International Journal of Geosciences, 2011, 2, 29-35
doi:10.4236/ijg.2011.21003 Published Online February 2011 (http://www.SciRP.org/journal/ijg)
Changes in Tropical Cyclone Number in the Western North
Pacific in a Warming Environment as Implied by Classical
Thermodynamics
Xiaogang Zhou1, Chongjian Liu2,3, Ying Liu2, Hui Xu4, Xiuming Wang1
1Training Centre, China Meteorological Administration, Beijing, China
2State Key Laboratory of Severe Weather, Chinese Academy of Meteorological Sciences, Beijing, China
3Shanghai Typhoon Institute, China Meteorological Administration, Shanghai, China
4National Meteoro logical Center, China Meteorologica l Administration, Beijing, Chi na
Received October 29, 2010; revised December 5, 2010; accepted January 1, 2011
Abstract
Observational analyses show that the equatorial trough in the western North Pacific (WNP) is a well-known
origin for tropical cyclones (TC) which have tended to weaken in intensity and decrease in number during
the last several decades under global warming. A scientific problem then arises as to why higher sea surface
temperatures (SSTs), one of the necessary conditions for typhoon genesis, can cause a weakened equatorial
trough and a decreased TC number. In this paper, the WNP is taken as an example to illustrate a possible
mechanism for the above-mentioned seemingly counterintuitive phenomena and explain the causality be-
tween the unusually heterogeneous pattern of SSTs in a warming environment and TC number in the WNP.
This mechanism is based substantially on the second law of thermodynamics.
Keywords: Second Law of Thermodynamics, Global Warming, Thermal Wind Relation, Sea Surface
Temperature
1. Introduction
A number of papers and the observational data have re-
vealed that a variety of devastating weather/climate
events have happened frequently over the world recently.
Here we may quote, as examples, the most serious
drought since 1940 occurred in the central western part
of the United States in 1998 with grain production drop-
ping by 38%, the warmest year 1999 experienced in
China in the last hundred years, the extraordinarily pow-
erful and deadly Hurricane Katrina with damages of
about $81 billion and fatalities over 1800 in 2005, and so
forth [1-5]. However, during this severe period, a coun-
terintuitive phenomenon was seen in that the tropical
cyclone (TC) numbers tended to decrease over some
oceanic basins while a rise in their sea surface tempera-
tures (SSTs) has been observed [6-8]. As a result, a sci-
entific problem arises as to why, under a background of
global warming, higher SSTs, implying more potential
energy which is one of the necessary conditions for ty-
phoon genesis, would cause decreased TC numbers?
In the recently published monograph [9] it is stated
that most numerical models indicate an overall decrease
in the number of storms attributable to greater atmos-
pheric stability and to a decrease in vertical mass flux.
However, the analysis in this paper for understanding the
observed counterintuitive phenomena is quite different
from those described in the previous works. This analysis
is based on fundamental dynamics rather than numerical
experiments whose results are inevitably affected by the
numerical model itself.
In this paper the western North Pacific (WNP) over
which the TC numbers tended to decrease with minor
fluctuations from late 1960s (Figure 1) is taken to illus-
trate a possible mechanism responsible for the conun-
drum. This paper is based on the observational results
shown in Figure 1 that are obtained from the Tropical
Cyclone Year Book or the CMA dataset covering 59
years as indicated in Ref. [10]. And, the relative vorticity
(RV) in Figure 1 is calculated via the definition formula
for RV (see Subsection 3.1 below), based on the National
Centers for Environmental Prediction/National Center

X. G. ZHOU ET AL.
30
Figure 1. The long term time series for the TC numbers in the WNP and in the basin west of 140˚E as well as the averaged
relative vorticity (10-5 s-1) in the monsoon trough ITCZ during 1949-2007 (see the text for details).
for Atmospheric Research (NCEP/NCAR) 2.5˚ × 2.5˚
(latitude–longitude grid) reanalysis data.
2. Results and Discussion
2.1. The Main Source of TC Genesis and the
ITCZ
According to the previous studies [11-13], 80% - 85% of
TCs originate in the ITCZ or just on its poleward side,
and the monsoon trough ITCZ located in the basin west
of 140˚E is the main origin of TCs over the WNP. Based
on the satellite images and the other data analyses, it is
noticed that 70% of the TCs originate from the cloud
clusters over the ITCZ and the monsoon trough in the
WNP [14,15]. The necessary conditions of TC genesis
and development include higher SSTs, stronger low level
vorticity, weaker vertical wind shear, and a higher latitu-
dinal position of the subtropical anticyclone ridge/ITCZ,
though these conditions are not equally important.
Among them theoretically low level vorticity should be
the fundamental factor for TC genesis since initial dis-
turbances are the embryo of TCs. In addition, the inten-
sity of the ITCZ as a main system generating TCs can be
described in terms of the RV e.g. use RV at 850 hPa for
defining the ITCZ, as is seen in Ref. [16]. Indeed the TC
numbers over the WNP and the basin west of 140˚E have
a high correlation with the RV around the ITCZ, as is
seen in Figure 1 where these numbers show almost syn-
chronous changes with those of the RV. The corre-
sponding correlation coefficients for the WNP and the
basin west of 140˚E are 0.6552 and 0.6614 at the 0.001
significance level, respectively. It is noticed, in [10], that
a 10-year running mean to the annual TC frequency data
and NCEP typhoon season mean wind data has been ap-
plied to get the long term time series of the averaged TC
numbers and RV at 925 hPa in the monsoon trough ITCZ
for the period 1949-2007, and, that July-October (JASO
hereafter) is defined as the typhoon season since JASO is
the most frequent season for TCs over the WNP. It will
therefore be a reasonable way to discuss the causality
between the TC frequency trend and warming SSTs over
the WNP via the ITCZ variability as the medium.
2.2. The ITCZ Variabilities
The analyses below are based on the NCEP/NCAR 2.5˚ ×
2.5˚ resolution reanalysis data for horizontal winds from
which the ITCZ fields in terms of RV are figured out via
the definition of RV at constant pressure layer
pp
p
vu
x
y









, (1)
where
p

, u and v are the RV, the latitudinal and longi-
tudinal velocities at constant pressure, respectively, as
well as 2.0˚ × 2.0˚ data for the SST fields [17]. All the
means are calculated against the period of JASO as men-
tioned above.
Figure 2 shows the streamlines fields superimposed

X. G. ZHOU ET AL.
31
on the positive RV at 925 hPa during JASO over the
North Pacific. This shows that the zones of positive RV
can indicate the general position of the convergence
zones in the streamlines fields. These convergence zones
should be able to represent the ITCZs since the ITCZ is
mainly formed by the trade winds converging [18,19].
As mentioned in Section 2, using RV at 850 hPa for de-
fining the ITCZ has been done [16]. However, the RV in
terms of 850 hPa is not continuous in some sections of
the ITCZ over the Pacific owing to its weaker intensity
(figures not shown here). Therefore the RV at 925 hPa
that is more continuous and smoother than that at 850
hPa is chosen instead in this paper.
The variation of the ITCZ over the WNP associated
with the reduction in the TC numbers under warming
SSTs during the last several decades might be caused by
Figure 2. Comparison of the streamlines fields superimposed on the positive RV at 925 hPa (contours in 10-5 s-1) during JASO
over the WNP between the first and last 20-year/30-year means (as marked above the respective panels).

X. G. ZHOU ET AL.
32
the following two factors: 1) the intensity of the mon-
soon trough ITCZ, the main origin of TCs over the WNP,
in terms of RV at 925 hPa was weakened and 2) the po-
sition of the ITCZ has shifted further south. The latter
can be seen in Figure 3 in which the central position of
the ITCZ is determined by singling out the points with
maximum positive relative vorticity values for each 2.5
longitudinal distance within the 100˚E - 140˚E area and
then averaging them, both of which would contribute to
the decrease in TC numbers over the WNP.
Next we will specifically discuss these two factors.
2.3. The Implication of SSTs Variation
Figure 4 shows consecutive 20-year means of SSTs over
the North Pacific for JASO during 1949-2008. It is seen
that the SSTs over the North Pacific gradually increase,
particularly the 28˚C isotherm, the critical temperature
for the warm pool [20], which has extended eastward.
This cross-equatorial area of warm water initially limited
to the western Pacific has extended into the eastern Pa-
cific. Since there is a close relationship between SSTs
and surface wind divergence/convection over the tropical
oceans or the ITCZs [21-23] the following questions are
then raised: how the SSTs or their gradient influence the
intensity of the ITCZ, and why the sea surface warming
around the western Pacific is not as dramatic as over the
central and eastern Pacific? The latter is relevant to the
first of the ITCZ variability factors mentioned above. A
potential clue can be found in the theory of modern
nonlinear non-equilibrium thermodynamics.
For an isolated thermodynamic system, the state func-
tion of the system, entropy s per unit mass, will sponta-
neously increase with time according to the second law
of thermodynamics, which can be expressed by the for-
mula [24,25]
d0
d
s
t (2)
and is usually called the spontaneous entropy increment
principle. As a result, an isolated system will spontane-
ously tend to homogenization. However, for an open
system with a diabatic heating rate Q transferred through
its boundaries, Equation 2 should be modified to
d
d
s
Q
tT
 (3)
where T is the temperature (in ˚K) of the system. The
nature of the second law of thermodynamics shows that,
if there exists initial differences, heat (particles) will be
spontaneously transferred (diffused) from areas with
higher T (concentration) to that with lower T (concentra-
tion). Any many-body system like the atmosphere or
ocean must be controlled by the second law of thermo-
dynamics and, in fact the entropy flow properties of at-
mospheric systems have been revealed via this law
[26-29].
Specifically, if there exist differences in temperature
spatially (say, on the sea surface), the original area of
warmer sea surface will diffuse its thermal energy (the
inner energy, proportional positively to temperature via
the formula of e = Cv T where e is the inner energy per
unit mass, Cv is the specific heat at constant volume and
T is temperature) to its surroundings with lower tem-
perature. As a consequence, compared to the surrounding
areas, the original warmer area (e.g., the warm pool) will
experience a weaker warming under global warming
since it will lose a certain amount of heat via the diffu-
sive process at the same time, and vice versa. Figure 4
shows the case for the North Pacific as an example in
which it is demonstrated that the SSTs around the mon-
soon trough ITCZ have a smaller increment of tempera-
ture while those over the adjacent ITCZ sections near the
central and eastern equatorial Pacific have larger incre-
ments. Because the ITCZ is mainly caused, at least in the
initial stages, by thermodynamic forcings such as the
gradient in SST which plays more of a role than the ab-
solute SST value with regard to convection and precipi-
tation [23], the monsoon trough ITCZ should indeed be-
come weaker in response to more uniform SSTs or a
weakened SST gradient.
2.4. The Effect of the SST Pattern on the ITCZ
Migration
As described above, in the warming environment the
higher SST area within the 28˚C isotherm has gradually
extended eastward (Figure 4) so as to form an apparent
zone of higher SSTs with a distinct gradient of nearly
north-south direction (y-direction) created on the both
northern and southern sides of this zone. Such a SST
Figure 3. An illustration of changes in the average position
of the ITCZ from 1949 to 2007. Here, the central position of
the ITCZ is determined from the points with maximum
positive RV along the longitudinal direction within 100˚E–
140˚E and then averaging their respective latitudinal posi-
tion.

X. G. ZHOU ET AL.
33
Figure 4. The consecutive 20-year-averaged SST fields (˚C) for the North Pacific south of 40˚N during the period from 1949
to 2008.
pattern will cause changes in the mean temperature Tm of
an air layer above the sea surface between p1 (e.g. 1000
hPa that is near the sea surface) and p2 (e.g. 925 hPa that
is used for defining the ITCZ in terms of RV in this pa-
per). As a result, in some regions to the north of the zone
of higher temperature, with the average temperature gra-
dient along the north-south direction m
T
y

 being smaller
than zero, a westerly wind component at higher levels
(e.g. at 925 hPa) should be superposed, due to gradient
and Coriolis forces.
Similarly, the latitudinal velocity to the south of the
zone should be superposed by an easterly component as
the gradient in SSTs in the southern regions is the re-
verse of that in the north. Thus, the RV, as is expressed
by pp
p
vu
x
y





 


, in the regions to the north of the
zone of higher temperature will be decreased since the
term u
y





becomes smaller while the term
p
v
x





changes little in this case. At the same time, the RV in
the regions to the south of the zone of higher temperature
will be increased owing to the reversed gradient in SSTs
or Tm there.
Taking the definition of ITCZ in terms of positive RV
into account, we might expect that the part of the ITCZ
to the north of the zone of high temperature will tend to
disappear as a result of a reduction in RV there and,
similarly initial ITCZ to the south will be enhanced and

X. G. ZHOU ET AL.
34
even extend south further. This could help to explain
why the ITCZ apparently migrates south (Figures 2,3).
3. Conclusions
As is well-known, the necessary conditions for TC gene-
sis are not equally important and, among them dynamical
factors such as low level vorticity and vertical wind shear
play a more important role than thermodynamic factors
such as SST and moist instability [30-32]. This study
shows that, warmer SSTs in the WNP can cause fewer
TCs, that is, warmer SSTs are only one of the necessary
conditions and so do not definitely lead to an increase in
TC numbers. This may be attributed to the heterogeneous
effects of complicated patterns of SSTs on RV as implied
by the second law of thermodynamics. This paper further
also suggests that low level vorticity associated with
ITCZ variations should be a fundamental factor for TC
genesis. Based on the analyses in this paper, a new way
of understanding the mechanism responsible for the cau-
sality between SSTs and TC occurrence frequency over
the WNP is then suggested. The WNP is only used as an
example in this study and the methodology illustrated
herein should be universal.
4. Acknowledgements
This work has been jointly supported by the National
Natural Science Foundation of China (40875029,
41075048, 40633016, and 40975036), 973 Program
(2009CB421500) and the Basic Research Project of the
State Key Laboratory of Severe Weather, Chinese
Academy of Meteorological Sciences (2008LASWZI01).
5. References
[1] D. R. Easterling, J. L. Evana, P. Y. Grosman, T. R. Karl,
K. E. Kunkel and P. Ambenje, “Observed Variability and
Trends in Extreme Climate Events: A Brief Review,”
Bulletin of the American Meteorological Society, Vol. 81,
No. 3, 2000, pp. 417-425.
doi:10.1175/1520-0477(2000)081<0417:OVATIE>2.3.C
O;2
[2] T. R. Karl, G. Kukla, V. N. Razuvayev, M. J. Changery,
R. G. Quayle, R. T. Heim Jr, D. R. Easterling and C. B.
Fu, “Global Warming: Evidence for Asymmetric Diurnal
Temperature Change,” Geophysical Research Letters,
Vol. 18, No. 12, 1991, pp. 2253-2256.
doi:10.1029/91GL02900
[3] M. Manton and J. Eral, “Trends in Extreme Daily
Rainfall and Temperature in Southeast Asia and the
South Pacific: 1961-1998,” International Journal of
Climatology, Vol. 21, No. 3, 2001, pp. 269-284.
doi:10.1002/joc.610
[4] S. W. Wang and D. Y. Gong, “Enhancement of the
Warming Trend in China,” Geophysical Research Letters,
Vol. 27, No. 16, 2000, pp. 2581-2584.
doi:10.1029/1999GL010825
[5] R. S. Cerveny, J. Lawrimore, R. Edwards and C. Landsea,
“Extreme Weather Records,” Bulletin of the American M-
eteorological Society, Vol. 88, No. 6, 2007, pp. 853-860.
doi:10.1175/BAMS-88-6-853
[6] C. Wang, S. K. Li and D. B. Enfield, “Atlantic Warm
Pool Acting as a Link between Atlantic Multidecadal Os-
cillation and Atlantic Tropical Cyclone Activity,” Geo-
chemistry, Geophysics, Geosystems, Vol. 9, 2008, pp. 1-17.
doi:10.1029/2007GC001809
[7] H. von Storch, “An Attempt to Homogeneously Describe
60 Years Statistics of TC Activity in East Asia: 1948-
2007,” Presented in 2008 Taiwan Climate Workshop, 18
November 2008, Taipei, Taiwan, China.
[8] J. L. McBride and H. Ramsay, “Relationship between
Tropical Cyclone Activity and Sea Surface Temperature
in the Southern Hemisphere,” Presented in 2nd Interna-
tional Summit on Hurricanes and Climate Change, May
31-June 5, 2009, Corfu, Greece (in “Aegean Conferences
Series-Vol. 41”; p. 23).
[9] J. B. Elsner and J. T. Hagger, “Hurricanes and Climate
Change,” Springer, 2009.
doi:10.1007/978-0-387-09410-6
[10] L. Ma and L. Chen, “The Relationship between Global
Warming and the Variation in Tropical Cyclone Fre-
quency over the Western North Pacific,” Journal of
Tropicalmeteorology, Vol. 15, No. 1, 2009, pp. 38-44.
[11] W. M. Gray, “Global View of the Origin of Tropical
Disturbances and Storms,” Monthly Weather Review, Vol.
96, No. 4, 1967, pp. 669-700.
[12] J. R. Bates, “Dynamics of Disturbances on the Intertropi-
cal Convergence Zone,” Quarterly Journal of the Royal
Meteorological Society, Vol. 96, No. 410, 1970, pp. 677-
701. doi:10.1002/qj.49709641010
[13] J. G. Charney, “Tropical Cyclonegenesis and the Forma-
tion of the Intertropical Convergence Zone, in Mathe-
matical Problems of Geophysical Fluid Dynamics,” In: W.
H. Reid, Eds., Lectures in Applied Mathematics, Ameri-
can Mathematical Society, New York, Vol. 13, 1971, pp.
335-368.
[14] L. M. Briegel and W. M. Frank, “Large-Scale Influences
on Tropical Cyclogenesis in the Western North Pacific,”
Monthly Weather Review, Vol. 125, No. 2, 1997, pp.
1397-1413.
doi:10.1175/1520-0493(1997)125<1397:LSIOTC>2.0.C
O;2
[15] E. A. Ritchie and G. J. Holland, “Large-Scale Patterns A-
ssociated with Tropical Cyclogenesis in the Western Pa-
cific,” Monthly Weather Review, Vol. 127, No. 9, 1999,
pp. 2027-2043.
doi:10.1175/1520-0493(1999)127<2027:LSPAWT>2.0.C
O;2
[16] S. C. Cha and J. L. Evans, “Comparison of the Structure
of the ITCZ in the West Pacific during the Boreal Sum-
mers of 1989–93 Using AMIP Simulations and ECMWF

X. G. ZHOU ET AL.
35
Reanalysis,” Journal of Climate, Vol. 15, No. 24, 2002,
pp. 3459-3568.
[17] E. Kalnay, et al., “The NCEP/NCAR 40-Year Reanalysis
Project,” Bulletin of the American Meteorological Society,
Vol. 77, No.3, 1996, pp. 437-471.
doi:10.1175/1520-0477(1996)077<0437:TNYRP>2.0.CO
;2
[18] J. Bjerknes, “Atmospheric Teleconnections from the
Equatorial Pacific,” Monthly Weather Review, Vol. 97,
No. 2, 1969, pp. 163-172.
doi:10.1175/1520-0493(1969)097<0163:ATFTEP>2.3.C
O;2
[19] J. R. Holton, J. M. Wallace and J. A. Young, “On
Boundary Layer Dynamics and the ITCZ,” Journal of the
Atmospheric Sciences, Vol. 28, No. 2, 1971, pp. 275-280.
doi:10.1175/1520-0469(1971)028<0275:OBLDAT>2.0.C
O;2
[20] C.-R. Ho, X.-H. Yan and Q. Zheng, “Satellite Obse-
rvations of Upper-Layer Variabilities in the Western Pac-
ific Warm Pool,” Bulletin of the American Meteorolo-
gical Society , Vol. 76, No. 5, 1995, pp. 669-679.
doi:10.1175/1520-0477(1995)076<0669:SOOULV>2.0.C
O;2
[21] N. E. Graham and T. P. Barnett, “Sea Surface Tempera-
ture, Surface Wind Divergence and Convection over
Tropical Oceans,” Science, Vol. 238, No. 4827, 1987, pp.
657-659. doi:10.1126/science.238.4827.657
[22] K.-M. Lau, H.-T. Wu and S. Bony, “The Role of
Large-Scale Atmospheric Circulation in the Relationship
between Tropical Convection and Sea Surface Tempera-
ture,” Journal of Climate, Vol. 10, No. 3, 1997, pp. 381-
392.
doi:10.1175/1520-0442(1997)010<0381:TROLSA>2.0.C
O;2
[23] R. S. Lindzen and S. Nigam, “On the Role of Sea Surface
Temperature Gradients in Forcing Low Level Winds and
Convergence in the Tropics,” Journal of the Atmospheric
Sciences, Vol. 44, 1987, pp. 2440-2458.
doi:10.1175/1520-0469(1987)044<2418:OTROSS>2.0.C
O;2
[24] I. Prigogine, “Introduction to Thermodynamics of Irreve-
rsible Processes,” Charles C. Thomas, 1955.
[25] S. R. de Groot and P. Mazur, “Non-Equilibrium Thermo-
dynamics,” North-Holland Publishing Company, 1962.
[26] C. Liu and Y. Liu, “An Attempt at Improving a Global
Spectral Model by Incorporating the Second Law of
Thermodynamics,” Geophysical Research Letters, Vol. 32,
2005, L03806.
doi:10.1029/2004GL021602
[27] C. Liu, Y. Liu and H. Xu, “A Physics-Based Diffusion
Scheme for Numerical Models,” Geophysical Research
Letters, Vol. 33, 2006, L12805.
doi:10.1029/2006GL025781
[28] Y. Liu and C. Liu, “Entropy Flow and the Evolution of a
Storm,” Entropy, Vol. 10, No. 4, 2008, pp. 430-440.
doi:10.3390/e10040430.
[29] H. Xu and C. Liu, “Entropy Flow Properties of a Ty-
phoon as Simulated by a Meso-Scale Model,” Europhys-
ics Letters, Vol. 83, No. 1, 2008.
doi:10.1209/0295-5075/83/18001
[30] M. Sugi, A. Noda and N. Sato, “Influence of Global
Warming on Tropical Cyclone Climatology: An Experi-
ment with the JMA Global Model,” Journal of the Mete-
orological Society of Japan, Vol. 80, No. 5, 2002, pp.
249-272. doi:10.2151/jmsj.80.249
[31] R. E. McDonald, D. G.Bleaken, D. R. Cresswell, V. D.
Pope and C. A. Senior, “Tropical Storms: Representation
and Diagnosis in Climate Models and the Impacts of Cli-
mate Change,” Climate Dynamics, 2005.
doi:10.1007/s00382-004-0491-0
[32] F. J. Chauvin, F. Royer and M. Deque, “Response of
Hurricane-Type Vortices to Global Warming as Simu-
lated by ARPEGE-Climate at High Resolution,” Climate
Dynamic, Vol. 27, No. 4, 2006, pp. 377-399.
doi:10.1007/s00382-006-0135-7