**3. Analysis**

Based on previous work done [12], variables selected for evaluation consisted of base-state variables and derived variables as listed in Section 2.1. Through the S-mode technique, only base-state variables were examined; therefore, only notable characterizations are summarized in the text below. The T-mode and cluster analysis technique; however, yielded numerous composite fields for consideration. To minimize this impact, the cluster from each RI group and each RI definition that contained the largest number of events (bolded in **Table 2**) is provided for discussion below.

#### **3.1. RI and non-RI S-mode maps**

As stated previously, S-mode analysis of the base-state meteorological fields was conducted first. **Table 1** shows that RPC1 contained the largest variance explained (roughly 24%), and the loading map (**Figure 3**) revealed that areas of higher heights in the northeast quadrant quadrant and over the storm center co-varied with higher MSLP, lower temperatures, lower moisture and latent heat content. A total of 16 events' RPC scores (**Table 3**) exceeded 2 standard deviations above the mean, suggesting strong positive correlation between those events and RPC1. Of these 16 events, six were classified as RI cases with the 25kt/24-hour definition of RI. In fact, the highest positive deviation (approximately 5 standard deviations above the mean) was an RI case, while the second largest positive deviations were a mixture of RI and non-RI events. These results suggest a blend of RI and non-RI events for RPC1. Similarly, RPC2 results (which explained approximately 12% of the variability) revealed lower heights in proximity of the storm center (**Figure 4**) co-varied with lower MSLP, cooler low-level temperatures in the southwest quadrant of the cyclone and overall higher specific humidity and latent heat flux values. Additionally, patterns revealing a wrap-around of moisture over the storm-center were revealed. However, only three of the eight events that exceeded 2 standard deviations from the mean were RI events, again showing the blending of RI and non-RI cases in these results. RPC3 (which explained approximately 7% of the total variance), exhibited higher heights colocated with higher MSLP, temperature, specific humidity, and latent heat flux over the storm center and to the south, but lower heights, temperature, specific humidity, and latent heat flux North of the storm center (**Figure 5**). This RPC profile, along with RPCs 4–6 (not shown), is indicative of baroclinic environmental influence associated with both storm types. These first three RPCs, explaining over half of the variability combined, demonstrated a recurring problem in the S-mode analysis, namely the inability to separate RI and non-RI events (as was seen in **Figure 2**).

tudes of diagnostic fields in RI and non-RI storms were utilized at each gridpoint from the study domains, yielding a spatial map of significance values associated with each variable tested. The resulting plots provided specific regions in the study domain where statistically significant magnitude differences between RI and non-RI storms existed for individual GEFS reforecast variables. These results provided insight not only into the scope of these magnitude differences but into the spatial locations of the differences, which complement the RPCA

32 Recent Developments in Tropical Cyclone Dynamics, Prediction, and Detection

Based on previous work done [12], variables selected for evaluation consisted of base-state variables and derived variables as listed in Section 2.1. Through the S-mode technique, only base-state variables were examined; therefore, only notable characterizations are summarized in the text below. The T-mode and cluster analysis technique; however, yielded numerous composite fields for consideration. To minimize this impact, the cluster from each RI group and each RI definition that contained the largest number of events (bolded in **Table 2**) is

As stated previously, S-mode analysis of the base-state meteorological fields was conducted first. **Table 1** shows that RPC1 contained the largest variance explained (roughly 24%), and the loading map (**Figure 3**) revealed that areas of higher heights in the northeast quadrant quadrant and over the storm center co-varied with higher MSLP, lower temperatures, lower moisture and latent heat content. A total of 16 events' RPC scores (**Table 3**) exceeded 2 standard deviations above the mean, suggesting strong positive correlation between those events and RPC1. Of these 16 events, six were classified as RI cases with the 25kt/24-hour definition of RI. In fact, the highest positive deviation (approximately 5 standard deviations above the mean) was an RI case, while the second largest positive deviations were a mixture of RI and non-RI events. These results suggest a blend of RI and non-RI events for RPC1. Similarly, RPC2 results (which explained approximately 12% of the variability) revealed lower heights in proximity of the storm center (**Figure 4**) co-varied with lower MSLP, cooler low-level temperatures in the southwest quadrant of the cyclone and overall higher specific humidity and latent heat flux values. Additionally, patterns revealing a wrap-around of moisture over the storm-center were revealed. However, only three of the eight events that exceeded 2 standard deviations from the mean were RI events, again showing the blending of RI and non-RI cases in these results. RPC3 (which explained approximately 7% of the total variance), exhibited higher heights colocated with higher MSLP, temperature, specific humidity, and latent heat flux over the storm center and to the south, but lower heights, temperature, specific humidity, and latent heat flux North of the storm center (**Figure 5**). This RPC profile, along with RPCs 4–6 (not shown), is indicative of baroclinic environmental influence associated with both storm types. These first three RPCs, explaining over half of the variability combined, demonstrated a recurring

results well.

**3. Analysis**

provided for discussion below.

**3.1. RI and non-RI S-mode maps**

**Figure 3.** S-mode RPC 1 loading patterns for geopotential height at 850 hPa (panel a) and specific humidity at 850 hPa (panel b) with respect to latitude/longitude relative to the storm center, as well as the associated RPC score time series (panel c). The product of the loading map and its time-series value for a case are in units of standard anomalies.


**Table 3.** RPC score values exceeding (±) 2 standard deviations above/below the mean.

**Figure 4.** Same as **Figure 3**, but for RPC 2.

**Figure 5.** Same as **Figure 3**, but for RPC 3.

Through this analysis, the inherent difficulty of classifying RI and non-RI storms is apparent, as the base-state fields considered seem to be equally present in RI and non-RI events for all RPCs. Despite this, the results suggest some modest classification ability of RI and non-RI events through the temperature and moisture patterns, as well as variables more indicative of environmental interaction (e.g. vorticity and static stability) as the largest influences on TC RI processes.

#### **3.2. RI and non-RI T-mode composites**

**Figure 4.** Same as **Figure 3**, but for RPC 2.

34 Recent Developments in Tropical Cyclone Dynamics, Prediction, and Detection

**Figure 5.** Same as **Figure 3**, but for RPC 3.

T-mode composites of the base-state meteorological fields, as well as derived fields including: divergence, relative vorticity, vertical speed and directional wind shears (see [18] for clarification on the difference), equivalent potential temperature, and static stability (as defined in [19]) were formulated next. The analysis below is broken down by variable.

**Figure 6.** Geopotential height (m), with respect to latitude/longitude relative to the storm center, composites at 850 hPa using 40kt/24-hours definition for cluster 2 RI (panel a) and cluster 3 non-RI (panel b). Permutation tests results (panel c–shaded areas are significant at α=0.05 or less) revealed nearly the entire map as significant in discriminating between RI and non-RI events.

#### *3.2.1. Geopotential height and mean sea level pressure characteristics*

The map types for RI and non-RI systems revealed a better lower to mid-level structure, with lower heights for a larger radius overall for RI systems. This suggests the RI core is physically distinct from its surrounding environment. In general, for all RI definitions at all height levels, the highest heights are in the northeast quadrant quadrant of the composites, with low-levels for all RI definitions also exhibiting higher heights around the core, indicative of deeper convection (**Figure 6**). In the mid-levels and low-levels for 30kt/24-hours (four out of the six RI clusters) and 40kt/24-hours (two out of the five RI clusters) definitions, all of the RI clusters contain lower heights over the storm core for a larger radius. Map types for MSLP reveal instances when RI composites exhibit a smaller diameter of lower MSLP over the storm center (cluster 6 for RI using 30kt/24-hours and cluster 2 for 40kt/24-hours) with tighter gradients. Comparing these results to non-RI composites, three of the seven clusters maintain a uniform appearance (30kt/24-hours) or even mirror a traditional midlatitude trough/ridge pattern (in one non-RI map type). It is important to note that two non-RI cases using the 40kt/24-hours definition had larger regions of lower MSLP, which is explainable given the frequency of strong (category 3 or 4) non-RI storms associated with this RI definition (12% of the non-RI dataset). Regardless, the dominant pattern among all clusters shows a tighter gradient in low-level geopotential height and MSLP surrounding the TC core in RI systems. Permutation testing revealed a magnitude difference most apparent with MSLP composites for all RI definitions, where RI cases are exhibiting a statistically significantly larger radius of lower heights and pressures than for the non-RI systems, especially for 25kt and 30kt definitions. These results are supported by permutation test results for geopotential heights, which reveal the storm center in the low- and mid- levels as statistically significant at the 95% level in distinguishing between RI and non-RI storms (**Table 4**). It is also notable that the region of significance for MSLP increases as the wind definition increases. In other words, the 40kt/24-hours has the entire permutation map exhibiting statistical significance suggesting geopotential heights are more distinct; however, this could be an artifact of the 40kt definition containing category 4 and 5 storms making up 70% of the dataset versus non-RI containing at most category 4 (4%).


Percent significance values greater than 70 are bolded.

**Table 4.** T-mode analysis results for geopotential height and MSLP. Magnitude difference (%) for RI greater than non-RI composites and percent significance results from permutation tests for each variable examined for each RI definition.

Diagnosing Tropical Cyclone Rapid Intensification Through Rotated Principal Component Analysis of... http://dx.doi.org/10.5772/63988 37


Percent significance values greater than 70 are bolded.

distinct from its surrounding environment. In general, for all RI definitions at all height levels, the highest heights are in the northeast quadrant quadrant of the composites, with low-levels for all RI definitions also exhibiting higher heights around the core, indicative of deeper convection (**Figure 6**). In the mid-levels and low-levels for 30kt/24-hours (four out of the six RI clusters) and 40kt/24-hours (two out of the five RI clusters) definitions, all of the RI clusters contain lower heights over the storm core for a larger radius. Map types for MSLP reveal instances when RI composites exhibit a smaller diameter of lower MSLP over the storm center (cluster 6 for RI using 30kt/24-hours and cluster 2 for 40kt/24-hours) with tighter gradients. Comparing these results to non-RI composites, three of the seven clusters maintain a uniform appearance (30kt/24-hours) or even mirror a traditional midlatitude trough/ridge pattern (in one non-RI map type). It is important to note that two non-RI cases using the 40kt/24-hours definition had larger regions of lower MSLP, which is explainable given the frequency of strong (category 3 or 4) non-RI storms associated with this RI definition (12% of the non-RI dataset). Regardless, the dominant pattern among all clusters shows a tighter gradient in low-level geopotential height and MSLP surrounding the TC core in RI systems. Permutation testing revealed a magnitude difference most apparent with MSLP composites for all RI definitions, where RI cases are exhibiting a statistically significantly larger radius of lower heights and pressures than for the non-RI systems, especially for 25kt and 30kt definitions. These results are supported by permutation test results for geopotential heights, which reveal the storm center in the low- and mid- levels as statistically significant at the 95% level in distinguishing between RI and non-RI storms (**Table 4**). It is also notable that the region of significance for MSLP increases as the wind definition increases. In other words, the 40kt/24-hours has the entire permutation map exhibiting statistical significance suggesting geopotential heights are more distinct; however, this could be an artifact of the 40kt definition containing category 4 and 5 storms making up 70% of the dataset versus non-RI containing at most category 4 (4%).

36 Recent Developments in Tropical Cyclone Dynamics, Prediction, and Detection

**T-mode analysis for geopotential height and MSLP**

**Permutation significance (%)**

**Mag. difference (%)**

**Permutation significance (%)**

**25kt/24-hours 30kt/24-hours 40kt/24-hours**

<5 11 <5 49 <5 **83**

<5 5.5 <5 19 <5 42

<5 13 <5 30 <5 12

<5 53 <5 **95** <5 **96**

**Table 4.** T-mode analysis results for geopotential height and MSLP. Magnitude difference (%) for RI greater than non-RI composites and percent significance results from permutation tests for each variable examined for each RI

**MSLP** <5 36 <5 **92** <5 **100**

**Mag. difference (%)**

**Variable Mag.**

**Geo. height 850 hPa**

**Geo. height 700 hPa**

**Geo. height 500 hPa**

**Geo. height 200 hPa**

definition.

**difference (%)**

**Permutation significance (%)**

Percent significance values greater than 70 are bolded.

**Table 5.** Same as **Table 4**, but for thermodynamic variables.

#### *3.2.2. Thermodynamic characteristics*

Specific humidity (25kt/24-hours and 30kt/24-hours) throughout the atmospheric profile contain larger magnitudes (see **Table 5**) for a greater diameter around the storm center and in the northeast quadrant quadrant for RI cases. RI TCs also contain maximum magnitude over the storm center in the mid- and upper- levels, or in the northeast quadrant quadrant, compared to non-RI cases which see a shift of the maximum magnitude towards the ENE region for 25kt/24-hours and 30kt/24-hours definition (**Figure 7**). Cross sections show drier air infiltrating through the inflow regions of the non-RI storm (west side of latitudinal cross section for 25kt/24-hours definition) compared to a more even distribution for RI clusters on either side of the storm center (**Figure 8**).

**Figure 7.** Specific humidity (kgkg−1) composites at 500 hPa using 30kt/24-hours definition for cluster 5 RI (panel a) and cluster 6 non-RI (panel b). Permutation tests results (panel c–shaded areas are significant at α=0.05 or less) revealed the storm center as significant in discriminating between RI and non-RI events.

Equivalent potential temperature (*θe*) fields show similar magnitudes among RI and non-RI cases, although the radius of maximum *θe* is larger with the RI map type, suggesting the potential energy over the storm center is the important feature here. Additionally, the *θe* field is largely symmetric around the storm center for RI map types (**Figure 9a**). However, for the non-RI using the 25kt/24-hours definition, the *θe* field is non-symmetric, instead showing a tilted core in the composite fields (**Figure 9b**). This tilt suggests a cutting off of the moisture source over the storm center, especially in the mid- and upper- levels. These results do not hold up as well for the 30kt/24-hours and 40kt/24-hours RI definitions, as there are non-RI composites which show symmetric latitudinal *θe* cross sections. While the more intense non-RI TCs have clustered together, distinguishing them from the non-RI group itself, it hinders classification ability using these RI definitions. Permutation tests revealed that at all pressure levels, for all RI definitions, the region directly over the storm center, as well as the inflow region for 25kt and 30kt definitions, is statistically significant at the 95% level in discriminating RI versus non-RI systems.

*3.2.2. Thermodynamic characteristics*

38 Recent Developments in Tropical Cyclone Dynamics, Prediction, and Detection

side of the storm center (**Figure 8**).

Specific humidity (25kt/24-hours and 30kt/24-hours) throughout the atmospheric profile contain larger magnitudes (see **Table 5**) for a greater diameter around the storm center and in the northeast quadrant quadrant for RI cases. RI TCs also contain maximum magnitude over the storm center in the mid- and upper- levels, or in the northeast quadrant quadrant, compared to non-RI cases which see a shift of the maximum magnitude towards the ENE region for 25kt/24-hours and 30kt/24-hours definition (**Figure 7**). Cross sections show drier air infiltrating through the inflow regions of the non-RI storm (west side of latitudinal cross section for 25kt/24-hours definition) compared to a more even distribution for RI clusters on either

**Figure 7.** Specific humidity (kgkg−1) composites at 500 hPa using 30kt/24-hours definition for cluster 5 RI (panel a) and cluster 6 non-RI (panel b). Permutation tests results (panel c–shaded areas are significant at α=0.05 or less) revealed the

Equivalent potential temperature (*θe*) fields show similar magnitudes among RI and non-RI cases, although the radius of maximum *θe* is larger with the RI map type, suggesting the potential energy over the storm center is the important feature here. Additionally, the *θe* field is largely symmetric around the storm center for RI map types (**Figure 9a**). However, for the

storm center as significant in discriminating between RI and non-RI events.

**Figure 8.** Latitudinal cross section for specific humidity (kgkg−1) composites 1000–850 hPa using the 25kt/24-hours definition for cluster 5 RI (panel a) and cluster 3 non-RI (panel b). Permutation tests (panel c–shaded areas are significant at α=0.05 or less) revealed the storm center and inflow region as statistically significantly different.

Static stability at 500 hPa, on average revealed magnitudes were approximately the same for all definitions between RI and non-RI storms. However, RI clusters, which contained stronger TCs (i.e. category 4 and 5s), had a closed off maximum static stability center over the core of the storm for all RI definitions (**Figure 10**). Permutation tests confirm stability in the mid-levels as statistically significant in discriminating between RI and non-RI systems for nearly the entire storm domain. Notably, for the 40kt/24-hours definition, the storm center in the low-levels was also significant, but is likely a result of higher magnitudes (i.e. category 5 cases) for these RI events.

**Figure 9.** Latitudinal cross section composites for equivalent potential temperature (K) 1000–300 hPa using the 25kt/24 hours definition for cluster 5 RI (panel a) and cluster 3 non-RI (panel b).

**Figure 10.** Static stability (K/Pa) composites at 500 hPa using 40kt/24-hours definition for cluster 2 RI (panel a) and cluster 3 non-RI (panel b). Permutation tests (panel c–shaded areas are significant at α=0.05 or less) revealed magnitude discrimination for nearly the entire storm domain.

#### *3.2.3. Kinematic characteristics*

**Figure 9.** Latitudinal cross section composites for equivalent potential temperature (K) 1000–300 hPa using the 25kt/24-

**Figure 10.** Static stability (K/Pa) composites at 500 hPa using 40kt/24-hours definition for cluster 2 RI (panel a) and cluster 3 non-RI (panel b). Permutation tests (panel c–shaded areas are significant at α=0.05 or less) revealed magnitude

hours definition for cluster 5 RI (panel a) and cluster 3 non-RI (panel b).

40 Recent Developments in Tropical Cyclone Dynamics, Prediction, and Detection

discrimination for nearly the entire storm domain.

The first kinematic field considered was upper-level (200 hPa) divergence. Divergence (25kt/24-hours and 30kt/24-hours) showed RI and non-RI clusters similar in both magnitude and region of greatest divergence in the northeast quadrant quadrant of the systems (**Figure 11**); however, the 40kt/24-hours definition revealed RI systems had 30% larger magnitude near the storm center and in the northeast quadrant quadrant. RI cases, for all definitions, tended to have a larger coverage area of the composite exhibiting divergence, despite the similarities in the spatial orientation of the divergence on the composite maps. Permutation tests supported the conclusion that divergence magnitude (**Table 6**), rather than spatial orientation, was the distinguishing characteristic between RI and non-RI storms at a 95% significance level.

**Figure 11.** Divergence (s−1) composites at 200 hPa using 30kt/24-hours definition shows an example of how cluster 5 RI (panel a) and cluster 6 non-RI (panel b) clusters are different in both magnitude and region of greatest divergence in the northeast quadrant quadrant of the systems. Permutation tests (panel c–shaded areas are significant at α=0.05 or less) revealed a region over the storm center as significant.

For relative vorticity, using both the 25kt/24-hours and 30kt/24-hours definitions, positive vorticity is noted in three out of the six RI clusters in proximity to storm center in the upper levels, which is notably absent from non-RI cluster map types. For the 40kt/24-hours definition, three out of five RI map types exhibited this feature as well, while only two out of seven non-RI map types showed the same positive vorticity area (**Figure 12**). Vorticity magnitudes were larger for RI TCs with all map types (at all levels) and definitions, and also the vorticity gradient near the center was steeper within the RI system versus the non-RI. The only exception was at 700mb, in which vorticity features are similar in both RI and non-RI. Permutation tests show that over the storm center, for all three pressure levels, all RI definitions, had a 95% level of significance in distinguishing RI from non-RI cases. Notably, the area of statistical significance around the storm center is larger in the mid- levels.


**Table 6.** Same as **Table 4**, but for kinematic variables.

Map types of vertical speed shear (850–200 hPa – **Figure 13**), thought to be undesirable for RI to occur, revealed weaker 200 hPa winds than the 850 hPa winds within the RI. This is indicative of a closed off environment around the core for the RI systems to a greater degree than the non-RI. Permutation tests revealed all but the southwest quadrant to be statistically significant at the 95% level at discriminating RI from non-RI systems for all RI definitions.

#### *3.2.4. Non-significant variables*

CAPE, CIN, vertical velocity at 850 hPa, latent heat flux, sensible heat flux, static stability at 850- and 700-hPa, and skin temperature composites, while all examined, did not reveal meaningful differences with regards to spatial orientation or magnitude for distinguishing between RI and non-RI cases. While some of the magnitudes were greater for RI clusters containing stronger systems (i.e. category 4 and 5 TCs), other non-RI clusters exhibited similar magnitudes which consisted mainly of tropical storm strength systems. Latent heat flux for example, revealed that for the 25kt/24-hour definition, more latent heat flux was available throughout the inflow region and around the core of the RI cases. However, with the 30kt/24 hour and 40kt/24-hour definitions, the main distinguishing feature seemed to only be higher magnitudes throughout the atmospheric profile. Otherwise, permutation tests surprisingly revealed the NW and northeast quadrant quadrant of the maps for all RI definitions as statistically significant at the 95% level for both CAPE and skin temperature. This is attributed to land influences of some TCs which were in proximity to land when the greatest intensification occurred. Results confirmed a lack of statistical significance in discriminating RI from non-RI with CIN, but confirmed a decent discrimination of magnitude with latent heat flux and sensible heat flux (**Table 5**). However, again, these results are likely being influenced by the proximity to land of some TCs, which would affect 1000 hPa level results for these variables.

three out of five RI map types exhibited this feature as well, while only two out of seven non-RI map types showed the same positive vorticity area (**Figure 12**). Vorticity magnitudes were larger for RI TCs with all map types (at all levels) and definitions, and also the vorticity gradient near the center was steeper within the RI system versus the non-RI. The only exception was at 700mb, in which vorticity features are similar in both RI and non-RI. Permutation tests show that over the storm center, for all three pressure levels, all RI definitions, had a 95% level of significance in distinguishing RI from non-RI cases. Notably, the area of statistical significance

**T-mode analysis for kinematic variables** 

**Permutation significance (%)** 

**Mag. difference (%)** 

**Permutation significance (%)** 

**25kt/24-hours 30kt/24-hours 40kt/24-hours** 

17 12 35 11 28 16

40 19 22 15 38 19

100 22 100 17 28 14

<5 23 <5 21 30 21

<5 12 <5 3.4 <5 8.5

47 **76** 30 **81** 33 **75**

Map types of vertical speed shear (850–200 hPa – **Figure 13**), thought to be undesirable for RI to occur, revealed weaker 200 hPa winds than the 850 hPa winds within the RI. This is indicative of a closed off environment around the core for the RI systems to a greater degree than the non-RI. Permutation tests revealed all but the southwest quadrant to be statistically significant

CAPE, CIN, vertical velocity at 850 hPa, latent heat flux, sensible heat flux, static stability at 850- and 700-hPa, and skin temperature composites, while all examined, did not reveal

at the 95% level at discriminating RI from non-RI systems for all RI definitions.

**Mag. difference (%)** 

around the storm center is larger in the mid- levels.

42 Recent Developments in Tropical Cyclone Dynamics, Prediction, and Detection

**Permutation significance (%)** 

**Variable Mag.**

**Vorticity 700 hPa**

**Vorticity 500 hPa**

**Vorticity 200 hPa**

**Divergence 200**

**Directional shear 850–200**

**Speed shear 850–200 hPa**

**hPa**

**hPa**

**difference (%)** 

Percent significance values greater than 70 are bolded.

**Table 6.** Same as **Table 4**, but for kinematic variables.

*3.2.4. Non-significant variables*

**Figure 12.** Relative vorticity (s−1) composites at 200 hPa using 40kt/24-hours definition for cluster 2 RI (panel a) and cluster 3 non-RI (panel b). Permutation tests (panel c–shaded areas are significant at α=0.05 or less) revealed the area over the storm center to be statistically significant in distinguishing between the two event types.

Overall, the T-mode analysis revealed the discriminating spatial and magnitude differences between RI and non-RI storms. As suspected through S-mode analysis, moisture and surface temperature patterns, as well as variables indicating environmental influence including geopotential heights in the upper levels, relative vorticity, divergence, and static stability in the mid-levels had the largest influences on TC RI processes.

**Figure 13.** Vertical speed shear (ms−1) composites at 850–200 hPa using 25kt/24-hours definition for cluster 5 RI (panel a) and cluster 3 non-RI (panel b). Permutation tests (panel c–shaded areas are significant at α=0.05 or less) revealed nearly the entire map as statistically significant.

#### **4. Conclusion**

Distinguishing meteorological characteristics of RI and non-RI storm structure is critically important in order to improve statistical model prediction of the onset of RI. This research made efforts to continue improvement in identifying relevant large-scale internal dynamics of TCs undergoing RI in the North Atlantic basin, specifically noting important diagnostic variables in three-dimensional space. Base-state, as well as composite derived, meteorological parameters were evaluated through both S-mode and T-mode RPCA for three RI definitions. Specifically with T-mode, hierarchical cluster analysis techniques were used to formulate map types for RI and non-RI systems. To understand the internal dynamics within these complex systems, variables examined included: geopotential heights, temperature, *u* and *v* wind components, specific humidity, MSLP, CAPE, CIN, latent heat flux, sensible heat flux, surface temperature, vertical velocity at 850 hPa, divergence at 200 hPa, relative vorticity, vertical directional and speed shear, equivalent potential temperature, and static stability.

Overall, the T-mode analysis revealed the discriminating spatial and magnitude differences between RI and non-RI storms. As suspected through S-mode analysis, moisture and surface temperature patterns, as well as variables indicating environmental influence including geopotential heights in the upper levels, relative vorticity, divergence, and static stability in

**Figure 13.** Vertical speed shear (ms−1) composites at 850–200 hPa using 25kt/24-hours definition for cluster 5 RI (panel a) and cluster 3 non-RI (panel b). Permutation tests (panel c–shaded areas are significant at α=0.05 or less) revealed

Distinguishing meteorological characteristics of RI and non-RI storm structure is critically important in order to improve statistical model prediction of the onset of RI. This research made efforts to continue improvement in identifying relevant large-scale internal dynamics of TCs undergoing RI in the North Atlantic basin, specifically noting important diagnostic variables in three-dimensional space. Base-state, as well as composite derived, meteorological parameters were evaluated through both S-mode and T-mode RPCA for three RI definitions.

nearly the entire map as statistically significant.

**4. Conclusion**

the mid-levels had the largest influences on TC RI processes.

44 Recent Developments in Tropical Cyclone Dynamics, Prediction, and Detection

S-mode analysis results demonstrated the difficulty of establishing characteristic attributes for classifying RI and non-RI storms, as the base-state fields considered were equally present in RI and non-RI events for all RPCs. Two of the six RPC groups contained cases that were indicative of strong, well-structured TCs, exhibiting what you would expect for a sustainable environment for TC continuation and strengthening, regardless of storm type. Whereas, four of the six RPC groups contained cases influenced by baroclinic environmental effects on TCs, which further aids in the positive/negative aspects of environmental influence on TCs. While stronger outflow can lower stability, enhancing the outflow, it can also be detrimental to a TC [20, 21]. Despite this, results indicated a modest classification ability of RI and non-RI events through the temperature and moisture patterns, as well as those variables that would be more indicative of environmental interaction.

T-mode analysis, on the other hand, revealed several important distinguishing spatial features between RI and non-RI systems. Most notably:


resistance to upward vertical motion, forcing subsidence over the storm center [5, 20], but also resistance to adverse effects of the environment, such as vertical shear and Rossby penetration depth, preventing tilting of the TC and allowing for maintenance of the vertical thermal structure [24, 25].


While results of the RPCA analysis confirm previous findings such as the importance of moisture supply, stability within the core, and stronger relative vorticity for RI systems, it also argues against research findings suggesting magnitude is the main distinguisher between RI and non-RI events [29]. Results presented suggest the symmetry of the equivalent potential temperature and specific humidity profiles throughout the atmospheric column, as well as the storm-centered placement of these variables, and stability, directly over the inner-core (instead of shifted to the east-northeast as with several non-RI composites given lower RI definitions) are significant in discrimination of these event types. While there were some shortcomings, such as proximity to land potentially influencing results in the low levels and the inability to fully resolve the inner-core due to model resolution, the results provide a framework of diagnosis for RI processes within TCs. This framework, combined with an improved statistical modelling scheme, will ideally be of use for improving TC intensity forecasts in operational meteorology.
