Physical Mechanisms Responsible for Track Changes and Rainfall Distributions Associated with Tropical Cyclone Landfall
Abstract and Keywords
As a tropical cyclone approaches land, its interaction with the characteristics of the land (surface roughness, topography, moisture availability, etc.) will lead to changes in its track as well as the rainfall and wind distributions near its landfall location. Accurate predictions of such changes are important in issuing warnings and disaster preparedness. In this chapter, the basic physical mechanisms that cause changes in the track and rainfall distributions when a tropical cyclone is about to make landfall are presented. These mechanisms are derived based on studies from both observations and idealized simulations. While the latter are relatively simple, they can isolate the fundamental and underlying physical processes that are inherent when an interaction between the land and the tropical cyclone circulation takes place. These processes are important in assessing the performance of the forecast models, and hence could help improve the model predictions and subsequently disaster preparedness.
Tropical cyclones (TCs), commonly known as hurricanes in the North Atlantic Ocean and typhoons in the western North Pacific Ocean, are one of the most destructive natural hazards on earth. They form and spend almost their entire lifetime over oceans, where they pose threats to all oceangoing vessels. Fortunately, in recent years, through adequate warnings with enough lead time, most of these vessels can avoid being hit by a TC. On the other hand, when a TC makes landfall, the very strong winds, heavy rain, and storm surge associated with its landfall can lead to severe loss of lives and property, irrespective of whether the track forecasts are accurate or not. Quite often, interaction between the TC circulation and the coastal land surface, which may consist of complex topography, can lead to unexpected movements of the TC as well as localized heavy rain that can couple with storm surge to produce severe flooding. Weakly-built structures could also be destroyed by the strong winds from the TC, which are often enhanced by local topography.
Among the three elements of track, convection (and hence rainfall), and winds (and hence storm surge), track is the most important one, because if the prediction of track is wrong, the forecasts of rainfall, winds, and storm surge occurring at a given location would also be incorrect. In this chapter, we therefore first present the current state of science in understanding the processes that are responsible for changes in the track associated with TC landfall. Physical processes that likely govern changes in the distribution of convection and rainfall as a TC approaches land are then discussed.
The interaction of the TC circulation with land also modifies the TC intensity (maximum wind speed near the earth’s surface) and the wind distribution. However, the availability of wind observations is limited, partly because winds can vary tremendously across small distances due to topography or different land use, and partly because extreme winds often destroy the anemometers so that “true” observations cannot be obtained. As a result, only limited observational or theoretical/numerical studies have been conducted, so that it is still difficult to describe or understand the types of changes in the intensity and wind distribution that could occur as a TC is about to make landfall. Nevertheless, this chapter attempts to summarize some of the work in this area. The hazard of storm surge associated with TCs is quite well understood, and so the basic theory is presented, together with a brief description of the approaches that have been used to predict the surges.
Theoretical Framework of Tropical Cyclone Motion
The fundamental processes that cause TC movement have been summarized in Chan (2005). In a baroclinic atmosphere, TC motion can be explained using the potential vorticity (PV) equation:(1)
where P1 is the value of the azimuthal wavenumber-1 PV, and Λ1 is an operator that extracts the azimuthal wavenumber-1 value of each of the quantities.
It has been shown by Wu and Wang (2000) from a theoretical, and Chan, Ko, and Lei (2002) from an observational, perspective that a TC tends to move toward a maximum in the value of (∂P1/∂t), which hereafter will be referred to as PV tendency (PVT). Thus, understanding how a TC moves is to evaluate the contributions from each of the terms in Equation (1). For each of the terms, as well as the total PVT, Wu and Wang (2000) proposed to estimate a vector that gives the direction and magnitude of its contribution to the overall motion vector. The larger the magnitude of the vector, the more important that component is, because the sum of these vectors, which is the vector representing TC motion, gives the direction and speed of TC motion.
In the following section, the relative contribution of each term in Equation (1) to the overall motion of the TC under different situations is examined.
Effects of Land-Sea Contrast on Tropical Cyclone Movement
Before a TC makes landfall, part of its circulation ahead of the TC center will already encounter the land that has greater friction and topography, if the latter exists. These differences will then directly affect the first two as well as the last terms on the right-hand side of Equation (1). In addition, the amount of moisture available would likely be less than that over the ocean. The convection, and subsequently the diabatic heating, distribution will therefore be altered, which will then modify the third term in Equation (1). It should be noted that topography, as well as the increase in friction, could also lead to different moisture distributions as well.
Wong and Chan (2006) performed a set of very simple experiments to investigate the effect of land-sea contrast on TC motion on an f plane. If there were no land-sea contrast, and with no terrain, a vortex on an f plane should remain stationary (Chan, 2005) (Figure 1a). However, in the presence of rough land (i.e., increased friction), the vortex is “attracted” toward land irrespective of the moisture available over land (Figures 1c and 1d). However, if the land is dry but not rough, no movement occurs (Figure 1b). In other words, a rougher surface is the crucial factor in causing this drift of the vortex toward land.
Wong and Chan (2006) explained this drift based on the vorticity equation. They showed that frictional differences between land and sea produce, near the earth’s surface, convergence on the onshore side and divergence on the offshore side. As a result, cyclonic and anticyclonic vorticities are generated in the mid troposphere on the offshore and onshore sides respectively, leading to a formation of a pair of gyres that are subsequently advected cyclonically by the TC circulation (Figure 2). The flow in between the gyres (the “ventilation flow”) then advects the TC southward. At the same time, the convergence on the onshore side and the subsequent advection leads to strong diabatic heating on the north side of the TC (Figure 3d). This cancels part of the horizontal advection effect produced by the ventilation flow (Figure 3b), so that the vortex eventually moves toward the southwest (Figure 3a). Note that the vertical advection term is apparently unimportant (Figure 3c).
The results of Wong and Chan (2006) are for a vortex in the Northern Hemisphere. Using a different numerical model, Li, Cheung, and Chan (2014) obtained similar results for a vortex in the Southern Hemisphere (Figure 4). It can therefore be concluded when a TC circulation is embedded in an area with a frictional contrast, the TC will drift toward the area with stronger friction, and toward the offshore side.
If the experiments are run on a beta plane (in which case a Northern Hemisphere TC with no land-sea contrast would move toward the northwest—see Chan and Williams ), the drift depends on the orientation of the coastline (Szeto & Chan, 2010). For a north-south-oriented coastline, the TC track shifts southward compared with the case with no land as a result of the processes discussed in the previous paragraphs for the f-plane case (Figure 5b). However, for an east-west-oriented coastline, the vortex now drifts to the right side of the track without any land (Figure 5a). Szeto and Chan (2010) explained this difference as follows: Because of the orientation of the coastline, the superposition of the beta gyres onto the land changes the location of the asymmetric convergence/divergence pattern that generates the land-induced gyres, which can be clearly seen by taking the difference between the experiments with and without the land-sea contrast (Figure 6). While the land-induced gyres are oriented in almost the north-south direction in a north-south-oriented coastline (Figure 6b), those for an east-west-oriented coastline have a northwest-southeast orientation (Figure 6a), thus creating a “ventilation” flow that advects the TC toward the northeast.
To examine further the contribution of differences in frictional contrast on TC track, Au-Yeung and Chan (2010) performed two experiments on an f plane with different roughness values over the land portion of the domain and found that a vortex tends to drift toward rougher land (Figure 7), which is caused by an increase in vertical advection (second term in Equation 1) in the area of rougher land (not shown).
To summarize, when at least part of the circulation of a TC encounters a difference in roughness, changes in the convergence/divergence pattern occur, which can lead to changes in the vertical motion (hence diabatic heating) and in the components of the PV equation (hence the relative vorticity). All these will produce a different PVT pattern that will cause the TC to move, in general, toward a surface of higher roughness.
Changes in the TC track in the presence of topography have been observed for a long time (e.g., Brand & Blelloch, 1974). To understand the mechanisms, many numerical studies have been performed. For example, Yeh and Elsberry (1993) imposed an easterly flow to push a TC toward an idealized terrain similar to that of Taiwan, and found that a TC approaching the northern part of this terrain is deflected to the north while a southward deflection occurs for a TC making landfall in the southern part because the background flow is modified by Taiwan’s topography. In an even simpler study, Kuo, Williams, Chen, and Chen (2001) showed that in the presence of an idealized topography of Taiwan, a vortex in a barotropic atmosphere tends to circulate clockwise around the topography, which the authors called the “topographic beta effect.” Other dynamic factors that might contribute to track changes have also been proposed. These include modification of the Froude and Rossby numbers of the basic flow (Lin, Chen, Hill, & Huang, 2005), channeling effect (Huang, Wu, & Wang, 2011; Jian & Wu, 2008), and blocking of the lower tropospheric flow (Chambers & Li, 2011, for the case of the Big Island in Hawaii). All of these factors will likely modify the background flow and/or the TC circulation, and hence change the PVT through horizontal advection.
In terms of diabatic heating, Hsu, Kuo, and Fovell (2013) found that TCs landing in the northern and southern parts of Taiwan move slower and faster respectively than the average because of the difference in rainfall distributions. They ran numerical experiments using different diabatic heating distributions and showed that the speed of the vortex is indeed modified. Wang, Chen, Kuo, and Huang (2013) also explained the slowing down of Typhoon Fanapi (2010) based on the asymmetric heating distribution.
Most of these previous investigations have either included a background flow or used an idealized terrain. The “pure” effect of real terrain on vortex motion cannot be ascertained. Results from case studies also cannot be generalized.
For these reasons, Tang and Chan (2014) did an experiment on a beta plane with no background flow for a TC near Taiwan. They found that as the onshore side of the TC circulation encounters the central mountain range of Taiwan and goes over to the lee side, conservation of PV leads to the formation of a cyclonic gyre. By the same argument, an anticyclonic gyre would form to the west of the offshore side. A pair of counter-rotating gyres is thus generated (Figure 8a). The TC circulation then rotates this pair of gyres cyclonically, so that by the time the TC moves closer to the island, the ventilation flow between the gyres pushes the TC northward (Figures 8b and d). Further rotation of the gyres changes the direction of the ventilation flow, and hence the TC moves back southward after making landfall on the island (Figure 8c).
Tang and Chan (2014) found that the deflection of the TC is not only caused by the horizontal advection of PV. Diabatic heating also contributes substantially when the TC is very close to the island (Figure 9), which is consistent with the conclusion of Hsu et al. (2013).
To investigate whether such deflection also exists when a TC encounters other mountain ranges, Tang and Chan (2014) also performed a similar experiment for the island of Luzon. They found a similar deflection (Figure 10a) and a similar set of gyres (Figure 10b), although the magnitude of the ventilation flow is weaker because the height of the mountain range in Luzon is not as high, and hence the deflection is not as large (see Figure 10a).
In their second study (Tang & Chan, 2015a), they showed that because the development of these gyres depends on the interaction between the TC circulation and topography, TCs that appear to be far away from Taiwan could also be affected, sometimes to an appreciable extent (Figure 11). For example, a TC moving into the South China Sea could still be deflected toward Taiwan (as in the TW125 and TW115 cases in Figure 11).
Clearly, the interaction described in these two studies depends on when the TC circulation starts to interact with the terrain, which means that the size of the TC is important. Indeed, Tang and Chan (2015b) showed that as the size becomes smaller, the TC has to be closer to the mountains before a track deflection would occur (Figure 12). However, the deflection for a medium-size TC (the example TWm15 in Figure 12) is actually the largest—see especially the inset panel in Figure 12. This is because the terrain-induced gyres advected by the TC circulation are at such a location as to produce the largest ventilation flow to push the TC northward. For a small TC, the ventilation flow is actually rather weak (not shown) and hence the deflection is smaller (TWs137 in Figure 12).
To summarize, interaction between the TC circulation and topography leads to the formation of a pair of counter-rotating gyres that will cause the TC to be deflected through the processes of both horizontal advection and diabatic heating. The extent of the deflection depends on the height of the topography, the size of the TC, and the relative position between the TC and the topography. It should be noted that all these results were obtained with no background flow. If an environment flow is present, it will also interact with the topography, and hence the track deflection becomes more complicated. Intuitively, this should depend on the strength of the environmental flow.
One significant implication of these results is that, in the numerical prediction of TC tracks, the representation of the land in terms of land use (and hence roughness, e.g., grassland versus urbanized area) and terrain height (e.g., Taiwan versus Luzon) must be as accurate as possible. Because the diabatic heating term also contributes substantially to the overall PVT especially close to landfall, it is also important that accurate moisture data be available. In addition, how the TC outer structure is represented in the model is crucial, as an erroneous representation of the TC size would lead to a wrong interaction with topography.
Convection and Rainfall Distributions Near Landfall
In addition to track changes, the distributions of convection and rainfall also change when a TC is approaching land. In this section, we summarize the main research results on such changes based on observations as well as numerical modeling.
Observational studies of rainfall associated with TC landfall date back to at least the 1950s, when Koteswaram and Gaspar (1956) and Miller (1958) found, based on rain gauge data along the coast, that rainfall associated with Northern Hemisphere TCs is generally heavier to the right side of the TC. Similar results were obtained by Powell (1982, 1987) for individual TCs in the Atlantic (e.g., Figure 13 for Hurricane Frederic in 1979) and by Yuan, Zhou, Huang, and Liao (2009) through examining radar data for a number of cases making landfall in China. Fung (2010) studied rain gauge data over South China and also found more rainfall over land on the onshore side.
On the other hand, some other studies found just the opposite, with rainfall being the maximum to the offshore side of the track near landfall for both the Northern (Blackwell, 2000; Parrish, Burpee, Marks, & Grebe, 1982; also Chan, Liu, Ching, & Lai, 2004—see the example in Figure 14) and Southern Hemispheres (May, Kepert, & Keenan, 2008; also Li, Cheung, Chan, & Tokuno, 2013—see the example in Figure 15). Liu, Chan, Cheng, Tai, and Wong (2007) analyzed satellite cloud-top temperatures, which were used as a proxy for deep convection, during the landfall of 18 TCs over South China, and concluded that the location of heaviest convection near landfall apparently depends on the direction of the vertical wind shear.
These contrasting results from different studies (i.e., whether more rainfall is on the onshore or offshore side) are likely a consequence of several factors. First, each study generally used one type of data (rain gauge, radar, satellite). The coverage of rain gauges is limited and confined to land. Radar data depict convection in the lower troposphere and not necessarily the rainfall on the ground. Satellite data also suffer from a similar problem. Second, because of the difficulty in retrieving data for a large number of cases, most of the observational studies were based on not too many TCs. The conclusion is therefore not robust and likely depends on the characteristics of the TCs studied and the environment in which the TCs were embedded, and hence cannot be generalized. Third, an important factor that apparently determines the rainfall distribution is vertical wind shear (Liu et al., 2007). Differences in vertical wind shear in different cases can therefore lead to differences in the rainfall asymmetries. Similar results were found by Wingo and Cecil (2010) using satellite data and in a recent study by Xu, Jiang, and Kang (2014) on TCs making landfall in southern China and the southeastern United States based on rain gauge data.
To understand the physical processes responsible for the rainfall asymmetries, many numerical studies have also been carried out, which are summarized in the next subsection.
Factors Affecting the Convection/Rainfall Distribution
Various theories have been proposed to explain the rainfall distribution associated with TC landfall. Dunn and Miller (1960) suggested that because of increased surface friction on the onshore side, low-level convergence is enhanced and hence more rainfall occurs. Based on numerical simulation results, Tuleya and Kurihara (1978—see Figure 16), Jones (1987), and Chen and Yau (2003) reached the same conclusion. However, simulations on an f plane made by Chan and Liang (2003) gave maximum rainfall in the front-left quadrant prior to landfall, but the maximum rotated to the front-right quadrant after landfall—see Figure 17. The main difference in their experiment compared with the previous ones is that the land is simulated to move toward the TC so that no asymmetry in the wind field is present due to the steering of the TC toward land. They explained this result in terms of dry-air intrusion and a subsequent change in the convective stability. In another f-plane simulation, Wong and Chan (2006) also showed that maximum rainfall is on the offshore side of the TC circulation, which is related to the direction of the vertical wind shear such that the strongest convection is located left of the downshear direction, consistent with the observational result of Liu et al. (2007).
In the Southern Hemisphere, Ramsay, Leslie, and Kepert (2009) found the rainfall simulated from a high-resolution mesoscale model associated with the landfall of Tropical Cyclone Larry (2006) in Australia to possess a pronounced maximum to the right (offshore) side of the TC prior to landfall in the inner core of the TC, and attributed that to the frictional asymmetry and subsequent advection of the hydrometeors by the cyclonic circulation of the TC. Li, Cheung, and Chan (2015) obtained similar results in their simulations of TCs in the Southern Hemisphere, with the rainfall distribution being to the right of the downshear direction of the vertical wind shear.
These numerical studies point to three factors that could affect the rainfall distribution: surface roughness, moisture availability, and vertical wind shear. Different relative contributions from these factors under different environmental conditions are likely the reason for the different observed rainfall distributions. The presence of topography (shape and height) is another important factor that could modify the left-right asymmetries in rainfall. In addition, environmental factors such as monsoonal flow and frontal boundaries, and microphysical processes such as conversion of different phases of hydrometeors, may also lead to changes in the rainfall distribution (see Elsberry et al., 2013, for a review).
The Physics Governing Track and Convection Changes
Figure 18 gives a schematic diagram showing the possible processes that likely contribute toward the changes in TC movement and its rainfall distribution as it approaches land through the interaction between its circulation and the land features. Such interaction is due to three main factors: surface roughness, moisture availability, and topography. Differences in surface roughness between land and sea, as well as the presence of topography, give rise to convergence/divergence at different locations, which will lead to changes in the vertical motion (and hence rainfall) and relative vorticity distributions. As a result of the latter, a pair of counter-rotating gyres is formed, establishing an atmospheric flow pattern that causes (1) changes in PVT mainly through horizontal advection of PV and diabatic heating (from convergence and moisture advection), and (2) the development of vertical wind shear that also affects the location of maximum diabatic heating. In addition, moisture availability and topography can change the distribution of convection, and vertical wind shear can develop from the presence of topography. These processes then cause the TC to move differently and the distribution of convection to be different compared with the case with no land or topography.
It is clear that the processes are very complex. A good understanding of such processes is therefore important in providing a good prediction of both the TC track and its rainfall distribution, which will reduce the hazards as well as the loss of lives and property as the TC makes landfall.
Changes in Intensity and Wind Distribution
The third change that occurs as a TC approaches land is its wind distribution, which includes its peak wind (intensity) and the radial and azimuthal variations of the wind speed. This section summarizes some of the studies in this aspect.
A TC generally weakens near and after landfall, and dissipates soon after that. The major physical processes responsible for such a phenomenon are as follows: First, compared with that over the open ocean, air over land is generally drier. At the same time, the land surface temperature is also lower than that of the sea for two reasons. As the outer rainbands move over land, the dry air near the land surface causes evaporation of the rain beneath the clouds, and hence a cooling of the land surface. The clouds will also block solar radiation from reaching the land surface. With lower temperature and lower moisture content, the equivalent potential temperature of air over land is thus lower, which when being drawn into the TC, will reduce the amount of convection of the TC as it is close to land. Such dry air flowing into one side of the eyewall could also reduce the integrity of the eyewall and hence the warming at the TC center cannot be easily maintained. These processes will lead to a weakening of the TC. Another factor is the increased friction over land so that as the outer circulation of the TC encounters land, the wind speed is reduced, which then reduces the amount of angular momentum that can be transported into the center of the TC, and hence the TC will weaken.
Occasionally, a TC can last a long time over land and even reintensify due to the injection of moisture either through advection or its movement over a body of water such as a large lake. Enhancement of the TC circulation can also occur if it moves close to a low-pressure trough.
Many individual case studies have been carried out through analyses of observations or numerical simulations to illustrate that one or more of the processes described above indeed occurred in a particular TC. In numerical simulations, sensitivities to various factors have also been investigated. However, with the exception of one study (Rappaport et al., 2010), the patterns of intensity change of TCs near landfall under various dynamic and thermodynamic conditions have yet to be systematically analyzed. While individual case simulations can provide insights into the processes responsible for that particular TC, generalization of the processes is not possible because the environment in which each TC is embedded is different. Simulations under different background environments and topography therefore need to be made to ascertain the relative contributions of various processes.
Although intensity is generally the parameter to evaluate when wind damage is considered, the radial and azimuthal distributions of wind are equally as important in hazard preparedness. Unfortunately, wind observations over the ocean and land are both scarce and scattered, which makes it difficult to study and understand such distributions in a systematic manner. The few studies that have been carried out are all case studies, the pitfalls of which have been pointed out in the previous subsection.
Clearly, increased friction over land will lead to a reduction in wind speed. However, wind speeds can be increased through channeling and downslope effects in regions with topography, as well as downbursts from heavy rain. But again, because these are all location specific, it is difficult to generalize the effect.
One possible effect has recently been identified through numerical simulation (Wong & Chan, 2007). In their simulation on an f plane, and assuming a dry atmosphere as well as a time-invariant axisymmetric mass field, a wind maximum is found to occur offshore at the time of TC landfall (Figure 19). They explained this maximum based on the gradient wind balance concept. As the swirling flow of the TC moves offshore, it suddenly encounters a smaller friction. As a result, the pressure-gradient force becomes larger than the sum of the Coriolis and centrifugal forces, which leads to a negative radial acceleration and subsequently a stronger tangential wind offshore of the TC center. When they remove the above assumptions and ran the full-physics model again, a similar maximum is found. Because such numerical experiments are idealized ones, this effect should be present in all TCs. However, such an effect has not been verified because of the difficulty in obtaining such near-shore observations.
The term “storm surge” generally refers to the rise in water level along the coast as a TC approaches, the causes of which can include the stress due to the strong winds, the atmospheric pressure deficit, and breaking waves. However, the actual observed water level can be different from this rise because of the astronomical tide. If the storm surge occurs at the same time as the astronomical high tide, the total water level can be much higher. Because of this, prediction of the actual sea-level rise will need to take into account both the storm surge and the astronomical tide.
The wind stress on the water is enhanced near the coast especially in the presence of an extensive continental shelf. The shape of the coastline can also play an important role in channeling or diverting the water to cause a higher sea-level rise than predicted in some areas. The atmospheric pressure deficit refers to the difference in the atmospheric pressure near the TC center versus the surrounding, which leads to a rise in the water level closer to the center.
Because the dynamical processes governing storm surge are quite well understood, not much research has been done in this area. Most of the work involves improving the design of the prediction models such as the grid resolution, two- versus three-dimensional models, and the coupling between the atmosphere and the ocean. As these are not related to the basic science, they are not described here. It suffices to say that increases in computational power have led to more accurate predictions of storm surge for many recent storms. However, because of our limited ability to predict the changes in the intensity and wind distributions (see the section “Changes in Intensity and Wind Distribution”), large errors in storm surge predictions can still occur.
As mentioned in the Introduction, tropical cyclones can bring a multitude of hazards as they come ashore. A good understanding of the physical mechanisms responsible for track changes, rainfall, and wind distributions is clearly important for improving the predictions of the hazards associated with TC landfall. However, the amount of research in this area is comparatively scarce compared with many other topics. This is likely because as a TC approaches land, its interaction with different land features (topography, land use, moisture availability, etc.) can vary greatly. Simulations with even rather high horizontal resolution may not capture such interactions correctly, so that verifications with observations become difficult, which might have prevented researchers from investigating the underlying physical processes.
Nevertheless, some of the results presented in this chapter suggest that, with simple models, it is possible to understand some of the fundamental physical mechanisms that may contribute toward track changes and variations in the rainfall distributions associated with TC landfall. These mechanisms are likely to be important in some real situations. For example, when a TC is in a weak environmental flow, surface friction and/or topographic effect can become dominant in modifying its track and be important in generating a vertical wind shear that could change the rainfall distribution. Understanding these basic mechanisms is also useful in the development of prediction models. Because the interaction with land and topography depends on the characteristics of the land surface and the vortex structure, proper representation of such characteristics and structure in the model is critical in producing a good forecast. These results can therefore provide a basis in examining the performance of the models and in modifying the model to improve the forecast accuracy.
Unfortunately, the lack of data is still limiting our ability to study the physical mechanisms responsible for the changes in intensity and wind distributions, which can impact on the predictions of storm surge. Wind observations are particularly problematic, as the atmospheric flow is strongly influenced by the shape and characteristics of the land surface within a very small area. More research efforts should therefore be focused in this area.
With the development and installation of new instrumentation (both in situ as well as remote), it is likely that we can better observe the wind and rainfall characteristics associated with TC landfall. The World Meteorological Organisation of the United Nations has recently established a research and development project, named UPDRAFT (Understanding and PreDiction of Rainfall Associated with landFalling Tropical cyclones), that aims at collecting all such observations as tropical cyclones approach the coast of China (where six to eight TCs make landfall every year), and then using these observations to study the physical processes that are responsible for the different rainfall distributions through analyses and simulations. Of course, the wind observations will also help in the understanding of the modifications of the TC wind structure due to different surface conditions. Hopefully, with more such observations, more researchers will devote their efforts in this important area to improve the predictions of tropical cyclone track and its associated hazards (wind, rainfall, and storm surge).
The author acknowledges his previous students and collaborators in contributing toward the various concepts and ideas presented in this chapter. The support from various research projects under the Research Grants Council of the Hong Kong Special Administrative Region Government of China is acknowledged. The manuscript was finalized while the author was a Visiting Fellow Commoner at Trinity College, University of Cambridge, UK, whose support is also much appreciated.
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