Evolving Perspectives on Abrupt Seasonal Changes of the General Circulation

(Rossby, 1951) wrote in a short note published in Tellus on cooperative research projects that "there is […] every reason to expect, during the next few years, an extremely vigorous development of Chinese meteorology and, as a result, many significant realistic contributions from that part of world". In addition to the establishment of the People's Republic of China, one reason Rossby must have had in mind when he wrote this was the return to China in 1950 of his three protègès: Tu-cheng YEH (Duzheng YE) and Yi-ping SHIEH (Yibing XIE) from the University of Chicago, and Chen-Chao KOO (Zhengchao GU) from the University of Stockholm. Both T.-C. YEH and C.-C. KOO went to the Institute of Geophysics and Meteorology of the Chinese Academy of Sciences. There, they were not only responsible for leading the meteorological research program, but they were also key figures in the establishment of a modern operational weather forecast system. Later in the 1950s, Rossby was able to see for himself the contributions his Chinese protègès had made, such as the first thorough analysis of the general circulation over eastern Asia, which was invited to be published in Tellus (Staff Members of the Section of Synoptic and Dynamic Meteorology, Institute of Geophysics and Meteorology, Academia Sinica, Peking, 1957, 1958; Staff Members of the Section of Synoptic and Dynamic Meteorology, Institute of Geophysics and Meteorology, Academia Sinica, 1958). However, the scope of meteorological research in China was not limited to topics directly related to China or East Asia, but extended to fundamental problems of the field. (Blumen and Washington, 1973) surveyed the research activities and developments in atmospheric dynamics and numerical weather predictions in China during 1949-66 and found "on the basis of accumulated evidence" that "the field of meteorology had become a well established and continually growing scientific activity." (Blumen and Washington, 1973) focused on cumulus and turbulent boundary layer dynamics and the dynamics of meso-, synoptic-, and planetary-scale motions, but they acknowledged that "a more exhaustive overview of the contributions made by Chinese meteorologists to the theory of the general circulation appears warranted."

Figure 1.  Chapter headings of "Some fundamental problems of the general circulation of the atmosphere" (Yeh and Chu, 1958).

Figure 2.  (continued)

Indeed, a unique contribution by Chinese meteorologists to the theory of the general circulation had been the monograph by Professor YEH and his colleague Pao-chen CHU, entitled "Some Fundamental Problems of the General Circulation of the Atmosphere" (Yeh and Chu, 1958). The chapter headings (Fig. 1) show the breadth of the contents and "give an idea of the broad sweep and ground-breaking nature of his ideas at this time" (Hoskins, 2014). The monograph was not only a survey of Chinese contributions, largely led by T.-C. YEH and C.-C. KOO, to the theory of the general circulation——it was also a survey of the contemporary theoretical advances in the world, organized by the two authors' vision of the nature of the general circulation. Many insights in (Yeh and Chu, 1958), such as the mechanisms responsible for the formation and maintenance of the mean meridional circulation and the westerly jet streams, the joint effects of topography and thermal forcing on the location of mean ridges and troughs (stationary waves), laid foundations for later advances in the theory of the general circulation (e.g., Held, 1983; Held et al., 2002; Kaspi and Schneider, 2011; Birner et al., 2013). Although the monograph was published only two years after the first successful numerical simulation of the general circulation by (Phillips, 1956), (Yeh and Chu, 1958) attempted as much as possible at the time to give an internally consistent picture of the general circulation. They assigned a central role in the maintenance of jets and the mean circulation to large-scale eddies and their transport of energy, angular momentum, and mass——insights that had grown out of Professor YEH's PhD thesis on energy dispersion in Rossby waves (Yeh, 1949).

A thorough summary of the (Yeh and Chu, 1958) monograph is beyond the scope of this paper; readers are referred to (Lu, 2016) for more details. (Lu, 2016) particularly emphasized the scientific style of (Yeh and Chu, 1958), who strove for conciseness in mathematics, lucidity in physics, and overall internal consistency in their quest to identify general laws from regional and special phenomena. Here, it suffices to mention that (Yeh and Chu, 1958) stressed, citing the then-unpublished results by Yeh, Dao, and Li, that the observed abrupt seasonal change of the general circulation over Asia may be an important and possibly broader phenomenon in need of a general explanation. The present paper focuses on this abrupt change of the general circulation, reviewing Professor Tu-cheng YEH's contributions along with recent advances. Professor YEH and his colleagues were decades ahead of their time in contemplating the universality of abrupt seasonal changes and in proposing model experiments to elucidate their mechanisms. Such model experiments have recently uncovered mechanisms involved in abrupt seasonal changes——mechanisms that are independent of inhomogeneities at the lower boundary, such as those arising from land-sea contrast or topography but that are regionally modulated by such inhomogeneities.

We first review the main results of (Yeh et al., 1959), referred to as Yeh-Dao-Li (1959) hereafter, in section 2. In section 3, we review results from statistically zonally symmetric numerical simulations that exhibit rapid seasonal transitions (Bordoni and Schneider, 2008; Schneider and Bordoni, 2008). Section 4 discusses the implications and open questions, followed by conclusions in section 5.

In a footnote of the Tellus paper led by T.-C. YEH, S.-Y. DAO, and C.-C. KOO on the general circulation over East Asia, the authors mentioned that "according to our recent study (to be published) the sudden northward shift of westerlies in June is not limited to Asia but it is a world-wide phenomenon, being earliest over Asia and latest over N. America. In the period from middle September to middle October, there is a world-wide sudden onset of westerlies southward" (Staff Members of the Section of Synoptic and Dynamic Meteorology, Institute of Geophysics and Meteorology, Academia Sinica, Peking, 1957). Subsequently, Yeh and Chu (1958, chapter 1) documented abrupt changes of the general circulation during June and October over the Middle East, Tibetan Plateau, the coast of East Asia, central Pacific, and North America, followed by a publication by Yeh, Dao, and Li in Acta Meteorologica Sinica in Chinese. The authors also prepared an English version of the paper for a volume celebrating Rossby's 60th birthday, which was eventually published in a volume commemorating Rossby because he suddenly died on 19 August 1957. The paper is entitled "The abrupt change of circulation over northern hemisphere during June and October" and is authored by T.-C. YEH, S.-Y. DAO, and M.-T. LI; we refer to it as Yeh-Dao-Li (1959). We base our introduction to Professor YEH's contribution to the description of abrupt changes of the general circulation on this version of their publication.

Although abrupt changes of the circulation had been observed over the South Asian monsoon region and the Middle East, it was Yeh-Dao-Li (1959) who first stated clearly, with the limited observational data available then, that the seasonal variation of zonal winds and associated circulation patterns is abrupt not only over the monsoon region, but that it may be a broader phenomenon at least in the Northern Hemisphere, and possibly also over the Southern Hemisphere. The main observations were summarized in the abstract of Yeh-Dao-Li (1959):

"In this paper we have shown that there is an abrupt change of the upper-air circulation over the Northern Hemisphere in June and October. In June this change is characterized by a sudden northward shift of the westerlies and easterlies. Associated with this[,] a marked change in the upper flow pattern takes place[,] followed by the establishment of the typical summer circulation. In October the abrupt change is characterized by a sudden southward shift of the westerlies and easterlies. This is also accompanied by a marked change in the upper flow pattern, after which the typical upper winter circulation is established.

The onset of the summer circulation is associated with the outbreak of the SW monsoon in India and Mai-yu in China and Japan and a rapid northward displacement of the intertropical convergence zone (ICZ). The onset of the winter circulation is followed by the retreat of the SW monsoon and the ICZ. The synoptic sequence of these development is described."

As an example, Fig. 2, adapted from Yeh-Dao-Li (1959, Figs. 2 and 8), depicts the abrupt northward shift of the westerlies and easterlies at the end of May and the southward shift of the circulation during October in the South Asian monsoon region. Note in particular the northward shift of upper-level easterlies at the monsoon onset (end of May) and their downward extension to the surface on the southern flank of the Tibetan Plateau, as well as the transition from easterlies to westerlies in the lower troposphere.

By considering abrupt seasonal changes of the circulation as a broad phenomenon, Yeh-Dao-Li (1959) went beyond the regional dynamics of monsoons, unlike previous work going back to (Halley, 1686), by not focusing exclusively on the underlying regional inhomogeneities at the lower boundary as the main factors responsible for the abrupt seasonal changes. They stated explicitly:

"Concerning the cause of the abrupt changes, we shall only propose the following reasons as a conjecture: From winter to summer the inclination of the sun over the Northern Hemisphere gradually increases. With this increase the temperature contrast between the equator and pole gradually decreases. When it has decreased to a certain value, a certain type of `instability' in the atmosphere appears and the abrupt change of the upper-air circulation takes place. From summer to winter the `reversed' sequence of events would occur. Since the temperature and velocity fields are not independent of each other, a sudden change of the temperature would also follow such a change of the circulation."

"To answer conclusively the above conjecture," Yeh-Dao-Li proposed "the following model experiment: In a rotating half sphere or two coaxial cylinders […] we heat differently the inner and outer part, then gradually decrease or increase the heating difference and observe whether we get the abrupt transition of the circulation as observed in the atmosphere."

Their conjecture about the mechanisms of the abrupt transitions and the proposed experiment did not assign central roles to topography and/or land-sea contrasts, but rather to a conjectured internal instability of the general circulation, which can be triggered by gradual variations of the differential heating between the equator and poles. Consistent with the view of (Yeh and Chu, 1958), who put large-scale eddies in a central position in the maintenance of the general circulation, it is likely that Yeh-Dao-Li also thought eddies would play a role in the conjectured instability of the general circulation.

It is remarkable that they took such a broad view of monsoon transitions as an instability, given they were working at a time when data were necessarily regional and systematic model experiments were in their infancy. Regime transitions of the general circulation were found around the time of Yeh-Dao-Li (1959) in the now classical laboratory experiments in rotating annuli by D. Fultz, R. Hide, and R. Pfeffer (see the review by Read et al., 2015). For instance, transitions between different circulation regimes, such as regular waves or irregular geostrophic turbulence, occur as varying parameters that relate to the thermal contrast between the inner and outer annulus or the rotation rate. However, the regime transitions observed in these laboratory experiments were different from the abrupt seasonal transitions of the general circulation seen in the atmosphere.

The advent of numerical general circulation models (GCMs) put the experiments proposed by Yeh-Dao-Li (1959) within easy reach. Indeed, numerical simulations successfully reproduce abrupt seasonal transitions of the general circulation (e.g., Zeng et al., 1988; Prell and Kutzbach, 1992; Wu et al., 1997; Chao and Chen, 2001). However, the setup of these simulations included lower-boundary inhomogeneities such as land-sea contrasts and topography, which prevented the modeling studies from identifying instabilities or other mechanisms that contribute to abrupt transitions but may be independent of lower-boundary inhomogeneities. Thus, these modeling studies were still not the numerical version of the model experiment proposed by Yeh-Dao-Li (1959) to test their conjecture about the mechanism of the observed abrupt seasonal transitions.

Only half a century after the publication of Yeh-Dao-Li (1959), GCM experiments corresponding to the laboratory experiment proposed by Yeh-Dao-Li (1959) were conducted (Bordoni and Schneider, 2008; Schneider and Bordoni, 2008), without the authors of these studies being aware of Yeh-Dao-Li's proposal decades earlier.

In the model experiment proposed by Yeh-Dao-Li (1959), the boundary conditions were to be axisymmetric and only the thermal contrast between the equator and the poles was to be varied gradually. Building on steady-state simulations by (Walker and Schneider, 2006), Schneider and Bordoni carried out just such numerical experiments with idealized GCMs, first in a dry GCM without a hydrologic cycle (Schneider and Bordoni, 2008), and then in a moist GCM with a hydrological cycle (Bordoni and Schneider, 2008). In the simulations with a hydrological cycle, the lower boundary is a homogeneous slab ocean whose thickness is varied from very thin (a swamp planet with low thermal inertia) to very thick (a thick ocean planet with high thermal inertia).

Abrupt seasonal transitions of the general circulation from an equinox to a solstice regime indeed occur in the simulations when the lower boundary has sufficiently low thermal inertia (Fig. 3a). They occur irrespective of the presence of a hydrological cycle and latent heat release (Schneider and Bordoni, 2008). That is, the onset or retreat of intense off-equatorial precipitation during the circulation transitions in the simulations is a byproduct of the circulation changes, not a driver of it. The transitions resemble the circulation transitions observed in Earth's atmosphere in the South Asian monsoon region at the onset (May/June) and retreat (September/October) of the summer monsoon, with abrupt changes in both precipitation (Fig. 3b) and zonal winds (Fig. 4). In particular, the simulated circulation changes at the transitions between the equinox and solstice regimes exhibit the same rearrangement of the zonal wind structure as that described by Yeh-Dao-Li (cf. Figs. 2 and Figs. 5c, d).

Figure 3.  Pentad-mean cross-sections of the zonal wind (m s^-1) along 90^°E (a) from May to June and (b) during October, 1956. E and W indict easterlies and westerlies, respectively. [Adapted from Figs. 2 and 8 of (Yeh et al., 1959)].

Figure 4.  (a) Zonal- and pentad-mean precipitation (color contours; units: mm d^-1; the interval is 2 mm d^-1 with maximum identified by cross) and sea-level air temperature (grey contours; the contour interval is 2 ^°C, with the solid line being 24 ^°C isoline) in aquaplanet simulation with a thin slab ocean [Reprinted from (Bordoni and Schneider, 2008)]. (b) Precipitation (color scale) and surface winds (vectors; The longest vector at 18^°S in September indicts a wind speed of 9.1 m s^-1 and vector components to the left and right indict westward and eastward wind components, respectively) averaged zonally over the South Asian monsoon sector (65^°-95^°E), in which the ITCZ (precipitation maxima) is marked by red lines[Reprinted from (Schneider et al., 2014)].

The key to understanding the dynamics of the circulation changes is a regime transition of the tropical meridional overturning circulation. During the equinox regime, the Hadley cells are close to symmetric about the equator, and the strength of the poleward flow in the upper branches is primarily controlled by the eddy angular momentum flux divergence in the upper troposphere (Fig. 5a). During the solstice regime, there is a strong cross-equatorial Hadley cell with an ascending branch in the summer hemisphere, while a second, much weaker Hadley cell is confined to the winter hemisphere (Fig. 5b). The strong cross-equatorial Hadley cell is much closer to the angular momentum-conserving regime described by (Schneider, 1977), (Held and Hou, 1980), (Lindzen and Hou, 1988), and (Plumb and Hou, 1992). In this regime, the poleward flow in the upper branches is more directly thermally controlled (by differential diabatic heating and eddy energy flux divergences) than mechanically controlled (by eddy angular momentum flux divergence).

Figure 5.  Seasonal cycle of the zonal- and pentad-mean near-surface zonal wind at 15^°N from observations in the Asian monsoon sector (green) and from aquaplanet simulations with a thin slab ocean (yellow) and with a thick slab ocean (red) [Reprinted from (Bordoni and Schneider, 2008)].

Figure 6.  Zonal- and temporal-mean circulation at two 20-day periods (a, c) before (Julian Day 101-120) and (b, d) after (Julian Day 145-165) monsoon onset in the aquaplanet simulation of (Bordoni and Schneider, 2008) with a thin slab ocean: (a, b) streamfunction of meridional overturning circulation (black contours; contour interval: 50× 10⁹ kg s^-1; solid contours for anticlockwise rotation and dashed contours for clockwise rotation), and transient eddy angular momentum flux divergence [color contours; contour interval: 0.6× 10^-5 m s^-2 in (a) and 1.2× 10^-5 m s^-2 in (b), with red tones for positive and blue tones for negative values]; (c, d) zonal wind (black contours; contour interval: 6 m s^-1) and the same eddy angular momentum flux divergence (color contours) as in (a, b) [Reprinted from (Bordoni and Schneider, 2008)].

The abrupt transition of the circulation in the simulations is one between these two regimes, as can be ascertained by computing a local Rossby number: R _o=-ζ/f, where ζ is the mean relative vorticity and f is the planetary vorticity in the upper branch of the overturning circulation. A larger R _o (close to 1) means the upper branch is closer to the angular momentum-conserving limit, and the strength of the circulation responds directly to the thermal forcing; a smaller R _o (close to 0) indicates an eddy-mediated regime in which the circulation strength is influenced by the eddy angular momentum fluxes and does not directly respond to the thermal forcing (Schneider, 2006; Walker and Schneider, 2006). (Bordoni and Schneider, 2008) found that R _o changes from less than 0.4 to larger than 0.7 during the transition between the equinox and solstice regimes in their aquaplanet simulation with a thin slab ocean. A similar transition in R _o occurs for the zonal-mean Hadley circulation (Walker and Schneider, 2006) and for the meridional overturning circulation in the South Asian monsoon sector in Earth's atmosphere (Bordoni and Schneider, 2008).

These simulation results and observations suggest that the monsoonal transitions in Earth's atmosphere may indeed arise through some kind of "instability in the atmosphere", as Yeh-Dao-Li (1959) surmised. The question is, what is the mechanism responsible for this "instability"? Several mechanisms appear to play a role. One is that a Hadley cell can amplify rapidly once it is in the angular momentum-conserving regime. The rapid amplification in this regime is made possible by the nonlinearity of the angular momentum balance, provided the thermal inertia of the atmosphere and surface is sufficiently low to allow rapid adjustments (Lindzen and Hou, 1988, Plumb and Hou, 1992). Another involves an eddy-mean flow feedback: as the ascending branch of a Hadley cell moves into the summer hemisphere, it moves along with the lower-level temperature (or, more precisely, moist static energy) maximum (Privè and Plumb, 2007a, b). Thermal or gradient wind balance implies that upper-level easterlies develop within the cross-equatorial Hadley cell, above the region where temperatures increase going meridionally towards the lower-level temperature maximum under the ascending branch. This region of upper-level easterlies extends from the ascending branch deep into the winter hemisphere (Figs. 5c and d)——similar to the zonal wind changes Yeh-Dao-Li described (Fig. 2). The upper-level easterlies shield the interior of the cross-equatorial Hadley cell from extratropical eddies with westerly phase speeds, which cannot propagate on the easterlies. This allows the cross-equatorial Hadley cell to be closer to the angular momentum-conserving regime, where it can amplify rapidly with strengthening differential heating (Schneider and Bordoni, 2008).

It is clear that these mechanisms act in the simulations as well as in observations. It is also clear that, in the simulations, they suffice to trigger rapid circulation transitions between the equinox and solstice regimes, with attendant rapid changes in zonal winds and precipitation that have traditionally been taken as defining monsoon transitions. A low thermal inertia of the surface and atmosphere is necessary for the circulation changes to occur rapidly; otherwise, the adjustments in temperature and zonal winds would be thermally damped. If these are indeed the essential mechanisms for monsoon transitions, they suggest the role of the subtropical land surfaces in the South Asian monsoon is primarily to offer a surface of low thermal inertia. Land-sea contrasts are not necessary for such monsoon transitions. The upshot is that the heating contrast between the Indian Ocean and the subtropical continental mass to the north is certainly helpful for triggering monsoon transitions, but it is not essential for monsoon transitions. Monsoon transitions can arise more universally through internal rearrangements of the circulation, confirming the conjecture in Yeh-Dao-Li's proposal. Nonetheless, it is without question that land-sea contrast and topographic features such as the Tibetan Plateau, which featured prominently in Professor Yeh's work, also play important roles (e.g., Boos and Kuang, 2010, Wu et al., 2012).

Simulation studies such as those we discuss in this paper have over the past decade substantially broadened our view of what controls monsoons. The description of their dynamics has evolved from being rooted in regional peculiarities to being understood from broader and more universal principles. Several new mechanisms controlling their dynamics have been identified, and new ones continue to be added, such as stationary-eddy effects, especially in the East Asian monsoon (e.g., Park et al., 2012; Shaw, 2014). What remains missing, more than half a century after Yeh-Dao-Li suggested to put the study of seasonal transitions on a systematic footing, is a comprehensive theoretical framework that describes quantitatively how the different mechanisms interact.

Such a framework would have to account for the effects of transient eddy energy and angular momentum fluxes, their interaction with the mean meridional circulation and zonal winds, and their modulation through stationary eddies. It would have to be able to provide answers to questions such as: (1) How does the strength and structure of a Hadley cell depend on external factors such as the solar declination angle? (2) What controls when and how rapidly the circulation undergoes transitions between the equinox and solstice regimes? (3) How and to what extent do surface inhomogeneities such as land-sea contrasts modulate the internal rearrangement of the atmospheric circulation during the seasonal transitions? A comprehensive theoretical framework should also provide an answer to the question originally posed by Yeh-Dao-Li: Can the seasonal transitions be understood as an instability of the circulation as forcing parameters move through a critical region? To quantitatively answer these questions, at a minimum we need a closed theory of the Hadley circulation that couples the dynamics of tropical overturning circulation to extratropical wave dynamics (Schneider et al., 2010).

Professor YEH and his colleagues were decades ahead of their time in hypothesizing that the abrupt seasonal transitions of the general circulation may be a circulation phenomenon that can occur independently of regional surface inhomogeneities, and that this can be probed in a model experiment that abstracts from surface inhomogeneities. (Yeh and Chu, 1958) had earlier expressed the view that the mean meridional circulation is largely controlled by eddies, so we may surmise that they would have been pleased with the more recent discovery of how important a role eddies appear to play in seasonal transitions of the general circulation, through their transports of angular momentum and energy (e.g., Walker and Schneider, 2006; Bordoni and Schneider, 2008; Schneider and Bordoni, 2008) as well as moisture (Boos and Kuang, 2010).

The question remains open as to how the many different processes contributing to seasonal circulation transitions are quantitatively linked. We are still missing a theoretical framework that consolidates our understanding of the general circulation into a set of mathematical equations that are amenable to analytical insight and that would allow us to answer, among other questions, whether the seasonal transition of the circulation can be understood as "a certain type of instability," as conjectured by Yeh-Dao-Li. Unlike in Professor YEH's time, progress towards reaching this goal is not impeded by difficulties to experiment with the general circulation systematically. Numerical models today give us the means to do so. There seems to be little that obstructs progress towards completion of the program began by pioneers such as ROSSBY, CHARNEY, and YEH: developing a comprehensive theory of the general circulation grounded in the universal laws of physics.