850 JOURNAL OF METEOROLOGICAL RESEARCH VOL.28

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2 850 JOURNAL OF METEOROLOGICAL RESEARCH VOL.28 tional capabilities. Synoptic meteorology is an extension of hydromechanics that involves applying hydromechanical principles to a specific fluid (namely, the atmosphere). The atmosphere is a slow-moving fluid with viscosity, compressibility, and phase transitions. These characteristics mean that the atmosphere has a high degree of complexity. Li (2011) divided the history of hydromechanics into four stages: (1) ancient hydromechanics based on practical experience; (2) classical hydromechanics based on Newtonian mechanics (including extensions to continuous media); (3) neoteric hydromechanics based on physical insight; and (4) contemporary hydromechanics based on modern technology. The history of synoptic meteorology can also be divided into four analogous stages: ancient synoptic meteorology, classical synoptic meteorology, neoteric synoptic meteorology, and contemporary synoptic meteorology. Objects studied in synoptic meteorology include both mid- and low-latitude weather, including largescale baroclinic weather systems and mesoscale convective systems. Synoptic meteorology uses diagnostic and analytic methods, as well as numerical simulations. The purview of synoptic meteorology is broad, so it is practically impossible for an article to discuss these topics comprehensively. However, a review of the history of synoptic meteorology reveals that frontal cyclones in mid and high latitudes have been a consistent topic of research from the early days of synoptic meteorology to the present. We use the evolution of frontal cyclone conceptual models to summarize the historical advance of synoptic meteorology, with reference to the four stages of advance in hydromechanics and the historical development of meteorological observational techniques. The first conceptual model of extratropical frontal cyclones was developed by Robert FitzRoy in This model (shown in Fig. 1) represents the embryonic stage of synoptic meteorology, and is one of the most important achievements of ancient synoptic meteorology. FitzRoy sailed around the world with Charles Darwin as a captain in the British Royal Navy, and later achieved the rank of Vice-Admiral. Based on records of winds and temperatures that he recorded in his logbook over many years, FitzRoy concluded that a storm is an anti-clockwise vortex composed of cold and warm air masses. Figure 1 reflects his understanding that the occurrence of a cyclone is closely related to the temperature difference between these warm and cold air masses, and highlights the confrontation between strong flows of warm and cold air within the storm. This model also shows penetration of the warm and cold air masses by cold and warm airflows, as well as wide regions of calm winds between the cold and warm airflows. Many of the phenomena described in Fig. 1 can be clearly seen in modern satellite water vapor images. Figure 1, which is based entirely on observations made without the assistance of radio communications or real-time weather maps, reflects the remarkable depth of FitzRoy s understanding of changes in winds and temperatures. It is worth pointing out that the cores of some of the cyclones shown in Fig. 1 contain both warm and cold air masses, while others contain only warm air mass. These sketches appear to contradict the conceptual cyclone model developed during the classical stage of synoptic meteorology, which held that the core of a cyclone in the occlusion stage is composed entirely 2. Ancient synoptic meteorology: The Fitz- Roy model Fig. 1. Conceptual model of extratropical cyclones developed by Admiral FitzRoy in The figure shows an anti-clockwise vortex with both cold (solid lines) and warm (dashed lines) air masses. [Adapted from Petterssen, 1958 (Chinese version)]

3 NO.5 TAO Zuyu, XIONG Qiufen, ZHENG Yongguang, et al. 851 of cold air; however, they are consistent with the modern conceptual model of explosive cyclones. This point is discussed below. The warm-core cyclone structure in the cyclone model drawn by FitzRoy is by no means fortuitous; on the contrary, it is drawn meticulously and intentionally from the basis of his personal observations. This model is therefore an outstanding example of the ancient stage of synoptic meteorology, which was largely based on practical experience. 3. Classical synoptic meteorology: The Norwegian model The Norwegian conceptual model of extratropical cyclones is summarized in Fig. 2. Developed approximately 100 yr ago by Bjerknes and Solberg (1922), this model represents the achievements of the classical stage of synoptic meteorology. This model differs from the ancient cyclone model in that it treats the front as a three-dimensional core and highlights the inseparability of the front and the cyclone. The front determines the three-dimensional structure of the cyclone, the distribution of rain and clouds within the storm, and even the entire life cycle of the cyclone. Fig. 2. (a 1 a 3) Frontal structure and (b) life cycle of the Norwegian cyclone model. [Adapted from Bjerknes and Solberg, 1922] This classical cyclone model, which is often called the frontal cyclone model, established the core idea that baroclinicity is the mechanism by which weather changes in mid and high latitudes. Despite the lack of upper-air observations (radio soundings) at the time of its development, the classical cyclone model is a three-dimensional model. It includes the horizontal (Fig. 2a 2 ) and vertical (Figs. 2a 1 and 2a 3 ) motions of air at upper levels, as well as the distributions of rain and clouds. Figure 2a 3 shows a vertical section across the warm and cold fronts, while Fig. 2a 1 shows a cross-section of the northern part of the cyclone that does not intersect the surface front. There is also an upper-level front with a warm air mass above and a cold air mass below, but this front does not touch the ground. This model regards the front as a substantial surface that determines the direction of vertical motion and the distribution of rain and clouds. The blocking effect of the cold front causes sinking of cold air to the rear of the front, while the impact effect of the cold front causes warm air to rise along the leading edge. The warm front causes warm air to climb up the underlying surface. The practice of inferring the upper-level structure of a cyclone from surface observations is called indirect upper-level meteorology (aerology). Figure 2b shows the life cycle of the frontal cyclone. The cyclone occurs along a static front in the east-west trough, with the center of the cyclone located at the turning point of this disturbance. The cold front moves eastward and southward as the cyclone deepens, while the warm sector of the cyclone gradually contracts until it disappears. The warm air ascends to upper levels, where it eventually forms an occluded cyclone. Nearly all textbooks on synoptic meteorology introduce this conceptual model, but it contains a serious flaw. From the hydromechanical point of view, continuity is a basic characteristic of a fluid. The assumption that the front acts as a substantial surface therefore cannot be established in hydromechanics, because treating the front as a substantial surface creates a zeroth-order discontinuity in temperature that violates the continuity of the fluid. In reality, the front

4 852 JOURNAL OF METEOROLOGICAL RESEARCH VOL.28 is a transitional region between the cold and warm air masses with a strong temperature gradient. The front is therefore a discontinuity in the temperature gradient (i.e., a first-order discontinuity in temperature). Schultz and Vaughan (2011) have questioned the very existence of the occlusion process in reality based on the continuity principle. Although the treatment of the front as a substantial surface is not tenable, the distributions of rain and clouds predicted by the Norwegian model still accord with observations. This model therefore still exerts profound influences on meteorologists today. 4. Neoteric synoptic meteorology: The Chicago model Similar to the neoteric stage of hydromechanics, the neoteric model of extratropical cyclones is based on deep physical insight. This model, which we call the Chicago model, is the three-dimensional baroclinic disturbance model proposed by Palmén and Newton (1969). The establishment of an upper-air observation network led to the discovery of disturbances in the westerly wind belt above surface cyclones (Fig. 3). The neoteric cyclone model is a three-dimensional model that includes not only the surface cyclone but also the anticyclone behind the cyclone. This model can therefore be called a baroclinic disturbance model. The upper-level trough is located behind the surface cold front and tilts westward (backward) in the vertical direction. This vertical structure accords with both hydrostatic balance and the thermal wind relationship. According to quasi-geostrophic theory, the thermal asymmetry of the backward-tilting baroclinic disturbance indicates a developing disturbance. The cold and warm advection corresponding to the cold and warm fronts act to enhance the amplitude of the upper-level disturbance (Holton, 1972; Tao et al., 2012). The most important aspect of this model is that it gives three trajectories of representative air parcel paths in a cyclone. Specifically, this model specifies the trajectories of warm air parcels ahead of the cold front, the trajectories of cold air parcels behind the cold front, and the trajectories of upper-level air parcels from locations behind the trough to locations ahead of the ridge. The speed of vertical air motion in a large-scale weather system is very small, approximately 0.1% of the speed of horizontal wind. Vertical velocities are therefore very difficult to observe directly. In the classical cyclone model, vertical motion is estimated by considering the front as a substantial surface, which violates hydromechanical theory. Furthermore, the anafront and katafront systems found in weather analyses cannot be reasonably explained under the assumption that fronts are substantial surfaces. Erik Palmén and contemporaries of the Massachusetts Institute of Technology advocated analysis of cyclones on isentropic surfaces. This type of analysis is based on the assumption that potential temperature is conserved over short periods. Vertical motion within the storm is then inferred by analyzing the slopes of isentropic surfaces and the directions of Fig. 3. (a) Three-dimensional stereograph and (b) twodimensional vertical cross-section from the model of frontal cyclones proposed by Palmén and Newton (1969). Solid lines show height contours at 300 hpa, while dashed lines show isobars at the surface. Double-shafted arrows show trajectories of cold and warm air near the cold front and their projections at surface. Double-dashed arrows show air parcel trajectories at upper levels from the rear of the trough to the front and their projections at 300 hpa.

5 NO.5 TAO Zuyu, XIONG Qiufen, ZHENG Yongguang, et al. 853 isentropic winds. The representative trajectories derived from the neoteric cyclone model reflect a profound understanding of quasi-geostrophic dynamics in the large-scale circulation. The trajectories of sinking cold air and rising warm air shown in Fig. 3 reflect the occurrence of sinking motion with cold temperature advection and rising motion with warm temperature advection under quasi-geostrophic balance. Cold advection is related to cold fronts, while warm advection is related to warm fronts. Both of these trajectories have distinct clockwise curvatures, and highlight that sinking motion is related to low-level divergence, while rising motion is related to upper-level divergence. The absolute magnitude of negative vorticity in diverging air parcels increases, so the curvature of the trajectories is anticyclonic. The trajectories therefore reflect both vertical motion under Dyne s mass-conservation principle and the relationship between divergence and relative vorticity articulated by the vorticity equation (i.e., divergence increases the absolute magnitude of negative vorticity). The baroclinic atmosphere includes an upperlevel westerly jet above the surface front. The wind speeds in this jet are much larger than the propagation speed of the disturbance. We can therefore infer that upper-level air parcels must move from locations behind the trough to locations ahead of the trough. As air parcels move from the trailing ridge to the trough, their vorticity changes from negative to positive. This increase in air parcel vorticity must be related to convergence. This means that trajectories behind the trough must sink toward the surface (as shown in Fig. 3). By contrast, the vorticity of air parcels moving from the trough to the leading ridge must change from positive to negative. This decrease of air parcel vorticity must be related to divergence, so trajectories ahead of the trough must rise. This overall picture of air parcel motion is consistent with the relationship between vertical motion and the vertical derivative of vorticity advection expressed in the quasi-geostrophic diagnostic equations. This three-dimensional baroclinic disturbance model based on observations and analyses (presented by Palmén and Newton in the book Atmospheric Circulation Systems; Palmén and Newton, 1969) is consistent with the diagram (shown in Fig. 4) of the secondary circulation in a back-tilting baroclinic disturbance presented by Holton in his widely used textbook An Introduction to Dynamic Meteorology (Holton, 1972). This consistency highlights the profound understanding of dynamical theory that underpins the neoteric cyclone model. 5. Contemporary synoptic meteorology: A cyclone model for the modern era The popular application of satellite imagery in the 1980s led to the discovery of spiral occluded frontal cloud belts in intensifying cyclones over the North Atlantic Ocean (Fig. 5a). Conceptual analysis (Figs. 5b and 5c) and scientific observations (including dropsondes released from airplanes and buoy stations on the ocean surface) as well as synoptic analysis (Figs. 6a c) showed very strong temperature gradients on both sides of the occluded front. These observations were inconsistent with the thermal structure of the occluded front predicted by the classical cyclone model, which considered the front to be a substantial surface. The cold front catches up to the warm front at the last Fig. 4. Schematic diagram of the secondary circulation associated with a developing baroclinic disturbance. (a) 500-hPa (solid line) and 1000-hPa (dashed lines) geopotential height contours, and surface fronts. (b) Vertical profile through line II in (a), indicating the direction of vertical motion. [Adapted from Holton, 1972]

6 854 JOURNAL OF METEOROLOGICAL RESEARCH VOL.28 Fig. 5. (a) Spiral occluded frontal cloud belts in an intensifying cyclone over the North Atlantic Ocean. (b, c) Conceptual models of the life cycle of a marine extratropical cyclone. Step (I) shows the initial development, step (II) the frontal fracture, step (III) the back-bent warm front and frontal T-shape, and step (IV) the warm-core frontal occlusion. (b) Shows sea-level pressure (solid lines), fronts (bold lines), and the cloud distribution (shaded). (c) Shows temperature (solid lines) and cold and warm air currents (solid and dashed arrows, respectively). [From Newton and Holopainen, 1990; their Fig ] stage of the cyclone life cycle, forming a so-called occluded front. The air masses on both sides of the occluded front are cold, so the temperature contrast should be small. The results of idealized numerical simulations of developing baroclinic disturbances under the primitive equations led to the development of a new cyclone conceptual model (Newton and Holopainen, 1990; Snyder et al., 1991). This model features a T-shaped frontal structure and a back-bent warm front. Back-bent warm fronts are frequently observed during the last stage of the cyclone life cycle, particularly in explosive marine and continental cyclones. For example, Xiong et al. (2013) showed the existence of a back-bent warm front in a cyclone over Mongolia. The contemporary and classical cyclone models are similar in that both indicate the co-existence of warm and cold fronts in the cyclone, and both break cyclone development into four stages. However, unlike the classical model, the cold and warm fronts in the center of the cyclone do not connect with each other in the contemporary model. By contrast, the two fronts form a T-shaped front structure. The warm front stretches westward and southward as the cyclone develops, and then twines in a spiral around the center of the cyclone. A warm front that undergoes this type of wrap-up process is called a back-bent warm front. Although the shape of this back-bent front is similar to that of the occluded front in the classical model, the back-bent warm front keeps its original temperature gradient. The characteristics of the back-bent front are therefore entirely different from those of the occluded front. The backward bend of the warm front in the contemporary cyclone model means that some warm air is drawn into the center of the cyclone. This process warms the air in the center of the cyclone relative to the surrounding air, and thus leads to the formation of a warm core. This phenomenon was also described in the ancient model developed by FitzRoy (Fig. 1). This indicates that the FitzRoy s model was both careful and (in many ways) comprehensive; however, the classical (Norwegian) model neglected the potential formation of a warm core. The reason for this oversight is related to the assumption that the front can be treated as a substantial surface. In this case, the occlusion process means that the core area of the cyclone must be occupied entirely by cold air. Cold core cyclones do not exist in nature (Schultz and Vaughan, 2011). The development of a back-bent warm front and the formation of a warm core can be illustrated by using high-resolution numerical model simulations and modern computer visualization techniques (Fig. 7) (Wang et al., 2000). Three-dimensional air parcel trajectories can be calculated explicitly based on the

7 NO.5 TAO Zuyu, XIONG Qiufen, ZHENG Yongguang, et al. 855 Fig. 6. (a) Geostationary Operational Environmental Satellite 7 (GOES-7) visible image at 1801 UTC 14 December 1988 with frontal positions superimposed. (b) Surface isobars (solid black lines; interval 4 hpa), isotherms (dashed gray lines; interval 4 ), and horizontal winds (pennant, full barb, and half-barb denote 25, 5, and 2.5 m s 1, respectively) at 1800 UTC 14 December The positions of ships (open circles) and buoys (dots) are also shown. (c) Flight section at 300 m above sea level with ship, buoy, and dropsonde data included. Temperature (solid lines; interval 2 ) and horizontal winds (as in (b)) are also shown. The area of this flight section is shown as a solid rectangle in (b). [From Schultz and Vaughan, 2011] distribution of hourly winds (u, v, w), rather than inferring them from physical insight as was done during construction of the neoteric cyclone model. Figure 8 (Zhang et al., 2006) shows two groups of trajectories that roughly correspond to those shown in Fig. 3. The first group of trajectories corresponds to warm and wet air parcels that ascend to the upper troposphere from surface locations ahead of the cold front. The second group corresponds to air parcels that are initially located behind the upper-level trough, which first sink and then rise as they travel across the trough toward the leading edge of the system. These two groups of trajectories share many features in common with the theoretical trajectories shown in Fig. 3. Specifically, the curvature of the trajectories shown in Fig. 3 is anticyclonic in the upper troposphere. The second group of trajectories shown in Fig. 8 sinks first and then rises after crossing the trough. The convergence and divergence of the simulated trajectories highlight the strong relationship between horizontal convergence and the direction of vertical motion. The trajectories shown here represent air parcel movement in a developing cyclone and a strengthening upper-level trough. The upper-level trough develops

8 856 JOURNAL OF METEOROLOGICAL RESEARCH VOL.28 are very difficult to describe conceptually based solely on physical understanding. Our current conceptual understanding of extratropical cyclones owes much to the development of computer technology and numerical modeling techniques. 6. Discussion and concluding remarks Fig. 7. Cloud top stereograph of a simulated cyclone system at 0100 UTC 2 June The 0.1 g kg 1 ice water content iso-surface is shown in color, and the wind fields at 1.5- and 12-km altitudes are shown as green arrows and red streamlines, respectively. [From Wang et al., 2000] Fig. 8. (a) As in Fig. 7, but including air parcel trajectories (shown as shaded strips). The shading indicates temperatures at different levels, with red colors (at low levels) indicating higher temperatures than blue colors (upper levels). (b) Air parcel trajectories. [From Zhang et al., 2006] into a cutoff low. The low-level warm front then bends backward, isolating the warm core. The complex dynamical processes that occur during this development The rate of advance in synoptic meteorology highlights the complexity of atmospheric motions. Weather systems develop on multiple scales simultaneously, with interactions among subsystems of many different scales. Although midlatitude cyclones are fundamentally large-scale baroclinic waves, latent heat feedbacks caused by mesoscale precipitation also affect their development. A convective system over the tropical ocean with an initial scale of dozens of kilometers could develop into a tropical cyclone with a scale of a thousand kilometers. Severe convective systems in midlatitudes, which may also have scales of dozens of kilometers, can generate tornadoes with scales of hundreds of meters. Studies of complicated nonlinear processes in the atmosphere are aided substantially by the use of modern massive numerical simulations. As examples, Fig. 9a shows the three-dimensional motion inside a typhoon using a high-resolution numerical model based on the nonhydrostatic primitive equations (Wang et al., 1999), while Fig. 9b shows a simulation of the formation of a tornado below a severe convective storm. In a typhoon, warm and moist air containing large amounts of unstable potential energy converges into the typhoon at sea level from all directions and then ascends (dashed-line segments in Fig. 9a). This ascent releases large amounts of energy into the atmosphere, so upward motion becomes very strong (red line segments and balls in the core of the typhoon). The air diverges eastward and westward as it nears the tropopause, entering the subtropical upper-level westerly jet and the tropical easterly jet along the south side of the Tibetan high. Tornadoes form at the base of strong convective systems with horizontal scales of dozens of kilometers and slow rotation. A large number of vortices with scales of dozens of meters each exist near the base of

9 NO.5 TAO Zuyu, XIONG Qiufen, ZHENG Yongguang, et al. 857 Fig. 9. (a) Air parcel trajectories from simulation of a typhoon system over the northern South China Sea on 1 May Dashed lines show 3-h trajectories, balls indicate the positions of air parcel trajectories within 72 h, and colors indicate upward (red) and downward (blue) vertical velocity. [From Wang et al., 1999]. (b) Video screenshot of a simulated tornado system. [Provided by Professor Xue Ming of University of Oklahoma] the cloud. The air pressure is relatively low within these vortices, so that pendent objects form in these regions of low pressure at the base of the cloud. These small-scale vortices are generally relatively weak, with short life spans. However, occasionally one of these vortices will intensify: the central pressure of the vortex drops sharply, and the pear-shaped bulge at the bottom of cloud develops into a tornado that touches down on the ground. These two examples above show that the numerical simulations that underpin the modern practice of synoptic meteorology can almost do anything (Wang et al., 1998; Wang et al., 2004; Chen et al., 2007). The core task of contemporary synoptic meteorology is to grasp the physical scientific understanding within the large amounts of data produced by numerical models. It is therefore necessary to learn and inherit the profound physical understanding gained during the neoteric stage of synoptic meteorology. A conceptual model represents a generalization of physical knowledge. Figure 10 shows a schematic diagram published in Proceedings of the Extratropical Cyclones Symposium organized in memory of Erik Palmén by the American Meteorological Society in 1988 (Newton and Holopainen, 1990). It shows physical understanding originating from observations, theory, and diagnosis (Shapiro et al., 1999). The essence of observations should be understood by using theory, while theory must be based on observations, and diagnosis links observations and theory. Even in modern times with the advent of powerful computers and big data, the continued advance of synoptic meteorology still requires the careful combination of observations, theory, and diagnosis. Acknowledgment. The authors wish to thank one of the reviewers who provided a very important paper (Schultz and Vanghan, 2011) published in Bulletin of the American Meteorological Society. Thispaper argues that modern research shows that occluded fronts and the occlusion process presented 90 yr ago in the Norwegian cyclone model do not exist in reality. Therefore, synoptic textbooks about the occlusion Fig. 10. Physical understanding and conceptual representation through the union of theory, diagnosis, and observation. [From Shapiro et al., 1999; their Fig. 1]

10 858 JOURNAL OF METEOROLOGICAL RESEARCH VOL.28 process need to be rewritten. This is one of the authors motivations to write this paper. REFERENCES Bjerknes, J., and H. Solberg, 1922: Life cycle of cyclones and the polar front theory of atmospheric circulation. Geophysisks Publikationer, 3, Chen Min, Tao Zuyu, Zheng Yongguang, et al., 2007: The front-related vertical circulation occurring in the pre-flooding season in South China and its interaction with MCS. Acta Meteor. Sinica, 65, (in Chinese) Holton, J. R., 1972: An Introduction to Dynamic Meteorology. Academic Press Inc., Li Jiachun, 2011: Flow everywhere. com/3.1/1111/01/ html. Accessed on 1 November (in Chinese) Newton, E. C., and E. O. Holopainen, 1990: Extratro- pical Cyclones The Erik Palmén Memorial Volume. Amer. Meteor. Soc., Boston, USA, Palmén, E., and C. W. Newton, 1969: Atmospheric Circulation Systems. Academic Press, Petterssen, S., (Translated by Cheng Chunshu), 1958: Weather Analysis and Forecasting. Science Press, Beijing, (in Chinese) Schultz, D. M., and G. Vaughan., 2011: Occluded fronts and the occlusion process A fresh look at conventional wisdom. Bull. Amer. Meteor. Soc., 92, Shapiro, M., H. Wernli, J. W. Bao, et al., 1999: A planetary-scale to mesoscale perspective of the life cycles of extratropical cyclones: The bridge between theory and observations. The Life Cycles of Extratropical Cyclones, Shapiro, M. A., and S. Gronas, Eds., Amer. Meteor. Soc., Snyder, C., C. S. William, and R. A. Rotunno, 1991: Comparison of primitive-equation and semigeostrophic simulations of baroclinic wave. J. Atmos. Sci., 48, Tao Zuyu, Zhou Xiaogang, and Zheng Yongguang, 2012: Theoretical basis of weather forecasting: Quasigeostrophic theory summary and operational applications. Adv. Meteor. Sci. Technol., 2, (in Chinese) Wang, H. Q., K. H. Lao, and W. M. Chan, 1999: A PC based visualization system for coastal ocean and atmospheric modeling. Proceedings of the Sixth International Estuarine and Coastal Modeling Conference, New Orlean, USA, doc/4.pdf. Wang Hongqing, Zhang Yan, Tao Zuyu, et al., 1998: Visualization of large five-dimensional complex data. Prog. Nat. Sci., 8, (in Chinese),,, et al., 2000: Visualization of the numerical simulation of a Yellow Sea cyclone. J. Appl. Meteor. Sci., 11, (in Chinese),, Zheng Yongguang, et al., 2004: Meteorological data visualization system. Acta Meteor. Sinica, 62, (in Chinese) Xiong Qiufen, Niu Ning, and Zhang Lina, 2013: Analysis of the back-bent warm front structure associated with an explosive extratropical cyclone over land. Acta Meteor. Sinica, 71, (in Chinese) Zhang Wei, Tao Zuyu, Hu Yongyun, et al., 2006: A study on the dry intrusion of air flows from the lower stratosphere in a cyclone development. Acta Sci. Nat. Univ. Pekin., 42, (in Chinese)