Changes in Tropical Cyclone Number in the Western North Pacific in a Warming Environment as Implied by Classical Thermodynamics

doi:10.4236/ijg.2011.21003

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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

E-mail: [email protected]

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.

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

















, (1)

where



, 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.

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.

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]

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

 (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.

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



 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

















, in the regions to the north of the

zone of higher temperature will be decreased since the

term u











becomes smaller while the term











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.

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).

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