1. Introduction
The first part of this study (Chan and Chan 2012, hereafter Part I) established the robust climatology of tropical cyclone (TC) size (the azimuthal mean radius of 17 m s−1 10-m wind from the TC center, R17) and strength (the mean total surface wind velocity within 1°–2.5° latitude radius from the TC center) over the western North Pacific (WNP) and the North Atlantic (NA) using the Quick Scatterometer (QuikSCAT) satellite data during the period of 1999–2009. It represents the largest dataset ever assembled for size studies. TCs over the WNP are found to have significantly larger size and higher strength than those over the NA. A strong relationship also exists between size and strength so that strength may be considered to be superfluous in the characterization of TC structure. The spatial, seasonal, and interannual variations of TC size were also investigated. The results suggested that TC lifetime and the seasonal subtropical ridge (STR) activities are potential factors that could affect TC size.
In this part, the mechanisms that may be responsible for TC size changes are explored. Based on Eliassen's balanced equations, Challa and Pfeffer (1980) used Sundqvist's (1970) axisymmetric numerical experiments to examine the growth rate and intensity of TCs under different imposed environmental forcing profiles and found different eddy momentum transports. Holland and Merrill (1984) made a simple study of the ways in which a cyclone can interact with its environment by using observations in the Australian/southwest Pacific region and a linear diagnostic version of Eliassen's balanced vortex equations. They suggested that the ultimate intensity, strength, or size of a cyclone is regulated by interactions with its environment. Merrill (1984) also hypothesized that changes in angular momentum (AM) transport forced by the synoptic environment may influence TC size.
Liu and Chan (2002) found TCs with different sizes to be associated with different synoptic flow patterns at 850 hPa using 6 years of data from European Remote Sensing 1 and 2 (ERS-1 and -2, respectively) satellites (1991–96) over the WNP. They observed that large TCs are likely influenced by southwesterly surges (bands of relatively high winds compared with those in the environment) or late-season (subtropical high to the east and continental anticyclone to the west) patterns, while small TCs are likely to be south of the dominant ridge or embedded in a monsoon gyre. Similarly, Lee et al. (2010) also concluded that the lower-tropospheric environment can determine the difference between large and small TCs over the WNP (during 2000–05) during their early stage of intensification: the existence of a strong lower-tropospheric southwesterly wind in the outer-core region south of the large TCs and a subtropical high north of the small TCs. In addition, in terms of inner-core kinetic energy, Maclay et al. (2008) suggested that internal forcing (i.e., secondary eyewall formation and eyewall replacement cycle processes) and external forcing from the synoptic environment (most likely the vertical shear) can affect the growth process. Through observational analyses and simulations, Chen et al. (2011, 2012) also argued that for TCs that only spin up strongly in the inner core (and thus stay small in size), internal dynamics dominate. On the other hand, they found that environmental influences are more critical for TCs that become large in size. Based on the results of idealized numerical simulations, Hill and Lackmann (2009) concluded that environmental humidity can also determine TC size. However, the mechanisms on how the environment can cause TC size change and its importance have yet to be identified.
Apart from the typical TC size (usually defined as R17), the inner-core TC size (defined as both the radius of maximum wind and the radius of the azimuthal mean damaging-force wind speed of 25.7 m s−1) has been studied by Xu and Wang (2010a,b). They found that the surface entropy flux outside the eyewall contributes to the activity of spiral rainbands and thus the TC inner-core size increases (Xu and Wang 2010a). The initial vortex size is found to be more important than the initial relative humidity of the environment in determining the inner-core size of mature TCs (Xu and Wang 2010b).
It is clear from the above review that no systematic or detailed observational study on the mechanisms that determine TC size change exists. The objective of this study is therefore to investigate the possible mechanisms that may be responsible for TC size changes over the WNP and NA through an examination of AM transports using the QuikSCAT and Climate Forecast System Reanalysis (CFSR) datasets. It is hypothesized that the change in TC size is related to a change in the lower-tropospheric AM transport across the TC.
Section 2 describes the data and methodology used in this study. The changes in AM transports associated with different changes in TC structure (intensity and size) are presented in section 3. Based on the AM transport concept, section 4 discusses the external dynamics on determining the TC size change, the possible changes in environmental synoptic flow patterns, and the relation between the TC movement and TC size associated with different transitions of TC size. Finally, section 5 concludes with a summary and a discussion.
2. Data and methodology
a. Data
The data, definitions, and study period used in this study are mainly based on those in Part I. These include 11 years of QuikSCAT data (1999–2009), which were used to retrieve and define TC size (R17), and best-track data from the Joint Typhoon Warning Center (JTWC) and the National Hurricane Center (NHC) that provide information on the TC center position and intensity over the WNP and NA, respectively. Rain-flagged QuikSCAT data were excluded and the TC center was estimated by the linear interpolation method according to the time at which the QuikSCAT swath was over the TC. Small and large TCs are defined using the 25th and 75th percentiles (Table 1). Complete details (e.g., data descriptions and selection criteria) can be found in Part I.
Size categories over the WNP and the NA. Unit: degrees latitude.
To estimate AM transports and to examine the synoptic flows around the TCs, the National Centers for Environmental Prediction (NCEP) CFSR data (37 vertical levels, the latitude, longitude, and time resolutions being 0.5° in latitude, 0.5° in longitude, and 6-hourly, respectively) were employed. These data were used instead of the NCEP–National Center for Atmospheric Research (NCEP–NCAR) reanalysis data (Kalnay et al. 1996) because the horizontal spatial resolution of these latter data is 2.5° latitude × 2.5° longitude, which is too low to resolve the AM flux (AMF) around a TC. In addition, CFSR data include all available conventional and satellite observations (Saha et al. 2010) so that they are more reliable and realistic than the NCEP–NCAR reanalysis data. According to Saha et al. (2010), “SeaWinds ocean surface vector wind data from the NCEP operational archives were assimilated in CFSR from 2001 until it went nonoperational in 2009.” In other words, it is consistent and appropriate to use CFSR data in studying TCs classified based on the QuikSCAT data.
b. Angular momentum
As the QuikSCAT might not sweep over the TCs at the exact synoptic times (0000, 0600, 1200, or 1800 UTC), the nearest 6-hourly CFSR data were used to analyze the AM transport. The tangential and radial winds were reconstructed into a 1° latitude × 22.5° azimuthal polar grid relative to the TC center where 0.5°–1.5° latitude and 348.75°–11.25° is the first ring sector. The AM flux at radii from 1° to 9° latitude for every 1° latitude interval (i.e., total of nine rings) and every vertical level were calculated using (4). It is difficult to use reanalysis data to investigate the direct effect of friction within the planetary boundary layer. Frank (1977) suggested that AM dissipation caused by friction is likely small above 900 hPa. Therefore, interpretations of results below this level might be problematic and only the AMFs above the boundary layer (900 hPa) are examined.
Because AM transport has been shown to contribute toward intensity change (e.g., Holland and Merrill 1984), the TCs were further divided into four categories: intensity increase and size increase (I↑S↑), intensity increase and size decrease (I↑S↓), intensity decrease and size increase (I↓S↑), and intensity decrease and size decrease (I↓S↓). To ensure that the categories are significantly separated and to make the results more pronounced, threshold values for the selection of intensity and size changes are set to 5 kt (consistent to the intensity interval in the JTWC and NHC best-track datasets; 1 kt = 0.5144 m s−1) and 0.1° latitude, respectively (accounting for 55% and 40% of the total over the WNP and NA, respectively). Cases with minimal intensity or size changes are therefore removed. It might also be useful in the future to examine specific cases in which the size changes significantly, but intensity changes little.
Statistics of the four categories of TC structure changes [intensity increase and size increase (I↑S↑), intensity increase and size decrease (I↑S↓), intensity decrease and size increase (I↓S↑), and intensity decrease and size decrease (I↓S↓)] between final and initial times (i.e., T2 minus T1, within a day) over the WNP. ΔI and ΔS denote the changes in intensity (kt) and size (degrees latitude), while σ(ΔI) and σ(ΔS) are the standard deviations of the ΔI and ΔS, respectively. The selection threshold values for the changes in TC intensity and TC size are set to be 5 kt and 0.1° latitude, respectively.
c. Synoptic flow
As the sample size over the WNP is much larger than that over the NA, only the synoptic flows of the cases over the WNP were studied. In addition to the above four categories (i.e., the categorization considering both TC intensity and size changes), two groups were also formed: a size-increase (+ΔS) group and a size-decrease (−ΔS) group (i.e., regardless of intensity change). Because Liu and Chan (2002) found that the synoptic flow patterns associated with large and small TCs are quite different, to obtain a detailed synoptic flow analysis, each group was further divided into several size transitions. The selection threshold value for the size change is set to 0.1° latitude. For +ΔS group, small to larger small (sS), small to medium (sM), small to large (sL), medium to larger medium (mM), medium to large (mL), and large to larger large (lL) TC transitions were further classified (Table 4). Similarly, for −ΔS group, small to smaller small (Ss), medium to small (Ms), medium to smaller medium (Mm), large to small (Ls), large to medium (Lm), and large to smaller large (Ll) TCs were also classified (Table 5). Finally, the synoptic flows of recurving and nonrecurving TCs were also studied and simply stratified by whether a TC moves eastward or westward between T2 and T1, respectively.
Size transitions of the +ΔS group, that is, final size is larger than initial size. Only the selection threshold value 0.1° latitude for the change in size is set.
Because the lower-tropospheric AM transport is found to be crucial in determining TC size change (see section 3), studying the lower-tropospheric synoptic flow patterns should provide a better understanding of this mechanism. The synoptic flow analysis was therefore performed by extracting the 850-hPa zonal and meridional winds within a ±20° latitude square from the TC center using the CFSR data. Composite synoptic flow patterns were then obtained by compositing the synoptic flows in each of the groups and transitions.
3. Changes in AM budget
a. WNP TCs
When both the TC intensity and size increase (I↑S↑), an increase of upper-level (~300–150 hPa, 1°–5° latitude radius) AAM export and an increase of lower-tropospheric (~850 hPa and below) AAM import (up-out-increase and low-in-increase pattern) are found (Fig. 1a). The changes in SRAMF and SCT are highly correlated with the change in AAMF (see Fig. 5). Similar correlations are also found in the other three categories (i.e., I↑S↓, I↓S↑, and I↓S↓; not shown). It is interesting that the changes in ARAMF and ACT of each category are found to be generally out-of-phase so that they tend to compensate each other and thus contribute very little to the changes in AAMF in terms of the AM transport pattern (see Figs. 1b, 2b, 3b, and 4b).
Radius–height cross-sectional composites of the change (i.e., T2 minus T1) in (a) AAMF and (b) its four components of I↑S↑ over the WNP (unit: 106 m3 s−2). Solid and dashed lines indicate positive and negative changes, respectively. Heavy solid line indicates zero change. Note that a positive change can imply an increase in AM export or decrease in AM import, while a negative change can imply an increase in AM import or decrease in AM export. Regions with dots denote a confidence level (change between T2 and T1 different from 0) being higher than 90%.
Citation: Monthly Weather Review 141, 11; 10.1175/MWR-D-12-00204.1
For I↑S↓, the upper-level (~250–150 hPa, 1°–4° latitude radius) AAM export increases but the lower-tropospheric (~900–650 hPa) AAM import decreases (up-out-increase and low-in-decrease pattern, Fig. 2a). In addition, an obvious change in AAM transport occurs at the midlevels. Although there is an increase in AAM import near the planetary boundary layer, the difference is not significant, which should be mainly due to the frictional effect. If the lower-tropospheric AAM transport above 900 hPa is examined, a significant decrease in AAM import is found.
As in Fig. 1, but for I↑S↓.
Citation: Monthly Weather Review 141, 11; 10.1175/MWR-D-12-00204.1
In I↓S↑, the upper-level (~200–150 hPa, 1°–5° latitude radius) AAM export decreases and the lower-tropospheric (~850 hPa and below) AAM import increases (Fig. 3a). This up-out-decrease and low-in-increase AAM transport pattern is also accompanied by a significant positive change in AAMF at the midlevels. In addition, the AAM transport patterns between I↑S↓ and I↓S↑ categories are found to be mostly out-of-phase (cf. Figs. 2a and 3a).
As in Fig. 1, but for I↓S↑.
Citation: Monthly Weather Review 141, 11; 10.1175/MWR-D-12-00204.1
Finally, when both the intensity and size decrease (I↓S↓), both the upper-level (~150–100 hPa, 1°–4° latitude radius) AAM export and the lower-tropospheric (~700 hPa and below) AAM import decrease (up-out-decrease and low-in-decrease pattern, Fig. 4a). As might be expected, almost opposite AAM transport patterns are found between I↑S↑ and I↓S↓ categories (cf. Figs. 1a and 4a).
As in Fig. 1, but for I↓S↓.
Citation: Monthly Weather Review 141, 11; 10.1175/MWR-D-12-00204.1
The “out-of-phase” AAM transport patterns found between I↑S↓ and I↓S↑ (cf. Figs. 2a and 3a) and between I↑S↑ and I↓S↓ (cf. Figs. 1a and 4a) imply that the factors affecting TC intensity and size are somewhat independent. Meanwhile, it is noted that the conditions associated with TC intensification could also be favorable for TC size growth because the sample size of I↑S↑ category is substantially larger than all of the others (Table 2). However, because the investigation of the relationship between TC intensification and size growth is not the objective of the present study, it is left for future work.
The results of all these four distinct categories give clear and consistent conclusions that when a TC intensifies (weakens), the upper-level export of AAM increases (decreases). Similarly, when a TC grows (shrinks), the lower-tropospheric import of AAM increases (decreases). In other words, it is apparent that changes in the upper-level AM export and lower-tropospheric AM import are important factors that relate to TC intensity and size, respectively. These are potential mechanisms that can lead to intensity and size changes during the lifetime of a TC. These results provide strong evidence to substantiate the similar mechanisms proposed by Holland and Merrill (1984) although they simply categorized and composited similar TCs at two different stages, that is, tropical storm and hurricane. In all the four categories, both the changes in SRAMF and SCT are shown to be the main AMFs that highly correlate with the change in AAMF (Fig. 5), especially in the lower troposphere (due to the similarity of the results, those from the other categories are not shown).
Correlation coefficient (shaded) and the mean difference (contour lines with interval 2 × 106 m3 s−2) between each component change in AMF (SRAMF, ARAMF, SCT, and ACT) and the change in AAMF for I↑S↑.
Citation: Monthly Weather Review 141, 11; 10.1175/MWR-D-12-00204.1
At a fixed radius r from the TC center, SRAMF depends only on 
The change in SCT, which depends on the changes in f0 and 
In fact, for example, in the I↑S↓ category (Fig. 2), the SRAMF and SCT changes in the lower troposphere are both positive, which suggests a net decrease in AM import. A similar physical interpretation can be made for the other three categories. In addition, similar conclusions can be made if the entire sample is only divided into growing and shrinking groups (i.e., regardless of intensity change). There is an increase in lower-tropospheric (~850 hPa and below) AM import in growing TCs (Fig. 6) and a decrease in lower-tropospheric (~700 hPa and below) AM import in shrinking TCs (Fig. 7), which again implies that the lower-tropospheric AM transport is crucial in determining TC size change. The changes in lower-tropospheric SRAMF and SCT in these two groups are also found to be highly correlated to the change in AAMF (not shown).
As in Fig. 1a, but for the +ΔS group (in this figure, only the selection threshold value 0.1° latitude for the change in size is set).
Citation: Monthly Weather Review 141, 11; 10.1175/MWR-D-12-00204.1
As in Fig. 6, but for the −ΔS group.
Citation: Monthly Weather Review 141, 11; 10.1175/MWR-D-12-00204.1
b. NA TCs
Similar results are found in NA TCs (cf. Figs. 1a, 2a, 3a, 4a, and 8) although the regions having 90% confidence level different from 0 are not as large as those over the WNP (probably due to the smaller sample sizes over the NA, Table 3). In the regions where the results are significant, up-out-increase and low-in-increase (Fig. 8a), up-out-increase and low-in-decrease (Fig. 8b), up-out-decrease and low-in-increase (Fig. 8c), and up-out-decrease and low-in-decrease (Fig. 8d) AAM transport patterns are also generally found in the I↑S↑, I↑S↓, I↓S↑, and I↓S↓ categories of NA TCs, respectively. Because of the high resemblance of the results between these two ocean basins, the individual components of AAMF over the NA are not shown. All these results suggest that the mechanisms of the AM transport on TC size and intensity discussed in the previous section (section 3a) are not only applicable to TCs over the WNP but also to those over the NA. Presumably, the same mechanisms will apply to TCs in the other ocean basins although further studies would be necessary to verify this.
The radius–height cross-sectional composites of the change in AAMF of (a) I↑S↑, (b) I↑S↓, (c) I↓S↑, and (d) I↓S↓ over the NA (unit: 106 m3 s−2). Solid and dashed lines indicate positive and negative changes, respectively. Heavy solid line indicates zero change. Note that a positive change can imply an increase in AM export or decrease in AM import, while a negative change an increase in AM import or decrease in AM export. Regions with dots denote a confidence level (change between T2 and T1 different from 0) being higher than 90%.
Citation: Monthly Weather Review 141, 11; 10.1175/MWR-D-12-00204.1
4. Synoptic flow patterns associated with different size transitions
Because the change in TC size is shown to be mainly influenced by the lower-tropospheric AM transport (see section 3), to investigate how the circulations around the TC contribute to the AM transport, the lower-tropospheric (850 hPa) synoptic flow patterns associated with different size transitions over the WNP were examined.
Southwesterly and easterly surges that are mainly driven by the southwesterly monsoon and the STR, respectively, are typically present in both the +ΔS and −ΔS TCs (Figs. 9a,b and 10a,b). Because of the beta effect, TCs in the WNP generally move northwestward so that they are farther away from the southwesterly monsoon that is usually present at low latitudes. Thus, the decrease of inflow in the southwest quadrant is generally found in all groups (+ΔS and −ΔS; see Figs. 9e and 10e), and transitions (sS, sM, mM, mL, lL, Ss, Ms, Mm, Lm, and Ll; see e.g., Figs. 11e, 12e, and 13e).
Composite lower-tropospheric (850 hPa) synoptic flow patterns of +ΔS group at (a) T1 and (b) T2. Vectors and dashed contours indicate the synoptic flow and isotachs of the total winds (contour interval: 4 m s−1), respectively. (c) Composite synoptic lower-tropospheric flow difference between T2 and T1 (i.e., T2 minus T1). (d),(e) Corresponding composite tangential and radial wind differences relative to the TC center (indicated by a cyclone symbol), respectively (contour interval: 1 m s−1). In (c), regions with dots denote that the changes in tangential or radial wind different from 0 have a confidence level higher than 90%. In (d) and (e), solid and dashed lines indicate positive and negative changes, respectively. Heavy solid line indicates zero change. Note that a positive change can imply an increase in cyclonic flow (outflow) or decrease in anticyclonic flow (inflow), while a negative change can imply an increase in anticyclonic flow (inflow) or decrease in cyclonic flow (outflow). Similarly, regions with dots denote a confidence level [in (d), tangential, in (e), radial, wind changes different from 0, respectively] being higher than 90%.
Citation: Monthly Weather Review 141, 11; 10.1175/MWR-D-12-00204.1
As in Fig. 9, but for the −ΔS group.
Citation: Monthly Weather Review 141, 11; 10.1175/MWR-D-12-00204.1
As in Fig. 9, but for the sS transition.
Citation: Monthly Weather Review 141, 11; 10.1175/MWR-D-12-00204.1
As in Fig. 9, but for the Mm transition.
Citation: Monthly Weather Review 141, 11; 10.1175/MWR-D-12-00204.1
As in Fig. 9, but for the lL transition.
Citation: Monthly Weather Review 141, 11; 10.1175/MWR-D-12-00204.1
a. Size-increase (+ΔS) group
A size increase (regardless of intensity change; samples based on Table 6) is associated with the development of two prominent lower-tropospheric anticyclonic flows, one to the southeast (most likely the subtropical high) and another one (but relatively weaker) to the west of the vortex (Fig. 9c). These two anticyclonic flows act as external factors to enhance the lower-tropospheric cyclonic 
Statistics of TC movement for +ΔS and −ΔS groups. V1 and V2 are the velocity of TC movement in meridional direction at T1 and T2, respectively. Here Δf0 denotes the change in Coriolis parameter between final and initial times (i.e., T2 minus T1). Only the selection threshold value 0.1° latitude for the change in TC size is set.
In addition, the development of these two anticyclonic flows lead to a substantial increase in inward υr and a decrease in outward υr to the southeast and northwest of growing TCs (Fig. 9e), respectively. Though decreases in inflow are found in the northeast and southwest quadrants of TC, the change in inward AAMF from the TC is still positive (not shown; with the change in AAMF being dominated by the changes in υθ; cf. Figs. 9d,e), which suggests more AM is brought into the TC in the lower troposphere (Fig. 6), and hence the size increases.
Moreover, the strengthening of the lower-tropospheric anticyclonic flow to the southeast of the vortex suggests that when a westward-moving TC grows, it tends to deflect to the right and move more northward so that it is likely to be situated at the western side of STR. In such a transition, the steering flows in the meridional direction should be significantly increased, which is consistent with the results shown in Table 6. A faster northward movement results in a larger EAM, and thus the larger the SCT and ACT in contributing to TC growth (see section 4d).
b. Size-decrease (−ΔS) group
During a size decrease (again regardless of intensity change; samples based on Table 6), the extent and the magnitude of the wind surges are found to be significantly reduced (cf. Figs. 10a,b) in the southwestern and northeastern parts of the TC. No significant strengthening/development in the lower troposphere of the anticyclonic flow or increase of the radial winds to the southeast of vortex (as in the +ΔS group) can be found. In contrast, large decreases of inflow are found in the southwest, southeast, and northeast quadrants of the TC (Figs. 10c,e). A shrinking TC is likely to be associated with a weakening of the STR (Fig. 10c) so that the cyclonic circulation at the outer-core region of the TC is reduced.
Although a small increase in cyclonic flow exists near the TC center (Fig. 10d), which could be due to internal dynamics, the forcings from the outer-core region seems to be more important in determining TC size. The development of an anticyclonic synoptic environment surrounding a TC (Fig. 10c) apparently substantially reduces the cyclonic flow and inflow at the outer core (Figs. 10d,e), and thus, the size decreases. It is noted that the origin of the development of anticyclonic synoptic environment in the −ΔS group is different from those discussed in the +ΔS group. Similar to +ΔS TCs, although a strong decrease in outflow is also found in the northwest quadrant of −ΔS TCs, the change in inward AAMF (considering both the changes in υθ and υr) associated with the TC is not positive (not shown), which suggests less AM is brought into the TC in the lower troposphere (Fig. 7), and hence the size decreases.
c. Small, medium, and large TCs of +ΔS and −ΔS groups
As mentioned in section 2c, a detailed study of the synoptic flows of different transitions (sS, sM, sL, mM, mL, lL, Ss, Ms, Mm, Ls, Lm, and Ll; samples based on Tables 4 and 5) was also made to examine the changes in the extent, the magnitude, and the dynamics of the environmental surges in each type of transition. Because of the similar physics and results, only one transition is shown in each of the size categories. They are sS (Fig. 11), Mm (Fig. 12), and lL (Fig. 13), which generally show how the synoptic flow patterns associated with small, medium, and large TCs evolve, respectively.
In general, small TCs are likely to be situated at the southwestern or equatorial side of STR (Figs. 11a,b), medium TCs tend to occur at the western side of STR (Figs. 12a,b), while large TCs are likely to be sandwiched between two anticyclones (Figs. 13a,b). Among the three TC sizes, the magnitudes of the wind surges near the large TC are the highest while those around the small TC are the least. These results, which are based on 11 years of data, further reinforce those found by Liu and Chan (2002) based only on 6 years of data.
For the size evolution, the size of a small growing TC likely increases when there is an increment in cyclonic wind to the east (Figs. 11c,d) and a decrease in outflow to the west (Figs. 11c,e) in the lower troposphere of the TC vortex. In such a situation, the western extent of the STR to the north-northwest (Figs. 11a,b) of small growing TCs seems to be weakened so that the outflow to its west decreases. For the medium shrinking TCs, the extent of the southwesterly surge and the anticyclone to the east weakens in the lower troposphere (Figs. 12a–c). A large decrease in cyclonic wind to the east (Fig. 12d) and significant decrease in inflow to the southeast (Fig. 12e) of the TC are also found. For the last example, a large growing TC is likely influenced by two lower-tropospheric increases in anticyclonic flows (Fig. 13c) with a stronger one to the east-southeast (most likely the subtropical high) and a weaker one to the west of the cyclone. These developments of the anticyclonic flows around the TC lead to increases in cyclonic spin (Fig. 13d) and inflow (Fig. 13e) to the TC.
In addition, significant increases of lower-tropospheric AM import are found in all the growing transitions (not shown). Similarly, decreases of lower-tropospheric import of AM (though not significant, probably due to the small sample size) are also found among small, medium, and large shrinking TCs (not shown). Therefore, the changes in lower-tropospheric synoptic flow patterns are in agreement with the lower-tropospheric AM transport.
All these results suggest that the lower-tropospheric AM transport concept concluded in section 3 is still valid even when the growing and shrinking TCs are now further divided into different size categories (small, medium, and large). In other words, no matter what the size category of the TC is, the change in the lower-tropospheric AM transport is important and applicable in determining the change in TC size.
d. Relation between TC movement and size
As discussed in the previous sections, the change in synoptic flow around the TC can affect TC movement that leads to AM change and consequently affects TC size. Generally, the moving speeds of different-sized TCs are found to be different (Table 7), especially for small and large TCs. The northward speed of large TCs is much higher (statistically significant at 99% confidence level based on a Student's t test) than that of small TCs while the westward speed of small TCs is generally larger (with a probability of 80% being within the confidence interval) than that of large TCs. These results suggest that large and small TCs tend to be steered by the western side and equatorial side of the STR, respectively. The northward-moving speed of large TCs is the largest among all sized categories (small, medium, and large) while that of small TCs is the smallest. This may suggest that the larger the northward speed, the larger the TC size would be. It is consistent with the results shown in Table 6 that the mean change in TC northward speed of growing TCs is significantly (at 90% confidence level) higher than that of the shrinking TCs. Note also that the change in f0 of growing TCs is larger than that of the shrinking TCs with a probability of 80% being within the confidence interval.
Mean TC locations and movement of different TC size categories; U and V denote the zonal and meridional velocities of TC movement, respectively.
These results are reasonable because the change in SCT (one of the important AM transport components in determining TC size variation) is mainly contributed by the changes in f0 and 
The TC movement and size variations between recurving and nonrecurving growing TCs are also found to be significantly different (Table 8). The northward-moving speed and the change in f0 of the recurving ones are higher (at 99% confidence level). In the lower troposphere, the recurving and growing TCs are likely dominated by an increase in westerlies and a strengthening of the STR on the western-northwestern side and the eastern side of the TC, respectively (Figs. 14a–c). Such a synoptic situation results in an increase in cyclonic flow to the south (Fig. 14d), an increase in inflow to the west, and an increase in outflow to the east of the TC (Fig. 14e).
Statistics for the mean TC preferences of the recurving and growing (R + ΔS), recurving and shrinking (R − ΔS), nonrecurving and growing (NR + ΔS), and nonrecurving and shrinking (NR − ΔS) TCs. U1 and U2 (V1 and V2) are the velocities of TC movement in zonal (meridional) direction at T1 and T2, respectively. Latitude indicates the latitudinal TC position and Δf0 denotes the change in Coriolis parameter between T2 and T1 (i.e., T2 minus T1). Only the selection threshold value 0.1° latitude for the change in size is set.
As in Fig. 9, but for the recurving and growing TCs.
Citation: Monthly Weather Review 141, 11; 10.1175/MWR-D-12-00204.1
However, if there is no significant increase in the westerlies, the recurving TC does not grow but actually shrinks (Table 8 and Fig. 15). The average eastward-movement speed of recurving and shrinking group is found to be slower than that of the recurving and growing group. The mean latitudinal position of the recurving and growing TCs, 25.4°N, is higher than (at 90% confidence level) that of the recurving and shrinking TCs, 23.6°N (Table 8). It is likely that the recurving and shrinking TC travels along the western/northwestern side of the eastward-retreating subtropical high but has not yet reached higher latitudes, so that the westerlies have not increased much. Therefore, this implies that the lower-tropospheric increase in westerlies from the west of the TC could be an important environmental factor that can lead a recurving TC to grow.
As in Fig. 9, but for the recurving and shrinking TCs.
Citation: Monthly Weather Review 141, 11; 10.1175/MWR-D-12-00204.1
e. Summary
Through a comparison between the mean of the tangential and radial wind differences of +ΔS and −ΔS TCs, distinct increases in cyclonic flow (Fig. 16a) and inflow (Fig. 16b) are generally found around and to the southeast quadrant of growing TCs, respectively. Moreover, changes in synoptic flow patterns associated with growing and shrinking TCs are found to be distinctly different. The developments of lower-tropospheric anticyclonic flows bordering the TC are likely to favor TC growth. The recurving TC also tends to grow if the lower-tropospheric westerlies to its west strengthen. In contrast, a weakening of the cyclonic flow surrounding the TC is likely to reduce TC size. To summarize, the changes in synoptic flow patterns around the TC are therefore suggested to be the important external dynamic factor that can potentially determine the evolution of TC size. Further studies are necessary to verify this conclusion using model simulations.
Differences between the mean of the lower-tropospheric (850 hPa) (a) tangential (positively shaded) and (b) radial wind (negatively shaded) differences (i.e., T2 minus T1) of +ΔS and −ΔS groups (i.e., +ΔS minus −ΔS) relative to the TC center (indicated by a cyclone symbol) with contour interval 1 m s−1.
Citation: Monthly Weather Review 141, 11; 10.1175/MWR-D-12-00204.1
Apart from the changes in 
5. Summary and discussion
a. Summary
This is a continuation of the Chan and Chan [2012 (Part I)] study, with the objective to investigate the possible mechanisms on how the tropical cyclone (TC) size changes over the western North Pacific (WNP) and the North Atlantic (NA) in terms of angular momentum (AM) transports based on the observational Quick Scatterometer (QuikSCAT) and the Climate Forecast System Reanalysis (CFSR) datasets. It is hypothesized that the change in TC size is related to the lower-tropospheric changes in AM transport across the TC. Changes in AM transport associated with different changes in TC structure (intensity and size) within 24 h are therefore investigated. TCs were classified into four distinct categories: intensity increase and size increase (I↑S↑), intensity increase and size decrease (I↑S↓), intensity decrease and size increase (I↓S↑), and intensity decrease and size decrease (I↓S↓). It is found that the AM transports from these four categories are consistent with the hypothesis, which is summarized in Fig. 17.
Schematic diagram of AAM transports for (a) I↑S↑, (b) I↑S↓, (c) I↓S↑, and (d) I↓S↓. Long dashed and long solid arrows denote the increase in import and export of AAM, respectively, while short dashed and short solid arrows indicate the decrease in import and export of AAM, respectively.
Citation: Monthly Weather Review 141, 11; 10.1175/MWR-D-12-00204.1
In this study, two important physical mechanisms are identified. The change in TC intensity is positively related to the change in the upper-level AM export while the change in TC size is positively proportional to the change in the lower-tropospheric AM import. The conditions favorable to TC intensification may also be beneficial for size growth. Among the results on the changes in individual AM fluxes (AMF) contributing to the total changes in the absolute AMF (AAMF), the symmetric relative AMF (SRAMF) and symmetric Coriolis torque (SCT) are found to be important components in determining the change in TC size.
In addition, results from the WNP and the NA are consistent with each other. Similar results were also found by Holland and Merrill (1984) (though the categorization method of the present study is much more meticulous) over the Australian/southwest Pacific region. It is suggested that the proposed mechanisms should also be applicable to other ocean basins although more work is needed to verify this.
The synoptic flow analyses among different transitions of TC size suggest that the extent, the intensity, and the dynamics of the environmental lower-tropospheric wind can affect TC size, which agrees with the AM transport concept. The developments of the lower-tropospheric anticyclonic flows bordering the TC (one to the west and one to the east-southeast; latter is most likely the subtropical high system) are favorable for TC growth. The recurving TC also tends to grow if there is the lower-tropospheric westerlies to its west strengthen. In contrast, the reduction of the outer-core cyclonic circulation of the TC (most likely due to the weakening of the subtropical high to the southeast) favors a shrinking of the TC. All in all, the change in synoptic flow patterns near the TC is likely the important external dynamic factor that can potentially determine the evolution of TC size. In addition, the northward TC movement could be another clue for predicting the variability of TC size. The change in lower-tropospheric AM transport mechanism in determining the change in TC size is also found to be applicable to all the sizes (small, medium, and large).
b. Discussion
After identifying the change in lower-tropospheric AM transport as an important factor responsible for the change in TC size, the next step is to determine the elements that contribute to this AM transport process, which is likely the synoptic flow. Liu and Chan (2002) made a preliminary investigation of the synoptic flow patterns associated with small and large TCs that occurred over the WNP between 1991 and 1996. Although they identified several synoptic flow patterns, they did not provide any physical explanation on why the size of a TC is small or large in a particular pattern. The mechanisms found in this study therefore complement their study. Although the resolution of the CFSR data (~0.5° latitude) may prevent a realistic analysis of the inner-core (within ~1.5° latitude radius from the TC center) TC structure (e.g., underestimation in intensity; Schenkel and Hart 2012), the conclusions presented in this study should be largely valid because the regions outside the inner core were mainly examined, where the data are generally acceptable despite some uncertainty depending on the data availability especially in the planetary boundary layer.
The synoptic flow patterns shown in the current study were categorized by different size transitions that only provide information on how the synoptic flow changes during TC size changes. Since there can be several characteristic synoptic flow patterns in each size category, the composites done in this study may smooth out those synoptic features. Therefore, these results are mainly used to provide a general picture on how the changes in lower-tropospheric winds (tangential and radial winds) are associated with different sizes of growing and shrinking TC. The detailed synoptic flow variations in different seasons and locations associated with different TC sizes have yet to be resolved and more work is needed (while it can be further resolved in this study, the sample size is too small to be representative).
Finally, while the present study concludes, based on observations, that the intensity change is related to the upper-level AM transport, the causal relationships between the AM changes and intensity changes have not been explicitly examined. The AM changes may have been related to internal forcing (e.g., convection in the eyewall), external factors (e.g., upper-tropospheric trough), or other factors yet to be identified. Interpretation of the results given here should only be considered to be tentative.
Although important mechanisms have been identified from observational and reanalysis data, numerical simulations should also be performed to demonstrate whether these mechanisms are physically plausible. Meanwhile, thermodynamic factors such as environmental humidity, which may also determine TC size as suggested by Hill and Lackmann (2009), also need to be examined to find the possible linkage between dynamic and thermodynamic factors. These will form the next step of the current study.
Acknowledgments
This study is from part of the first author's Ph.D. work, which is supported by the Research Studentship from City University of Hong Kong and the Hong Kong Research Grants Council Grant CityU 100209. Most of the data analyses and visualizations are postprocessed by the NCAR Command Language Version 6.0.0 (http://dx.doi.org/10.5065/D6WD3XH5). The authors thank the editor, Professor Pat Harr, an anonymous reviewer, and Professor Kevin Cheung (the second reviewer) for their constructive comments on the manuscript.
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