Abstract

The monsoon circulation, which is generally considered to be driven by the landmass–ocean thermal contrast, like a gigantic land–sea breeze circulation, exhibits a phase reversal in its vertical structure; a monsoon high aloft over a continental thermal low is juxtaposed with a midoceanic trough underlaid by an oceanic anticyclone. This classic monsoon circulation model is well matched by the monsoon circulation depicted with the observational data prior to the First Global Atmospheric Research Program (GARP) Global Experiment (FGGE). However, synthesizing findings of the global circulation portrayed with the post-FGGE data, it was found that some basic features of major monsoon circulations in Asia, North America, South America, and Australia differ from those of the classic monsoon circulation model. Therefore, a revision of the classic monsoon theory is suggested. With four different wave regimes selected to fit the horizontal dimensions of these monsoon circulations, basic features common to all four major monsoons are illustrated in terms of diagnostic analyses of the velocity potential maintenance equation (which relates diabatic heating and velocity potential) and the streamfunction budget (which links velocity potential and streamfunction) in these wave regimes. It is shown that a monsoon circulation is actually driven by the east–west differential heating and maintained dynamically by a balance between a vorticity source and advection. This dynamic balance is reflected by a spatial quadrature relationship between the monsoon divergent circulation and the monsoon high (low) at upper (lower) levels.

1. Introduction

Because a landmass has a lower heat capacity than water, a continent warms up more rapidly during the summer by radiative heating than the adjacent ocean. This land–ocean differential heating may be able to maintain the warm-air ascending motion over the continent and the cold-air descending motion over the ocean. A secondary circulation is consequently established by these vertical motions coupled with a landward motion in the lower troposphere and a sea-bound return flow at upper levels. The low-level cross-isobar flow, which is directed towards low pressure over the continent, induces motions parallel to the isobars through the Coriolis force to form the cyclonic motion around the continental thermal low and convergence of moisture that maintains cumulus convection. The ascending motion over this thermal low produces divergence at upper levels where anticyclonic flows are generated. Three basic ingredients are included in this commonly accepted maintenance mechanism of a summer monsoon circulation (e.g., Wallace and Hobbs 1977; Holton 1992): 1) the land–ocean differential heating, 2) a monsoon high (oceanic trough) at upper levels and a thermal low (anticyclone) over the continent (ocean) at lower levels, and 3) the coincidence of a monsoon high (thermal low) with a divergent (convergent) center. A schematic diagram of the classic monsoon circulation model formed by these features is presented in Fig. 1.

Fig. 1.

An idealized summer monsoon circulation depicted by Wallace and Hobbs (1977). Tropical continents are represented by islands, while the high (H) and low (L) systems near sea level (lower plane) and 200 mb (upper plane) are portrayed by geopotential contours. Cross-isobar divergent (convergent) flows (short arrows) and vertical motions in the midtroposphere (vertical arrows)

Fig. 1.

An idealized summer monsoon circulation depicted by Wallace and Hobbs (1977). Tropical continents are represented by islands, while the high (H) and low (L) systems near sea level (lower plane) and 200 mb (upper plane) are portrayed by geopotential contours. Cross-isobar divergent (convergent) flows (short arrows) and vertical motions in the midtroposphere (vertical arrows)

The summer monsoon system portrayed by the observational data prior to the First Global Atmospheric Research Program (GARP) Global Experiment (FGGE) within the context of the global tropical circulation (e.g., Krishnamurti 1971a,b; Krishnamurti et al. 1973) is well reflected by the schematic circulation in Fig. 1. Based on the third feature of the classic monsoon circulation theory, Holton and Colton (1972) and Virji (1982) pointed out that the monsoon anticyclone can not be maintained by a simple Sverdrup balance between stretching and advection of planetary vorticity. A subgrid-scale convection process should be included to reach a vorticity budget balance. However, due to improvements of observations over oceans and data assimilation systems during and after the FGGE, a spatial quadrature relationship emerges from the monsoon anticyclone and the monsoon divergent circulation (delineated by velocity potential) in the post-FGGE assimilated data (e.g., Hoskins et al. 1989; Schubert et al. 1990). It seems that the maintenance of a monsoon anticyclone can be elucidated by a Sverdrup balance with the post-FGGE data. The monsoon climate variability constitutes one of the major themes in the Climate Variability and Predictability (CLIVAR) Program (WCRP 1998). Undoubtedly, a basic prerequisite to the success of the research initiative in the monsoon climate variability is an accurate maintenance mechanism of the monsoon circulation. Thus, revisiting the classic monsoon maintenance theory with the recent assimilation data is needed.

An effort is undertaken by this study to explore the maintenance mechanism of four major monsoon systems in Asia, North America, South America, and Australia with the National Centers for Environmental Prediction–National Center for Atmospheric Research (NCEP–NCAR) reanalysis data (Kalnay et al. 1996). The West African monsoon is not included in this study because this monsoon's vertical development is limited by the midtropospheric Saharan high (Rodwell and Hoskins 1996). Shown by our analysis, monsoon circulations over these regions are basically driven by the east–west differential heating and maintained by a Sverdrup balance. A revision of the classic monsoon maintenance mechanism is therefore suggested. The purpose of this study is to report results of our analysis and the revision of this maintenance mechanism. For this purpose, this paper is organized in the following manner. An overview of the global monsoon system depicted with the prior (post) FGGE data and the NCEP–NCAR reanalysis is presented in section 2. The diagnostic scheme and the data used to examine the maintenance mechanism of major monsoons are described in section 3. The next two sections are devoted to the analysis of two major monsoon systems in the Northern Hemisphere and another two in the Southern Hemisphere. Finally, concluding remarks are given in section 6.

2. Summer monsoon circulations

Some salient features of summer monsoon circulations pertaining to the present study were observed by previous studies, which analyzed either the prior- or post FGGE data. These circulation features will be briefly highlighted in support of the need to revise the classic monsoon circulation theory.

a. Prior (post) FGGE

Using extensive data collected at 200 mb for the 1967 summer, Krishnamurti (1971a,b) portrayed the global tropical circulation in terms of streamfunction and velocity potential. The Tibetan high, represented by a 200-mb streamfunction center, coincides with a divergent center indicated by a 200-mb velocity potential maximum. That is, centers of vorticity and divergence over the Tibetan region are out of phase. Evidently, the Tibetan anticyclone cannot be maintained by a Sverdrup balance (between advection and stretching of planetary vorticity). To obtain a proper simulation of this monsoon high, Holton and Colton (1972) incorporated a subgrid-scale dissipation in their diagnostic model. In contrast, a spatial quadrature relationship appears during the summer season in the upper-level streamfunction and velocity potential of the European Centre for Medium-Range Weather Forecasts (ECMWF) analyzed data (Hoskins et al. 1989; Schubert et al. 1990). An east–west circulation maintained by the North African cooling and the western Pacific–Asian monsoon heating may be inferred from the global ω (500 mb) and vertically integrated diabatic heating fields prepared by Hoskins (1996). The juxtaposition of the Tibetan anticyclone with ascending motions to its east and descending motions to its west agrees dynamically with the spatial quadrature relationship between this monsoon high and the velocity potential, required by the Sverdrup balance.

The North American monsoon circulation including an upper-level monsoon anticyclone and a lower-level thermal monsoon low centered over northwest Mexico (e.g., Higgins et al. 1997) is driven by the land–sea thermal contrast (Barlow et al. 1998). As revealed by Krishnamurti's (1971b) depiction of the global tropical circulation, the North American monsoon anticyclone coincides with a divergent center. On the other hand, it is inferred from Hoskins' (1996) global ω (500 mb) and diabatic heating that there is an east–west circulation across the North American monsoon region maintained by the eastern North Pacific cooling and the western North Atlantic–southwest United States heating. The juxtaposition of the North American monsoon anticyclone with ascending motions to its east and descending motions to its west resembles the relationship between the Tibetan anticyclone and the east–west circulation of the Asian monsoon.

Krishnamurti et al. (1973) extended the depiction of the global tropical circulation to include the 1969 northern winter. The upper-level Australian monsoon in the tropical circulation comprises a dipole of monsoon highs (one on each side of the equator) coupled with a divergent center located over Indonesia. This upper-level monsoon dipole is overlaid by a dipole of low-level monsoon lows shown by Sumi and Murakami (1981) with the FGGE data. Based on Gill's (1980) symmetric solution with respect to the equator, Chen et al. (1989) argued that the Australian monsoon circulation is maintained by the diabatic heating over the ocean east of Australia. Actually, the Australian monsoon's high and low are spatially in quadrature with the monsoon divergent circulation, which is maintained by a heating center to the east and a cooling center to the west of Australia. This east–west differential heating is consistent with Gunn et al.'s (1989) low-value outgoing longwave radiation (OLR; ≤220 W m−2) centers observed during the Bureau of Meteorology Research Centre (BMRC) Australian Monsoon Experiment (AMEX) and diabatic heating centers of Hoskins et al. (1989) and McBride (1998).

For the tropical South American monsoon, the Bolivian high–south Atlantic trough (Nordeste low) system, shown in Krishnamurti et al.'s (1973) tropical circulation, is in phase with the divergent and convergent centers across this monsoon region. Analyzing cloud winds, Virji (1981) reconfirmed this in-phase relationship between the Bolivian high and the divergent center. Handicapped by the same difficulty of Holton and Colton (1972), Virji (1982) introduced a subgrid-scaled process to balance the vorticity budget over tropical South America. In contrast, using the Goddard Earth Observing System (GEOS)-1 data (Schubert et al. 1993), Lenters and Cook (1997) was able to identify a quadrature relationship between the Bolivian high and the tropical South American divergent circulation, which is maintained by the eastern south Pacific cooling and the tropical South American heating. Later, based on this differential heating, Chen et al. (1999) substantiated this quadrature relationship through the Sverdrup balance.

In summary, the monsoon anticyclone and the monsoon divergent circulation depicted by the prior-FGGE data are spatially in phase, while those with the post-FGGE data are in quadrature. This disparity in the spatial relationship will be confirmed with the NCEP–NCAR reanalyses.

b. NCEP–NCAR reanalyses

Three major monsoon highs (Tibetan, North American, and North African) in the Northern Hemisphere summer (Krishnamurti 1971b) are clearly seen in the 200-mb streamline superimposed on the charts of the Climate Prediction Center (CPC) Merged Analysis of Precipitation (CMAP) rainfall (Fig. 2a), although the first and last one almost merge together. The North American high and the Tibet–North Africa anticyclone are separated by two midoceanic troughs (thick-dashed lines in Fig. 2a) over the North Pacific and North Atlantic. The monsoonal characteristics of a tropical circulation are reflected by a phase reversal in its vertical structure (White 1982). Two oceanic anticyclones reside below the two midocean troughs, as expected. Aligned with the oceanic anticyclones are the Indian monsoon trough, the North American thermal low, and the Saharan heat low over the three tropical continents (Fig. 2b) with the three upper-level anticyclones aloft.

Fig. 2.

Streamline charts superimposed with CMAP rainfall (shaded areas) (Xie and Arkin 1997) during the northern summer (JJA) at (a) 200 mb and (b) 850 mb, and the southern summer (JF) at (c) 200 mb and (d) 850 mb. The Australian monsoon onset occurs in late Dec (McBride 1987) while the Bolivian high reaches its maximum intensity in Jan (Chen et al. 1999). We use the 2-month (Jan–Feb) mean fields to portray the Southern Hemisphere summer circulation

Fig. 2.

Streamline charts superimposed with CMAP rainfall (shaded areas) (Xie and Arkin 1997) during the northern summer (JJA) at (a) 200 mb and (b) 850 mb, and the southern summer (JF) at (c) 200 mb and (d) 850 mb. The Australian monsoon onset occurs in late Dec (McBride 1987) while the Bolivian high reaches its maximum intensity in Jan (Chen et al. 1999). We use the 2-month (Jan–Feb) mean fields to portray the Southern Hemisphere summer circulation

During the southern summer, the upper-level anticyclones (Australian, Bolivian, and south African) appear over three tropical continents in the Southern Hemisphere (Fig. 2c). These anticyclones are separated by three distinct midocean troughs (thick-dashed lines in Fig. 2c) over the South Pacific, the South Atlantic trough, and the Indian Ocean (Krishnamurti et al. 1973). Corresponding to the first two upper-level anticyclones are the Australian monsoon trough and the Chaco low east of the Andes (Satyamurty et al. 1998) (Fig. 2d). Underneath the south African high, a major surface low system similar to other major monsoons is absent, but there is a T-shape intersection between the east–west-oriented inter-ocean convergence and the north–south-oriented intertropical convergence zone (van Heerden and Taljaard 1998).

Except for the West African monsoon, some common features emerge from these monsoon circulations: 1) the monsoon consists of an upper-level anticyclone and a low-level thermal low, and 2) the upper-level anticyclones are separated by midocean troughs, while the low-level thermal lows are divided by oceanic anticyclones. These features are consistent with those portrayed by the schematic summer monsoon circulation in Fig. 1.

Figure 3 shows the global divergent circulations in the upper and lower troposphere, (χ, VD) (200 mb) and (χ, VD) (850 mb), superimposed with diabatic heating/cooling (which is computed by the residual method of the thermodynamic equation presented in section 3). The heating centers in the northern summer (Fig. 3a) match well with the upper-level divergent centers over the western tropical Pacific and Atlantic, and tropical Africa, while the cooling centers coincide with convergent centers over the eastern tropical Pacific and Atlantic, and North Africa. It is inferred from this contrast that divergent circulation is driven by the diabatic heating. These upper-level divergent (convergent) centers are coupled with corresponding centers of opposite polarity in the low-level divergent circulation (Fig. 3b). The overhead sun migrates to the Southern Hemisphere in the southern summer and so do the diabatic heating centers and corresponding centers of divergent circulation. Thus, upper-level divergent centers agree with diabatic heating centers over the western tropical Pacific, eastern South America, and the Indian Ocean (Fig. 3c), while convergent centers correspond to the cooling centers over the southeast Indian Ocean, the tropical South Atlantic, and the eastern subtropical Pacific. Like northern summer, centers of the low-level divergent circulation with opposite polarity to their upper-level counterparts stand out in Fig. 3d.

Fig. 3.

Divergent circulation (χ, VD) superimposed with diabatic heating () during the northern summer (JJA) at (a) 200 mb and (b) 850 mb, and during the winter (JF) at (c) 200 mb and (d) 850 mb. Positive (negative) values of larger (smaller) than 1°C day−1 (−1°C day−1) are heavily (lightly) shaded. Contour intervals of χ (velocity potential) are 2 × 106 m2 s−1 in (a) and 106 m2 s−1 in (b)–(d)

Fig. 3.

Divergent circulation (χ, VD) superimposed with diabatic heating () during the northern summer (JJA) at (a) 200 mb and (b) 850 mb, and during the winter (JF) at (c) 200 mb and (d) 850 mb. Positive (negative) values of larger (smaller) than 1°C day−1 (−1°C day−1) are heavily (lightly) shaded. Contour intervals of χ (velocity potential) are 2 × 106 m2 s−1 in (a) and 106 m2 s−1 in (b)–(d)

The relationship between diabatic heating (cooling) and divergent circulation derived from Fig. 3 may be summarized as follows: Centers of diabatic heating (cooling) driving monsoon circulations are not always located over continents (oceans) as shown in Fig. 1, but most of them are over the western (eastern) tropical Pacific and Atlantic where deep cumulus convections are enhanced (suppressed) by warm (cold) sea surface temperatures. As expected by Holton and Colton (1972), a spatial quadrature relationship actually exists between monsoon anticyclones (Fig. 2) and divergent (convergent) centers [depicted by χ(200 mb) in Fig. 3]. Since a monsoon trough (continental thermal low) resides underneath a monsoon high, this trough also straddles a dipole of two χ(850 mb) cells, which spatially correspond to a dipole of two χ(200 mb) cells with the opposite polarity. Apparently, the spatial quarter-phase shift between the monsoon high (trough) and the monsoon secondary circulation is missing from the classic monsoon circulation (Fig. 1). It is conceivable that this spatial quadrature phase relationship has an important dynamic implication; the actual mechanism of the monsoon maintenance evidently differs from the classic one presented in Fig. 1.

3. Diagnostic scheme and data

Three basic features of the monsoon circulation are derived from Figs. 2,–3:

  1. The divergent circulation of a monsoon system is driven by the east–west differential heating in such a way that diabatic heating (cooling) center coincides with the upper-level divergent (convergent) center of the monsoon circulation.

  2. A monsoon system consists of a monsoon anticyclone in the upper troposphere and a monsoon (or continental thermal) low in the lower troposphere.

  3. The monsoon high (low) and the upper- (lower)-level divergent circulation are spatially in quadrature.

The mechanism for maintaining a major monsoon circulation must be able to explain these three basic monsoon features. Feature 1 is the relationship between diabatic heating and planetary-scale divergent circulation. Since the tropical global circulation is well portrayed by streamfunction and velocity potential (e.g., Krishnamurti 1971a,b; Krishnamurti et al. 1973), features 2 and 3 can be illustrated by the relationship between these two variables. Suggested by this inference, the search of the monsoon maintenance mechanism is performed with the following diagnostic scheme, which includes two components.

a. Relationship between diabatic heating and divergent circulation

Combining the continuity and thermodynamic equations, one obtains the velocity potential (χ) maintenance equation (Chen and Yen 1991a,b):

 
formula

where σ, V, T, cp, p, and are static stability, velocity vector, temperature, specific heat with constant pressure, pressure, and diabatic heating, respectively. Since thermal advection is generally much smaller than diabatic heating in the Tropics (e.g., Chen and Baker 1986), Eq. (1) may be approximated by

 
χχ,
(2)

which provides a link between diabatic heating and velocity potential to illustrate feature 1 of the monsoon circulation. Diabatic heating was estimated by the residual method of thermodynamic equation following our previous study (Chen and Baker 1986). Results were verified against those generated directly by the Goddard global data assimilation system (Schubert et al. 1993).

b. Relationship between divergent circulation and streamfunction

The vorticity equation without vertical advection and dissipation is

 
formula

The inverse Laplace transform of the simplified vorticity equation, that is, the streamfunction budget equation (Holton and Colton 1972; Sanders 1984) may be expressed as

 
formula

where ( )R and ( )D are rotational and divergent components of wind fields, and uz is zonal-mean wind. For convenience, let us define ψAψA1 + ψA2 + ψA3 and ψχψχ1 + ψχ2 + ψχ3. Any streamfunction tendency that satisfies the following criteria are neglected: Var(ψAn)/Var(ψA) < 15%, and Var(ψχn)/Var(ψχ) < 15%, where Var( ) = variance of ( ). Features 2 and 3 of a monsoon system will be elucidated by the simplified streamfunction budget equation.

Every major monsoon system has a different horizontal dimension. For example, the Tibetan high is formed primarily by ultralong waves 1 and 2 (Holton and Colton 1972), while the Bolivian high is constituted by the medium-wave (2–6) regime (Chen et al. 1999). Therefore, a proper Fourier scale separation is incorporated into the diagnosis so that the basic dynamics of a monsoon circulation can be properly isolated.

The NCEP–NCAR reanalyses (Kalnay et al. 1996) for the 1979–2000 period were used in this study. The NCEP assimilation system employed for the reanalysis project is a spectral model with a horizontal resolution of T62 and a vertical resolution of 28 sigma levels. The reanalyses used in our diagnosis were projected on a 2.5° × 2.5° horizontal resolution and a 28 pressure-level vertical resolution. Linear terms of Eqs. (2) and (3) were computed with monthly mean reanalyses, while the nonlinear terms were evaluated with the daily data. The ω (p-vertical motion) fields generated directly by the NCEP–NCAR reanalyses are utilized in constructing the east–west circulation. The scale separation was performed with the one-dimensional Fourier analysis along the longitudinal direction, and applied to any necessary field variable and every term in Eqs. (2) and (3).

4. Maintenance of Northern Hemisphere summer monsoons

a. Asian monsoon

Following Holton and Colton (1972), we focused our diagnosis on the wave 1–2 regime designated by ( )L. However, the following statistics, Var(χL)/Var(χ) ≥ 90% and Var(χL)/Var(χ) ≥ 90% at 200 and 850 mb, respectively, lead us to approximate Eq. (2) in the long-wave regime by

 
χLχL.
(4)

This approximation is well supported by the comparison between the χ (Fig. 3) and χL (Fig. 4) fields. The superimposition of (200 mb) on χL(200 mb) indicates that the divergent circulation of the Asian monsoon is driven primarily by the east–west differential heating between the heating in the western tropical Pacific and the cooling in North Africa (first monsoon feature). This differential heating is opposite to the classic monsoon circulation model (Fig. 1). The direction of the east–west circulation (shown later) in response to this differential heating is also opposite to that of the classic monsoon model.

Fig. 4.

Contribution from diabatic heating to divergent circulation (χ, ∇χ) at (a) 200 mb and (b) 850 mb in the long-wave (waves 1–2) regime during northern summer (JJA). Contour interval ofχL are (a) 2 × 106 m2 s−1 and (b) 106 m2 s−1

Fig. 4.

Contribution from diabatic heating to divergent circulation (χ, ∇χ) at (a) 200 mb and (b) 850 mb in the long-wave (waves 1–2) regime during northern summer (JJA). Contour interval ofχL are (a) 2 × 106 m2 s−1 and (b) 106 m2 s−1

Variances of eddy streamfunction explained by ψL are over 90% at 200 and 850 mb. Thus, conspicuous features of the Asian summer monsoon presented in Fig. 2 are well represented by ψL in Fig. 5. A vertical phase reversal of tropical stationary waves (White 1982; second monsoon feature) emerges from the contrast between ψL (200 mb) (Fig. 5a) and ψL (850 mb) (Fig. 5c). The spatially quadratic relationship between the monsoon high (low) and the tropical divergent circulation (third monsoon feature) is revealed from the ψL and χL fields at 200 and 850 mb. Actually, this quadratic feature can be also demonstrated by superimposing the east–west circulation (uD, −ω) (30°N) on the ψL (30°N) cross section (Fig. 5b). The updraft branch of the monsoon east–west circulation appears on the east side of the Tibetan high, while the downdraft branch of this circulation exists on the west side of this anticyclone. What is the dynamic mechanism in maintaining features 2 and 3 of the summer Asian monsoon implicated by the spatial relationship between the tropical divergent circulation (χ) and rotational flow (ψ) of the Asian monsoon system? This question will be answered by the ψL budget analyses at both upper and lower levels.

Fig. 5.

Streamfunction of the long-wave (waves 1–2) regime, ψL, at (a) 200 mb, and (c) 850 mb, and (b) the longitude–height cross section at 30°N, ψL (30°N), superimposed with the east–west circulation (uD, −ω)L (30°N). Positive values of ψL are shaded, while contour intervals of ψL are 4 × 106 m2 s−1 in (a), (b) and 2 × 106 m2 s−1 in (c)

Fig. 5.

Streamfunction of the long-wave (waves 1–2) regime, ψL, at (a) 200 mb, and (c) 850 mb, and (b) the longitude–height cross section at 30°N, ψL (30°N), superimposed with the east–west circulation (uD, −ω)L (30°N). Positive values of ψL are shaded, while contour intervals of ψL are 4 × 106 m2 s−1 in (a), (b) and 2 × 106 m2 s−1 in (c)

Following the criteria set in section 3, the simplified ψL budget is shown in Fig. 6. As inferred from the opposite spatial polarity between ψLχ12(=ψLχ1 + ψLχ2) and ψLA2, the ψL field is maintained by the counteraction between these two streamfunction tendencies, namely,

 
0 ≃ ψLA2 + ψLχ12,

which corresponds to the following simplified vorticity equation,

 
0 ≃ υψβ + ∇·(fVD)
(5)

for both upper and lower levels. Based on the spatial structure of χL(≅χL) (Fig. 4) and ψL (Fig. 5), one may assume,

 
formula

where Ly and k are the meridional scale of χL and the longitudinal wavenumber, respectively. Substituting Eq. (6) into Eq. (5) and making some simple rearrangement, one obtains

 
ψL = ALχLe/2,
(7)

where AL = α tan(αky) + (CI/CRx)(1 + α), α = π/(2Lyk), CRx = β/k2, and CI = f/k. The spatial quadrature relationship between ψL and χL is represented by the factor of e/2 (second monsoon feature). Since χL (Fig. 4) has a phase reversal in its vertical structure, ψL should also possess a vertical phase reversal following χL (third monsoon feature).

Fig. 6.

Streamfunction budgets of the long-wave (waves 1–2) regime: (a) ψLχ12(200 mb) (b) ψLA2(200 mb), (c) ψLχ12(850 mb), and (d) ψLA2(850 mb). Positive values of all variables are shaded. Contour intervals are 50 m2 s−2 in (a), (b) and 25 m2 s−2 in (c), (d)

Fig. 6.

Streamfunction budgets of the long-wave (waves 1–2) regime: (a) ψLχ12(200 mb) (b) ψLA2(200 mb), (c) ψLχ12(850 mb), and (d) ψLA2(850 mb). Positive values of all variables are shaded. Contour intervals are 50 m2 s−2 in (a), (b) and 25 m2 s−2 in (c), (d)

It becomes clear that the summer Asian monsoon presented in Figs. 4 and 5 is maintained by the following mechanism: The east-west circulation of the Asian monsoon induced by the east–west differential heating and coupled with the global divergent circulation [through Eq. (4)] maintains the Tibetan anticyclone and the Indian monsoon trough through the modified Sverdrup balance [Eq. (5)].

b. North American monsoon

The North American monsoon is much smaller in its horizontal dimension and intensity than the Asian monsoon (Tang and Reiter 1984). This contrast is often considered as a result of the size of the North American continent, but a different perspective is suggested by the following observations. First, as shown in Fig. 3, the zonal scale of the east–west differential heating between the Caribbean Sea and the eastern tropical Pacific is much smaller than that between the western tropical Pacific and North Africa. The response of the North American circulation to the former differential heating is expected to be smaller in its horizontal dimension. Second, the wavenumber-1 component explains about 60%–80% of the 200-mb eddy streamfunction variance in the northern Tropics (Krishnamurti 1971a). This wave component of ψ(200 mb) [ψ(850 mb)] (not shown) exhibits a ridge (trough) over the Tibetan Plateau (northern India) and a trough (ridge) over North America. Evidently the vertical structure of wavenumber-1 component is in phase with the Asian monsoon, but out of phase with the North American monsoon. The development of the latter monsoon is suppressed by this wave.

Since its horizontal dimension is smaller, does the North American monsoon possess all three basic features of a major monsoon circulation? Clearer features of the North American monsoon may be attained by focusing the analysis on the medium-wave (waves 2–8) regime designated by ( )M. Since more than 95% of the χM variance is explained by χM at both levels, χMχM is a good approximation. It is also revealed from the (χM, ) fields (Fig. 7) particularly at 200 mb that the negative χM center over the Caribbean Sea and the positive χM center over the eastern tropical Pacific are coincident with heating and cooling centers, respectively. As expected, the divergent circulation of the North American monsoon is driven by the east–west differential heating between the two oceans (first monsoon feature), instead of that between the warm continent and the cold ocean shown in the classic monsoon model (Fig. 1).

Fig. 7.

Same as in Fig. 4 except for a medium-wave (wave 2–8) regime. Contour intervals of χM are 106 in (a), (c) and 4 × 105 m2 s−1 in (b), (d)

Fig. 7.

Same as in Fig. 4 except for a medium-wave (wave 2–8) regime. Contour intervals of χM are 106 in (a), (c) and 4 × 105 m2 s−1 in (b), (d)

The North American monsoon high flanked by the two midocean troughs and the North American thermal low juxtaposed with two oceanic anticyclones are clearly depicted by ψM (200 mb; Fig. 8a) and ψM (850 mb; Fig. 8c), respectively. The vertical phase reversal of the North American monsoon circulation (second monsoon feature) is observed by contrasting these two variables across the North American continent. Superimposed on the ψM (30°N) cross section in Fig. 8b is the east–west circulation (uD, −ω)M (30°N) with its updraft branch centered over the Caribbean Sea and its downdraft branch over the eastern tropical Pacific. A spatial quadrature relationship between this east–west circulation and the North American monsoon circulation represented by ψM (30°N) is exactly the same as that of the Asian monsoon. This spatial quadrature relationship (third monsoon feature) can be also inferred from the contrast between χM (Fig. 7) and ψM (Fig. 8).

Fig. 8.

Same as in Fig. 5 except for a medium-wave (waves 2–8) regime. Contour intervals of ψM are 2 × 106 m2 s−1 in (a) and 106 m2 s−1 in (b), (c)

Fig. 8.

Same as in Fig. 5 except for a medium-wave (waves 2–8) regime. Contour intervals of ψM are 2 × 106 m2 s−1 in (a) and 106 m2 s−1 in (b), (c)

As required by criteria of section 3, the simplified ψM budget of the North American monsoon is presented in Fig. 9. Both the North American monsoon high and thermal low are maintained by counteractions of dynamic processes expressed by the following two simplified streamfunction budget equations:

 
formula

where ψMA12 = ψMA1 + ψMA2 and ψMχ12 = ψMχ1 + ψMχ2. The corresponding vorticity equations are

 
formula

In the upper subtropics, the zonal flow effectively advects the vorticity of medium-scale waves, and the divergent meridional wind of the medium-wave regime is strong enough to advect the planetary vorticity. Based on the structure of χM (Fig. 7) and ψM (Fig. 8), let us assume

 
formula

where LMy is a meridional scale of χM. Substituting Eq. (10) into Eqs. (8) and (9), and rearranging resultant equations, one obtains

 
formula

where AM = [α tan(αky)cR + cI]/(cRuZ), BM = (cI/cRx), and cR = β/[k2 + (2π/LMy)2]. The spatial quadrature relationship between χM and ψM of the North American monsoon (second monsoon feature) is represented by the factor e/2. As inferred from χM (Fig. 7), the monsoon divergent circulation represented by χM has a phase reversal across North America. Based on Eq. (11), the ψM field also undergoes a vertical phase reversal (third monsoon feature) as revealed in Fig. 8.

Fig. 9.

Same as in Fig. 6 except for the medium-wave (waves 2–8) regime. Contour intervals are 30 m2 s−2 in (a), (b) and 20 m2 s−2 in (c), (d)

Fig. 9.

Same as in Fig. 6 except for the medium-wave (waves 2–8) regime. Contour intervals are 30 m2 s−2 in (a), (b) and 20 m2 s−2 in (c), (d)

The analysis in this section shows that the three basic monsoon features emerge from the summer North America circulation after removing the wave-1 component (which is a suppressing factor to the development of the North American monsoon). The maintenance mechanism of the Asian monsoon is applicable to this monsoon.

5. Maintenance of Southern Hemisphere summer monsoons

For the summer in the Southern Hemisphere, we are concerned only with the monsoon circulations of tropical South America and Australia. The structure and maintenance of planetary-scale circulation at upper levels, particularly the Bolivian high, were already analyzed by Chen et al. (1999). The major characteristics of these two monsoons may be revealed/inferred from Chen et al.'s analysis. To avoid redundancy, it suffices to highlight their findings pertaining to the present study supplemented with results of the new analysis.

a. South American monsoon

In search of the structure and maintenance mechanism of the Bolivian high, Chen et al. (1999) split the asymmetric component of the upper-level South Hemisphere circulation into two wave regimes, wave-1 and the medium-wave (waves 2–6) regime. Variables in these two wave regimes are designated by ( )l and ( )m. Some of the basic features in these two regimes pertaining to the current study are:

  1. The Bolivian high, which is basically formed by the medium-wave regime, is modulated by the long-wave regime.

  2. Velocity potential in the medium-wave regime (χm) is related spatially in quadrature with the streamfunction of this wave regime (ψm) across tropical South America.

  3. A vertical phase reversal in the midtroposphere appears in the South American tropical circulation depicted by ψm of the medium-wave regime.

  4. The divergent circulation portrayed by χm is maintained primarily by diabatic heating, that is χm (200 mb) ≃ χm (200 mb).

  5. the maintenance of the Bolivian high is dynamically well explained by a Sverdrup balance.

The χm(850 mb) field (not shown) explains 98% of the χm(850 mb) variance. Therefore, χm(850 mb) ≃ χm(850 mb) is a good approximation. The superimposition of on χ in Fig. 3 indicates that the divergent circulation of the tropical South American circulation is driven by the east–west differential heating between the diabatic heating east of the Andes and the diabatic cooling over the eastern tropical Pacific (first monsoon feature), like the classic monsoon model in Fig. 1. For the wave-1 regime, the convergent center of χl(200 mb) is located over eastern Brazil (Chen et al. 1999, their Fig. 5), but is not strong enough to suppress the development of the South American monsoon circulation.

Corresponding to the juxtaposition of the Bolivian high with the midocean troughs (Fig. 10a), the surface low pressure over tropical South America aligned with the two oceanic anticyclones is well represented by ψm(850 mb) in Fig. 10c. The contrast between short wave trains of ψm(200 mb) and ψm(850 mb) across this region reveals a vertical phase reversal of the tropical South American circulation (second monsoon feature). The east–west circulation (uD, −ω)m (20°N) superimposed on the ψm (20°N) cross section (Fig. 10b) exhibits an updraft (downdraft) branch of this circulation east (west) of the Bolivian high coupled with the 200-mb divergent (convergent) center and the 850-mb convergent (divergent) center. Like the other two Northern Hemisphere summer monsoon circulations, the tropical South American monsoon bears all three basic monsoon features. The spatial quadrature relationship between χm and ψm (third monsoon feature) actually indicates that the maintenance mechanism of this monsoon differs from the classic monsoon circulation theory.

Fig. 10.

Same as in Fig. 5 except for a medium-wave (waves 2–6) regime. Contour intervals of ψm are 2 × 106 m2 s−1 in (a) and 106 m2 s−1 in (b), (c)

Fig. 10.

Same as in Fig. 5 except for a medium-wave (waves 2–6) regime. Contour intervals of ψm are 2 × 106 m2 s−1 in (a) and 106 m2 s−1 in (b), (c)

Chen et al.'s (1999, their Fig. 10) ψm (200 mb) budget analysis gives the simplified budget equation:

 
0 ≃ ψmA2 + ψmχ1,
(12)

which also fits the ψm (850 mb) budget (not shown). The corresponding vorticity equation is

 
0 ≃ −υmRβf∇  ·  VmD,
(13)

which is a modified Sverdrup balance (by replacing υm with υmR). Based on the spatial structure of χm (Chen et al. 1999, their Fig. 5) and ψm (Figs. 10a and 10c), let us assume

 
χm = Χmeikx and ψm = Ψmeikx.
(14)

Substituting Eq. (14) into Eq. (13) with some simple rearrangement, one obtains

 
ψm = Bmχme/2,  at both 200 and 850 mb,
(15)

where Bm = cI/cRx. A quarter-wave shift between χm and ψm across tropical South America is represented by the factor of e/2. Following the vertical phase reversal of χm (indicated by the χ fields across tropical South America in Figs. 3c,d), ψm undergoes a vertical phase reversal. The simplified Sverdrup balance explains the last two basic monsoon features of the tropical South American circulation.

In summary, the revised maintenance mechanism of a monsoon circulation (illustrated in Figs. 5b and 8b) is applicable to the South American monsoon (revealed from Fig. 10b), as it portrayed in the medium-wave regime.

b. Australian monsoon

It was shown by Chen et al. (1999) that the upper-level summer circulation in the tropical Southern Hemisphere can be well represented by zonal waves 1-6, which is denoted by ( )T. Variances of χT explained by χTQ at 200 and 850 mb are over 90% and χTχT is thus a good approximation. The (χ, ) field in Fig. 3 reveals that the divergent circulation of the Australian monsoon is driven by the east–west differential heating in a manner different from the classic monsoon circulation model (Fig. 1). The upper- (lower)-level divergent (convergent) center of this circulation is located on the upstream (downstream) side of the upper- (lower)-level monsoon easterlies (westerlies) over the western South Pacific (i.e., the warm-pool region). The contrast between the upper- and lower-level ψT around Australia (Figs. 11a,c) clearly shows a vertical phase reversal of the Australian monsoon circulation (second monsoon feature). Superimposing on the ψT (15°S) anomalies in Fig. 11b, the east–west circulation (uD, −ω)T (15°S) exhibits its updraft (downdraft) branch east (west) of the monsoon high (low). The third basic feature of the Australian monsoon is reflected by this spatial relationship. In contrast, the spatial quadrature relationship between χT and ψT may not be clear by a direct comparison between Figs. 2 and 3, for example. According to Chen et al. (1999), basic dynamics of wave-1 and medium-wave regimes are not exactly the same. The second and third monsoon features of the Australian monsoon should be explained in these two wave regimes, separately.

Fig. 11.

Same as in Fig. 5, except for the total wave (waves 1–6) regime. Contour intervals of ψT are 2 × 106 m2 s−1 in (a) and 106 m2 s−1 in (b), (c)

Fig. 11.

Same as in Fig. 5, except for the total wave (waves 1–6) regime. Contour intervals of ψT are 2 × 106 m2 s−1 in (a) and 106 m2 s−1 in (b), (c)

1) Long-wave regime

Extending Chen et al.'s (1999)  ψl budget analysis to cover 850 mb, we may approximate the ψl budget equations as follows:

 
formula

The vorticity equations corresponding to these two ψl budget equations are

 
formula

Based on spatial structure of ψT (Fig. 11) and χ (Fig. 3), one may assume

 
formula

Substituting Eq. (18) into Eqs. (16) and (17) and making some rearrangement of resultant equations, we obtain

 
formula

where Al = {α tan(αky)cR + [(1 + α2)/(1 + 16α2)]cI}/(cRuRZ) and Bl = α tan(αky) + [(1 + α2)/(1 + 16α2)](cI/cRx). The spatial quadrature relationship between χl and ψl is determined by the factor of e/2 in Eq. (19). As inferred from the χ fields in Fig. 3, χl undergoes a vertical phase reversal, and so does ψl.

2) Medium-wave regime

The medium waves are usually not so strong in the χ fields across Australia as that across tropical South America and its vicinity. A scale separation should be applied to this variable so that a clear view of its function can be obtained. Between 60°E and 150°W in the tropical Southern Hemisphere (0°–40°S), χmχm is still a good approximation. The divergent circulation of the Australian monsoon in this wave regime is primarily driven by the east–west differential heating. The Australian monsoon high aligned with the two oceanic troughs and the Australian monsoon low with the two oceanic anticyclones are discernable in the ψm anomalies of Fig. 10. The vertical phase reversal of ψm is observed in the ψm (15°S) longitude–height cross section. A spatial quadrature relationship between χm and ψm of this monsoon is reflected by the east–west circulation of the medium-wave regime (uD, −ω)m (15°S) across Australia (Fig. 10) with an updraft (downdraft) branch east (west) of the Australian ψm anomalies. These two basic features of the Australian monsoon in the medium-wave regime can be explained by the vorticity budget analysis shown in section 5b.

Although some dynamic features of the medium-wave regime may be blurred by the long-wave regime, three basic features of a monsoon circulation appear in both (χl, ψl) and (χm, ψm) fields across Australia. Since the Australian monsoon is formed by these two wave regimes, the Australian monsoon evidently possesses all three basic monsoon features. As shown in Fig. 11b, this monsoon is maintained by the revised maintenance mechanism.

6. Concluding remarks

Derived from prior FGGE studies, a major monsoon circulation exhibits three basic features: 1) The divergent circulation of a monsoon is maintained by the east–west differential heating (continental heating and oceanic cooling); 2) A phase reversal appears in the vertical structure of a monsoon circulation; and 3) The monsoon anticyclone (depicted by streamfunction ψ) and the monsoon divergent center indicated by velocity potential are coincident, namely the centers of vorticity and divergence are out of phase. These features agree with the classic monsoon circulation model (Fig. 1). In contrast, the structure and maintenance of monsoon circulations revealed from the post-FGGE data and the modern reanalyses differ from the classic monsoon circulation model in features 1 and 3. The divergent circulation of a monsoon system is often maintained by an east–west differential heating other than continental heating and oceanic cooling (feature 1). As expected by Holton and Colton (1972), a spatial quadrature relationship exists between the monsoon anticyclone and divergent circulation to meet a balance between stretching and advection of vorticity (feature 2). It is manifest from a planetary-scale perspective that basic dynamics of major monsoon circulations depicted by the prior- and post-FGGE data are different from each other. What may be the maintenance mechanism of a monsoon circulation? To answer this question, a simple diagnostic scheme consisting of the velocity-potential (χ) maintenance equation and the streamfunction (ψ) budget equation was applied in this study. Feature 1 of a monsoon is illustrated by the former budget equation, while features 2 and 3 are explained by the simplified vorticity dynamics obtained from the latter budget analysis. Four major monsoon circulations (Asian, North American, South American, and Australian) are examined in this study. Since spatial dimensions of these monsoons are not the same, a Fourier scale separation was applied to variables depicting their structure and dynamics. Major findings of our analysis are as follows.

  1. The horizontal heat advection is generally insignificant in the Tropics. Diabatic heating is therefore a primary forcing needed to maintain divergent circulation. Thus, χχ (velocity potential contributed by diabatic heating ) is a good approximation. Based on this relationship, we found that every monsoon divergent circulation is driven/maintained by a different east–west differential heating:

    • Asian monsoon: heating over the western tropical Pacific and cooling over North Africa.

    • North American monsoon: heating over the western tropical Atlantic and cooling over the eastern tropical Pacific.

    • Tropical South American monsoon: heating east of the Andes and cooling over the eastern tropical south Pacific.

    • Australian monsoon: the oceanic heating over the western tropical Pacific (warm pool) and the oceanic cooling over the eastern Indian Ocean.

  2. Neglecting dynamic processes contributing less than 15% of the variance of streamfunction tendencies induced by vorticity source (ψχ) and vorticity advection (ψA), we simplified the velocity potential maintenance and streamfunction budget equations. A simple relationship between potential function and streamfunction is derived from these simplified budget equations: 
    ψ = Cχe/2.
    The spatial quadrature relationship between the monsoon χ and ψ fields is represented by the factor of e/2. In order to satisfy the mass continuity, the divergent circulation depicted by χ exhibits a vertical phase reversal. It is inferred from this ψχ relationship that ψ also undergoes a phase reversal in its vertical structure.

Combining these two findings, one can easily obtain the following relationship between the monsoon circulation and diabatic heating:

 
ψ = e/2.

This ψχ relationship is consistent with Hoskins and Rodwell's (1995) demonstration that a linearized general circulation model with a prescribed diabatic heating (without mountains) is able to reproduce the summer upper-tropospheric circulation with a realistic monsoon anticyclone, and the North Pacific and North Atlantic troughs. Findings of this study summarized earlier lead us to revise the classic maintenance mechanism of major monsoon circulations. The east–west circulation associated with a monsoon circulation (as shown in Figs. 5a, 8a, 10b, and 11b) is driven/maintained by the planetary-scale east–west differential heating. Through vortex stretching, this east–west circulation generates negative (positive) vorticity at the upper (lower) levels by its updraft branch and the reverse process by its downdraft branch. The generated vorticity by this dynamic process is then counteracted by horizontal advection of planetary vorticity. A monsoon high (low) is maintained through this counteraction, which is basically a Sverdrup balance.

The climate variability of global monsoons (Asia–Australia, North/South America, and Africa) forms three principal research areas (G2–4) of the Climate Variability and Predictability Programme (WCRP 1998). Various mechanisms responsible for the monsoon climate variability of different regions have been proposed in the past two decades. For the Asian monsoon, its interannual variation may be caused by the following mechanisms: Sea surface temperature changes over the western tropical Indian Ocean (e.g., Shukla 1987) and the central-eastern tropical Pacific (associated with the ENSO activity) (e.g., Palmer et al. 1992, Chen and Yen 1994; Ju and Slingo 1995), the anomalous snow coverage of central Asia and the Tibetan Plateau (e.g., Vernekar et al. 1995), and the soil moisture change over the monsoon region (e.g., Meehl 1994). These mechanisms were tested by numerical simulations of atmospheric general circulation models. Australia, Indonesia, and New Guinea are adjacent to the so-called warm pool in the western tropical Pacific. It has been observed that interannual variations of the Australian monsoon onset and rainfall are closely related to the ENSO cycle (Alan 1983; McBride and Nicholls 1983; Holland 1986; Drosdowsky 1996).

A number of studies (e.g., Andrade and Sellers 1988; Carleton and carpenter 1990; Higgins et al. 1998; Higgins and Shi 2000; Yu and Wallace 2000; and others) were made to link the interannual variation in the rainfall of the North American monsoon system (NAMS) to the SST variation over the eastern tropical Pacific. In contrast, the possible association between Atlantic SST and the NAMS climate variability has not been well explored. Giannini et al. (2000) recently found that ENSO manifests itself in the tropical atmosphere as a zonal seesaw in sea level pressure between the equatorial Pacific and Atlantic Oceans. An anomalous Walker circulation coupled with this pressure seesaw provides a mean for the interaction between the two basins. As revealed from the global precipitation change associated with the ENSO (Ropelewski and Halpert 1987), precipitation over tropical South America is strongly modulated by ENSO events. This impact is reflected by the overall strength of the South American monsoon system and the rainfall pattern (e.g., Aceituno 1988; Kousky and Kayano 1994). During extreme El Niño (La Niña) phases, the ascending motion over tropical South America is weakened (strengthened) and rainfall is reduced (increased). In other words, the east–west circulation connecting the eastern tropical Pacific and tropical South America may be intensified (weakened) during La Niña (El Niño).

In search of causes responsible for interannual variations of the major monsoon climate systems, numerous mechanisms were suggested and proposed. However, these efforts were hampered by the lack of clear and accurate maintenance mechanisms of major monsoon circulations. The new mechanism revealed from our diagnosis in this study provides a new dynamic underpinning of a monsoon circulation, which would facilitate our endeavor for exploring the cause of the monsoon climate variability.

Acknowledgments

This study is supported by the NSF Grant ATM-9906454. Comments and suggestions offered by Dr. Glenn White and a reviewer were helpful in our revision of this paper. The computational assistance of Mr. Jung-Chieh Hsieh, the typing support of Ms. Judy Huang, and the editing assistance of Mr. Brad Temeyer are highly appreciated.

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Footnotes

Corresponding author address: Tsing-Chang (Mike) Chen, Atmospheric Science Program, Department of Geological and Atmospheric Sciences, Iowa State University, 3010 Agronomy Hall, Ames, IA 50011. Email: tmchen@iastate.edu