# Comparisons of the Generalized Potential Temperature in  Moist Atmosphere with the Equivalent Potential Temperature in Saturated Moist Atmosphere

Authors: Yushu Zhou; Liping Liu; Guo Deng
Journal: Advances in Meteorology
 (2009)

---

## Abstract

The real tropospheric atmosphere is neither absolutely dry nor completely saturated. It is in general moist but not saturated. Here the generalized potential temperature (GPT) was introduced to describe this humid feature of real moist atmosphere. GPT's conservation property in moist adiabatic process was discussed and proved. Comparisons of GPT in moist atmosphere with the equivalent potential temperature (EPT) in saturated moist atmosphere
were made by analyzing three torrential rain cases occurring over Jianghuai Valleys in 2003, the north China in 2004, and with the typhoon Fung-Wong in 2008, respectively. Results showed that the relative humidity is not up to 100% even in torrential rain systems, the saturated condition for EPT is not always held, and thus GPT can describe the moisture concentration and moisture gradient better than EPT. The GPT's definition includes the process that the air changes from dry to moist, then up to saturated. Therefore, potential temperature (PT) and EPT can be considered as its two special status. Similar as PT and EPT, GPT can be used to study atmospheric dynamic and thermodynamic processes more generally because of its conservation property in moist adiabatic process.


---

## Body

## 1. Introduction

Potential  temperature (abbreviated as
PT and denoted byθ) is an important
parameter for dry atmosphere and can be used for comparing the thermodynamic
discrepancy of air parcels under different pressure. However if latent heat
release is involved, θ is not conservative. So the equivalent
potential temperature (abbreviated as EPT and denoted by θe), conserved in the saturated and moist
adiabatic expansion, is introduced to describe saturated atmosphere [1]. For its
conservation property, θe has been widely used in many studies of moist
atmospheric processes, such as the analysis of stability [2], the
extratropical cyclone [3] as well as the investigation of squall line [4],
frontal surface, and rainbands [5, 6]. Although widely applied, both PT and EPT
have their own scopes of application: PT is suitable for absolutely dry air and
EPT in general for the absolutely saturated, moist air only. But the real
atmosphere is neither totally dry nor completely saturated. It is moist but
unsaturated. Gao et al. [7] defined the atmospheric state that the air is
saturated somewhere but not everywhere as the nonuniform saturation. To avoid
confusing the two air states, here the moist atmosphere is defined as the moist
but unsaturated air, which is more similar to the real one. So the conservation
of PT and EPT may not properly be applied to the moist atmosphere.Other than the absolutely dry or
completely saturated air, the moist atmosphere is the real object of atmospheric
research. Because the phase changes and microphysical processes are hard to
observe and estimate, progress in these fields is very slow. Xie [8] advocated
the work of the moist atmospheric dynamics in 1970s. Since then many Chinese
scholars pursued in this area [9–11] but the works are still relatively
insufficient. In other countries, investigations about the dynamics of moist air have been carried out.
For example, Tripoli and Cotton [12] argued that PT for the mixture of ice-water θil has a big advantage over θ in identifying atmospheric deep convective
systems; Pointin [13] emphasized the thermodynamic impacts of precipitation and
defined the moist equivalent temperature (θq) substituting T and PT in modeling calculations; in the perspective of
entropy, Hauf and Höller [14] considered that the different forms of PT could be
expressed by a universal physical variable, namely, the  entropic temperature θs.
By introducing the concept of virtual temperature Tρ into thermodynamic process on the basis of ice
phase interaction, Ooyama  [15, 16] derived a set of direct,
consistent criteria of dynamics and thermodynamics, which are connected with
the parameterization of physical processes. In order to analyze the potential
impacts of the change of potential vorticity with the help of ice crystal,
Rivas Soriano and García Díez [17] derived a tendency equation for the generalized potential
vorticity qg with the help of θs and drew a conclusion that inhomogeneous
heating is associated with the development of connective system. Under the
nonstatic, moist, and rainy atmosphere, Schubert et al. [18],
utilizing the physical quantity θρ proposed by Ooyama [15], discussed
the new potential vorticity theory. Not using the approach of parameterization
of physical processes, Bannon [19] provided a set of moist air equations to
predict the short- or long-term weather by means of integrating the original
dynamic equations. The works mentioned above in addition to Betts  [20] and
Persson [21] applied a large number of variables and empirical constants for
describing the properties of the real atmosphere in which dry air, water vapor,
and hydrometeors (liquid water) coexist. However, these various approaches
resulted in implicit physical meanings of new variables and complicated
calculations, and thus are inconvenient for practical analyses, thereby not
widely used in operations.Gao et al.  [7] introduced a
parameter, called the generalized potential temperature and denoted as θ*,
into the atmospheric framework, which is connected with specific humidity
reflecting the traits of the actual atmosphere—neither absolutely dry nor totally saturated.
By adding two variables, namely, specific humidity and saturation specific
humidity, which are already in the expression of EPT, into the formula of θ*,
the easily calculated and novel parameter θ* is proposed, having shown great potential in
the real weather analyses. Furthermore, with the help of θ*,
a series of analysis and prediction approaches have been tested, including
analyzing and identifying heat wave weathers during the summer season of Beijing
[22], and
diagnosing rainstorms in the nonuniformly saturated flow by adopting the
ageostrophic Q vector [23]. However these works have not directly
touched whether and how GPT may physically conserve. Suppose GPT is conserved
in the adiabatic process of real moist atmosphere, just as PT in the dry
adiabatic process and EPT in the saturated moist adiabatic process, the basis
and scope of application can further be guaranteed. Therefore, this paper focuses
on exploring GPT’s physical meanings, demonstrating its conservation in moist
atmosphere and further comparing its distribution with those for EPT in a
variety of torrential rain cases, because the moist atmosphere and
precipitation processes are focuses in this paper.


## 2. The Definition of GPT and Its Conservation Law for Moist Atmosphere

The expression of GPT for the
nonuniformly saturated air, introduced by Wang and Luo  [9], can be written as θ*(T,p)=θ(T,p)exp((Lqs·(q/qs)k)/cpmT), here, T is the
atmospheric temperature, p is the pressure, θ is the potential temperature (PT) of dry air, q and qs are the specific humidity and the saturated
specific humidity, respectively, L and cpm are the latent heat per unit mass of
condensation and the specific heat per unit mass at constant pressure of moist
air, and the (q/qs)k, known as the function of condensation
probability, is a reflection of the humidity of the real air. When air is dry (q=0), GPT means PT, namely, θ*(T,p)=θ(T,p);
When air is saturated (q=qs), GPT turns into EPT, namely, θ*(T,p)=θ(T,p)exp(Lqs/cpmT)=θe;
when q varies from 0 to qs, θ* has a value between θ and θe,
which can manifest the changes of the air from dry to moist, then up to
saturated. PT and EPT are the two extremes of GPT.


### 2.1. Physical Discussions of the Condensation Probability Function in Moist Atmosphere

On the basis of the molecular
statistics, if the specific humidity of the air isq,
the specific humidity of an infinitesimal part q′ probably does not equal q but follows a certain statistical distribution [24].
According to the observations, due to a large number of condensation nucleuses
in the air, some parts of the air condense (usually condensation starts as the
relative humidity (RH) reaches 76%) before the relative humidity is near 100%.
Commonly, the higher the value of RH is, the easier the vapor condenses, which
means the degree of condensation of vapor increases with the increasing
humidity. In order to apply this microphysical property of moist air to
weather analyses, it is reasonable to add a weighted function y into EPT without changing its
dimension, so a new parameter is derived as the form of θ*=θexp((L/CpT)qsy).
This weighted function y, indicating the coexistent feature of dry and moist
air, should satisfy the following conditions: y=0 in absolute dry air and y=1 in totally saturated moist air. Hence, based on the facts that the
condensation increases with the increasing humidity, y must be a dimensionless parameter but is associated with
humidity. In order to apply this theory into the synoptic system diagnosis and
approach, the form of power function y=(q/qs)k is adopted in our study. According to
the numerical simulation and data analysis [24], the condensation feature can
be perfectly described when k is settled
by 9. Obviously, there are many other forms of y in addition to y=(q/qs)k.The real atmosphere is
neither absolutely dry nor completely saturated, therefore it is rational to
introduce the condensation probability function and further study the dynamic
and thermodynamic processes of the moist air.


### 2.2. The Conservation of GPT

In view of the small
changes of a closed system, the first law of thermodynamics can be expressed by(1)δU=δQ+δW,where δU is the increment of the internal energy for
the system, δQ is the heat which the system gains in the
process, and δW is the work done to the system. Applying the
equation of state, (1) can be written as(2)δU=TδS−pδV. Here, S is the entropy. Another form of (2) is(3)δH=TδS+Vδp, where H is the enthalpy of the system. Owing to (2)
and (3) involving the state equation, for whatever processes (irreversible or
reversible), (1)–(3) can satisfy the conditions. Considering the
reversible process, the following equation holds:(4)δQ=TδS,δW=−pδV.As to the
ideal gas per unit mass, its internal energy and enthalpy can be expressed by(5)U=cvT,(6)H=cvT+RT=cpT. Here, cv and cp=cv+R are the specific heat per unit mass at
constant volume and pressure, respectively. Suppose the change of cv has nothing to do with T.Equation (6) and V=1/ρ=RT/p are substituted into (3), thus(7)TδS=cpδT−RTpδp. On the both
sides of (7) multiplied by 1/T, we get(8)δS=cpTδT−Rpδp=cpδ(lnT)−Rδ(lnp). When the air
parcel becomes saturated, specific humidity q is equal to qs(T,p).
Suppose a vapor parcel is lifted with an increment of δz,
the change of saturated specific humidity is |δqs|=−δqs.
The related latent heat is(9)δQ=−Lδqs. In this
process, liquid water drops out of the air parcel and is not involved in the
course of heat balance. Under this assumption, it is a nonadiabatic process.
Comparing to the heat still left in the parcel, however the heat taken out by
liquid water can be ignored. Thus the process can be considered
pseudo-adiabatic [25].Based on the property of nonuniform
saturation, the latent heat release can be expressed as(10)δQ=−Lδ(qs·y).Furthermore, employing the
appropriate form ofy, it yields(11)δQ=−Lδ(qs·(qqs)k).Taking (4) into (8), we get(12)cpmδ(lnT)−Rvδ(lnp)=δQT=−Lδ(qs·(q/qs)k)T, where cpm is the specific heat of moist air under
constant pressure and Rv is the specific gas constant of vapor.From the curve change ofqs(T,p) based on the long-term observations (not
shown; see Zhao and Gao [26]), the inequality qs(q/qs)k≪100g·kg−1 holds under most temperature and pressure
conditions. Thus inequality Lqs·(q/qs)k/(cpmT)≪1 always holds. The right-hand term of (12) can
be approximately expressed as −δ(Lqs·(q/qs)k)/T.
The approximation can also be verified from the derivation of the GPT’s
conservation. Hence the following inequality always holds in real atmosphere:(13)qs·(qqs)k<qs. So the
assumption for introducing EPT is the sufficient conditions for inducing GPT.Moreover, ignoring the individual
change ofcpm,
(12) can be transformed into(14)δ(cpmlnT−Rvlnp+L(qs·(q/qs)k)T)=0. Integrating (14), taking exponential operation with the help of κ=Rv/cpm,
the following equation is obtained:(15)θ*(T,p)≡T(p0p)κexp(Lqs·(q/qs)kcpmT)=const, which is
conservative. Equation (15) can further be transformed into(16)θ*(T,p)=θ(T,p)exp(Lqs·(q/qs)kcpmT). Similar to
the deriving approach of the equation of PT, it is easy to obtain the one for
moist atmosphere:(17)cpmTθ*dθ*dt=Qd.From (17), a conclusion can be drawn
that GPT is also conserved in the moist adiabatic process. It should be pointed
out that all assumptions in deriving the GPT’s conservation are necessary
conditions for EPT’s conservation. From this point of view, in addition to its conservation,
GPT can manifest more accurately the variation of humidity for the real moist
atmosphere than EPT.


## 2.1. Physical Discussions of the Condensation Probability Function in Moist Atmosphere

On the basis of the molecular
statistics, if the specific humidity of the air isq,
the specific humidity of an infinitesimal part q′ probably does not equal q but follows a certain statistical distribution [24].
According to the observations, due to a large number of condensation nucleuses
in the air, some parts of the air condense (usually condensation starts as the
relative humidity (RH) reaches 76%) before the relative humidity is near 100%.
Commonly, the higher the value of RH is, the easier the vapor condenses, which
means the degree of condensation of vapor increases with the increasing
humidity. In order to apply this microphysical property of moist air to
weather analyses, it is reasonable to add a weighted function y into EPT without changing its
dimension, so a new parameter is derived as the form of θ*=θexp((L/CpT)qsy).
This weighted function y, indicating the coexistent feature of dry and moist
air, should satisfy the following conditions: y=0 in absolute dry air and y=1 in totally saturated moist air. Hence, based on the facts that the
condensation increases with the increasing humidity, y must be a dimensionless parameter but is associated with
humidity. In order to apply this theory into the synoptic system diagnosis and
approach, the form of power function y=(q/qs)k is adopted in our study. According to
the numerical simulation and data analysis [24], the condensation feature can
be perfectly described when k is settled
by 9. Obviously, there are many other forms of y in addition to y=(q/qs)k.The real atmosphere is
neither absolutely dry nor completely saturated, therefore it is rational to
introduce the condensation probability function and further study the dynamic
and thermodynamic processes of the moist air.


## 2.2. The Conservation of GPT

In view of the small
changes of a closed system, the first law of thermodynamics can be expressed by(1)δU=δQ+δW,where δU is the increment of the internal energy for
the system, δQ is the heat which the system gains in the
process, and δW is the work done to the system. Applying the
equation of state, (1) can be written as(2)δU=TδS−pδV. Here, S is the entropy. Another form of (2) is(3)δH=TδS+Vδp, where H is the enthalpy of the system. Owing to (2)
and (3) involving the state equation, for whatever processes (irreversible or
reversible), (1)–(3) can satisfy the conditions. Considering the
reversible process, the following equation holds:(4)δQ=TδS,δW=−pδV.As to the
ideal gas per unit mass, its internal energy and enthalpy can be expressed by(5)U=cvT,(6)H=cvT+RT=cpT. Here, cv and cp=cv+R are the specific heat per unit mass at
constant volume and pressure, respectively. Suppose the change of cv has nothing to do with T.Equation (6) and V=1/ρ=RT/p are substituted into (3), thus(7)TδS=cpδT−RTpδp. On the both
sides of (7) multiplied by 1/T, we get(8)δS=cpTδT−Rpδp=cpδ(lnT)−Rδ(lnp). When the air
parcel becomes saturated, specific humidity q is equal to qs(T,p).
Suppose a vapor parcel is lifted with an increment of δz,
the change of saturated specific humidity is |δqs|=−δqs.
The related latent heat is(9)δQ=−Lδqs. In this
process, liquid water drops out of the air parcel and is not involved in the
course of heat balance. Under this assumption, it is a nonadiabatic process.
Comparing to the heat still left in the parcel, however the heat taken out by
liquid water can be ignored. Thus the process can be considered
pseudo-adiabatic [25].Based on the property of nonuniform
saturation, the latent heat release can be expressed as(10)δQ=−Lδ(qs·y).Furthermore, employing the
appropriate form ofy, it yields(11)δQ=−Lδ(qs·(qqs)k).Taking (4) into (8), we get(12)cpmδ(lnT)−Rvδ(lnp)=δQT=−Lδ(qs·(q/qs)k)T, where cpm is the specific heat of moist air under
constant pressure and Rv is the specific gas constant of vapor.From the curve change ofqs(T,p) based on the long-term observations (not
shown; see Zhao and Gao [26]), the inequality qs(q/qs)k≪100g·kg−1 holds under most temperature and pressure
conditions. Thus inequality Lqs·(q/qs)k/(cpmT)≪1 always holds. The right-hand term of (12) can
be approximately expressed as −δ(Lqs·(q/qs)k)/T.
The approximation can also be verified from the derivation of the GPT’s
conservation. Hence the following inequality always holds in real atmosphere:(13)qs·(qqs)k<qs. So the
assumption for introducing EPT is the sufficient conditions for inducing GPT.Moreover, ignoring the individual
change ofcpm,
(12) can be transformed into(14)δ(cpmlnT−Rvlnp+L(qs·(q/qs)k)T)=0. Integrating (14), taking exponential operation with the help of κ=Rv/cpm,
the following equation is obtained:(15)θ*(T,p)≡T(p0p)κexp(Lqs·(q/qs)kcpmT)=const, which is
conservative. Equation (15) can further be transformed into(16)θ*(T,p)=θ(T,p)exp(Lqs·(q/qs)kcpmT). Similar to
the deriving approach of the equation of PT, it is easy to obtain the one for
moist atmosphere:(17)cpmTθ*dθ*dt=Qd.From (17), a conclusion can be drawn
that GPT is also conserved in the moist adiabatic process. It should be pointed
out that all assumptions in deriving the GPT’s conservation are necessary
conditions for EPT’s conservation. From this point of view, in addition to its conservation,
GPT can manifest more accurately the variation of humidity for the real moist
atmosphere than EPT.


## 3. The Comparison of the Distribution for EPT and GPT in Heavy Rainstorm

Recently Gao et al. [22] derived the
generalized potential vorticity (GPV) with GPT and diagnosed heat wave
weathers during the summer seasons in Beijing.
However they have not yet further applied them to analyze torrential rain
events. In this paper, we intend to diagnose GPT’s distribution within various
heavy rain storms and show that GPT has evident advantages over EPT.


### 3.1. The Distribution of EPT and GPT in Yangtze River and Huaihe River Basin Torrential Rains

The Meiyu is a typical weather
phenomenon along the Yangtze River and Huaihe River basins
during the early summer season. The comparison of the distribution for EPT and
GPT will be made within these Meiyu frontal rainstorms. In late June and middle
July, 2003, strong rainstorm and flood disaster occurred in Yangtze
River and Huaihe River basins. The onset of Meiyu was on 21st June and the outset on 22nd July. The precipitation mainly occurred
during two periods, one from 21st to 28th June when the
rainfall was almost concentrated in the Yangtze River basin with a center at the middle
Yangtze River, and the other lasting from 29th June to 11th July when the extensive rainbelt was located at Huaihe River basin.
Detailed surface precipitation observations can be found in Zhou et al. [27]. We
focus on the second period here.Figure1 shows the distributions of
averaged EPT and GPT at 850 hPa from 29 June to 11 July 2003. Over mainland China,
PT is generally smooth and shows weak spatial gradient (Figure omitted). As PT
does not include the vapor term, the expected band of vapor gradient associated
with the Meiyu front cannot be seen. From Figure 1(a), a large gradient zone of EPT elongates from 30° to 33°N, apparently indicating the feature of vapor gradient across the
Meiyu front. But the region of high humidity, due to the moisture
transportation by the southwest monsoon, is located in the south side of Meiyu
front. In Figure 1(b), the high-value regions of GPT and its strong gradient are
located to the south of 33°N from Japan to the Bay of Bengal,
which results from the inclusion of specific humidity. No matter how much vapor
the atmosphere contains, the content of moisture is surly to be imaged with
GPT. So GPT tends to show advantages over EPT.Distributions of the
averaged (a) EPT and (b) GPT at 850 hPa from 29th June to 11th July in 2003
(unit in K; isoline interval of EPT and GPT: 2; isoline interval of RH: 10%). The
blank zone is the Tibetan Plateau.
(a)(b)Seen from the meridional
cross-section (Figure2), the distinct gradient of EPT (Figure 2(a)) lies in the region north of 33°N, which is the
confluence zone of the warm and moist air from southwest as well as the dry and
cold air from the north, forming the famous Meiyu front in early summer in East Asia. Similar to EPT, two narrow dense zones of GPT
isopleths with large vapor gradient exist near the position at 30°N and 33°N, respectively, but the gradient is much larger than that of EPT,
which implies plentiful water vapor content concentrated between these two
large moist gradient zones. According to the RH isopleths (the dashed lines in Figure 2(b)),
the large value zones of GPT gradient coincide well with the regions of RH up
to 80%, and GPT’s gradients coincide with those of RH well than EPT’s, indicating
that the expression of GPT involving the moist vapor humidity could reflect the
feature of moisture concentration better than EPT during the Meiyu period. Similarities
can be found in the Meiyu frontal rainstorms in the Yangtze River basin in 1998 and 1999 as well
as the one in the Huaihe River basin
in 2007. The
observations also indicate that the RH can hardly reach 100%, even in the
flooding. So the introduction of GPT for the moist air is capable of describing
the distribution of vapor  and  thermodynamic  property of real atmosphere.Meridional
cross-sections of the averaged (a) EPT and (b) GPT (solid line) and RH (dashed
line) along 115°E from 29th June to 11th
July in 2003 (unit in K; the intervals: 2, 3, resp.; the interval of
RH: 10%).
(a)(b)


### 3.2. The Distribution of EPT and GPT in the Torrential Rain of North China and in a Typhoon Fung-Wong in 2008

The above cases show the contrast
among EPT for saturated moist air and GPT for moist atmosphere during the Meiyu
period. China
is also often experiencing high-frequent and wide-range torrential rains, so it
is necessary to make a comparison with other forms of rainstorms. The heavy
rainfall occurring in North China in
August 2004 and Typhoon Fung-wong in 2008 is taken as examples. From 11th to 13th August 2004, a heavy rain occurred in North
China. Several past studies have simulated and analyzed this event [26].
We thus here only focus on the distributions of these three variables during
the event.An obvious wet trough with the
southwest to northeast orientation can also be discerned in Figure3(a). This trough corresponds to the
high-value zone of EPT, indicating that the moisture is transported into the
rainfall zone, and the gradient of EPT is accordant with that of RH.  For the distribution of GPT, in addition to
the coincidence between the two dense gradient zones of GPT (solid line in Figure 3(b))
and RH (dashed line in Figure 3(b)), the southwest-northeast moist trough is also
apparent. The center of large values of GPT occurred with RH higher than 90%, which
is much clearer than that of EPT. The more significant center and gradients in
both sides of the rainbelt for GPT suggest the existence of high moisture
concentration.Distributions of
(a) EPT and (b) GPT (solid line) and RH (dashed line) at 700 hPa on 12UTC August
2004 (unit in K; the intervals: 4, 4, resp.; the interval of RH: 10%).
(a)(b)From the meridional cross
sections, similar to Figure3, a wedge shaped the distribution of EPT from the
upper to middle levels, a sign of abundant latent heat release through the
whole atmospheric layer (Figure 4(a)).
Obviously, to the north of 38°N (the south side of the
strong rainfall region), the EPT values in the mid-lower levels are higher than
those north of 42°N, and the EPT gradient in
the north and south rainfall zones coincides with the zone of moisture gradient
(dashed lines in Figure 4(b)). For the GPT, its isolines extend from the upper to
lower air in the heavy rain zones, indicating plentiful water vapor above the rain
region. Furthermore, the high-value GPT center overlaps with the high RH center,
which is up to 90%. And the large value center of GPT is much narrower than
that of EPT. Comparing Figure 4(a)
with Figure 4(b), the EPT above the
heavy rainfall zones (34~37°N) does not reveal a dry region with RH
lower than 20%. The EPT isolines stretch northward and downward, while the GPT
isolines stretch downward in the south of the dry regions and then northward,
finally forming a small ridge extending to the downside and a weak trough of
GPT occurring in the region that RH is smaller than 20%. The spatial
distribution of GPT is much closer to the distribution of water vapor than EPT.Meridional
cross-sections of (a) EPT and (b) GPT (solid line) and RH (dashed line) along 117°E at 12UTC 12th August 2004 (unit in K;
the intervals: 2, 4, resp.; the interval of RH: 10%).
(a)(b)The above analysis is on a heavy
rainfall event occurring in North China. In
the following, the features of Typhoon Fung-wong with plenty of water vapor are
discussed in detail. As the first strong typhoon landed in China
in 2008, Fung-wong
is special for its large size, large-range influence, and high water vapor
content. Particularly it had an imbalanced shape with clouds primarily seen in the
south of the center during its early stage. The thick clouds were always
located at its southeastern quadrant, accompanied by plenty of water vapor
supply, inducing torrential rain with high intensity, large scopes, and
long-time influence.At 14UTC on July
25th, 2008, formed over the east ocean of Philippines, Fung-wong moved westward.
Subsequently, it evolved into a severe tropical storm at 08UTC
on 26th and into a typhoon at 20UTC on 27th. After landing
over the Hualian area of Taiwan
at 0630UTC 26th, Fung-wong continued to move northwestward. At 22UTC
28th, it landed at the town of Donghan in Fuqing city of Fujian
Province again with the central pressure of 975 hPa and the central maximum wind
speed of nearly 33 m s-1 (12-grade), and then moved northwestward but decreased gradually. In the
afternoon of 30th, it weakened into a tropical storm depression in
the northwest of Jiangxi
Province with its center shifting
southwestward slowly and passing through the southeast of Anhui  Province. Fung-wong caused heavy
precipitation and flooding in the southeastern coastal region of southern China as well as Jiangxi  Province. From the isobaric chart at 850 hPa
at 00UTC 28th July, the wind field of Fung-wong (the center located around
23°N, 121°E) had an asymmetrical structure (Figure
5(a)), and the high wind
zones, surrounded by abundant water vapor, were situated in its south, east, and
north parts. At the same time the RH over the west Pacific
Ocean is up to 90%. Moreover, the high-value region of RH within
Fung-wong reached 100%. This asymmetrical structure cannot be seen in PT because PT had a relatively smooth structure (Figure 5(b)). As to
the EPT (Figure 5(c)),
the thermodynamic asymmetrical structure of Fung-wong circulation is evident.
The southeastern part of Fung-wong corresponds to the high-value zones of EPT
(reflecting the high-humidity center), which is also the high-value areas of
the EPT gradient, while the central region of Fung-wong is relatively dry. Figure
5(d) shows much denser isopleths for GPT reaching its maximum and high gradient
in the region of RH up to 90%, which indicates that the gradient of GPT is larger
than that of EPT. Considering that the thermodynamic circulation reveals the
most clearest in the GPT distribution and the GPT’s high-value zones overlap
the region of RH up to 90%, the conclusion can be drawn that GPT not only
is able to reflect the thermodynamic structure but also has advantage over PT and
EPT in showing the distribution of water vapor fields.Distributions of (a)
wind field (solid: velocity, arrows: wind vector, unit in m s-1), (b) PT (solid
line) and RH (dashed line), (c) EPT, and (d) GPT at 850 hPa at 00UTC 28th July in
2008 (unit in K; the intervals: 2, 2, 4, resp.; the interval of RH: 10%).
(a)(b)(c)(d)The meridional cross-section (Figure6)
further indicates that water vapor around the eyewall is plentiful from lower
levels up to higher levels, with RH reaching above 90% from sea surface to above
350 hPa (dashed line in Figure 6(b)). However, RH near the central of the typhoon is smaller
than that of eyewall, about 80%, which shows that water vapor content is convergent
around the eyewall but it is relatively dry in eyewall, consisting with a general
distribution of moisture for typhoon. Since EPT includes the water vapor term,
the isopleths around the eyewall of the typhoon form a steep shape, the
convective instability zones stretch up to 650 hPa, and EPT has a V-shape
pattern from higher levels downward to 800 hPa near the center of typhoon (Figure 6(a)).
Compared to the steep GPT isolines (Figure 6(b)), the instability regions is as
clear as the EPT’s, but the gradient for EPT is not so large as the GPT’s.
Moreover, accompanying the two gradients bands for GPT, the maximum zone
overlaps with the highest water vapor values of the typhoon eyewall at 900 hPa
levels. The gradient belt for GPT is more obvious than EPT’s at the regions
that RH is over 90%, that is, the two regions from 17~20°N and
25~27°N in Figure 6(b).Distribution of (a)
EPT and (b) GPT (solid line) and RH (dashed line) along 121°E at 00UTC 28th July 2008 (unit in K; the
intervals: 2, 4, resp.; the interval of RH: 10%).
(a)(b)From the heavy Meiyu front rainfall
of Yangtze River and Huaihe River basin to North China rainstorm and to the typhoon Fung-wong, the comparisons of the EPT and GPT
distributions indicate that the GPT is able to reflect the effects of moisture
and water vapor gradient better than EPT.


## 3.1. The Distribution of EPT and GPT in Yangtze River and Huaihe River Basin Torrential Rains

The Meiyu is a typical weather
phenomenon along the Yangtze River and Huaihe River basins
during the early summer season. The comparison of the distribution for EPT and
GPT will be made within these Meiyu frontal rainstorms. In late June and middle
July, 2003, strong rainstorm and flood disaster occurred in Yangtze
River and Huaihe River basins. The onset of Meiyu was on 21st June and the outset on 22nd July. The precipitation mainly occurred
during two periods, one from 21st to 28th June when the
rainfall was almost concentrated in the Yangtze River basin with a center at the middle
Yangtze River, and the other lasting from 29th June to 11th July when the extensive rainbelt was located at Huaihe River basin.
Detailed surface precipitation observations can be found in Zhou et al. [27]. We
focus on the second period here.Figure1 shows the distributions of
averaged EPT and GPT at 850 hPa from 29 June to 11 July 2003. Over mainland China,
PT is generally smooth and shows weak spatial gradient (Figure omitted). As PT
does not include the vapor term, the expected band of vapor gradient associated
with the Meiyu front cannot be seen. From Figure 1(a), a large gradient zone of EPT elongates from 30° to 33°N, apparently indicating the feature of vapor gradient across the
Meiyu front. But the region of high humidity, due to the moisture
transportation by the southwest monsoon, is located in the south side of Meiyu
front. In Figure 1(b), the high-value regions of GPT and its strong gradient are
located to the south of 33°N from Japan to the Bay of Bengal,
which results from the inclusion of specific humidity. No matter how much vapor
the atmosphere contains, the content of moisture is surly to be imaged with
GPT. So GPT tends to show advantages over EPT.Distributions of the
averaged (a) EPT and (b) GPT at 850 hPa from 29th June to 11th July in 2003
(unit in K; isoline interval of EPT and GPT: 2; isoline interval of RH: 10%). The
blank zone is the Tibetan Plateau.
(a)(b)Seen from the meridional
cross-section (Figure2), the distinct gradient of EPT (Figure 2(a)) lies in the region north of 33°N, which is the
confluence zone of the warm and moist air from southwest as well as the dry and
cold air from the north, forming the famous Meiyu front in early summer in East Asia. Similar to EPT, two narrow dense zones of GPT
isopleths with large vapor gradient exist near the position at 30°N and 33°N, respectively, but the gradient is much larger than that of EPT,
which implies plentiful water vapor content concentrated between these two
large moist gradient zones. According to the RH isopleths (the dashed lines in Figure 2(b)),
the large value zones of GPT gradient coincide well with the regions of RH up
to 80%, and GPT’s gradients coincide with those of RH well than EPT’s, indicating
that the expression of GPT involving the moist vapor humidity could reflect the
feature of moisture concentration better than EPT during the Meiyu period. Similarities
can be found in the Meiyu frontal rainstorms in the Yangtze River basin in 1998 and 1999 as well
as the one in the Huaihe River basin
in 2007. The
observations also indicate that the RH can hardly reach 100%, even in the
flooding. So the introduction of GPT for the moist air is capable of describing
the distribution of vapor  and  thermodynamic  property of real atmosphere.Meridional
cross-sections of the averaged (a) EPT and (b) GPT (solid line) and RH (dashed
line) along 115°E from 29th June to 11th
July in 2003 (unit in K; the intervals: 2, 3, resp.; the interval of
RH: 10%).
(a)(b)


## 3.2. The Distribution of EPT and GPT in the Torrential Rain of North China and in a Typhoon Fung-Wong in 2008

The above cases show the contrast
among EPT for saturated moist air and GPT for moist atmosphere during the Meiyu
period. China
is also often experiencing high-frequent and wide-range torrential rains, so it
is necessary to make a comparison with other forms of rainstorms. The heavy
rainfall occurring in North China in
August 2004 and Typhoon Fung-wong in 2008 is taken as examples. From 11th to 13th August 2004, a heavy rain occurred in North
China. Several past studies have simulated and analyzed this event [26].
We thus here only focus on the distributions of these three variables during
the event.An obvious wet trough with the
southwest to northeast orientation can also be discerned in Figure3(a). This trough corresponds to the
high-value zone of EPT, indicating that the moisture is transported into the
rainfall zone, and the gradient of EPT is accordant with that of RH.  For the distribution of GPT, in addition to
the coincidence between the two dense gradient zones of GPT (solid line in Figure 3(b))
and RH (dashed line in Figure 3(b)), the southwest-northeast moist trough is also
apparent. The center of large values of GPT occurred with RH higher than 90%, which
is much clearer than that of EPT. The more significant center and gradients in
both sides of the rainbelt for GPT suggest the existence of high moisture
concentration.Distributions of
(a) EPT and (b) GPT (solid line) and RH (dashed line) at 700 hPa on 12UTC August
2004 (unit in K; the intervals: 4, 4, resp.; the interval of RH: 10%).
(a)(b)From the meridional cross
sections, similar to Figure3, a wedge shaped the distribution of EPT from the
upper to middle levels, a sign of abundant latent heat release through the
whole atmospheric layer (Figure 4(a)).
Obviously, to the north of 38°N (the south side of the
strong rainfall region), the EPT values in the mid-lower levels are higher than
those north of 42°N, and the EPT gradient in
the north and south rainfall zones coincides with the zone of moisture gradient
(dashed lines in Figure 4(b)). For the GPT, its isolines extend from the upper to
lower air in the heavy rain zones, indicating plentiful water vapor above the rain
region. Furthermore, the high-value GPT center overlaps with the high RH center,
which is up to 90%. And the large value center of GPT is much narrower than
that of EPT. Comparing Figure 4(a)
with Figure 4(b), the EPT above the
heavy rainfall zones (34~37°N) does not reveal a dry region with RH
lower than 20%. The EPT isolines stretch northward and downward, while the GPT
isolines stretch downward in the south of the dry regions and then northward,
finally forming a small ridge extending to the downside and a weak trough of
GPT occurring in the region that RH is smaller than 20%. The spatial
distribution of GPT is much closer to the distribution of water vapor than EPT.Meridional
cross-sections of (a) EPT and (b) GPT (solid line) and RH (dashed line) along 117°E at 12UTC 12th August 2004 (unit in K;
the intervals: 2, 4, resp.; the interval of RH: 10%).
(a)(b)The above analysis is on a heavy
rainfall event occurring in North China. In
the following, the features of Typhoon Fung-wong with plenty of water vapor are
discussed in detail. As the first strong typhoon landed in China
in 2008, Fung-wong
is special for its large size, large-range influence, and high water vapor
content. Particularly it had an imbalanced shape with clouds primarily seen in the
south of the center during its early stage. The thick clouds were always
located at its southeastern quadrant, accompanied by plenty of water vapor
supply, inducing torrential rain with high intensity, large scopes, and
long-time influence.At 14UTC on July
25th, 2008, formed over the east ocean of Philippines, Fung-wong moved westward.
Subsequently, it evolved into a severe tropical storm at 08UTC
on 26th and into a typhoon at 20UTC on 27th. After landing
over the Hualian area of Taiwan
at 0630UTC 26th, Fung-wong continued to move northwestward. At 22UTC
28th, it landed at the town of Donghan in Fuqing city of Fujian
Province again with the central pressure of 975 hPa and the central maximum wind
speed of nearly 33 m s-1 (12-grade), and then moved northwestward but decreased gradually. In the
afternoon of 30th, it weakened into a tropical storm depression in
the northwest of Jiangxi
Province with its center shifting
southwestward slowly and passing through the southeast of Anhui  Province. Fung-wong caused heavy
precipitation and flooding in the southeastern coastal region of southern China as well as Jiangxi  Province. From the isobaric chart at 850 hPa
at 00UTC 28th July, the wind field of Fung-wong (the center located around
23°N, 121°E) had an asymmetrical structure (Figure
5(a)), and the high wind
zones, surrounded by abundant water vapor, were situated in its south, east, and
north parts. At the same time the RH over the west Pacific
Ocean is up to 90%. Moreover, the high-value region of RH within
Fung-wong reached 100%. This asymmetrical structure cannot be seen in PT because PT had a relatively smooth structure (Figure 5(b)). As to
the EPT (Figure 5(c)),
the thermodynamic asymmetrical structure of Fung-wong circulation is evident.
The southeastern part of Fung-wong corresponds to the high-value zones of EPT
(reflecting the high-humidity center), which is also the high-value areas of
the EPT gradient, while the central region of Fung-wong is relatively dry. Figure
5(d) shows much denser isopleths for GPT reaching its maximum and high gradient
in the region of RH up to 90%, which indicates that the gradient of GPT is larger
than that of EPT. Considering that the thermodynamic circulation reveals the
most clearest in the GPT distribution and the GPT’s high-value zones overlap
the region of RH up to 90%, the conclusion can be drawn that GPT not only
is able to reflect the thermodynamic structure but also has advantage over PT and
EPT in showing the distribution of water vapor fields.Distributions of (a)
wind field (solid: velocity, arrows: wind vector, unit in m s-1), (b) PT (solid
line) and RH (dashed line), (c) EPT, and (d) GPT at 850 hPa at 00UTC 28th July in
2008 (unit in K; the intervals: 2, 2, 4, resp.; the interval of RH: 10%).
(a)(b)(c)(d)The meridional cross-section (Figure6)
further indicates that water vapor around the eyewall is plentiful from lower
levels up to higher levels, with RH reaching above 90% from sea surface to above
350 hPa (dashed line in Figure 6(b)). However, RH near the central of the typhoon is smaller
than that of eyewall, about 80%, which shows that water vapor content is convergent
around the eyewall but it is relatively dry in eyewall, consisting with a general
distribution of moisture for typhoon. Since EPT includes the water vapor term,
the isopleths around the eyewall of the typhoon form a steep shape, the
convective instability zones stretch up to 650 hPa, and EPT has a V-shape
pattern from higher levels downward to 800 hPa near the center of typhoon (Figure 6(a)).
Compared to the steep GPT isolines (Figure 6(b)), the instability regions is as
clear as the EPT’s, but the gradient for EPT is not so large as the GPT’s.
Moreover, accompanying the two gradients bands for GPT, the maximum zone
overlaps with the highest water vapor values of the typhoon eyewall at 900 hPa
levels. The gradient belt for GPT is more obvious than EPT’s at the regions
that RH is over 90%, that is, the two regions from 17~20°N and
25~27°N in Figure 6(b).Distribution of (a)
EPT and (b) GPT (solid line) and RH (dashed line) along 121°E at 00UTC 28th July 2008 (unit in K; the
intervals: 2, 4, resp.; the interval of RH: 10%).
(a)(b)From the heavy Meiyu front rainfall
of Yangtze River and Huaihe River basin to North China rainstorm and to the typhoon Fung-wong, the comparisons of the EPT and GPT
distributions indicate that the GPT is able to reflect the effects of moisture
and water vapor gradient better than EPT.


## 4. Conclusion

A further exploration of the
properties and application of the GPT introduced by Gao et al.  [7] is carried
out in this paper. The physical significance of the condensation probability
function invoked in the definition of GPT is discussed, including the derivation
of the conservation property of GPT for the nonuniformly saturated atmosphere,
tending to enhance GPT’s theoretical basis for the moist atmosphere. In the
real atmosphere, the air changes from dry state to moist and then to saturated.
The introduction of GPT can exactly describe this process. Furthermore GPT can conveniently be
applied in the operational analyses of synoptic system. The different
distributions among EPT and GPT are compared and analyzed during the periods of
Mei-yu heavy rainfall, North China rainfall,
and typhoon Fung-wong. The diagnosis results show that GPT, compared with EPT,
can manifest the effects of moist concentration and moist gradient more
efficiently in heavy rain events. Meanwhile, similar to the EPT in saturated
air, GPT is conserved in the moist atmosphere. So like EPT, it can be widely
used in studying the dynamic and thermodynamic properties of moist atmosphere
in the future.



---

*Source: 105265-2009-05-06.xml*