyclone track with respect to its mean motion
vector (e.g., Jordan and Stowell, 1955; Lawrence and Mayfield, 1977;
Muramatsu, 1986; Itano et al., 2002; Hong and Chang, 2005). The periods of
track oscillations range from less than an hour to a few days (Holland and
Lander, 1993). In this study, the small-scale oscillation with amplitudes
comparable to the eye size and periods of several hours is referred to
as the trochoidal motion of the tropical cyclone center. Willoughby (1988)
showed that a pair of rotating mass and sink source could lead to trochoidal
motion with periods ranging from 2 to 10 h. Flatau and
Stevens (1993) argued that
wave-number-one instabilities in the outflow layer of tropical cyclones could
cause trochoidal motion. Nolan et al. (2001) found that the small-amplitude
trochoidal motion is associated with the instability of the wave-number-one
component of tropical cyclone circulation due to the presence of the
low-vorticity eye. The instability in their three-dimensional simulation with
a baroclinic vortex quickly led to substantial inner-core vorticity
redistribution and mixing, displacing the vortex center that rotates around
the vortex core. Our spectral analysis indicates two peaks of the
fluctuations of the tropical cyclone motion centered at 5 and 9 h (figure
not shown), suggesting that the trochoidal motion is simulated in our
high-resolution numerical simulation.
Fluctuations (deviation from the 9 h running mean) of (a) the
tropical cyclone speed (black solid), the PVT speed (black dashed) and the
difference between the tropical cyclone speed and the conventional steering
(red solid), and (b) the difference between the tropical cyclone speed and
the conventional steering (red solid), and the difference between the
contribution of the HA term and the conventional steering (black).
Figure 12 shows the oscillation of the tropical cyclone track with respect to
the 9 h running mean track for the periods 6–18 and 59–70 h. We can see
that the displacement from the mean track is usually less than 6 km with a
period of several hours in this study. This displacement is less than the
size of the tropical cyclone eye. In general, the tropical cyclone center
rotates cyclonically relative to the mean track position, in agreement with
previous observational and numerical studies (Lawrenece and Mayfield, 1977;
Muramatsu, 1986; Itano et al., 2002; Willoughby, 1988; Nolan et al., 2001).
In association with the trochoidal motion of the tropical cyclone center, as
suggested by Nolan et al. (2001), substantial potential vorticity
redistribution and mixing can be observed in the inner-core region (Fig. 13).
During the period of 13–18 h, the tropical cyclone eye generally looks like
a triangle, but the orientation of the triangle changes rapidly, suggesting
the potential vorticity redistribution and mixing in the eye.
The trochoidal motion is well indicated in the translation speed estimated
with the PVT approach. Figure 14a shows the fluctuations of tropical cyclone
speed, the PVT speed, and the difference between the tropical cyclone speed
and the conventional steering, in which the 9 h running mean has been
removed. We can see that the fluctuations of tropical cyclone motion are well
represented in the PVT speed. Moreover, the consistency between the
fluctuations of tropical cyclone motion and those with the conventional
steering removed suggests that the small-amplitude oscillation of the
tropical cyclone motion cannot be accounted for by the conventional steering.
Figure 14b further compares the time series of tropical cyclone motion
relative to the conventional steering with the time series of the
contribution of the HA term relative to the conventional steering. The two
time series are correlated with a coefficient of 0.60. We can see that the
contribution of the HA term plays an important role in the fluctuations.
Since the non-steering effect can well account for the fluctuations
(Fig. 14a), Fig. 14b suggests that the VA and DH tend to reduce the magnitude
of the fluctuations.
Summary
In this study, we addressed two fundamental questions regarding the steering
principle that has been widely applied to tropical cyclone forecasting and
research for about a century (Fujiwara and Sekiguchi, 1919; Bowie, 1922). One
is why the conventional steering plays a dominant role in tropical cyclone
motion, and the other is when tropical cyclone motion deviates considerably
from the steering. The PVT diagnosis approach proposed by Wu and Wang (2000)
is used with the output from a high-resolution numerical experiment. It is
found that the PVT approach can well estimate tropical cyclone motion,
including the small-amplitude trochoidal motion relative to the mean tropical
cyclone track.
The effect of the conventional steering flow that is averaged over a certain
radius from the tropical cyclone center and a deep pressure layer (e.g.,
850–300 hPa) actually represents the combined contribution from both the
advection of the symmetric potential vorticity component by the asymmetric
flow (HA1) and the advection of the wave-number-one potential vorticity
component by the symmetric flow (HA2), although the contribution of the HA1
term is literally the effect of steering (Wu and Wang, 2001a, b). The
conventional steering generally plays a dominant role in tropical cyclone
motion since the contributions from other processes are largely cancelled out
due to the coherent structure of tropical cyclone circulation.
The trochoidal motion of the tropical cyclone center is simulated in the
numerical experiment with amplitudes smaller than the eye radius and periods
of several hours. The tropical cyclone center rotates cyclonically around the
mean track, in agreement with previous observational and numerical studies
(Lawrenece and Mayfield, 1977; Muramatsu, 1986; Itano et al., 2002;
Willoughby, 1988; Nolan et al., 2001). It is found that the small-amplitude
trochoidal motion cannot be accounted for by the effect of the conventional
steering, although the contribution of the HA term plays an important role in
the fluctuations. In agreement with previous studies (Willoughby, 1988; Nolan
et al., 2001), we suggest that the small-amplitude trochoidal motion results
from the asymmetric dynamics of the tropical cyclone inner core. It is also
found that the instantaneous speed of tropical cyclone motion can
considerably deviate from the conventional steering, while the latter better
represents tropical cyclone motion when averaged over a reasonable time
period.
Data availability
The underlying research data were the output of a numerical experiment and available on request by contacting the first author.
Acknowledgements
Many thanks go to Christopher W. Landsea of the National Hurricane Center
for providing us the early references on the steering principle. This
research was jointly supported by the National Basic Research Program of
China (2013CB430103, 2015CB452803), the National Natural Science Foundation
of China (grant no. 41275093) and the project of the specially appointed
professorship of Jiangsu Province. We appreciate C.-C. Wu and two
anonymous reviewers for their constructive comments.
Edited by: H. Wernli
Reviewed by: C.-C. Wu and two anonymous referees
References
Bender, M. A.: The effect of relative flow on the asymmetric structure
in the interior of hurricanes, J. Atmos. Sci., 54, 703–724, 1997.
Bowie, E. H.: Formation and movement of West Indian hurricanes.
Mon. Weather Rev., 50, 173-179, 1922.
Carr, L. E. and Elsberry, R. L.: Observational evidence for
predictions of tropical cyclone propagation relative to steering, J.
Atmos. Sci., 47, 542–546, 1990.
Chan, J. C.-L.: An observation al study of physical processes
responsible for tropical cyclone motion, J. Atmos. Sci., 41,
1036–1048, 1984.
Chan, J. C.-L. and Gray, W. M.: Tropical cyclone motion and
surrounding flow relationship, Mon. Weather Rev., 110, 1354–1374, 1982.
Chan, J. C-L. and Williams, R. T.: Analytical and numerical studies of
beta-effect in tropical cyclone motion, Part I: Zero mean flow, J.
Atmos. Sci., 44, 1257–1265, 1987.
Chan, J. C.-L., Ko, F. M. F., and Lei, Y. M.: Relationship between
potential vorticiy tendency and tropical cyclone motion, J. Atmos.
Sci., 59, 1317–1336, 2002.
Choi, Y., Yun, K.-S., Ha, K.-J., Kim, K.-Y., Yoon, S.-J., and Chan, J.-C.-L.:
Effects of Asymmetric SST Distribution on Straight-Moving Typhoon Ewiniar
(2006) and Recurving Typhoon Maemi (2003), Mon. Weather Rev., 141,
3950–3967, 2013.
Dong, K., and C. J. Neumann, 1986: The relationship between tropical cyclone
motion and environmental geostrophic flows, Mon. Weather Rev., 114, 115–122,
1986.
Duchon, C. E.: Lanczos filtering in one and two dimensions, J.
Appl. Meteor., 18, 1016–1022, 1979.
Dudhia, J.: Numerical study of convection observed during the winter
monsoon experiment using a mesoscale two-dimensional model, J.
Atmos. Sci., 46, 3077–3107, 1989.
Fiorino, M. and Elsberry, R. L.: Some aspects of vortex structure
related to tropical cyclone motion, J. Atmos. Sci., 46, 975–990, 1989.
Flatau, M. and Stevens, D.: The Role of Outflow-Layer Instabilities in
Tropical Cyclone Motion, J. Atmos. Sci., 50, 1721–1733, 1993.Fovell, R. G., Corbosiero, K. L., Seifert, A., and
Liou, K.-N.: Impact of cloud-radiative processes on
hurricane track, Geophys. Res. Lett., 37, L07808,
10.1029/2010GL042691, 2010.
Frank, W. and Ritchie, E. A.: Effects of vertical wind shear on the
intensity and structure of numerically simulated hurricanes, Mon. Weather Rev., 129, 2249–2269, 2001.
Franklin, J. L., Feuer, S. E., Kaplan, J., and Aberson, S. D.: Tropical
cyclone motion and surrounding flow relationship: Searching for beta gyres
in Omega dropwindsonde datasets, Mon. Weather Rev., 124, 64–84, 1996.
Fujiwhara, S. and K. Sekiguchi: Estimated 300 m isobars and the
weather of Japan, J. Meteor. Soc. Japan, 38, 254–259, 1919 (in Japanese).
Holland, G. J.: Tropical cyclone motion: Environmental interaction
plus a beta effect, J. Atmos. Sci., 40, 328–342, 1983.
Hong, S. Y. and Lim, J. O. J.: The WRF single-moment 6-class microphysics
scheme (WSM6)[J], J. Korean Meteor. Soc., 42, 129–151, 2006.Hong, J.-S. and Chang, P.-L.: The trochoid-like track in Typhoon Dujuan
(2003), Geophys. Res. Lett., 32, L16801, 10.1029/2005GL023387, 2005.
Houze, R. A.: Clouds in tropical cyclones, Mon. Weather Rev.,
138, 293–344, 2010.
Hsu, L.-H., Kuo, H.-C., and Fovell, R. G.: On the Geographic
Asymmetry of Typhoon Translation Speed across the Mountainous Island of
Taiwan, J. Atmos. Sci., 70, 1006–1022, 2013.
Huang, Y.-H., Montgomery, M. T., and Wu, C.-C.: Concentric eyewall
formation in Typhoon Sinlaku (2008) – Part II: Axisymmetric dynamical
processes, J. Atmos. Sci., 69, 662–674, 2012.
Itano, T., Naito, G., and Oda, M.: Analysis of elliptical eye of Typhoon
Herb (T9609) (in Japanese with English abstract), Sci. Eng. Rep.
Natl. Def. Acad., 39, 9–17, 2002.
Kain, J. S. and Fritch, J. M.: Convective parameterization for
mesoscale models: the Kain-Fritch scheme. The representation of cumulus
convection in numerical models, Meteorol. Monogr., 46,
165–170, 1993.
Lawrence, M. B. and Mayfield, B. M.: Satellite observations of
trochoidal motion during Hurricane Belle 1976, Mon. Weather
Rev., 105, 1458–1461, 1977.
Marks Jr., F. D., Houze Jr., R. A., and Gamache, J. F.: Dual-aircraft
investigation of the inner core of Hurricane Norbert, Part I: Kinematic
structure, J. Atmos. Sci., 49, 919–942, 1992.
Mlawer, E. J., Taobman, S. J., Brown, P. D., Iacono, M. J., and Clough, S. A.: Radiative transfer for inhomogeneous atmosphere: RRTM, a validated
correlated-k model for the longwave, J. Geophys. Res., 102,
16663–16682,
1997.
Muramatsu, T.: Trochoidal motion of the eye of Typhoon 8019,
J. Meteor. Soc. Japan, 64, 259–272, 1986.
Neumann, C. J.: Global overview, Global Guide to Tropical
Cyclone Forecasting, World Meteor. Org., 1.1–1.56, 1993.
Noh, Y., Cheon, W. G., Hong, S.-Y., and Raasch, S.: Improvement of the
K-profile model for the planetary boundary layer based on large eddy
simulation data, Bound.-Layer Meteor., 107, 401–427, 2003.
Nolan, D. S., Montgomery, M. T., and Grasso, L. D.: The wavenumber-one
instability and trochoidal motion of hurricane-like vortices, J.
Atmos. Sci., 58, 3243–3270, 2001.
Oda, M., Nakanishi, M., and Naito, G.: Interaction of an Asymmetric Double
Vortex and Trochoidal Motion of a Tropical Cyclone with the Concentric
Eyewall Structure, J. Atmos. Sci., 63, 1069–1081, 2006.
Riehl, H., and Burgner, N. M.: Further studies on the movement and
formation of hurricanes and their forecasting, Bull. Amer. Meteor.
Soc., 31, 244–253, 1950.Riemer, M.: Meso-β-scale environment for the stationary band
cpmplex of verticall-sheared tropical cyclones, Q. J. R. Meteorol.
Soc., 142, 2442–2451, 2016.
Simpson, R. H.: On the movement of tropical cyclones, Trans.
Amer. Geophy. Union, 27, 641–655, 1946.
Velden, C. S. and Leslie, L. M.: The basic relationship between
tropical cyclone intensity and the depth of the environmental steering layer
in the Australian region, Weather Forecast., 6, 244–253, 1991.
Wang, B. and Li, X.: The beta drift of three-dimensional vortices: A
numerical study, Mon. Weather Rev., 120, 579–593, 1992.
Wang, B., Elsberry, R. L., Wang, Y., and Wu, L.: Dynamics of tropical
cyclone motion: A review, Sci. Atmos. Sin., 22, 1–12, 1998.
Wang, C.-C., Chen, Y.-H., Kuo, H.-C., and Huang, S.-Y.: Sensitivity of
typhoon track to asymmetric latent heating/rainfall induced by Taiwan
topography: A numerical study of Typhoon Fanapi (2010), J.
Geophys. Res.-Atmos., 118, 3292–3308, 2013.
Wang, Y. and Holland, G. J.: The beta drift of baroclinic vortices,
Part I: Adiabatic vortices, J. Atmos. Sci., 53, 411–427, 1996a.
Wang, Y. and Holland, G. J.: The beta drift of baroclinic vortices.
Part II:Diabatic vortices, J. Atmos. Sci., 53, 3737–3756, 1996b.
Wang, Y. and Holland, G. J.: Tropical cyclone motion and evolution in
vertical shear, J. Atmos. Sci., 53, 3313–3332, 1996c.
Willoughby, H.: Linear motion of a shallow-water, barotropic vortex,
J. Atmos. Sci., 45, 1906–1928, 1988.
Wong, M. L. M. and Chan, J. C. L.: Tropical cyclone motion in response to
land surface friction, J. Atmos. Sci., 63, 1324–1337, 2006.
Wu, C.-C. and Emanuel, K. A.: Potential vorticity diagnostics of
hurricane movement, Part I: A case study of Hurricane Bob (1991),
Mon. Weather Rev., 123, 69–92, 1995a.
Wu, C.-C. and Emanuel, K. A.: Potential vorticity diagnostics of
hurricane movement, Part II: Tropical Storm Ana (1991) and Hurricane Andrew
(1992), Mon. Weather Rev., 123, 93–109, 1995b.
Wu, C.-C., Huang, Y.-H., and Lien, G.-Y.: Concentric eyewall formation
in Typhoon Sinlaku (2008) – Part I: Assimilation of T-PARC data based on
the Ensemble Kalman Filter (EnKF), Mon. Weather Rev., 140, 506–527, 2012.
Wu, L. and Wang, B.: A potential vorticity tendency diagnostic
approach for tropical cyclone motion, Mon. Weather Rev., 128,
1899–1911, 2000.
Wu, L. and Wang, B.: Movement and vertical coupling of adiabatic
baroclinic tropical cyclones, J. Atmos. Sci., 58, 1801–1814, 2001a.
Wu, L. and Wang, B.: Effects of convective heating on movement and
vertical coupling of tropical cyclones: A numerical study, J. Atmos.
Sci., 58, 3639–3649, 2001b.Wu, L., Braun, S. A., Halverson, J., and Heymsfield, G.: A numerical
study of Hurricane Erin (2001), Part I: Model verification and storm
evolution, J. Atmos. Sci., 63, 65–86, 2006.
Wu, L., Liang, J., and Wu, C.-C.: Monsoonal Influence on Typhoon
Morakot (2009), Part I: Observational analysis, J. Atmos. Sci., 68,
2208–2221, 2011a.
Wu, L., Zong, H., and Liang, J.: Observational analysis of sudden
tropical cyclone track changes in the vicinity of the East China Sea,
J. Atmos. Sci., 68, 3012–3031, 2011b.
Yu, H., Huang, W., Duan, Y. H., Chan, J. C. L., Chen, P. Y., and Yu, R. L.: A
simulation study on pre-landfall erratic track of typhoon Haitang (2005),
Meteorol. Atmos. Phys., 97, 189–206, 2007.